U.S. Department of the Interior

U.S. Geological Survey

USGS Open-File Report 2013–1165

CGS Special Report 228

Southern California Earthquake Center Publication 1792

The Uniform California Earthquake Rupture Forecast, 

Version 3 (UCERF3)—The Time-Independent Model

M ≥ 6.7 Earthquake

Participation Rates (per year)

10 10 10 -6 -4 -2

34oN

38oN

42oN

122°W 120°W 118°W
COVER 

3D perspective view of California, showing the average long-term rate at which different areas of the state participate in M≥6.7 earthquake 

ruptures. Black rectangles represent explicitly modeled faults (for UCERF3 Fault Model 3.1). Ruptures associated with the Cascadia 

megathrust are not shown.
Uniform California Earthquake Rupture Forecast,

Version 3 (UCERF3)—The Time-Independent Model

By Edward H. Field, Glenn P. Biasi, Peter Bird, Timothy E. Dawson, Karen R. Felzer, David D. Jackson, 

Kaj M. Johnson, Thomas H. Jordan, Christopher Madden, Andrew J. Michael, Kevin R. Milner, Morgan T. 

Page, Tom Parsons, Peter M. Powers, Bruce E. Shaw, Wayne R. Thatcher, Ray J. Weldon, II, and Yuehua 

Zeng (Working Group on California Earthquake Probabilities) 

U.S. Geological Survey Open-File Report 2013–1165

California Geological Survey Special Report 228

Southern California Earthquake Center Publication 1792

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia 2013

For product and ordering information:

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For more information on the USGS—the Federal source for science about the Earth,

its natural and living resources, natural hazards, and the environment:

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Suggested citation:

Field, E.H., Biasi, G.P., Bird, P., Dawson, T.E., Felzer, K.R., Jackson, D.D., Johnson, K.M., Jordan, T.H., 

Madden, C., Michael, A.J., Milner, K.R., Page, M.T., Parsons, T., Powers, P.M., Shaw, B.E., Thatcher, 

W.R., Weldon, R.J., II, and Zeng, Y., 2013, Uniform California earthquake rupture forecast, version 3 

(UCERF3)—The time-independent model: U.S. Geological Survey Open-File Report 2013–1165, 97 p., 

California Geological Survey Special Report 228, and Southern California Earthquake Center Publication 

1792, http://pubs.usgs.gov/of/2013/1165/.

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain 

copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured 

from the copyright owner.
 

STATE OF CALIFORNIA

EDMUND G. BROWN JR.

GOVERNOR

THE NATURAL RESOURCES AGENCY

JOHN LAIRD 

SECRETARY FOR NATURAL RESOURCES

DEPARTMENT OF CONSERVATION

MARK NECHODOM 

DIRECTOR

CALIFORNIA GEOLOGICAL SURVEY 

JOHN G. PARRISH, Ph.D. 

STATE GEOLOGIST
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Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

v

Table of Contents

List of Abbreviations Used in this Report....................................................................................................................... ix

Contributors to UCERF3 ................................................................................................................................................ x

Executive Committee (ExCom)................................................................................................................................... x

Key Contributors......................................................................................................................................................... x

Management Oversight Committee (MOC) ................................................................................................................ x

Scientific Review Panel (SRP)................................................................................................................................... xi

UCERF3 Deformation Model Evaluation Committee ................................................................................................. xi

California Earthquake Authority Multidisciplinary Research Team ............................................................................ xi

External Evaluation of UCERF3 ................................................................................................................................xii

Abstract..........................................................................................................................................................................1

Introduction ....................................................................................................................................................................2

Background ................................................................................................................................................................2

Model Framework.......................................................................................................................................................5

Model Uncertainties....................................................................................................................................................7

Participants, Review, and Consensus Building...........................................................................................................8

Fault Models.................................................................................................................................................................11

Definition ..................................................................................................................................................................11

Fault Zone Polygons.................................................................................................................................................11

Logic Tree Branches ................................................................................................................................................12

Development Process ..............................................................................................................................................12

Deformation Models .....................................................................................................................................................15

Geologic Slip Rate Constraints.................................................................................................................................15

Geologic Deformation Model ....................................................................................................................................16

Deformation Models from Joint Inversion of Geodetic and Geologic Data ...............................................................17

Creep and Aseismicity..............................................................................................................................................19

Implied Moment Rates..............................................................................................................................................22

Logic Tree Branch Weights ......................................................................................................................................26

Earthquake Rate Models and the “Grand Inversion”....................................................................................................26

Methodology.............................................................................................................................................................27

Implementation Ingredients ......................................................................................................................................29

Inversion Setup and Associated Gridded Seismicity ................................................................................................41

Gardner-Knopoff Aftershock Filter............................................................................................................................49

Results .....................................................................................................................................................................50

Sensitivity Tests........................................................................................................................................................80

Discussion....................................................................................................................................................................84

Improvements Over UCERF2...................................................................................................................................85

Model Limitations......................................................................................................................................................87

Future Improvements ...............................................................................................................................................89

Conclusions and Recommendations............................................................................................................................90

Acknowledgements ......................................................................................................................................................91

References...................................................................................................................................................................92

Data and Resources ....................................................................................................................................................97

U3_FaultSectionData: ..............................................................................................................................................97

U3_PreInversionAnalysisTable:................................................................................................................................97

U3 Supplementary Figures:......................................................................................................................................97

 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

vi

Figures

1. 3D perspective view of California, showing the 2,606 fault sections (black rectangles) of UCERF Fault 

Model 3.1 (FM 3.1) ............................................................................................................................. 5

2. Diagram of the four main model components of the UCERF3 framework................................................. 7

3. Diagram of UCERF3 long-term model logic-tree branches with weights given in parentheses................. 9

4. Diagrams illustrating the definition and creation of fault zone polygons ...................................................13

5. Perspective map diagrams of California showing UCERF3 Fault Model (FM) 3.1, and fault sections 

unique to FM 3.1 and FM 3.2... .........................................................................................................17

7. Maps of California showing slip-rate models............................................................................................18

8. Diagrams illustrating the adjustments to moment rate and slip rate due to creep ....................................22

9. Maps showing spatial distribution of off-fault moment rates (first column) for the three UCERF3 

deformation models that provide such estimates (for Fault Model 3.1 only), together with that 

implied by the UCERF2 forecast model (including both gridded sources and type C zones). ...........24

10. Maps showing the spatial distribution of moment rates implied by the UCERF2 smoothed seismicity 

model and the new UCERF3 smoothed seismicity model, compared to the average UCERF3 

deformation model.............................................................................................................................25

11. Map showing UCERF3 Fault Model 3.1 sections divided into an integral number of equal length 

subsections........................................................................................................................................28

12. Graphs showing the magnitude-area (top) and slip-length (bottom) relationships used in UCERF3......32

13. Graph of mean rupture profile based on a stack of 13 mapped surface ruptures...................................33

14. Maps showing the various off-fault spatial seismicity probability density functions (SpatialPDF) used 

in UCERF3 for setting gridded seismicity...........................................................................................40

15. Graphs showing examples of the various regional magnitude-frequency distributions (MFDs) 

considered in setting up the Characteristic Inversion Model branches ..............................................44

16. Graph showing magnitude-frequency distributions implied by the Gutenberg-Richter hypothesis .........47

17. Plots showing application of the Gardner-Knopoff aftershock filter in UCERF3 .....................................50

18. Magnitude-frequency distributions (MFDs) for the entire California region for all UCERF3 logic tree 

branches, with comparison to mean results from UCERF2 ...............................................................53

19. Maps showing average subsection slip rate misfits for both UCERF3 (Fault Model 3.1) and UCERF2 

(Fault Model 2.1), shown as ratios of final implied slip rates divided by deformation model slip 

rates, and averaged over all logic tree branches ...............................................................................56

20. Latitudinal plots showing slip rate and paleoseismic data fits for the southern San Andreas Fault, for 

both UCERF3 and UCERF2 ..............................................................................................................58

21. Histogram of observed rupture lengths from a global data compilation of 258 earthquakes ..................59

22. Map showing the rate at which the Cucamonga Fault coruptures (participates) with other fault 

sections for the branch-averaged UCERF3 model (for Fault Model 3.1) ...........................................60

23. Histogram of the coefficient of variation (COV) for average slip per event, where each sample is the 

standard deviation of slip on a subsection divided by the mean slip, taken among all subsections 

for the reference logic-tree branch inversion......................................................................................61

24. Graphs showing the distribution of regional moment rates implied by UCERF3 logic tree branches .....62

25. Graphs showing example fault-section participation magnitude-frequency distributions (MFDs) 

averaged over all logic tree branches, and weighted accordingly......................................................64

26. Plots showing cumulative magnitude-frequency distributions (MFDs) for selected regions ...................65

27. Maps showing ratios of UCERF2 and UCERF3 results..........................................................................67

28. Branch-averaged participation rate maps for UCERF3 and UCERF2, and for the ratio of the two 

(UCERF3/UCERF2)...........................................................................................................................68

29. Latitudinal plots showing average model-implied segmentation on the San Andreas Fault system for 

UCERF2 and UCERF3 ......................................................................................................................69
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

vii

30. Graphs illustrating the hazard-curve example for PGA at the Redding site listed in table 13.................73

31. Comparison of UCERF2 and UCERF3 for 2-percent-in-50-year PGA ...................................................78

32. Branch ratio maps showing the influence of each deformation model on 2-percent-in-50 year peak 

ground acceleration. ..........................................................................................................................79

33. Graph showing number of above-water-level ruptures as a function of the number of simulated 

annealing runs averaged ...................................................................................................................81

34. Graphs showing cumulative participation magnitude-frequency distribution statistics for 200 

simulated annealing runs on the reference branch ............................................................................82

35. Number of above-water-level ruptures for branch-averaged solutions as a function of the number of 

simulated annealing runs on each branch .........................................................................................83

36. Peak ground acceleration (PGA) hazard curves for the Los Angeles and San Francisco sites listed 

in table 14, obtained by varying equation-set weights on the UCERF3 reference branch. ................84

Tables

1. List of appendixes to this report. ............................................................................................................... 6

2. Working Group on California Earthquake Probabilities consensus-building activities, 2009–2013. .........10

3. Moment rates for the various types of sources in UCERF2......................................................................19

4. Moment rates (in units of 1019 N⋅m/yr) for the UCERF3 deformation models, plus implied values 

of maximum magnitude (Mmax) and mean recurrence interval (MRI) of M≥8 events8.........................20

5. The grand inversion system of equations used in solving for the long-term rate of fault-based ruptures. 30

6. Magnitude-area and slip-length model combinations used in UCERF3*..................................................33

7. Event rate estimates and mean recurrence intervals (MRIs) at paleoseismic sites..................................36

8. Example values from the probability of paleoseismic detection model ( ) used in equation set 2 

of the inversion...................................................................................................................................37

9. Average slip data from appendix R ..........................................................................................................37

10. Probability of observing surface slip (Pr

paleo−slip−proxy)......................................................................38

11. Evaluation metrics currently available in the UCERF3 framework..........................................................52

12. Average cumulative magnitude-frequency distributions for UCERF3 and UCERF2...............................54

13. Number of fault sections, total moment rate (in units of 1018 N⋅m/year), and event rates (per year) 

inside the three subregion boxes shown in figure 27..........................................................................66

14. Ratios of UCERF3 to UCERF2 ground motion exceedance values for varios sites, intensity 

measures, and return periods*. ..........................................................................................................74

15. Influence of different logic-tree branches. ..............................................................................................77

16. Key assumptions made in UCERF3, most of which have at least implicit or partial representation on 

our logic tree.......................................................................................................................................89
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

viii

Appendixes 

A. Updates to the California Reference Fault Parameter Database—Uniform California Earthquake Rupture 

Forecast, Version 3 Fault Models 3.1 and 3.2 by Timothy E. Dawson

B. Geologic-Slip-Rate Data and Geologic Deformation Model by Timothy E. Dawson and Ray J. Weldon, II

C. Deformation Models for UCERF3 by Tom Parsons, Kaj M. Johnson, Peter Bird, Jayne M. Bormann, 

Timothy E. Dawson, Edward H. Field, William C. Hammond, Thomas A. Herring, Rob McCaffrey, ZhenKang Shen, Wayne R. Thatcher, Ray J. Weldon, II, and Yuehua Zeng

D. Compilation of Creep Rate Data for California Faults and Calculation of Moment Reduction Due to 

Creep by Ray J. Weldon, II, David A. Schmidt, Lauren J. Austin, Elise M. Weldon, and Timothy E. 

Dawson

E. Evaluation of Magnitude-Scaling Relationships and Depth of Rupture by B.E. Shaw

F. Distribution of Slip in Ruptures by Glenn P. Biasi, Ray J. Weldon, II, and Timothy E. Dawson

G. Paleoseismic Sites Recurrence Database by Ray J. Weldon, II, Timothy E. Dawson, Glenn P. Biasi, 

Christopher Madden, and Ashley R. Streig

H. Maximum Likelihood Recurrence Intervals for California Paleoseismic Sites by Glenn P. Biasi

I. Probability of Detection of Ground Rupture at Paleoseismic Sites by Ray J. Weldon, II, and Glenn P. Biasi

J. Fault-to-Fault Rupture Probabilities by Glenn P. Biasi, Tom Parsons, Ray J. Weldon, II, and Timothy E. 

Dawson

K. The UCERF3 Earthquake Catalog by K.R. Felzer

L. Estimate of the Seismicity Rate and Magnitude-Frequency Distribution in California from 1850–2011 by 

K.R. Felzer

M. Adaptive Smoothed Seismicity Model by K.R. Felzer

N. Grand Inversion Implementation and Testing by Morgan T. Page, Edward H. Field, Kevin R. Milner, and 

Peter M. Powers

O. Gridded Seismicity Sources by Peter M. Powers, and Edward H. Field

P. Models of Earthquake Recurrence and Down-Dip Edge of Rupture for the Cascadia Subduction Zone by 

Arthur D. Frankel and Mark D. Petersen

Q. The Empirical Model by K.R. Felzer

R. Compilation of Slip-in-the-Last-Event Data and Analysis of Last Event, Repeated Slip, and Average 

Displacement for Recent and Prehistoric Ruptures by Christopher Madden, David E. Haddad, J. Barrett 

Salisbury, Olaf Zielke, J. Ramón Arrowsmith, Ray J. Weldon, II, and Javier Colunga

S. Constraining Epidemic Type Aftershock Sequence (ETAS) Parameters from the Uniform California 

Earthquake Rupture Forecast, Version 3 Catalog and Validating the ETAS Model for Magnitude 6.5 or 

Greater Earthquakes by Jeanne L. Hardebeck

T. Defining the Inversion Rupture Set Using Plausibility Filters by Kevin R. Milner, Morgan T. Page, Edward 

H. Field, Thomas Parsons, Glenn P. Biasi, and Bruce E. Shaw
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

ix

List of Abbreviations Used in this Report 

Abbreviation Definition

2in50 PGA 2-percent-in-50-year peak ground acceleration

ABM Average block model

BSSC Building Seismic Safety Council

CEA California Earthquake Authority

CEPEC California Earthquake Prediction Evaluation Council

CGS California Geological Survey

COV Coefficient of variation

EllsworthB Ellsworth B magnitude-area relationship (WGCEP, 2003)

ERF Earthquake rupture forecast

ETAS Epidemic type aftershock sequence

ExCom Executive Committee

FM Fault model

GPS Global Positioning System

GR Gutenberg-Richter

HanksBakun08 Hanks and Bakun (2008) magnitude-area

InSAR Interferometric synthetic aperture radar

LA Los Angeles

MFD Magnitude-frequency distribution

MOC Management Oversight Committee

MRI Mean recurrence interval

MRT Multidisciplinary Research Team

NEHRP National Earthquake Hazards Reduction Program

NEPEC National Earthquake Prediction Evaluation Council

NSHMP National Seismic Hazard Mapping Program

OEF Operational earthquake forecasting

Off-fault spatial seis PDF 

(or SpatialPDF)

Spatial distribution of off-fault gridded seismicity set by 

choosing one of the spatial probability density maps

OpenSHA Open-source, Java-based platform for conducting Seismic 

Hazard Analysis

PGA Peak ground acceleration

PSHA Probabilistic seismic hazard analysis

RELM Regional earthquake likelihood models

SA Spectral acceleration

SAF San Andreas Fault

SCEC Southern California Earthquake Center

SF San Francisco

Shaw09mod Modified version of Shaw (2009) magnitude-area 

relationship, as justified in appendix E (this report)

SpatialPDF (or Off-Fault 

Spatial Seis PDF)

Spatial distribution of off-fault gridded seismicity set by 

choosing one of the spatial probability density maps

SRP Scientific Review Panel

USGS United States Geological Survey

UCERF Uniform California Earthquake Rupture Forecast

WGCEP Working Group on California Earthquake Probabilities
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

x

Contributors to UCERF3

The following groups were involved in the development of UCERF3: 

Executive Committee (ExCom)

The ExCom is responsible for convening experts, reviewing options, making 

recommendations, and orchestrating implementation of the model and supporting databases. The 

role of the ExCom is not to advocate specific model components, but to ensure that a minimum 

set of models is considered that spans the range of viability.

Edward (Ned) Field (Chair) U.S. Geological Survey 

Timothy Dawson California Geological Survey

Andrew Michael U.S. Geological Survey 

Tom Parsons U.S. Geological Survey 

Ray Weldon University of Oregon

Key Contributors

These are individuals who contributed in a major way, either by providing expert opinion 

or specific model components. 

Ramón Arrowsmith Arizona State University 

Glenn Biasi University of Nevada, Reno

Peter Bird University of California, Los Angeles

Karen Felzer U.S. Geological Survey 

Jeanne Hardebeck U.S. Geological Survey 

Dave Jackson University of California, Los Angeles

Kaj Johnson Indiana University 

Christopher Madden Oregon State University 

Kevin Milner Southern California Earthquake Center

Morgan Page U.S. Geological Survey 

Peter Powers U.S. Geological Survey 

Bruce Shaw Columbia University (Lamont Doherty) 

Wayne Thatcher U.S. Geological Survey 

Yuehua Zeng U.S. Geological Survey

Management Oversight Committee (MOC)

The MOC is in charge of resource allocation and approving project plans, budgets, and 

schedules. The MOC is also responsible for seeing that the models are properly reviewed and 

delivered.

Thomas Jordan (Chair) Southern California Earthquake Center Director

Tom Brocher U.S. Geological Survey 

Jill McCarthy U.S. Geological Survey 

Chris Wills California Geological Survey
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

xi

Scientific Review Panel (SRP)

The SRP is an independent but participatory body of experts who decide whether the 

WGCEP has considered an adequate range of models, given the forecast duration of interest, and 

that logic tree branch weights have been set appropriately. 

Bill Ellsworth (Chair) U.S. Geological Survey 

Duncan Agnew Scripps Institution of Oceanography 

Ramón Arrowsmith Arizona State University 

Yehuda Ben-Zion University of Southern California 

Greg Beroza Stanford University 

Mike Blanpied U.S. Geological Survey 

Arthur Frankel U.S. Geological Survey 

Sue Hough U.S. Geological Survey 

Warner Marzocchi Instituto Nazionale di Geofisica e Vulcanologia, Italy

Hamid Haddadi California Geological Survey

Rick Schoenberg University of California, Los Angeles

David Schwartz U.S. Geological Survey 

UCERF3 Deformation Model Evaluation Committee

These are individuals are responsible for evaluating the suite of deformation models 

proposed in UCERF3 and assigning relative weights to each in the final model. 

Tom Parsons (Chair) U.S. Geological Survey 

Jack Boatwright U.S. Geological Survey 

Timothy Dawson California Geological Survey

Arthur Frankel U.S. Geological Survey 

Jim Dieterich University of California, Riverside 

Dave Jackson University of California, Los Angeles

Wayne Thatcher U.S. Geological Survey 

Ray Weldon University of Oregon

Chris Wills California Geological Survey

California Earthquake Authority Multidisciplinary Research Team

Shawna Ackerman California Earthquake Authority 

Bob Anderson California Seismic Safety Commission

Bruce Patton California Earthquake Authority 

Badie Rowshandel California Geological Survey
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

xii

External Evaluation of UCERF3

The National Earthquake Prediction Evaluation Council (NEPEC) and the California 

Earthquake Prediction Evaluation Council (CEPEC) were asked, upon the conclusion of the 

project, to evaluate the quality and integrity of the process by which the UCERF3 timeindependent earthquake model and forecast had been constructed. Both councils affirmed that 

the work had been carried out in an appropriate manner taking, into account input from a broad 

cross-section of the earthquake research community, and that the SRP had managed a thorough 

review and quality control process throughout the project. Letter reports from the NEPEC and 

CEPEC are included on the following pages of this report. 

As members of the USGS National Seismic Hazard Map Steering Committee, 

the following also provided comments on the applicability of UCERF3 in the 2014 seismic 

hazard maps: John Anderson (chair), Norm Abrahamson, Ken Campbell, Michael Hamburger, 

Bill Lettis, Nilesh Shome, Ray Weldon, Chris Wills, and Martin Chapman. 

NEPEC members current and active during the UCERF3 project 

Terry Tullis* (Chair) Brown University 

William Leith (Co-chair) U.S. Geological Survey 

Ramón Arrowsmith Arizona State University

Nick Beeler* U.S. Geological Survey 

David Jackson University of California, Los Angeles 

Bruce Shaw Columbia University 

William Ellsworth U.S. Geological Survey 

Susan Hough U.S. Geological Survey 

Evelyn Roeloffs* U.S. Geological Survey 

John Vidale* University of Washington 

Andrew Michael U.S. Geological Survey 

Allan Rubin* Princeton University 

Roland Bürgmann* University of California, Berkeley

*Member of UCERF3 final review subcommittee 

CEPEC members who participated in the external evaluation of UCERF3

John G. Parrish (Chair) California Geological Survey 

Lucy M. Jones U.S. Geological Survey 

Tom Heaton California Institute of Technology 

Rui Chen California Geological Survey 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

xiii

PROF. JOHN VIDALE, DIRECTOR

Pacific Northwest Seismic Network

E-MAIL: VIDALE@UW.EDU

MONDAY, AUGUST 19, 2013 

DR. SUZETTE KIMBALL, ACTING DIRECTOR

U.S. Geological Survey

Reston, Virginia 20192

Dear Dr. Kimball,

This letter conveys the approval by the National Earthquake Prediction Evaluation Council 

(NEPEC) of the process used by the Scientific Review Panel (SRP) to oversee the timeindependent Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3). As you are 

aware, UCERF3 is a joint undertaking of the U.S. Geological Survey, the California Geological 

Survey, and the Southern California Earthquake Center, with support from the California 

Earthquake Authority.

NEPEC was asked by the USGS Earthquake Hazards Program on August 8 to 

evaluate whether the process by which the UCERF3 forecast was made is sound, such that the 

model should be of sufficient quality for use in hazard assessments for public policy. This 

conforms to NEPEC's role defined at the start of the UCERF3 project in 2009. In particular, we 

were asked to examine the make-up of the SRP, the nature of the SRP reviews, and how the 

working group responded to those reviews. We were not asked to undertake an independent 

review of UCERF3 itself, as this was carried out by the SRP over a period of several years. 

The six members of NEPEC signing this letter did not have a central role in development of 

UCERF3; the rest of the NEPEC members did participate significantly in the UCERF3 effort, 

and were recused from contributing to this letter aside from the chance to comment on it. In 

response to those comments, we changed some sentences for clarity, but this has not altered the 

opinion conveyed in this letter. 

For this assessment, NEPEC has received annual updates on progress, and we were provided 

with a letter from the SRP Chair outlining that group's activities, with documentation of SRP 

reviews and working-group responses to those reviews, and with access to the current draft of the 

UCERF3 report that is in preparation for publication. Some of us examined portions of that

report in the process of our review. The SRP reports document the issues with the UCERF3 

components and approaches that arose between June 2010 and April 2013. The May 2013 

document from the working group summarizes how UCERF3 was revised in response to the 

final SRP review with respect to the prior version (3.2). 

The new model UCERF3 improves on its predecessor UCERF2 in numerous ways. It has a 

more complete database of California faults, includes additional geological observations of past 

earthquake dates and fault configurations, and has incorporated improved and updated 

"deformation models" to improve estimates of the movement along those faults. The classes of 

earthquake frequency-magnitude relations considered have been broadened. A numerical 

inversion algorithm has been used to estimate recurrence rates of a comprehensive suite of 

possible damaging earthquakes, which is the information needed to estimate the probability of 

shaking exceeding specific levels. The inversion scheme allows most available geodetic, 

geological, and seismicity data to be used to develop a self-consistent forecast of future 

California seismic events based on best-available science. UCERF3 is developed using a more 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

xiv

flexible computational platform than UCERF2 so that additional data can be more easily

incorporated. For the long term, the more flexible foundation of UCERF3 provides a better 

roadmap than did UCERF2 to further refine future hazard assessments as field measurements 

improve and scientific ideas evolve.

UCERF3 was implemented by leading seismic hazard experts, with broad and extensive 

participation across the U.S. earthquake mitigation community. UCERF3 was vetted openly and 

with input from other specialists and users, and their feedback was heeded to test and improve 

initial models. In a crucial detail, a comprehensive and well-documented logic tree was 

developed to take account of alternative scientific views on many aspects of the hazard. In 

response to a question in our charge, we affirm that the SRP is composed of exceedingly wellqualified and appropriate experts. 

We are grateful to those involved in the creation of UCERF3 for their diligent and skilled 

efforts, which will lead to improved guidance for zoning, insurance rates, and public 

information. In particular we approve of the work and processes used by the SRP to guide the 

development of UCERF. 

John E. Vidale, member, NEPEC, signing also for Nicholas M. Beeler, Roland Bürgmann, Evelyn Roeloffs, Allan M. 

Rubin, Chair Terry E. Tullis.
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

xv

 E DMUND G . B ROWN , J R .

GOVERNOR

California Earthquake 

Prediction 

Evaluation Council 

August 16, 2013

Suzette M. Kimball, Ph. D. Mark Ghilarducci, Director

Acting Director Governor’s Office of Emergency Services

United States Geological Survey Cal-OES Headquarters

12201 Sunrise Valley Dr. 3650 Schriever Avenue

Mail Stop 101 Mather, CA 95655

Reston, VA 20192

Re: Evaluation of the Scientific Review Process in Developing UCERF-3 

Dear Acting Director Kimball & Director Ghilarducci:

The Working Group on California Earthquake Probabilities (WGCEP) commenced its research and development of 

the Uniform California Earthquake Rupture Forecast, Version 3 (UCERF-3), early in 2010. Just prior to that, the 

California Earthquake Prediction Evaluation Council (CEPEC) met jointly with the National Earthquake Prediction 

Evaluation Council (NEPEC) and concluded that the role of these Councils would be to evaluate the process by 

which the UCERF-3 Scientific Review Panel (SRP) conducted its technical oversight of the work being done by the 

WGCEP. In addition, a review of the UCERF-3 development process by CEPEC and NEPEC is required by the 

California Earthquake Authority as a condition of its providing major funding for the project.

On August 8, 2013 the CEPEC received a formal request from Dr. Michael L. Blanpied, Associate Coordinator for 

the United States Geological Survey (USGS) Earthquake Hazards Program, to conduct an evaluation of the review 

process by which the SRP guided and critiqued the work of the WGCEP, and to determine the quality, integrity, and 

adequacy of that review process. CEPEC undertook this charge following a recommendation from its Chair and 

concurrence from the Director of the California Office of Emergency Services (Cal-OES). Four of the eight CEPEC 

members participated in the review; three others excused themselves because of their active participation in the 

WGCEP and SRP.

Following the CEPEC assessment of the SRP reviews conducted of the WGCEP, CEPEC provides the following 

comments:

• As reflected in the six SRP review reports, the SRP offered constructive comments and practical 

recommendations at several stages over the course of the UCERF-3 project. It provided 

invaluable guidance that spanned a wide range of project matters, including project organization, 

management, and oversight. The SRP encouraged the WGCEP to engage the potential user 

groups and stakeholders and to coordinate with the National Seismic Hazard Mapping Program at 

an early stage in the project. This facilitated the adoption of the UCERF-3 in the 2014 revision of 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

xvi

the National Seismic Hazard Maps and the potential acceptance of the UCERF-3 by the general 

seismological and engineering community.

• The reviews conducted by the SRP were timely, thorough, and instructive. The SRP reviews have 

great technical depth and contained considerable details.

The CEPEC concludes that the reviewing process followed by the SRP in its quality control oversight of the work of 

the WGCEP in developing the UCERF-3 model resulted in an appropriate model to represent the present 

understanding of the earthquake processes.

Sincerely,

John G. Parrish, Ph. D., PG

Chair – CEPEC

cc: Mike Blanpied, USGS

cc: CEPEC
Uniform California Earthquake Rupture Forecast,

Version 3 (UCERF3)—The Time-Independent Model

By Edward H. Field, Glenn P. Biasi, Peter Bird, Timothy E. Dawson, Karen R. Felzer, David D. Jackson, 

Kaj M. Johnson, Thomas H. Jordan, Christopher Madden, Andrew J. Michael, Kevin R. Milner, Morgan T. 

Page, Tom Parsons, Peter M. Powers, Bruce E. Shaw, Wayne R. Thatcher, Ray J. Weldon, II, and Yuehua 

Zeng (Working Group on California Earthquake Probabilities)1

Abstract

In this report we present the time-independent component of the Uniform 

California Earthquake Rupture Forecast, Version 3 (UCERF3), which provides authoritative 

estimates of the magnitude, location, and time-averaged frequency of potentially damaging earthquakes in 

California. The primary achievements have been to relax fault segmentation assumptions and to 

include multifault ruptures, both limitations of the previous model (UCERF2). The rates of all 

earthquakes are solved for simultaneously, and from a broader range of data, using a systemlevel “grand inversion” that is both conceptually simple and extensible. The inverse problem is 

large and underdetermined, so a range of models is sampled using an efficient simulated 

annealing algorithm. The approach is more derivative than prescriptive (for example, magnitudefrequency distributions are no longer assumed), so new analysis tools were developed for 

exploring solutions. Epistemic uncertainties were also accounted for using 1,440 alternative logic 

tree branches, necessitating access to supercomputers. The most influential uncertainties include 

alternative deformation models (fault slip rates), a new smoothed seismicity algorithm, 

alternative values for the total rate of M≥5 events, and different scaling relationships, virtually all 

of which are new. As a notable first, three deformation models are based on kinematically 

consistent inversions of geodetic and geologic data, also providing slip-rate constraints on faults 

previously excluded because of lack of geologic data. The grand inversion constitutes a systemlevel framework for testing hypotheses and balancing the influence of different experts. For 

example, we demonstrate serious challenges with the Gutenberg-Richter hypothesis for 

individual faults. UCERF3 is still an approximation of the system, however, and the range of 

models is limited (for example, constrained to stay close to UCERF2). Nevertheless, UCERF3 

removes the apparent UCERF2 overprediction of M6.5–7 earthquake rates and also includes 

types of multifault ruptures seen in nature. Although UCERF3 fits the data better than UCERF2 

overall, there may be areas that warrant further site-specific investigation. Supporting products 

may be of general interest, and we list key assumptions and avenues for future model 

improvements. 

________________ 

1

For affiliations of authors, see preceding section, “Contributors to UCERF3.”
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

2

Introduction

Background

The 38 million residents of California live among some of the most active earthquake 

faults in the United States, so efforts to promote public safety and community resilience require

credible assessments of the earthquake hazard. The best tool for quantifying the earthquake 

threat is probabilistic seismic hazard analysis (PSHA; see list of abbreviations in the front matter 

of the report), which quantifies the likelihood that ground shaking will exceed various levels 

during a given time period (Cornell, 1968). End-users of PSHA include those charged with landuse planning, building-code revisions, disaster preparation and recovery, emergency response, 

and the design of lifelines and critical facilities, as well as organizations that promote public 

education for risk mitigation (National Research Council, 2011). 

One of the two main modeling components of PSHA is an earthquake rupture forecast 

(ERF), which quantifies the probability of all damaging fault-rupture events in a region, for a 

given timespan, above some magnitude threshold, and at some level of discretization deemed 

adequate for hazard assessment. ERFs are also useful for choosing earthquake-planning 

scenarios (for example, Wald and others, 2005) and for quantifying what events might be 

unfolding in an earthquake early warning system (for example, Cua and others, 2009). 

Two different entities have traditionally developed official ERFs for California. One is 

the National Seismic Hazard Mapping Program (NSHMP) of the United States Geological 

Survey (USGS), which has developed statewide, time-independent (long-term) models for use in 

the national seismic hazard maps (for example, Algermissen and others, 1982; Frankel and 

others, 1996, 2002). The other official ERFs were from the Working Groups on California 

Earthquake Probabilities (WGCEP; 1988, 1990, 1995, and 2003), which developed timedependent models based on Reid’s (1911) elastic-rebound theory (where probabilities drop on a 

fault after experiencing a rupture and build back up with time as tectonic stresses reaccumulate). 

These WGCEP models, however, only covered a subset of California; see Field (2007) for a 

review.

The 1994 Northridge earthquake led to an insurance-availability crisis, which prompted 

the California legislature to create the California Earthquake Authority (CEA), a publicly 

managed provider of residential earthquake insurance that is funded primarily by participating 

private insurance companies (www.earthquakeauthority.com). CEA currently holds about twothirds of all such policies in California, making it one of the largest residential earthquake 

insurance providers in the world. The enabling legislation for CEA states that insurance rates 

shall be based on the “best available science” and that any statewide variability in insurance rates 

must reflect actual risk differentials. These requirements created the demand for a timedependent forecast based on uniform methodologies across the state, which was lacking in the 

official models developed previously. Consequently, a new WGCEP effort was commissioned in 

September 2004 and charged with developing a Uniform California Earthquake Rupture Forecast 

(UCERF). The project was collaborative between the USGS, the California Geological Survey 

(CGS), and the Southern California Earthquake Center (SCEC), with significant funding from 

CEA. This working group came to be known as WGCEP 2007. 

The first model developed by WGCEP 2007 was a prototype, UCERF1 (Petersen and 

others, 2007), assembled from available components without conforming to a consistent timedependent methodology statewide. The final consensus model, UCERF2, was released to the 

public in April 2008 as a USGS open-file report including 16 appendixes (Working Group on 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

3

California Earthquake Probabilities, 2008), and other supplementary materials, 

(www.SCEC.org/ucerf2), and was then published in Bulletin of the Seismological Society of 

America (Field and others, 2009). UCERF2 was the first statewide, time-dependent model that 

used consistent methodologies, data-handling standards, and uncertainty treatment in all regions. 

The entire model was implemented in OpenSHA (Field and others, 2003), an open-source, 

object-oriented computational framework for seismic hazard, which enabled unprecedented 

flexibility with respect to PSHA calculations for any or all of the alternative time-dependent 

components. The development was also fully coordinated with the NSHMP, and the timeindependent version of UCERF2 was adopted for use in the 2008 USGS national seismic hazard 

maps (Petersen and others, 2008a). 

Although WGCEP 2007 was successful in terms of stated goals, a number of issues were 

identified in the “Model Limitations and Opportunities for Future Improvements” section of the 

report. The most salient of these were (1) to relax segmentation assumptions and include 

multifault ruptures and (2) to incorporate spatiotemporal clustering for the time-dependent 

forecasting of aftershocks and other triggered earthquake sequences. Both of these issues were 

subsequently—and dramatically—exemplified following the UCERF2 publication, by events 

including the 2011 M9 Tohoku earthquake with respect to segmentation (see, for example, 

Kagan and Jackson, 2013), the 2011 M6.3 Christchurch earthquake in terms of spatiotemporal 

clustering (for example, Kaiser and others, 2012), and both the 2010 M7.2 El Mayor-Cucapah

and 2012 M8.6 Sumatra earthquakes in regard to multifault ruptures (for example, Hauksson and 

others, 2011; Meng and others, 2012). 

A persistent problem in WGCEP and NSHMP studies of California seismicity has been 

the overprediction, or “bulge,” in the modeled event rates between M6.5 and 7.0 (for example, 

the “earthquake deficit” described by WGCEP 1995). The UCERF2 rates also showed a bulge in 

this magnitude range, requiring ad hoc adjustments to lower them to within the 95-percent 

confidence bounds of observed rates. WGCEP 2007 speculated that the relaxation of strict 

segmentation would provide a better solution to the bulge problem, and they noted that the 

multifault ruptures observed in the 1992 Landers, California, and 2002 Denali, Alaska, 

earthquakes supported this hypothesis. 

In addition to the 2011 M6.3 Christchurch earthquake, which demonstrated that 

aftershocks could be more damaging than their main shock (Kaiser and others, 2012), the 2009 

L’Aquila, Italy, earthquake also exemplified the potentially dire effects of earthquake triggering 

(van Stiphout and others, 2010). In fact, an international commission convened in the aftermath 

of the latter earthquake (Jordan and others, 2011) concluded that we need to move more 

aggressively toward Operational Earthquake Forecasting (OEF), which, by definition, would 

include both authoritative, real-time forecasts, as well as official protocols for communicating 

implications to the public (Jordan and others, 2011). Furthermore, OEF is now listed as one of 

the strategic-action priorities of the USGS, with a goal of providing “effective situational 

awareness” during hazardous events, with core responsibilities including issuing warnings and 

providing timely information to emergency managers, the media, and the public (Holmes and 

others, 2013, p. 32–33). 

Recognizing the limitations of UCERF2 and the rapid pace of earthquake forecasting

research, the USGS, CGS, and SCEC reconstituted WGCEP in 2010 and, with support from 

CEA, charged it with developing a new model, UCERF3. This report presents the resultant timeindependent component of UCERF3, in which we have relaxed segmentation and included 

multifault ruptures via a generalized inversion approach. A number of other issues have been 

addressed as well, and virtually all datasets have been revised and updated. Four different 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

4

UCERF3 models were developed, evaluated, and formally reviewed during the course of this 

project: versions 3.0, 3.1, 3.2, and 3.3, where the latter is the final time-independent model 

presented here (abbreviated as “UCERF3” below). Although a detailed version history is not 

provided in this report, the more important changes are discussed in the context of lessons 

learned. 

The spatial domain of UCERF3 is the same as that used for UCERF2, shown by the 

polygon surrounding California in figure 1. This is sometimes referred to as the “RELM” region, 

because it was first adopted for the purpose of developing and testing alternative forecasts in the 

Regional Earthquake Likelihood Models (RELM) project (Field, 2007; Schorlemmer and others, 

2007). RELM has since expanded into the Collaboratory for the Study of Earthquake 

Predictability (Zechar and others, 2010), and the continued use of this evaluation region will 

greatly facilitate formal, independent testing of UCERF3. 

As with its predecessor, UCERF3 development has been coordinated with the NSHMP, 

and the time-independent component presented here has been formally recommended for use in 

the 2014 revisions to national seismic hazard maps. The model for the Cascadia subduction zone, 

which extends partway into northern California from Oregon and Washington, was developed by 

a separate NSHMP working group. Coordination with UCERF3 was achieved via joint 

participation in workshops (table 2). Because the Cascadia model is largely decoupled from 

UCERF3 and is described in appendix P (this report), we do not discuss it here. 

A number of key products were developed for UCERF3, most of which are represented 

in the various appendixes listed in table 1. Each appendix was reviewed by the UCERF3 

Scientific Review Panel (SRP) and often by additional experts selected by the SRP. Although 

some of these appendixes have also been published as peer-reviewed journal papers, we refer to 

these appendixes here by the corresponding letter given in table 1. All are noteworthy 

achievements in and of themselves, and many will be of broader interest. For example, the 

UCERF3 deformation models (appendix C, this report) can be used in developing physics-based 

earthquake simulators (for example, Tullis and others, 2012).

The time-dependent components of UCERF3 will be the topic of future reports. For 

instance, we are attempting to include spatiotemporal earthquake clustering by merging a pointprocess Epidemic Type Aftershocks Sequence model (ETAS; Ogata, 1988) into our finite-faultbased framework. Our ultimate aim is to deploy UCERF3 as part of an operational earthquake 

forecast, although doing so will require additional work with respect to real-time network 

interoperability. Other goals for the time-dependent model include addressing self-consistency 

issues with respect to elastic-rebound probability calculations in unsegmented models (Field and 

others, 2009) and further investigating the implications of apparent seismicity rate changes with 

respect to the likelihood of large damaging earthquakes (the “empirical” model of WGCEP 2003 

and in UCERF2; see, for example, Reasenberg and others, 2003). Prototypes of all these 

components have been developed and reviewed, but final implementation awaits the necessary 

completion of the long-term model presented here.

The different approach taken in developing UCERF3 necessitated an extensive set of 

PSHA calculations, both for logic-tree sensitivity tests and for determining adequacy with 

respect to averaging over stochastic elements of the long-term model. This unanticipated 

requirement delayed the project, but the fact that we include hazard calculations is a notable first 

among WGCEPs. Although the UCERF3 platform now lends itself to continual updates and 

improvements, the features and options included here were dictated by deadlines of the Building 

Seismic Safety Council (BSSC). 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

5

Figure 1. 3D perspective view of California, showing the 2,606 fault sections (black rectangles) of 

UCERF Fault Model 3.1 (FM 3.1). Colors indicate the long-term rate at which each area participates 

in M≥6.7 earthquakes, averaged over all 720 UCERF3 logic tree branches for FM 3.1, and including

aftershocks. The entire colored area represents the UCERF model region, which comprises 

California and a buffer zone. The white boxes define the San Francisco Bay area and Los Angeles 

regions used in various calculations, and the white line crossing the state is our definition of 

northern versus southern California. The Cascadia megathrust is not shown on this map; it and the 

Mendocino transform fault (which is shown) extend beyond the UCERF model region. 

Model Framework

The UCERF3 framework, like that of UCERF2, has been constructed from the four main 

model components shown in figure 2. The fault model gives the physical geometry of the larger, 

known, and more active faults; the deformation model gives slip-rate and creep estimates for

each fault section, as well as deformation rates of the modeled faults (if available); the 

earthquake rate model gives the long-term rate of all earthquakes throughout the region (at some 

level of discretization); and the earthquake probability model gives the likelihood that each event 

will occur during a specified time span, perhaps conditioned on additional information such as 

date of last event. The first three of these model components are discussed here (in subsequent 

sections below). These are sufficient for time-independent PSHA, as the assumed Poisson 

probability model depends only on long-term rates. Truly time-dependent probability models, 

based on renewal and clustering processes, will be the topic of future publications. 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

6

Table 1. List of appendixes to this report.

Appendix Title Authors

A Updates to the California Reference Fault Parameter 

Database—Uniform California Earthquake Rupture 

Forecast, Version 3 Fault Models 3.1 and 3.2

Dawson, T.E.

B Geologic-Slip-Rate Data and Geologic Deformation 

Model

Dawson, T.E., and Weldon, R.J., II

C Deformation Models for UCERF3 Parsons, T., Johnson, K.M., Bird, 

P., Bormann, J.M., Dawson, T.E., 

Field, E.H., Hammond, W.C., 

Herring, T.A., McCaffrey, R., 

Shen, Z.-K., Thatcher, W.R., 

Weldon R.J., II, and Zeng, Y.

D Compilation of Creep Rate Data for California Faults 

and Calculation of Moment Reduction Due to Creep

Weldon, R.J., II, Schmidt, D.A., 

Austin, L.J., Weldon, E.M., and 

Dawson, T.E.

E Evaluation of Magnitude-Scaling Relationships and 

Depth of Rupture

Shaw, B.E.

F Distribution of Slip in Ruptures Biasi, G.P., Weldon, R.J., II, and 

Dawson, T.E.

G Paleoseismic Sites Recurrence Database Weldon R.J., II, Dawson, T.E., 

Biasi, G.P., Madden, C., and 

Streig, A.R.

H Maximum Likelihood Recurrence Intervals for 

California Paleoseismic Sites

Biasi, G.P.

I Probability of Detection of Ground Rupture at 

Paleoseismic Sites

Weldon, R.J., II, and Biasi, G.P.

J Fault-to-Fault Rupture Probabilities Biasi, G.P., Parsons, T., Weldon 

R.J., II, and Dawson, T.E.

K The UCERF3 Earthquake Catalog Felzer, K.R.

L Estimate of the Seismicity Rate and MagnitudeFrequency Distribution in California from 1850–2011Felzer, K.R.

M Adaptive Smoothed Seismicity Model Felzer, K.R.

N Grand Inversion Implementation and Testing Page, M.T., Field, E.H., Milner, 

K.R., and Powers, P.M.

O Gridded Seismicity Sources Powers, P.M., and Field, E.H.

P Models of Earthquake Recurrence and Down-Dip 

Edge of Rupture for the Cascadia Subduction Zone

Frankel, A.D., and Petersen, M.D.

Q The Empirical Model Felzer, K.R.

R Compilation of Slip-in-the-Last-Event Data and 

Analysis of Last Event, Repeated Slip, and Average 

Displacement for Recent and Prehistoric Ruptures

Madden, C., Haddad, D.E., 

Salisbury, J.B., Zielke, O., 

Arrowsmith, J.R., Weldon R.J., II, 

and Colunga, J.

S Constraining Epidemic Type Aftershock Sequence 

(ETAS) Parameters from the Uniform California 

Earthquake Rupture Forecast, Version 3 Catalog and 

Validating the ETAS Model for Magnitude 6.5 or 

Greater Earthquakes

Hardebeck, J.L.

T Defining the Inversion Rupture Set Using Plausibility 

Filters

Milner, K.R., Page, M.T., Field, 

E.H., Parsons, T., Biasi, G.P., and 

Shaw, B.E.

*All appendixes can be cited as independent elements of the USGS Open File Report on UCERF3.
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

7

We acknowledge there are situations where the distinction in figure 2 can break down, 

such as when differentiating a “multifault rupture” (in the earthquake rate model) from the case 

where one fault very quickly triggers another (in the earthquake probability model). The 

distinction nevertheless remains both a modeling convenience and a practical necessity to the 

extent that building codes remain based on long-term rates of events.

Figure 2. Diagram of the four main model components of the UCERF3 framework.

This modularization also aids in the implementation of alternative models (for example,

logic-tree branches discussed below) and in the replacement of model elements with new 

components. Building on OpenSHA, WGCEP 2007 put considerable effort into developing an 

open-source, object-oriented, and extensible “UCERF cyberinfrastructure,” including the use of 

distributed data resources and flexible analysis tools. UCERF3 represents a dividend on these 

investments, which we have augmented with new computational capabilities, including the 

harnessing of supercomputers to solve for earthquake rates and generate large numbers of hazard 

curves.

Model Uncertainties

Because of a lack of consensus on how to forecast earthquakes, it is important that our 

model adequately portray epistemic uncertainties, which represent our incomplete understanding 

of how the earthquake system works, as well as the aleatory uncertainties, which represent the 

inherent randomness assumed in any given model of the system (Senior Seismic Hazard 

Analysis Committee, 1997). The history of WGCEPs can be viewed as a progression of 

including more and more epistemic uncertainties. For example, WGCEP 1988 did not consider a 

possible recurrence of the two largest historical events (the great 1857 and 1906 earthquakes), 

whereas WGCEP 2003 represented a quantum leap in having 10,000 different models for the 

Bay Area alone. 

As in UCERF2, we represent epistemic uncertainties using a logic tree structured 

according to the four main model components. Our final branch options and associated weights 

for the UCERF3 time-independent model are shown in figure 3. Note that some branch options 

are given zero weight but are shown nonetheless, in case practitioners want to reconsider their 

applicability in special (for example, site-specific) studies. The set of nonzero-weighted branches 

gives rise to 1,440 different UCERF3 models. 

UCERF3 represents an important step in the WGCEP quest for a more complete 

representation of epistemic uncertainty. For example, rather than assuming or prescribing 

earthquake-generating attributes of the various seismic sources, as in previous NSHMP and 

WGCEP models, we take a more derivative approach to system-level behavior by solving for a 

much wider range of models that are consistent with the data. Of course UCERF3 is still a crude 

approximation of the actual system (for example, imposing strict separation between “on-fault” 

and “off-fault” earthquakes). Because “all models are wrong, but some are useful” (Box, 1979), 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

8

the relevant question for practitioners is whether UCERF3 is a better representation of future 

earthquake activity than UCERF2 for the purpose of managing seismic risk.

Participants, Review, and Consensus Building

The organizational structure used in this study is similar to WGCEP 2007, comprising an 

Executive Committee (ExCom), a Management Oversight Committee (MOC), a Scientific 

Review Panel (SRP), and a large group of contributing experts. The ExCom was responsible for 

convening experts, reviewing options, and making decisions about model components. The 

MOC allocated resources and approved project plans, budgets, and schedules; it also oversaw the 

model review and delivery processes. The SRP is an independent, participatory body of experts 

that reviewed the project plans, research results, and model elements. In particular, the SRP 

provided WGCEP with guidance regarding model viability and the range of models needed to 

adequately represent epistemic uncertainties. Other WGCEP contributors include research 

scientists, resource experts, model advocates, and information technology professionals. 

Members of these groups are listed in the “Contributors to UCERF3” section. We also note that 

CEA’s Multidisciplinary Research Team (MRT) participated in UCERF3 reviews, but they were 

not directly involved in the model development nor any decisions about branch options. 

The discussion of model options and consensus building has been achieved through a 

series of community workshops (table 2), which included participants from the broader 

community. Some workshops focused on the scientific ingredients going into UCERF3, while 

others were aimed at informing user communities and getting their feedback. Numerous smaller 

working group meetings are not listed in table 2. 

Though all participants influenced decisions with respect to logic-tree branches and their

weights, including the SRP, the ExCom had responsibility for the final decisions. In the case of 

deformation models, where the ExCom felt that special expertise was needed, an ad hoc 

evaluation committee was convened to advise on branch weights (discussed in the “Logic Tree 

Branch Weights” section). The entire UCERF3 process was monitored by representatives of the 

National Earthquake Prediction Evaluation Council (NEPEC), which formally advises the USGS 

Director, and the California Earthquake Prediction Evaluation Council (CEPEC), which formally 

advises the California Office of Emergency Services. 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

9

Figure 3. Diagram of UCERF3 long-term model logic-tree branches with weights given in 

parentheses. The branches are organized by the basic model components in figure 2: fault models 

(green), deformation models (purple), and earthquake rate models (blue). The branches and 

weighting decisions, as well as reference branch values for sensitivity tests (bold typeface), are 

described in the sections for each component. UCERF3 has a total of 1,440 nonzero branches.
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

10

Table 2. Working Group on California Earthquake Probabilities consensus-building activities, 

2009–2013.

Date Activity Description

2013

June 21 UCERF3 Time-Independent Model (report #9) submitted

Feb. 21 Workshop on use of UCERF3 in the USGS National Seismic Hazard Map

Feb. 13–14 UCERF3 fault-by-fault evaluation meeting #3

Jan. 25 UCERF3 fault-by-fault evaluation meeting #2

Jan. 24 UCERF3 fault-by-fault evaluation meeting #1

2012

Oct. 17–18 California workshop of the National Seismic Hazard Mapping Project (NSHMP)

July 9 UCERF3 Model Framework (report #8) submitted

May 8–9 Scientific Review Panel meeting

Apr. 30 Review of Preliminary UCERF3 Model (report #7) submitted

Mar. 31 Preliminary UCERF3 Model (report #6) submitted

Mar. 21–22 Cascadia subduction zone workshop

Jan. 26 UCERF3 deformation model meeting

Jan. 24-25 Earthquake Hazards Program northern California workshop

Jan. 5-6 WGCEP all-hands meeting

2011

Dec. 15 Cascadia subduction zone workshop

Oct. 25 Joint UCERF3 and NGA-W2 workshop on common issues

Oct. 24 UCERF3 plan overview (emphasizing the grand inversion for users)

Sept. 30 Final UCERF3 Plan (report #5) submitted

Sept. 11–14 SCEC annual meeting

June 30 SRP Review of Proposed UCERF3 Plan (report #4) submitted

June 13–14 Scientific Review Panel meeting

June 11 Workshop on distribution of slip in large earthquakes

June 10 Workshop on instrumental and historical seismicity

June 9 Workshop on the use of physics-based simulators

June 8 Workshop on time-dependent models

June 4–5 Workshop on UCERF3 deformation models

May 31 Proposed UCERF3 Plan (report #3) submitted

Apr. 8 Statewide fault model and paleoseismic data workshop (in southern California)

Apr. 6 Statewide fault model and paleoseismic data workshop (in northern California)

Mar. 2–3 Distribution of slip in large earthquakes meeting

Jan. 12 WGCEP all-hands meeting

2010

Dec. 31 UCERF3 Methodology Assessment—Proposed Solutions to Issues (report #2) submitted

Nov. 18–19 Cascadia subduction zone workshop

Nov. 10–12 Scientific Review Panel meeting

Nov. 3–4 CEPEC/NEPEC meeting

Sept. 12–15 SCEC annual meeting

Aug. 2 Fault-to-fault jumps task meeting

June 30 UCERF3 Methodology Assessment—Issues and Research Plan (report #1) submitted

Apr. 1–2 Workshop on incorporating geodetic surface deformation data in UCERF3

Feb 17–18 WGCEP all-hands meeting

2009Dec. 1–2 UCERF3 kick-off and planning meeting
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

11

Fault Models 

The UCERFs are primarily fault-based earthquake rupture forecasts, in that most large 

earthquakes (~80 percent) occur on the possible rupture surfaces defined by a fault model (fig. 

2). The fault database developed for UCERF2 has been updated with both revisions and 

additions, with special consideration being given to fault endpoints for the purpose of defining 

multifault rupture possibilities. Full details are given in appendix A (this report), and a summary 

of the more important changes is presented here. 

Definition

A fault model gives the spatial geometry of the larger, active faults throughout the region, 

with alternative models representing epistemic uncertainties in the fault system geometry. By 

definition, a fault model is composed of a list of fault sections, where each fault section is 

represented by:

• Fault section name (for example, “San Andreas (Parkfield)”)

• Fault trace (list of latitudes, longitudes, and depths for the upper fault edge)

• Upper and lower seismogenic depth estimates

• Average dip estimate 

• Average rake estimate (although this can be modified by a deformation model)

• Fault zone polygon (an areal representation of a fault zone)

Because distinct fault sections are defined only to the extent that one or more of these 

attributes vary along strike, some sections can be quite long (for example, the northern San 

Andreas Fault has only four sections). The complete master list of fault sections for California is 

given in the Fault Section Database, which is part of the California Reference Geologic Fault 

Parameter Database. Some fault section entries in this database are mutually exclusive (for 

example, representing alternative representations). The list of fault sections in a given fault 

model is therefore considered to be a complete, viable representation of the large, known, and 

active faults throughout the region. 

Fault Zone Polygons

The fault zone polygon attribute, described in appendix O (this report), is new to 

UCERF3, and is intended for specifying: 

• Whether the fault section represents a simple surface or a broader, braided system of faults;

• The area over which the deformation-model slip rate applies;

• The faults to which observed microseismicity is attributed;

• The area over which elastic-rebound-based probability reductions are applied after an earthquake; 

and

• Whether a future large earthquake is identified as a rupture of a UCERF3 modeled fault.

A retrospective example of the identification problem is whether the 2010 El MayorCucapah earthquake (Hauksson and others, 2011) was an event on the UCERF2 Laguna Salada 

Fault source, or whether it was part of the background seismicity. With the addition of fault zone 

polygons in UCERF3 this distinction is not ambiguous, or at least a lot less so. 

In UCERF3, each fault section represents a proxy for all events that nucleate inside its 

fault zone polygon. Polygons based on geologic considerations (fig. 4A) were assigned to each 

fault section in appendix A (this report), thereby satisfying the first bullet above. However, for 

some faults such as the San Andreas, this zone gets as narrow as 1 km on each side of the fault, 

which is too thin for the other intended uses listed above. This reflects the fact that there is no 

single polygon definition that will perfectly satisfy all intended uses.
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A fault zone width was effectively defined in UCERF2 based on standards established 

previously by the NSHMP in distinguishing fault-based sources from gridded, off-fault 

seismicity. Specifically, the maximum magnitudes for gridded seismicity were previously 

reduced in the vicinity of fault-based sources to avoid overlap with the minimum magnitude of 

fault sources (for example, Petersen and others, 2008b). Although this led to a checkerboard 

pattern for the zones around faults (according to the grid cells assigned to each fault), the average 

width of their zones was about 12 km on either side of vertically dipping faults. 

WGCEP has therefore adopted a default width of 12 km on both sides of vertically 

dipping faults, with this tapering to the surface projection for faults dipping less than 50 degrees. 

More specifically, fault zone polygons are the combination (or union) of three independently 

defined polygons (fig. 4B): the geologically defined polygon for the fault; the surface projection 

of the fault if dipping; and a buffer on either side of the fault trace. The width of the buffer 

polygon on either side of a fault trace scales linearly from 0 km at 50 ̊ dip to 12 km at 90 ̊ dip 

(fig. 4C). This provides vertical faults with a broad zone of influence that scales down as dip 

decreases and the area of the surface projection polygon increases. Figure 4B demonstrates how 

the three polygons are combined. This fault zone definition is both consistent with past NSHMP 

practice and avoids the checkerboard pattern. It is still somewhat arbitrary, however, so potential 

hazard implications of this choice need to be considered carefully in any given application, as we 

will illustrate below.

Logic Tree Branches

UCERF3 comprises two alternative fault models: FM 3.1 and FM 3.2, which are 

analogous to the fault model alternatives FM 2.1 and FM 2.2 used in UCERF2. These two new 

models, shown in figure 5, represent alternative representations of several fault groups. Reducing 

all possible combinations to just two models introduces artificial correlation between the 

alternatives for different faults; however, the groupings are judicious choices for minimizing the 

number of logic-tree branches (every additional fault model requires 720 new logic-tree 

branches), and the PSHA calculations discussed below indicate adequacy for at least the most 

common hazard metrics.

Development Process

Fault models FM 3.1 and 3.2 were developed in coordination with the Statewide 

Community Fault Model project, which builds on SCEC’s Community Fault Model development 

(Plesch and others, 2007). Two workshops were held to solicit feedback from the broader 

community in April of 2011 (table 2). Relative to UCERF2, the primary modifications are (1) 

153 new faults sections were added, mostly in northern California, and about 95 fault sections 

were revised (the numbers are not exact because some are a bit of both); (2) fault endpoints were 

reexamined by reviewing more detailed geologic maps, to enable better quantification of 

multifault rupture probabilities; and (3) connector fault sections were added between larger faults 

where deemed appropriate, to enable multifault ruptures or, where needed, to define block 

boundaries for the deformation models. Figure 5 shows the fault sections that were added, 

modified, or left unchanged from UCERF2. Further details on how these fault models were 

constructed are given by in appendix A (this report). 
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Figure 4. Diagrams illustrating the definition and creation of fault zone polygons. A, Perspective view 

of the Garlock, southern San Andreas, and San Jacinto fault systems, color coded by slip rate (other 

faults in this region are not shown). Downdip projections of the faults are stippled, and the 

geologically defined surface polygons are solid. The geologic polygons typically extend to 1 km on 

either side of the fault traces, but in many places are much broader to accommodate additional 

mapped surface features. B, Schematic diagram of the union of geologic, surface projection, and 

trace buffer polygons to form the “complete” fault zone polygon used in UCERF3. The exemplified

fault dips at ~70o, so the buffer polygon extends to 6 km on either side of the fault trace. The dashed 

orange lines in the complete polygon mark the subdivisions used to define polygons for the 

individual fault sections. C, Strike-perpendicular cross section of a fault showing how dip variations 

influence the widths of the trace buffer, the surface projection, and the complete fault zone polygon 

used in UCERF3.
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Figure 5. Perspective map diagrams of California showing UCERF3 Fault Model (FM) 3.1 (top), and 

fault sections unique to FM 3.1 (middle) and FM 3.2 (bottom). Fault sections are colored to identify 

those that were added (red), modified (green), and unchanged (blue) since UCERF2. Some of the 

modifications are relatively trivial (for example, name change only); see appendix A (this report) for 

precise details. Type C zones applied in UCERF2 (orange polygons) are labeled with their modeled 

deformation rates. The Cascadia subduction zone is not shown here, but is given in appendix P (this 

report).
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Deformation Models

The rate of large events in fault-based ERFs depends directly on fault slip rates, which 

can be derived from measured and dated geologic offsets and perhaps interpolated or 

extrapolated along faults. Slip rates can also be obtained by modeling geodetic measurements 

such as Global Positioning System (GPS) observations (fig. 6). Because it is impossible to 

identify all faults, another contribution to hazard can be “off-fault” deformation (in quotes here 

because this deformation is at least partially occurring on unmodeled faults), which can be 

inferred from observed seismicity and (or) GPS observations. 

Only about 30 percent of UCERF2 faults had measured slip-rate estimates, and most 

others had an estimate from only a single location. UCERF2 deformation models were therefore 

based on expert-opinion evaluation of geologic and geodetic data. In addition to on-fault slip 

rates, off-fault deformation was represented by a set of geographic polygons, referred to as “type

C zones,” each of which was assigned an effective slip rate (fig. 5, top panel). As an a posteriori

check, UCERF2 deformation models were summed across various transects to confirm that total 

plate tectonic rates were well matched.

For UCERF3, we have developed four different deformation models. One is a 

geologically “pure” model (uninfluenced by GPS observations), while the other three are 

kinematically consistent models that directly include both geologic and geodetic constraints. By 

using these models, we minimize relying on expert opinion to broker discrepancies between 

geodetic and geologic data, as was done in UCERF2. Importantly, this approach has provided 

data-driven slip rate estimates for faults with no prior assigned rates (which were excluded from 

UCERF2) and has filled in slip rates along faults with sparse observations. The latter three 

models also provide off-fault strain rate maps, allowing us to abandon the UCERF2 type C 

zones. 

Geologic Slip Rate Constraints

Because UCERF2 expert-opinion slip rates were influenced by both geologic and 

geodetic data, an effort was made in UCERF3 to extract and compile the geologic-only 

constraints at points on faults where such data exist (appendix B, this report). In addition to 

geologic slip rates, appendix B also includes the supporting data, such as information about the 

site location, offset features, dating constraints, number of events, reported uncertainties, 

comments—and separate qualitative ratings of the offset features, dating constraints, and overall 

slip rate. In the majority of cases, these data were compiled from the original sources, although 

extensive use was also made of the written summaries included in the USGS Quaternary Fault 

and Fold Database (U.S. Geological Survey, 2013; earthquake.usgs.gov/hazards/qfaults;

Machette and others, 2004). 

Given the number of Quaternary active faults in California, the dataset of geologic slip 

rates is somewhat sparse. The compilation includes ~230 reported slip rates, of which about 150 

reported rates are ranked as moderately to well constrained. Of the ~350 fault sections in the 

UCERF3 fault model, only about 150 fault sections are directly constrained by slip rate data (fig. 

7B). This emphasizes the fact that slip rates in previous models, as well as in the pure geologic 

model here, are often extrapolated over long distances and that values for most fault sections are 

not directly constrained by geologic data. 
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Geologic Deformation Model

One of the new UCERF3 deformation models is a purely geologic model that includes no 

constraints from geodesy or plate motion models (appendix B, this report). As with the other 

deformation models, the output is an estimated slip rate at all points on the model faults. Where 

available, these slip rates were assigned using the revised geologic data in appendix B; 

elsewhere, best-estimate values were taken from UCERF2, except where the latter included 

hybrid slip rates (from both geology and geodesy) or where the old slip rates were inconsistent 

with other types of data, such as the USGS rate category and published slip rates. 

A number of fault sections had no previously assigned slip rate, and these were simply 

excluded from UCERF2. Such sections have been assigned to a rate category in UCERF3, based 

primarily on recency of activity, but also on geomorphic expression and comparison to similar, 

nearby faults with slip rate constraints. The following criteria were applied when using recency 

of activity to assign slip rate bounds: 

• Active in Quaternary (<1.6 million years) 0.0 to 0.2 mm/yr 

• Active in Late Pleistocene (< ~130,000 years) 0.2 to 1.0 mm/yr 

• Active in Holocene (< ~11,000 years) 1.0 to 5.0 mm/yr 

Very few faults were placed into the last category, primarily because the fastest slipping 

faults are already well characterized throughout California. The exceptions to this are offshore 

faults, which are difficult to study. In the absence of other data, the best estimate for each 

category was selected using a relationship between the number of UCERF fault sections and 

known slip rates. This weighted mean approach is described in appendix B (this report). The 

Geologic deformation model is displayed in figure 7C. Table 3 lists the moment rate 

contributions from the various types of sources in UCERF2, and table 4 lists the implied moment 

rates for the new deformation models. Of particular note is that the new faults (UCERF2 faults 

that lacked slip rates plus the new faults added to UCERF3) constitute a collective moment rate 

of 0.27×1019 N⋅m/yr (for FM 3.1), which is more than half of the total off-fault moment rate in 

UCERF2 (0.47×1019 N⋅m/yr). The latter represents the off-fault background and type C zone 

contributions in table 3. Discounting the added faults, the moment rate of the UCERF3 Geologic 

deformation model is about 1 percent above that of the UCERF2 model. 
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Figure 6. Maps showing GPS velocity vectors for California. A, Distribution of UCERF3 GPS velocity 

vectors for California, referenced to the North America Plate (from appendix C, this report). B, The 

residual velocities computed as the difference between observed GPS velocities and those 

predicted by the UCERF2 Deformation Model 2.1. The velocity scales of the two plots are the same. 

The residual vectors indicate that UCERF2 generally underestimates the average statewide 

deformation rate, particularly in the most populated parts of the state.

Deformation Models from Joint Inversion of Geodetic and Geologic Data

Several workshops and meetings were convened to address the UCERF3 goal of deriving 

slip rates and off-fault strain maps from kinematically consistent inversions of GPS and geologic 

data (table 2). Appendix C (this report) describes both the GPS database, shown here in figure 6, 

as well the three UCERF3 deformation models developed by inverting those data together with 

the geologic constraints: 

• NeoKinema. A model obtained by inverting geologic, geodetic, and principal stress data

using the finite element method of Bird (2009) to estimate the long-term velocity field both 

on and off faults. It is not based on a block geometry. 

• Zeng. A model by Zeng and Shen (unpublished work) representing faults as buried 

dislocations in a homogeneous elastic half space. Each fault segment slips at a solved-for slip 

rate beneath a locking depth, except at a few segments where shallow creep is allowed. A 

continuity constraint allows adjustment between more and less block-like deformation. The 

model here is on the less-block-like end of that spectrum. 

• Averaged Block Model (ABM). A model constructed by averaging five different block 

models using a kinematically consistent method. The input models were updates of 

McCaffrey’s DefNode (McCaffrey, 2002; 2005), Hammond’s block model (Hammond and 
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others, 2011), Johnson’s quasi-block model (Johnson and Fukuda, 2010), and special (more 

block-like) versions of NeoKinema and Zeng’s model. The averaging used the slip rates from 

all five block-model inversions as “data” in a unified block model inversion. Residual inblock strain that results from slip on block boundaries is mapped onto identified faults using 

a buried-dislocation approach as described above for the Zeng model (for details, see 

appendix C, this report). The leftover strain that cannot be reasonably accommodated on 

faults is the “off-fault” portion. 

Figure 7. Maps of California showing slip-rate models. A, Fault slip rates for the UCERF2 

Deformation Model 2.1. B, Sites of geologic slip-rate constraints. C–F, Fault slip rates for the four 

UCERF3 deformation models for Fault Model 3.1.

Each deformation model provides slip-rate estimates for every UCERF3 fault section. 

Each also provides off-fault deformation in the form of strain rate tensors on a 0.1o×0.1o grid 

covering California, which is converted to an off-fault moment rate grid as described in appendix 
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C (this report). All three models were constrained by a consensus GPS velocity field constructed 

for this purpose (appendix C), as well as by the geologic slip rate constraints from appendix B

(this report). The slip rates for these deformation models are shown in figure 7. The new fault 

zone polygons described above were not used in the deformation modeling process here. 

Table 3. Moment rates for the various types of sources in UCERF2.

[ , given in units of 1019 N⋅m/yr or 1026 dyne⋅cm/yr]

5

Source Type Moment Rate ( ) Percent of Total Seismic Percent of Total

CA faults 1 1.73 76% 73%

Non-CA faults 2 0.07 3% 3%

Off-faults background 3 0.37 16% 16%

C Zones (seismic) 4 0.10 5% 4%

C Zones (aseismic) 4 0.10 4%

Total (seismic) 2.27 100%

Total (including aseismic) 2.37 100%

1

Value reflects the 10 percent reduction for smaller earthquakes (generally <6.5, which are treated as background 

seismicity) and aftershocks. The UCERF2 faults are only a subset of UCERF3 fault model, to which about 160 new 

fault sections have been added.

2

Faults outside of California (in Nevada and Oregon), but within the UCERF model region.

3

Value does not include type C zones or deep seismicity near Cascadia (in the NSHMP file agrd_deeps_out) but 

does include aftershocks and the special areas for Brawley (1.6 × 1016 N·m/yr), Mendocino (3.7 × 1017 N·m/yr), 

and Creeping San Andreas Fault (1.9 × 1016 N·m/yr).

4

Half the moment rate in type C zones was assumed aseismic in UCERF2.

5

Values in this table were compiled by running the OpenSHA method 

UCERF3.utils.UCERF2_MFD_ConstraintFetcher.computeMomentRates(). 

Creep and Aseismicity

In this report, the term “creep” refers to interseismic creep, which operates over decadal 

and longer time periods, rather than the postseismic creep that follows most earthquakes. 

Appendix D (this report) documents observations of creep on California faults and develops a 

new methodology to estimate seismic moment rate reductions due to creep. It approximately 

doubles the number of creep estimates that were available in UCERF2, primarily by utilizing 

interferometric synthetic aperture radar (InSAR) and dense geodetic network data. Appendix D 

also applies a model developed by Savage and Lisowski (1993) to infer how creep extends to 

depth, and it examines observations of microrepeating earthquakes (recognized as repeatedly 

rupturing asperities embedded within a creeping fault surface) to see if they are consistent with 

the model-predicted creep reduction with depth.
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Table 4. Moment rates (in units of 1019 N⋅m/yr) for the UCERF3 deformation models, plus implied values of maximum magnitude (Mmax) 

and mean recurrence interval (MRI) of M≥8 events8. [ABM, average block model; %, percent. Also listed are UCERF2 values, and the notes give important comparison details] 

Fault

Model

Deformation 

Model

On-fault

1 

On-fault

increase 

from 

UCERF2 2

On-fault

for new 

faults 3

% from 

new 

faults

change 

on 

UCERF2 

faults 4

Off- fault

 5

Off-fault

change 

from 

UCERF2 

Total 

(including 

off-fault 

aseismic)

Total 

increase 

over 

UCERF2 6

% of 

total off 

faults

Mmax 7 

MRI

M≥8 

(years) 8

3.1

ABM 1.93 11% 0.35 18% -9% 0.92 44% 2.85 20% 32% 8.41 207

Geologic 2.02 17% 0.27 13% 1%

NeoKinema 1.76 1% 0.32 18% -17% 1.02 60% 2.78 17% 37% 8.39 214

Zeng 1.88 9% 0.28 15% -8% 0.88 37% 2.76 16% 32% 8.38 216

3.2

ABM 1.92 11% 0.37 19% -10% 0.92 44% 2.84 20% 33% 8.41 207

Geologic 2.02 17% 0.28 14% 1%

NeoKinema 1.75 1% 0.32 18% -17% 1.04 63% 2.79 18% 37% 8.39 213

Zeng 1.88 9% 0.29 16% -8% 0.88 37% 2.76 16% 32% 8.38 216

2.1 UCERF2 1.73 0% 0.00 0% 0% 0.64 0% 2.37 0% 27% 8.15 385 1

Value includes fault-specific downdip widths and creep-based moment-rate reductions; default is 0.1 where no creep data exist. For reference, the average lower 

seismogenic depth is ~12 km in the UCERF3 Fault Models; with surface creep the average seismogenic thickness is ~11 km. Note that UCERF3 does not include 

most of the UCERF2 “Non-CA Faults” listed in table 30, so contributions from these are included “off fault” here. The value of 1.73 listed for UCERF2 includes 

a 10-percent reduction for small earthquakes and aftershocks (table 30), but this is compensated by UCERF3 applying the default aseismicity of 0.1 (which was 

zero in UCERF2). 

2

These are the on-fault values divided by the value of 1.73 for UCERF2. 3

Moment-rate contributions from only the more than 150 new fault sections added in UCERF3 (not included in UCERF2). For the geologic model with Fault 

Model 3.1, 49 percent percent of the increase (0.28 × 1019 N·m/yr) is from the following two new faults: Cerro Prieto (0.083 × 1019 N·m/yr) and Mendocino 

(0.054 × 1019 N·m/yr). 4

Change in on-fault moment rate for the same faults as used in the UCERF2 model. 5

Values from off-fault strain rates given in appendix C, which assume a seismogenic thickness of 11 km. The UCERF2 value includes contributions from both 

“C-Zones (aseismic)” and “Non-CA Faults” (table 30), the latter because most of the “Non-CA Faults” have been excluded in UCERF3. 6

Relative to the UCERF2 total value of 2.37× 1019 N·m/yr (table 30), which includes contributions from “C-Zones (aseismic)” in table 30. The UCERF3 on-fault 

values have aseismic contributions removed, but there may be aseismic contributions in the UCERF3 off-fault values. 7

Implied values computed assuming a truncated Gutenberg-Richter distribution constrained to have the observed rate of 7.9 M≥5 events per year (appendix L,

this report) and a b-value of 1.0. 8

Values in this table compiled by running the following OpenSHA method on 04/24/13:UCERF3.analysis.DeformatioNmodelsCalc.calcMoRateAndMmaxDataForDefModels().
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As in UCERF2, the aseismicity factor is defined as the fraction of rupture area, between 

the upper and lower seismogenic depths, that is reduced by creep, while the coupling coefficient

defines what fraction of the slip rate is fully seismic (not due to creep). Nonzero aseismicity 

factors primarily reduce rupture magnitudes (due to area reduction), whereas coupling 

coefficients less than 1.0 reduce event rates (due to the slip-rate reduction). Both reduce moment 

rates.

Only aseismicity factors were applied in UCERF2, and only about 20 percent of 

UCERF2 fault sections had nonzero values. Furthermore, UCERF2 aseismicity factors were 

computed as the surface creep rate divided by the total average slip rate, a ratio hereafter referred 

to as the “creep fraction.” It is now understood, however, that most creep is shallow and 

decreases rapidly with depth. By integrating over a depth-dependent creep model, we have 

developed a new relationship for moment rate reduction versus creep fraction (appendix D, this 

report). The result, plotted in figure 8, shows that the moment rate reduction increases less 

rapidly with creep fraction than in UCERF2; the latter is a straight line with a slope of 1.0. For 

each fault section, the partitioning between aseismicity factor and coupling coefficient depends 

on the creep fraction. For creep fractions less than 0.9: 

aseismicity factor = creep fraction

coupling coefficient = 1.0

For creep fractions between 0.9 and 0.95, or for creep fractions between 0.9 and 1.0 on the San 

Andreas creeping section:

aseismicity factor = 0.9 

coupling coefficient = 1.0 – 10 × (creep fraction – 0.9) 

That is, coupling coefficient varies linearly from 0.0 to 0.5 for creep fractions between 

0.9 and 0.95, with the relatively complicated functional form being needed to avoid double 

counting (fig. 8B). Values are capped for creep fractions above 0.95 according to: 

aseismicity factor = 0.9 

coupling coefficient = 0.5

As discussed in appendix N (this report), the transition threshold at 0.9 was chosen to 

ensure that the Parkfield segment of the San Andreas gets an area reduction consistent with the 

magnitude 6.0 events that have historically occurred on that fault section. Slip rate reductions on 

highly creeping faults act to limit the rate of throughgoing ruptures (for example, see appendix N 

for discussion of the San Andreas creeping section). The dependence on long-term slip rates (fig. 

8A) implies that the moment rate reductions vary among the deformation models (average 

aseismicity factor and coupling coefficient values are listed for each fault section on the 

“OrigSlipRatesEtc” sheet of the U3_FaultSectionData file given in the Data and Resources

section). 
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Figure 8. Diagrams illustrating the adjustments to moment rate and slip rate due to creep. A, The 

UCERF3 creep model, which specifies moment rate reduction as a function of the ratio of creep rate 

to slip rate. B, The moment rate reductions in the UCERF3 creep model are applied in two ways—

as an aseismicity factor, which reduces seismogenic area, and as a coupling coefficient, which 

reduces the slip rate. Details are discussed in the “Creep and Aseismicity” section.

In UCERF2, the moment rate reduction was set to zero for faults with no creep data.

However, it is very difficult to recognize creep on most California faults where slip rates are on 

the order of a few mm/yr, especially for low creep fractions. To account for this observational 

bias, UCERF3 applies a default aseismicity factor of 0.1 where data are lacking, which is the 

approximate average over all fault sections that have data, including those that are known not to 

creep. This implies a default 10 percent reduction in area and, consequently, in moment rate. 

Implied Moment Rates

Moment rate statistics for the UCERF3 deformation models are compared with UCERF2 

in table 4. The total moment rates for the UCERF3 deformation models range from 2.76×1019

N⋅m/yr to 2.85×1019 N⋅m/yr, which is a 16 to 20 percent increase over the UCERF2 value of 

2.37×1019 N⋅m/yr; the latter includes both the seismic and aseismic contributions listed in table 

4. This increase is consistent with the residuals shown in figure 6B, which are independent of the 

UCERF3 models. Also listed are the implied Mmax and mean recurrence intervals for M≥8 events 
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23

(assuming a truncated Gutenberg-Richter [GR] distribution), none of which appear to be 

unreasonable from a total moment rate perspective.

The on-fault moment rates for the UCERF3 models imply an increase between 1 and 17 

percent relative to UCERF2, all of which is the result of adding new faults (total moment rate 

changes considering only the same faults vary between +1 and -17 percent). For the geologic 

deformation model, 49 percent of the new-fault increase comes from just two fault section 

additions: Cerro Prieto (0.083×1019 N⋅m/yr) and Mendocino (0.054×1019 N⋅m/yr). 

Compared to UCERF2, off-fault moment rates increased from 37 to 60 percent among 

the new models. However, these total off-fault moment rates are not used as a direct constraint in 

UCERF3 (total moment rates are actually implied by other logic tree choices, as discussed 

below). In terms of the percentage of the total moment rate that is off-fault, the new deformation 

models have values between 32 and 37 percent, a bit higher than the UCERF2-implied value of 

27 percent. 

Figure 9 shows the spatial distribution of the off-fault and total moment rates given by 

the three GPS-based models (the geologic deformation model does not provide off-fault 

deformation), as well as total moment rate ratios with respect to UCERF2 and the UCERF3 

average. In general, the UCERF3 models are in better agreement with each other than with 

UCERF2, at least for off-fault moment rates. The ratios with UCERF2 show biggest differences 

near the edges of the RELM region.

The total deformation model moment-rate distributions can be compared to smoothed 

seismicity, which was used in UCERF2 for setting off-fault earthquakes rates. As discussed in 

more detail below, two smoothed seismicity models are used in UCERF3, one from UCERF2, 

based on a 50-km Gaussian smoothing function, and a new model based on an adaptive 

smoothing approach given in appendix M (this report). Figure 10 compares the moment rate 

maps implied by these two smoothed seismicity models with that of the average UCERF3 

deformation model (see figure caption for some important assumptions). The differences can be 

explained by one or more of the following: problems with the deformation models; temporal 

seismicity rate changes not reflected in the earthquake catalog; inadequate aftershock 

declustering in the smoothed seismicity maps; spatially dependent aseismicity; catalog 

completeness issues in some areas; the existence of characteristic magnitude-frequency 

distributions on faults; Gutenberg-Richter b-value and (or) maximum magnitude variability; or 

that there is no significant difference given overall uncertainties. We had originally hoped to set 

off-fault event rates using smoothed seismicity, and to then set maximum magnitudes to match 

the spatial variability of off-fault moment rates from the deformation models. This does not 

work, however, because some areas would need magnitudes greater than 10 to satisfy both the 

seismicity and deformation model moment rates.
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Figure 9. Maps showing spatial distribution of off-fault moment rates (first column) for the three 

UCERF3 deformation models that provide such estimates (for Fault Model 3.1 only), together with 

that implied by the UCERF2 forecast model (including both gridded sources and type C zones). 

Total moment rates (that is, including faults) are shown in the second column, and ratios with 

respect to the average UCERF3 results are shown in the third column (giving equal weight to each 

model, rather than the branch weights shown in figure 3). Ratios with respect to UCERF2 are shown 

in the fourth column. Details on how UCERF3 off-fault moment rate maps were computed, such as 

an assumed seismogenic thickness of 11 km, are given in appendix C (this report). 
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Figure 10. Maps showing the spatial distribution of moment rates implied by the UCERF2 smoothed

seismicity model (Petersen and others, 2008b) and the new UCERF3 smoothed seismicity model 

(appendix M, this report), compared to the average UCERF3 deformation model (described in figure 

9). The smoothed seismicity maps have the same total moment rate as the UCERF3 average, and 

they essentially assume a Gutenberg-Richter distribution with the same maximum magnitude 

everywhere. Also shown are ratios of the smoothed seismicity maps to the UCERF3 average 

(bottom row).
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Logic Tree Branch Weights

A complete description of deformation-model weighting is given in appendix C (this 

report), only a brief summary of which is provided here. All the UCERF3 deformation models fit 

their input datasets within overall observational uncertainties. The models generally fit the 

geologic observations better than the geodetic data, mostly because the former were given higher

weight to avoid strong along-fault slip rate variations that can occur when overfitting geodetic 

data. By design, the geologic deformation model fits the geologic data averages exactly. 

However, the geologic constraints on a significant fraction of California faults (~30 percent) are 

very weak to nonexistent, which was the primary reason to commission geodetic models in the 

first place. NeoKinema represents the best fit to GPS data, with average misfits three times lower 

than for the ABM and Zeng deformation models. The Zeng deformation model applies the 

minimum possible changes to geologic constraints in fitting GPS data and is explicitly 

constrained to stay within geologic bounds on most faults. 

In addition to consistency with geologic and geodetic data, appendix C (this report) also 

ranks the models in terms of overall moment rate, fit to plate-tectonic rates and directions, and 

the amount of off-fault deformation. All information was given to an ad hoc expert committee 

for evaluation and weighting. Members had varying opinions with respect to the value of each 

evaluation metric, which led to a wide range of suggested branch weights, but most members 

gave more credence to geologic observations. 

The models underwent further evaluation, review, and fine tuning following the ad hoc 

committee’s deliberations, with three fault-by-fault review meetings being particularly influential 

(table 2). The final UCERF3 weights are (also shown in figure 3): NeoKinema (30 percent), 

Zeng (30 percent), ABM (10 percent), and geologic (30 percent).

The ABM deformation model has the lowest weight because it tends to have relatively 

high slip rates at its block boundaries, which might be an artifact of the approach. The Zeng 

deformation model reflects minimal changes to geologic constraints; therefore the collective 

weight for the “more geologic” models is 0.6, and that for the “more geodetic” models (ABM 

and NeoKinema) is 0.4. This balance reflects our perspective on the applicability of short-term 

geodetic signals versus relatively long-term geologic slip rates in determining earthquake 

likelihoods in California. Whether the optimum balance should vary with forecast duration is a 

question for further study. We also note that final UCERF3 models do not necessarily match all 

slip rates exactly, because these constraints are weighed against others in the inversion described 

below. These deformation models’ weights are therefore a priori, and subject to effective 

modification.

Earthquake Rate Models and the “Grand Inversion”

The earthquake rate component of the UCERF3 model framework (fig. 2) defines the 

long-term rate of all possible earthquake ruptures above the magnitude threshold, M≥5, and with 

a discretization sufficient to represent hazard. Each earthquake rate model comprises two types 

of sources: ruptures with dimensions larger than the seismogenic depth occurring on explicitly 

modeled faults (supraseismogenic on-fault ruptures); and other earthquakes, modeled as 

seismicity on a 0.1o×0.1o geographic grid with each cell assigned a magnitude-frequency 

distribution (MFD) of earthquake nucleation rates. The gridded seismicity is separated into 

events inside a fault zone polygon (subseismogenic on-fault ruptures), and those outside all fault 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

27

zone polygons (off-fault ruptures). Cells partly inside and partly outside a fault zone polygon are 

fractionally apportioned. The complete bookkeeping details are given in appendix O (this report).

In UCERF2, the models for each fault were constructed separately, and background 

seismicity was then added. The UCERF3 procedure solves for the rates of all events 

simultaneously using the inversion method of Field and Page (2011), which builds on the work 

of Andrews and Schwerer (2000). This unified, system-level approach enables the relaxation of 

fault segmentation and the inclusion of multifault ruptures, two major goals of UCERF3. Its 

implementation has been dubbed the “grand inversion.” Aftershocks are included in the 

UCERF3 long-term rate model. To facilitate certain applications, we provide a procedure for 

removing aftershocks that is consistent with previous NSHMP practice.

Methodology

We first consider only those ruptures that occur on the faults included in the UCERF3 

fault and deformation models and only model events that have rupture lengths greater than or 

equal to the local seismogenic thickness. To relax segmentation, we subdivide each fault section 

into S equal-length subsections with lengths that are about half the seismogenic thickness, 

resulting in S=2606 for FM 3.1 (fig. 11) and 2664 for FM 3.2. The surfaces of possible ruptures 

are taken to be the complete set of two or more contiguous fault subsections. Requiring at least 

two subsections ensures that the minimum rupture lengths are approximately equal to the 

seismogenic thickness. The rupture set is filtered by retaining only ruptures that pass all of the 

following “plausibility” criteria, as detailed in appendix T (this report): 

• All fault sections connect within 5 km or less, as assessed in appendix J (this report). 

• Ruptures cannot include a subsection more than once. 

• Ruptures must contain at least two subsections of any main fault section, unless the only 

way two fault sections can connect is through a single-subsection connector, as described 

in appendix T (this report). 

• Ruptures can only jump between fault sections at their closest points (in 3D). 

• The maximum azimuth change between neighboring subsections is 60o, except for leftlateral to right-lateral connections such as Garlock to the San Andreas. 

• The maximum azimuth change between the first and last subsection is 60o, except for 

left-lateral to right-lateral connections such as Garlock to the San Andreas. 

• The maximum cumulative rake change (summing over each neighboring subsection pair) 

is 180o, based on rakes of the geologic deformation model to ensure rupture-set 

consistency. 

• The maximum cumulative azimuth change, computed by summing absolute values over 

each neighboring subsection pair, is less than 560o (a filter that reduces “squirreliness”; 

that is, many changes of azimuth).

• Branch points (potential connections between main fault sections) must pass a Coulomb 

criterion that earthquake triggering between the two fault sections is physically 

reasonable, as described in appendix T (this report). 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

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Figure 11. Map showing UCERF3 Fault Model 3.1 sections divided into an integral number of equal 

length subsections (lengths equal to, or just less than, half the section’s seismogenic thickness). All 

subsections shown in green are connected to all others in green without jumping more than 5 km 

between faults.

This filtering produces 253,706 and 305,709 unique “viable” ruptures for FM 3.1 and FM 

3.2, respectively. In comparison, mapping the UCERF2 ruptures onto their nearest equivalents in 

the FM 3.1 yields only 7,773 ruptures. The much larger UCERF3 rupture set reflects the high 

connectivity of California’s fault system—nearly all the fault sections connect to each other 

without jumping more than 5 km (green subset in figure 11). Again, it is believed that ignoring 

this connectivity in UCERF2 may have contributed to an overprediction of moderate sized 

earthquake rates. In any case, UCERF2 generally lacks types of multifault ruptures that have 

been seen in nature.

It is important to note, however, that UCERF3 rupture sets are still an approximation of 

the system. For example, the 5-km fault separation cutoff, which is based on both theoretical and 

empirical studies (Harris and Day, 1993; Wesnousky, 2006), presumes knowledge of fault 

connectivity at depth that we do not have. Of the “viable” ruptures that pass the above test, one 

could almost certainly identify at least a few that are in some ways less likely than ruptures that 

have been filtered out. The relevant question is whether the current approach is a better 

approximation than largely ignoring multifault ruptures (as in UCERF2). Moreover, seismic 

hazard is more sensitive to the combined magnitude-frequency distribution of nearby faults, 

rather than to the details of individual ruptures, as will be discussed below. 

The inversion method estimates the long-term rates of the R viable ruptures {fr : r = 1, 2, 

..., R} by solving the system of equations described in table 5. The equations can be weighted by 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

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the uncertainties in the data and (or) by the degree of belief in the importance of a particular 

constraint. Conceptually, this approach is simpler, more objective, and more reproducible than 

that adopted in UCERF2. For example, the (largely artificial) distinction between type A and 

type B faults has been dropped, and type C zones have been merged into off-fault seismicity.

In addition to setting equation-set weights, subjectivity is also involved in assigning 

weights to alternative logic tree branches. Both of these, however, can be guided by how well the 

models fit the data. What the grand inversion really represents is a system-level framework for 

both incorporating expert opinion and for identifying a more complete range of models that are 

consistent with all available data. The framework is also extensible, in that other equations-set 

constraints could easily be added to the list in table 5; as we said repeatedly during development 

and review—tell us what you don’t like about a result and you have given us a new inversion 

constraint. 

In an exploratory study, Field and Page (2011) solved the inverse problem by the 

nonnegative least squares algorithm of Lawson and Hanson (1974). This algorithm is not 

computationally feasible for an inversion using the statewide system of faults. Therefore, we 

have developed a parallelized code that can efficiently solve very large equation sets by 

simulated annealing, as described in appendix N (this report). Owing to the stochastic nature of 

the algorithm, simulated annealing can also provide a range of models that sample the solution 

space of the inverse problem, which generally is underdetermined, or mixed-determined at best. 

This sampling can be used to represent the epistemic uncertainty associated with model 

nonuniqueness. 

Appendix N also discusses a number of important inversion implementation details, 

including the tuning of equation-set weights, the sensitivity of the results to those weights, final 

misfits with respect to the various data constraints, reproducibility tests based on synthetic 

datasets, and alternative simulated annealing algorithms. 

Implementation Ingredients

This section describes the various data and models used in the grand inversion, organized 

according to the equation sets of table 5. 

Slip Rate Balancing (Equation Set 1)

Equation set 1 of table 5 involves satisfying the fault section slip rates (vs) defined by the 

given deformation model. Doing so requires knowledge of the average slip on the s

th subsection 

in the r

th rupture (Dsr), where the average is over multiple occurrences of the event, and where 

the slip value is that at midseismogenic depths. Using such slip rate matching, rather than the 

moment rate balancing of previous WGCEPS, avoids potential depth-of-rupture ambiguities. We 

first compute the average slip for a given rupture, Dr, and then partition this among the 

subsections to get Dsr. 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

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Table 5. The grand inversion system of equations used in solving for the long-term rate of faultbased ruptures, where fr represents the frequency or rate of the rth rupture. 

[Important implementation details, such as equation-set weighting, are given in appendix N (this report)] 

Equation set Description

�Dsrfr = vs

R

r=1

(1) Slip Rate Balancing: vs is the subsection slip rate (from a 

deformation model) and Dsr is the slip on the sth subsection in 

the rth event, averaged over multiple occurrences of the rupture 

and as measured at mid-seismogenic depth.

�GsrPr

paleofr = fspaleo

R

r=1

(2) Paleoseismic Event Rate Matching: is a 

paleoseismically inferred event rate estimate, Gsr specifies 

whether the rth rupture utilizes the sth subsection (0 or 1), and 

is the probability that the rth rupture would be seen in a 

paleoseismic trench.

Rs

m = Rs−1 m + Rs+1 m

2

(3) Fault Section Smoothness Constraint: This enables forcing 

the nucleation rate, R, in the mth magnitude bin to vary 

smoothly along a fault section, where the s-1 and s+1 

subsections are adjacent to the sth subsection.

λrfr = 0 (4) Improbability Constraint: This allows us to force relatively 

improbable events to have a lower rate (for example, based on 

multi-fault rupture likelihoods). A higher value of adds more 

misfit for a given rupture rate, forcing the inversion to 

minimize that rupture rate further.

fr = fr

a−priori (5) A Priori Constraint: This constrains the rates of particular 

ruptures to target values, either on an individual basis (for 

example, make Parkfield occur every ~25 years) or for a 

complete rupture set (for example, as close as possible to those 

in UCERF2).

�Mgr

m fr = Rgm

R

r=1

(6) Regional MFD Constraint: This enables forcing a geographic 

region, g, to have a specified magnitude-frequency distribution 

(MFD), such as Gutenberg-Richter. Rg

m represents the 

nucleation rate for the mth magnitude bin in the gth region. 

Matrix Mgr

m fr contains the product of whether the rth rupture 

falls in the mth magnitude bin (0 or 1) multiplied by the fraction 

of that rupture that nucleates in the gth region. 

�Msr

mfr = Rsm

R

r=1

(7) Fault Section MFD Constraint: This enables forcing 

subsections to have specific nucleation MFDs. Rs

m is the 

nucleation rate for the mth magnitude bin on the sth subsection. 

Matrix Msr

mfr contains the product of whether the rth rupture 

falls in the mth magnitude bin (0 or 1) multiplied by the fraction 

of that rupture that nucleates on the sth subsection.
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

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The magnitude of each rupture is computed from a magnitude-area relationship, M(Ar). In 

UCERF2 the Hanks and Bakun (2008) and Ellsworth B (Working Group on California 

Earthquake Probabilities, 2003) relationships were used with equal weights. For UCERF3, we

have also included a slightly modified version of the Shaw (2009) relationship, as justified in 

Shaw (2013) and appendix E (this report). These three relationships, referred to hereafter as 

HanksBakun08, EllsworthB, and Shaw09mod, are plotted in figure 12, and their functional forms 

are as follows:

M = 3.98 + log(A) if A ≤ 537 km2 (M ≤ 6.71) HankBakun08 

M = 3.07 + (4 3⁄ )log(A) if A > 537 km2 (Hanks and Bakun, 2008) 

M = 4.2 + log(A) EllsworthB 

(WGCEP, 2003) 

M = 3.98 + log(A) + (2/3)log �

2 Max�1.0,�A/Wo

2�

1+Max�1.0,� A

7.4Wo

2��

� Shaw09mod 

(Shaw, 2009, 2013) 

where M is magnitude, A is area (km), and Wo is the original downdip width (unreduced by 

aseismicity).

Two different approaches are used to get Dr for each rupture. One, used in UCERF2, 

involves converting the magnitude from the M(Ar) relationship to moment and then dividing by 

the rupture area Ar and shear modulus μ to get Dr: 

where Mor is the moment of the r

th rupture. The shear modulus (μ) is assumed to be 3.0×1010 Pa 

throughout this report. 

Because Ar is based on the depth of microseismicity, Dr might be an overestimate if slip 

extends below such depths in larger ruptures. Therefore, an alternative is to obtain Dr using one 

of two viable slip-length scaling relationships, which have been derived from surface-slip 

observations (Shaw, 2013) and updated here in appendix E (this report) using the enhanced 

UCERF3 surface slip database in appendix F (this report). The first, which assumes slip scales as 

the square root of length, is given as:

 Dr = 0.22�Lr SqrtLength 

The second, which assumes constant stress drop, is given as:

 Dr = 0.151 � 7

3Lr

+ 1

30�

−1

ConstStressDrop

where Dr is average slip in meters and Lr is length in km. Appendix E (this report) gives the full 

functional forms in terms of physical parameters. Neither of these relationships is applicable 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

32

when the average aseismicity factor is ≥0.2; in such cases, Dr is obtained from magnitude and 

area, as described above. 

Examples obtained using these two slip-length models, as well as using the three 

magnitude-area relationships above, are given in figure 12 (bottom). The slip-length models 

generally give a smaller Dr for longer ruptures, which could be real (for example, due to slip 

penetrating below the depth of microseismicity) or it could represent a bias in slip measurements 

(for example, surface values being lower than those at seismogenic depths). Adding these sliplength relationships therefore provides an element of epistemic uncertainty not included in 

UCERF2.

Figure 12. Graphs showing the magnitude-area (top) and slip-length (bottom) relationships used in 

UCERF3, which are documented in appendix E (this report). The M(A)-derived slip-length curves at 

the bottom assume an average seismogenic thickness of 11 km in converting area to length.
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

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As discussed in appendix E (this report), some magnitude-area and slip-length 

relationship combinations are incompatible with the underlying assumptions. For example, using 

HanksBakun08 to get magnitude from area and then using ConstStressDrop to get slip from 

length can lead to unreasonably large widths for long ruptures..

Table 6 lists the combinations allowed in UCERF3, together with their associated 

weights, which are also shown in figure 3. All branches are given equal weight in UCERF3.

Table 6. Magnitude-area and slip-length model combinations used in UCERF3*

Magnitude-Area 

Relationship

Slip-length Relationship Branch

Weight

EllsworthB EllsworthB 20%

HanksBakun08 HanksBakun08 20%

Shaw09mod Shaw09mod 20% 

EllsworthB SqrtLength 20%

Shaw09mod ConstStressDrop 20% 

*See appendix E (this report) for equations and explanations. 

We need to partition Dr among the subsections used by each rupture to get Dsr, which 

again represents the average over multiple occurrences of the rupture. As discussed in appendix 

F (this report), the preferred choice is the observationally based “tapered-slip” (square-root-sine) 

model of Weldon and others (2008), which is shown in figure 13. This tapered-slip model was 

applied in UCERF2 when solving for the rate of ruptures on type A faults. The assumption here 

is that intraevent, along-strike slip variability averages out over multiple occurrences to yield the 

tapered shape. In UCERF3 this tapered-slip model is also applied to multifault ruptures, 

implying that there is no pinching out of the average slip at fault stepovers. 

Figure 13. Graph of mean rupture profile based on a stack of 13 mapped surface ruptures. The stack 

was obtained by normalizing the observed profiles to unit length and averaging them with their 

reflections about the midpoint. The details of this analysis are presented in UCERF2, appendix E 

(Weldon and others, 2008).

The choice of Dsr model should be consistent with how slip rates vary in the deformation 

model; for example, if slip is persistently low at fault stepovers, then the slip rates should be 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

34

lower there too. Because the deformation models do not resolve such along-strike slip rate 

variations, applying a multi-rainbow shape is not warranted, especially given the epistemic 

uncertainty about what is happening at seismogenic depths. However, because the deformation 

model slip rates do not ramp down toward the ends of faults that terminate (that is, where there 

are no connections to other faults), applying the tapered slip might artificially introduce a higher 

rate of smaller earthquakes to satisfy slip rates at these endpoints. To minimize this potential 

problem, UCERF3 also uses use a uniform (boxcar) slip distribution (Dsr = Dr) as an alternative 

logic tree branch, and the two options are given equal weight. A more correct solution may be to 

taper both the slip and the slip rates at fault terminations or intersections. Better observations are 

needed to constrain how the multifault slip functions actually vary in nature. 

The UCERF3 framework is capable of applying the WGCEP (2003) Dsr model, in which 

the slip is proportional to the slip rate of each subsection. However, this option is given zero 

weight for the same reasons it was excluded in UCERF2—lack of observational support and 

implications that some ruptures cannot happen. There is some evidence to support a 

characteristic slip model where the amount of slip on a subsection is similar for all ruptures

(Hecker and others, 2013), but applying this would be difficult because of very limited 

observational constraints, which would require the propagation of large epistemic uncertainties 

that have unknown spatial correlations. Instead, we compare the slip-per-event implications of 

UCERF3 with the results from Hecker and others (2013).

Because the inversion is solving for the rate of seismogenic thickness and larger ruptures, 

the slip rates in equation set 1 need be reduced to account for the moment released in 

subseismogenic events. This correction differs between Characteristic and Gutenberg-Richter

logic tree branches (listed under Inversion Model in figure 3), details of which are given in the 

“Inversion Setup and Associated Gridded Seismicity” section. 

Paleoseismic Event Rate Matching (Equation Set 2)

Equation set 2 matches event rates derived from paleoseismic trench studies. Not all 

ruptures that occur beneath a site are paleoseismicially observable, so we use the factor Pr

paleo to 

specify the probability that the r

th rupture will be seen in a trench study. In UCERF3, there are 

two types of event rate constraints: direct event rates derived from paleoseismically observed 

dates of events; and proxy event rates obtained from average slip-per-event data, where the 

proxy rate equals slip rate divided by the average slip. We distinguish fr

paleo and Prpaleo for 

these two data types as fr

paleo−event−rate and Prpaleo−event−rate

 versus fr

paleo−slip−proxy and 

Pr

paleo−slip−proxy, respectively.

Appendix G (this report) provides an updated compilation of event dates for various 

paleoseismic studies in California, and appendix H (this report) provides estimates of the mean 

paleoseismic event rates, fr

paleo−event−rate, implied by these data. The updated rates are 

compared with values used in UCERF2 in table 7, where we now have 31 constraints (9 more 

than in UCERF2). 

A new model for the probability of seeing a given rupture in a trench, Pr

paleo−event−rate, 

is given in appendix I (this report). The probability depends on both the average slip of the 

rupture, Dr, and the position of the site relative to the nearest end of the rupture, implying that 

one is less likely to observe surface offsets near the ends of a rupture, consistent with the tapered 

slip model. Table 8 lists representative values for Pr

paleo−event−rate. In principle, this could be 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

35

done on a trench-by-trench basis to account for the unique depositional environment at each site. 

The probability model adopted in UCERF3, however, is generic. 

Appendix R (this report) provides a compilation of average slip-per-event data, derived 

from either offset features or paleoseismic trench studies where available for California faults. 

These are reproduced here in table 9, which also lists the associated proxy event rates, 

fr

paleo−slip−proxy, implied by each deformation model. Although measurement uncertainties are 

given for the average slips in appendix R, the associated confidence bounds are not listed in table 

9 because they do not reflect the additional uncertainty due to the limited sampling of events. 

Appendix R also provides a model for Pr

paleo−slip−proxy, which represents a simple linear 

interpolation between the values listed here in table 10. 

Fault Section Smoothness Constraint (Equation Set 3)

A problem we encountered in an earlier version of the model (UCERF3.0) was that, in 

satisfying the above paleoseismic event rates, the inversion would simply put a high (or low) rate 

of events right at the paleoseismic sites. This produced artificially sharp peaks and troughs in the 

rate of events along strike. Equation set 3 mitigates this behavior by providing an along-fault 

smoothing constraint that minimizes curvature in the along-fault rate of events. We apply this 

smoothing only to fault sections that have one or more paleoseismic event-rate constraints, and 

confine it to the internal subsections of that section. That is, we do not apply this smoothing 

beyond the ends of fault sections, because this would require additional assumptions and careful 

bookkeeping at fault branches. 

Improbability Constraint (Equation Set 4)

Improbability constraints can force a lower rate on any designated event or event type, 

such as multifault ruptures involving large jumps. Appendix J (this report) summarizes the 

various observational and theoretical studies that can guide the assignment of improbability 

constraints. However, the Coulomb stress-transfer calculations given in appendix T (this report) 

were used to cull the total UCERF3 rupture set down to a subset deemed viable. Furthermore, the 

rates of multifault ruptures are already constrained in the inversion by both slip rate balancing 

(larger ruptures consume more slip) and by the regional GR constraint (larger events have lower

collective rates), rendering an improbability constraint somewhat redundant. We therefore have 

not applied any improbability constraints in UCERF3, and this choice is supported by results 

presented below.
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Table 7. Event rate estimates and mean recurrence intervals (MRIs) at paleoseismic sites from appendix H (this report), based on the data 

compilation in appendix G (this report).

[Comparisons to UCERF2 MRIs are also listed for sites that had data in that study. The “16%” and “84%” columns represent the 68-percent confidence bounds 

for the mean estimates] 

Site Lat Lon Mean Rate

(per yr) 16% 84% MRI (yr) 16% 84% UCERF2

Calaveras fault - North 37.5104 -121.8346 1.62E-03 1.16E-03 2.24E-03 618 446 859 445

Compton 33.9660 -118.2629 3.76E-04 2.46E-04 5.72E-04 2658 1748 4059

Elsinore - Glen Ivy 33.7701 -117.4909 5.58E-03 4.63E-03 6.77E-03 179 148 216 291

Elsinore Fault - Julian 33.2071 -116.7273 3.08E-04 5.35E-05 5.62E-04 3251 1779 18702 1193

Elsinore - Temecula 33.4100 -117.0400 9.81E-04 5.23E-04 1.88E-03 1019 533 1914 741

Elsinore - Whittier 33.9303 -117.8437 3.13E-04 5.45E-05 5.73E-04 3197 1747 18358 1256

Frazier Mountian, SSAF 34.8122 -118.9034 6.73E-03 4.97E-03 9.09E-03 149 110 201

Garlock Central (all events) 35.4441 -117.6815 6.97E-04 4.59E-04 1.06E-03 1435 941 2178 729

Garlock - Western (all events) 34.9868 -118.5080 8.13E-04 5.29E-04 1.25E-03 1230 798 1889 711

Green Valley - Mason Road 38.2341 -122.1619 3.41E-03 2.50E-03 4.66E-03 293 215 399

Hayward fault - North 37.9306 -122.2977 3.14E-03 2.52E-03 3.92E-03 318 255 396 363

Hayward fault - South 37.5563 -121.9739 5.97E-03 5.24E-03 6.80E-03 168 147 191 210

N. San Andreas - Alder Creek 38.9813 -123.6770 1.15E-03 2.01E-04 2.11E-03 870 474 4984

N. San Andreas - Santa Cruz 36.9626 -121.6981 9.10E-03 7.04E-03 1.18E-02 110 85 142 115

N. San Andreas - Fort Ross 38.5200 -123.2400 3.27E-03 2.74E-03 3.88E-03 306 258 366 360

N. San Andreas - North Coast 38.0320 -122.7891 3.79E-03 3.03E-03 4.73E-03 264 211 330 248

N. San Andreas -Offshore Noyo 39.5167 -124.3333 5.33E-03 4.63E-03 6.14E-03 188 163 216

Puente Hills 33.9053 -118.1104 2.85E-04 2.32E-04 3.52E-04 3506 2842 4313

San Gregorio - North 37.5207 -122.5135 9.81E-04 1.72E-04 1.80E-03 1019 554 5824 480

Rodgers Creek 38.2623 -122.5334 3.07E-03 1.99E-03 4.79E-03 325 209 503

San Jacinto - Hog Lake 33.6153 -116.7091 3.21E-03 2.41E-03 4.28E-03 312 234 416 233

San Jacinto - Superstition 32.9975 -115.9436 1.97E-03 1.07E-03 3.65E-03 508 274 938 402

S. SAF- Carrizo Bidart 35.2343 -119.7887 8.72E-03 6.49E-03 1.17E-02 115 86 154

S. San Andreas – Burro Flats 33.9730 -116.8170 4.87E-03 3.68E-03 6.41E-03 205 156 272 234

S. San Andreas - Coachella 33.7274 -116.1701 5.60E-03 4.16E-03 7.55E-03 179 132 241

S. San Andreas - Indio 33.7414 -116.1870 3.61E-03 2.81E-03 4.61E-03 277 217 357 358

S. San Andreas - Pallett Creek 34.4556 -117.8870 6.70E-03 5.45E-03 8.26E-03 149 121 184 136

S. San Andreas - Pitman Canyon 34.2544 -117.4340 5.76E-03 4.47E-03 7.41E-03 174 135 224 261

S. San Andreas - Plunge Creek 34.1158 -117.1370 4.87E-03 3.67E-03 6.28E-03 205 159 272 361

S. SAF M. Creek - 1000 Palms 33.8200 -116.3010 3.83E-03 3.07E-03 4.80E-03 261 208 326 303

S. San Andreas - Wrightwood 34.3697 -117.6680 9.43E-03 7.97E-03 1.12E-02 106 90 125 98
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Table 8. Example values from the probability of paleoseismic detection model ( ) used in 

equation set 2 of the inversion, from appendix I (this report).

Average Slip

(Dr, meters)

Magnitude

(approximate)

Probability of Detection

(“Dist” is fractional distances from end of rupture)

Dist = 0.05 Dist = 0.25 Dist = 0.5

0.08 5.5 0.01 0.02 0.02

0.16 6.0 0.06 0.11 0.14

0.88 6.5 0.53 0.62 0.64

2.04 7.0 0.80 0.82 0.83

3.20 7.5 0.95 0.96 0.97

4.36 8.0 0.98 0.99 0.99

Table 9. Average slip data from appendix R (this report), where the first 17 rows are from table 5

therein (average slip from offset features), and the last 6 rows (shaded) are from table 6 therein

(based on paleoseismic trench studies).

[Also listed are the proxy mean event rates and proxy mean recurrence intervals implied by each deformation 

model] 

Fault 

Section, 

Subsection #

Lat2 Lon2

Average 

Slip

(m)

ABM Geologic NeoKinema Zeng

Proxy

Rate

Proxy

MRI

Proxy

Rate

Proxy

MRI

Proxy

Rate

Proxy

MRI

Proxy

Rate

Proxy

MRI

San Andreas 

(Carrizo) 

rev, 1 35.24 -119.79 3.52 7.57E-03 132 9.11E-03 110 8.52E-03 117 6.79E-03 147

San Andreas 

(Carrizo) 

rev, 5 35.05 -119.56 4.06 6.47E-03 155 7.89E-03 127 7.38E-03 135 5.88E-03 170

San Andreas 

(Carrizo) 

rev, 6 35.01 -119.50 4.61 5.66E-03 177 6.95E-03 144 6.50E-03 154 5.18E-03 193

San Andreas 

(Cholame) 

rev, 8 35.65 -120.20 2.50 1.06E-02 94 1.28E-02 78 9.47E-03 106 1.02E-02 98

San Andreas 

(Coachella) 

rev, 4 33.64 -116.06 2.99 6.12E-03 163 6.29E-03 159 5.16E-03 194 6.21E-03 161

San Andreas 

(Coachella) 

rev, 10 33.44 -115.82 3.20 5.73E-03 174 5.89E-03 170 4.83E-03 207 5.82E-03 172

San Andreas 

(Mojave S), 

2 34.64 -118.35 2.87 6.05E-03 165 1.07E-02 94 8.87E-03 113 6.56E-03 152

San Andreas 

(Mojave S), 

3 34.62 -118.28 2.85 6.08E-03 164 1.07E-02 93 8.92E-03 112 6.60E-03 152

Elsinore 

(Julian), 5 33.24 -116.78 1.12 2.99E-03 334 2.52E-03 396 1.23E-03 815 2.18E-03 458

Garlock 

(West), 10 35.13 -118.22 4.68 8.66E-04 1155 1.53E-03 654 1.15E-03 873 3.37E-04 2971

Garlock 

(West), 12 35.20 -118.09 3.46 1.23E-03 813 2.07E-03 484 1.55E-03 646 4.55E-04 2199
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

38

Fault 

Section, 

Subsection #

Lat2 Lon2

Average 

Slip

(m)

ABM Geologic NeoKinema Zeng

Proxy

Rate

Proxy

MRI

Proxy

Rate

Proxy

MRI

Proxy

Rate

Proxy

MRI

Proxy

Rate

Proxy

MRI

Garlock 

(Central), 15 35.57 -117.15 3.11

1.12E03 8922.12E03 4721.68E03 5952.27E03 441

San Jacinto 

(Anza) rev, 

1 33.68 -116.82 1.87

4.61E03 2177.05E03 1425.97E03 1686.46E03 155

San Jacinto 

(Anza) rev, 

5 33.51 -116.55 1.44

5.99E03 1679.15E03 1097.74E03 1298.38E03 119

San Jacinto 

(Clark) rev, 

0 33.47 -116.48 2.94

1.92E03 5212.57E03 3901.56E03 6411.99E03 504

San Jacinto 

(Clark) rev, 

1 33.43 -116.41 2.50

2.25E03 4443.01E03 3321.83E03 5462.33E03 429

San Jacinto 

(Clark) rev, 

4 33.31 -116.21 1.30

2.48E03 4043.52E03 2843.52E03 2844.49E03 223

Compton, 2 33.97 -118.26 2.80

2.85E04 35103.03E04 33032.89E04 34563.97E04 2516

Puente Hills, 

2 33.91 -118.11 2.77

2.05E04 48723.06E04 32644.02E04 24854.34E04 2304

Puente Hills, 

2 33.91 -118.11 2.93

1.94E04 51662.89E04 34613.80E04 26344.09E04 2443

San Andreas 

(Carrizo) 

rev, 0 35.27 -119.83 5.42

4.91E03 2045.91E03 1695.53E03 1814.40E03 227

San Andreas 

(Mojave S), 

13 34.37 -117.67 3.15

5.51E03 1819.72E03 1038.08E03 1245.98E03 167

San Andreas 

(Mojave S), 

9 34.46 -117.89 6.00

2.89E03 3465.10E03 1964.24E03 2363.14E03 319

1

Sections, subsections correspond to Fault Model 3.1.

2

Location (Lat, Lon) is approximately halfway down the trace of fault subsection listed in column 1.

Table 10. Probability of observing surface slip (Pr

paleo−slip−proxy) as given in appendix R (this 

report). [Values are linearly interpolated between those listed] 

Slip

(Dsr, meters)

Probability of 

Detection

0.0 0.0

0.25 0.1

≥2.0 0.95

Total Regional Rate of M≥5 Events

A fundamental parameter and logic-tree branch choice is the total rate of M≥5 events per 

year, denoted RM≥5

total, that occur within the UCERF3 model region (shown in figure 1). The 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

39

seismicity analysis in appendix L (this report) determines seismicity rates using data for the time 

periods 1850–2011 (historical and instrumental) and 1984–2011 (modern instrumental catalog). 

We use the UCERF2 catalog completeness thresholds calculated by Felzer (2008) for eight 

different regions and over a variety of different eras based on changes in data availability with 

time. One modification is a drop in the 1850–1865 completeness threshold from M8.0 to M7.4, 

based on the determination that an M>7.4 earthquake would probably have been felt over a 

sufficiently wide area to have been noted, despite the sparse population. The lower magnitude 

cutoff has also been reduced from M4 in UCERF2 to M2.5 here, and all rate calculations include 

the UCERF2 corrections for magnitude uncertainties and rounding errors (Felzer, 2008). 

The rates for each era have been averaged together, weighted linearly by era duration.

This differs from the Weichert (1980) method applied by the NSHMP and used in the UCERF2 

smoothed seismicity model, where each era is weighted by the number of earthquakes contained. 

The Weichert (1980) method produces a more accurate result if the underlying rates are the same 

in each era. However, if the seismicity rate changes with time, as implied by the empirical 

models of WGCEP 2003 and 2007, the Weichert (1980) method produces a result that is heavily 

skewed towards the instrumental era. When computing an observed seismicity rate for UCERF2, 

the Weichert method was applied in three long time periods, and the results from those three 

time periods were averaged. This somewhat minimizes the effect of the weighting by the number 

of events in the Weichert method. By using more and smaller time periods in UCERF3, we have 

completely eliminated the assumptions of constant rate.

The 1850–2011 rate averages for each region were summed to obtain the total regional 

rate. A new global analogue model has also been used to account for possible temporal rate 

variations, leading to the following branch options for RM≥5

total: 6.5 events/yr (10 percent weight), 

7.9 events/yr (60 percent weight), 9.6 events/yr (30 percent weight). The preferred value (7.9) is 

5 percent greater than the value of 7.5 given in UCERF2 (see Felzer, 2008), and the branchaveraged UCERF3 value (8.3) is 11 percent greater than the UCERF2 value. In addition to 

dropping the Weichert method completely, part of this difference comes from 5 years of 

additional data and from decreasing the lower magnitude cutoff. Asymmetric weights are used

here because the post-1850 era is more likely to be below, rather than above, the true average 

rate, especially given the lack of any M≥8 events during this time period. 

It is important to note that the UCERF2 observed value of 7.5 was not used as an explicit 

constraint in that model, with the final implied UCERF2 value (~5.8 M≥5 events per year) being 

determined primarily by the smoothed seismicity model (see Petersen and others, 2008b). 

Therefore, the gridded seismicity component of UCERF2 is more consistent with recent 

seismicity rates, and thereby effectively includes the empirical time-dependent models of 

WGCEP 2003 and 2007. We believe the long-term rates are more appropriate for the UCERF3 

earthquake rate model, especially given that users will be able to apply any empirical model 

correction that makes it into the forthcoming time-dependent components. As a consequence, the 

preferred UCERF3 rate (7.9) is 36 percent greater than the effective UCERF2 model rate (5.8), 

and the UCERF3 branch-averaged rate (8.3) is 43 percent greater. 

Off-Fault Spatial Seis PDF

The spatial distribution of off-fault gridded seismicity is set by choosing one of the 

spatial probability density maps shown in figure 14 (referred to as the Off-Fault Spatial Seis PDF

logic-tree branch in figure 3, sometimes abbreviated as SpatialPDF here). One option is the 

UCERF2 smoothed seismicity map (fig. 14A) from the UCERF2, appendix J (Petersen and 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

40

others, 2008b), which is based on the Frankel (1995) methodology. This represents M≥4 events 

smoothed using 2D Gaussian kernel with a sigma of 50 km, and a somewhat narrower, 

anisotropic smoothing near a few active faults. 

Figure 14. Maps showing the various off-fault spatial seismicity probability density functions 

(SpatialPDF) used in UCERF3 for setting gridded seismicity (referred to as the Off-Fault Spatial Seis 

PDF logic tree branch in figure 3). Values in each map sum to unity. A, The UCERF2 Smoothed 

Seismicity model. B, The UCERF3 Smoothed Seismicity model of Felzer (appendix M, this report), 

which has a higher resolution, adaptive smoothing kernel. C, SpatialPDF implied by the average of 

the off-fault moment rate maps from appendix C (this report), which includes the Average Block 

Model, NeoKinema, and Zeng deformation models, and averages over maps for both Fault Models 

3.1 and 3.2.

Another SpatialPDF option is the “UCERF3 Smoothed Seismicity” map shown in figure 

14B, which was developed by Felzer (appendix M, this report) using the adaptive smoothing 

algorithm of Helmstetter and others (2007). Specifically, this considers M≥2.5 events, and the 

sigma of a 2D Gaussian smoothing kernel is determined by the distance to the n

th closest 

earthquake, where n=8 was chosen here based on optimization tests given in appendix M. Such 

higher resolution smoothing has had superior performance in the formal RELM tests (for 

example, Zechar and others, 2013) and is more consistent with surveys of precariously balanced 

rocks (for example, Brune and others, 2006). Nevertheless, UCERF2 smoothing may be more 

appropriate for the larger events that dominate hazard (M>6), and (or) for the longer term 

forecasts of interest for building codes. 

A third SpatialPDF option is to use the off-fault moment-rate map associated with the 

chosen deformation model (appendix C, this report), which was shown previously in figure 9, or 

the average of the three models that provide off-fault estimates (fig. 14C). The specification of 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

41

SpatialPDF branch weights differs between the Characteristic and Gutenberg-Richter Inversion 

Model options (fig. 3) and will therefore be discussed in the section on “Inversion Setup and 

Associated Gridded Seismicity”.

Fraction of Seismicity On Versus Off Faults

Like previous WGCEP and NSHMP models, the UCERF3 framework explicitly 

differentiates between fault-based sources and off-fault (gridded) seismicity, starting with the 

deformation model. The fraction of observed seismicity attributable to on-fault versus off-fault 

events is implied by both the choice of SpatialPDF (fig. 14) and the fault zone polygons (as a 

proxy for all events within). Summing the PDF values inside all fault zones implies the following 

percentage of on-fault seismicity:

• 53 percent for UCERF2 smoothed seismicity paired with Fault Model 3.1 

• 58 percent for UCERF2 smoothed seismicity paired with Fault Model 3.2 

• 53 percent for UCERF3 smoothed seismicity paired with Fault Model 3.1 

• 59 percent for UCERF3 smoothed seismicity paired with Fault Model 3.2 

None of the deformation models are used to calculate the percentage of on-fault seismicity

because doing so requires assuming the MFD at each location, as well as the fraction of moment 

that is released aseismically, both on- and off-fault.

Maximum Off-Fault Magnitude (Mmax

off−fault)

Another logic tree choice is the assumed maximum magnitude of off-fault seismicity, 

Mmax

off−fault. The three branch options applied in UCERF3 are 7.3, 7.6, and 7.9, with weights of 

10, 80, and 10 percent, respectively (fig. 3). For UCERF2, Mmax

off−fault was spatially variable, 

being 7.6 in the type C zones and 7.0 for gridded seismicity elsewhere, with a custom reduction 

near faults to avoid double counting with fault-based sources. As such, Mmax

off−fault has increased 

in UCERF3 for areas away from faults and outside type C zones, driven in part by the 2010 M7.2 

El Mayor-Cucapah earthquake exceeding the UCERF2 background-seismicity value of 7.0 

(although whether this event was on- or off-fault is ambiguous in UCERF2, as noted above). 

Branch weights were based on expert-opinion consensus, with the low weight at M7.3 being 

driven by high, implied off-fault aseismicity (when comparing consequent moment rates to the 

deformation model values in table 4), and the low weight at M7.9 reflecting a lack of evidence 

for such events (even though they are rare). The fact that three Mmax

off−fault options are provided 

is an improvement over UCERF2, which only had a single branch for off-fault seismicity.

Inversion Setup and Associated Gridded Seismicity

Here we describe the “Characteristic” versus “Gutenberg-Richter” branch options for the 

Inversion Model (fig. 3), including their conceptual motivation, how the remaining inversion 

constraints are constructed, and how the gridded seismicity is specified for each option. A 

supplementary file U3_PreInversionAnalysisTable, given in the “Data and Resources” section, 

lists many of the metrics discussed here for each potential logic tree branch.

Characteristic Branches

These branches represent the possibility that faulting is governed by “characteristic 

behavior,” which has come to mean one or more of the following: segmentation of faulting, in 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

42

which ruptures persistently terminate at certain locations; an increased rate of events at higher 

magnitudes compared to an extrapolation of the Gutenberg-Richter magnitude frequency 

distribution from smaller magnitudes; and a narrow range of slip from event to event at a point 

on a fault. In principle, these attributes could be implemented as direct constraints in the grand 

inversion. However, distilling the essence of a characteristic model into independent inversion 

constraints has proven difficult. 

For the UCERF3 model presented here, the Characteristic branch is defined by forcing, 

via equation set 7, each fault subsection to stay as close as possible to an a priori characteristic 

nucleation MFD, in which there is an increased rate of higher magnitude events. For both the 

new faults and those designated as type B in UCERF2, the total nucleation MFD for each fault 

section was constructed by putting one-third of the moment rate into a Gutenberg-Richter 

distribution and two-thirds into a characteristic distribution. For the Gutenberg-Richter 

component the minimum magnitude was set by the smallest supraseismogenic rupture on that 

section; maximum magnitude was set by the total fault section area and the chosen magnitudearea relationship; b-value was set as 1.0 (aftershocks are included); and a-value was set to satisfy 

one-third of the section slip rate, reduced for subseismogenic ruptures as quantified below. 

The characteristic component is represented with a single magnitude at the GutenbergRichter maximum magnitude, with an event rate that satisfies two-thirds of the slip rate (also 

reduced for subseismogenic ruptures). No aleatory variability in magnitude is given for the 

characteristic portion, although such variability can be added later for hazard calculations, as was 

done in UCERF2. The total characteristic nucleation MFD (the sum of both the GutenbergRichter and characteristic portions) is generally consistent with past NSHMP models. However, 

it is not exactly the same as that for type B faults in UCERF2, because the latter had branches 

both for connecting more type B faults (into megafaults) and for setting b-value to zero on the 

Gutenberg-Richter portion. These latter options were introduced in UCERF2 only to mitigate an 

overprediction of event rates near M6.7 (the bulge problem), which is handled directly in the 

UCERF3 grand inversion. 

For fault sections that were designated as type A in UCERF2, the characteristic 

nucleation MFD constraint is defined as that implied by UCERF2, averaged over all branches. 

This approach preserves the extra attention given to type A faults in UCERF2. The resultant 

characteristic nucleation MFD derived for each fault section is then divided evenly among the 

associated subsections (for use in equation set 7), which provides some along-fault smoothness 

in event rates along the main fault sections. Depending on the weight assigned to equation set 7, 

the grand inversion tries to stay as close as possible to these characteristic nucleation MFDs.

For the regional MFD constraint in equation set 6, a target MFD for the entire region is 

first constructed from the chosen regional rate, RM≥5

total, and the implied regional maximum 

magnitude, Mmax. The latter is computed from the largest area rupture in the fault system (given 

the chosen deformation model and magnitude-area relationship). The target MFD is further 

assumed to be a perfect truncated Gutenberg-Richter distribution with a b-value of 1.0. This total 

MFD, an example of which is shown as the black curve in figure 15, is then partitioned into a 

supraseismogenic on-fault MFD for use in the regional MFD constraint of equation set 6, as well 

as MFDs for the subseismogenic on-fault seismicity and the truly off-fault seismicity.

Because a fault section is a proxy for all ruptures that nucleate within its fault zone 

polygon, the total rate of events for each fault section is determined by multiplying RM≥5

total by the 

sum of SpatialPDF values inside the section’s fault zone polygon. Summing these rates over all 

fault sections gives the total rate of on-fault events (listed above, and illustrated on left side of 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

43

orange curve in figure 15A). Following UCERF2, the MFD for subseismogenic, on-fault ruptures 

is assumed to be Gutenberg-Richter up to the minimum magnitude of supraseismogenic ruptures. 

In UCERF2 this supraseismogenic transition was M6.5, except where the characteristic 

magnitude was less, whereas in UCERF3 the transition is fault-section dependent, owing to 

variations in seismogenic widths. Below the minimum supraseismogenic magnitudes, the total 

on-fault target MFD (orange curve in figure 15A) must be parallel to the total target (black curve) 

and offset by the difference between RM≥5

total and the total off-fault rate. Above the maximum 

magnitude of the off-fault events, Mmax

off−fault, the total target on-fault MFD (orange curve) must 

match the total regional target (black curve). In other words, the total on-fault target MFD has a 

b-value of 1.0 above and below these two transition points and assumes a straight-line 

interpolation in between (in log-rate space), meaning a constant, lower b-value at intermediate 

magnitudes (fig. 15A).

The truly off-fault MFD (green curve in figure 15A) is simply the difference between the 

total target MFD (black curve) and the total on-fault target MFD (orange curve). The 

supraseismogenic, on-fault MFD, shown as the blue line in figure 15B, is the total on-fault target 

(orange curve) minus the total subseismogenic on-fault MFD (cyan curve, which represents the 

sum of all subseismogenic, on-fault MFDs described above). 

The supraseismogenic, on-fault MFD (blue curve in figure 15B) summarizes the total of 

all regional MFD constraints represented by equation set 6. In principle, this total could be 

broken into arbitrarily small subregions, but uncertainties on the rates in smaller areas impose 

practical limits. For UCERF3, the total MFD was divided into just two regional constraints, one 

for northern and one for southern California. Furthermore, equation set 6 is applied as an 

equality constraint below magnitude 7.85, and as an inequality constraint at higher magnitudes 

(appendix N, this report). The latter allows the final solution MFD to roll off more quickly than 

the target if allowed or required by the other data constraints.

The total gridded seismicity for UCERF3 (gray line in figure 15B) is the sum of the offfault MFD (green) and the total subseismogenic on-fault MFD (cyan). This result is generally 

consistent with the total UCERF2 gridded seismicity (magenta line in figure 15B), though 

smoother in shape and exhibiting lower rates at some magnitudes (consistent with the added

UCERF3 faults taking moment rate from the gridded seismicity). The red line in figure 15B

shows the total MFD for fault-based sources in UCERF2, which by itself exceeds the total 

regional target around M7.0—the “bulge” described in the UCERF2 report—which is eliminated 

in the grand inversion by imposing the constraints of equation set 6. The brown line in figure 

15B is the total MFD for UCERF2 (which equals magenta plus red). 

Up to this point, the deformation-model moment rates (table 4) have not been used in 

constructing the various target MFDs. A useful pre-inversion diagnostic is to compute implied 

coupling coefficients, defined here as the moment rate of the target MFD divided by the 

deformation model moment rate from table 4. These diagnostics are listed separately for the total 

on-fault and off-fault model components, and for all logic tree branches, in the 

U3_PreInversionAnalysisTable. These implied coupling coefficients can exceed 1.0 if the target 

MFD implies more moment rate than exists in the deformation model.
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

44

Figure 15. Graphs showing examples of the various regional magnitude-frequency distributions 

(MFDs) considered in setting up the Characteristic Inversion Model branches. See labels and main 

text for an explanation of each curve. This example is for the reference branch, which is shown with

bold elements in figure 3. A, Illustration of the total target Gutenberg-Richter, total on-fault target, 

and truly off-fault MFDs. B, Illustration of the subseismogenic on-fault, supraseismogenic on-fault 

target, total gridded seismicity, and equivalent MFDs from UCERF2.
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

45

The off-fault coupling coefficients implied for a given deformation model depend 

primarily on the choice of RM≥5

total and Mmax

off−fault, and to a lesser extent on the SpatialPDF. The 

values implied from UCERF3 range from 0.17 (for NeoKinema deformation model with 

RM≥5

total = 7.6, Mmax

off−fault = 7.3, UCERF3 Smoothed Seismicity, and the Shaw09mod 

magnitude-area relationship) to 0.62 (for Geologic deformation model with RM≥5

total = 9.6, 

Mmax

off−fault = 7.9, UCERF2 Smoothed Seismicity, and the EllsworthB magnitude-area 

relationship); values for all braches are given in the U3_PreInversionAnalysisTable. These 

coupling coefficients imply off-fault moment rate reductions of 38 to 83 percent (relative to that 

predicted by the deformation models). One could alternatively tune Mmax

off−fault to some desired 

coupling coefficient. However, off-fault coupling coefficients are essentially unconstrained, and 

the parameterization in terms of Mmax

off−fault is more intuitive for most hazard analysts. The 

possibility of using the implied off-fault coupling coefficients in deciding a posteriori branch 

weights is not pursued here, although as noted above, it was a consideration in assigning the 

lower Mmax

off−fault value of 7.3 a relatively small weight (10 percent). 

The on-fault coupling coefficients implied by the deformation models are more 

potentially useful to modify the model. Values greater than 1.0 are remedied by the inversion 

rolling off the final MFD more rapidly at highest magnitudes relative to the target. Values less 

than 1.0 imply the slip rates are higher than can be accommodated by the target MFD, and the 

UCERF3 logic tree consequently has four Fault Moment Rate Fix options for this: 

• Apply Implied Coupling Coefficient—reduce the slip rates on all fault sections by the 

implied coupling coefficient. 

• Relax MFD Constraint—permit an overprediction “bulge” in the final MFD if needed to 

satisfy slip rates.

• Apply Both Options—apply both of the above. 

• Do Nothing—let the inversion decide where to reduce slip rates in matching the target 

MFD.

For UCERF3, only the Do Nothing option is given nonzero weight, because fault 

moment rate reductions are not an important issue for the characteristic models (the majority of 

implied on-fault coupling coefficient values are greater than 1.0, with the lowest being 0.86;

U3_PreInversionAnalysisTable). This means the inversion will decide whether and where to 

reduce slip rates (balancing this against the other constraints in the inversion). An alternative 

approach might be to target specific faults with site-specific coupling coefficients. Indeed, the 

exclusion of the Mendocino, Cerro Prieto, and Brawley Faults from previous NSHMP models 

was apparently done for this reason. However, we presently lack any basis for applying faultspecific coupling coefficients (beyond those already applied), and we want to avoid excluding 

any major faults from consideration. 

The Relax MFD Constraint might still be appealing in order to relax the regional GR 

constraint (because there is some chance the UCERF2 bulge is real, even though there is no 

supporting evidence for it). The result of doing so, however, is quite consistent with keeping the 

GR constraint, but applying the highest branch option for RM≥5

total (9.6 events per year); that is, the 

Relax MFD Constraint tends to increase rates at all magnitudes equally (appendix N, this report), 

so we effectively have this option in the model. 

The logic tree in figure 3 gives the following two branches for the characteristic Inversion 

Model: 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

46

• Characteristic UCERF2 Constrained—This applies the fault-section nucleation MFD 

constraints described above for equation set 7. Note that rupture rates are prevented from 

going to zero by enforcing a minimum “water-level” rate, which is the rupture rate for a 

GR starting-model multiplied by 0.01 (see appendix N, this report).

• Characteristic Unconstrained—No fault section MFD constraints are applied here. This 

model is more underdetermined, so a larger set of inversion runs are needed to sample the 

solution space; results can either be averaged or used to sprout additional subbranches of 

the logic tree.

Currently only the first of these options is given non-zero weight for two reasons: to stay 

as close as possible to UCERF2, and because the second option requires much more extensive 

exploration of the solution space, which we did not have time to conduct. 

The fault slip rates are reduced in the inversion according to the moment rate implied by 

subseismogenic, on-fault ruptures. This reduction was originally done on a fault section basis, 

but high rates of observed seismicity in some areas produced subseismogenic MFDs that had 

moment rates greater than those assigned to the fault section, leading to negative corrected 

moments. Therefore, only a systemwide average is applied to reduce slip rates for 

subseismogenic ruptures in UCERF3. The reduction for each logic tree branch is derived by 

dividing the moment rate of the subseismogenic MFD (cyan curve figure 15B) by the total onfault moment rate from the deformation model (table 4); the values among branches here vary 

from 4.1 to 10 percent (U3_PreInversionAnalysisTable).

The off-fault gridded seismicity sources are defined by partitioning the associated MFD 

(green curve figure 15A) among the regional grid cells that are outside fault zone polygons, 

weighted by the relative spatialPDF value in each grid cell. The Characteristic branches use 

either the UCERF2 or UCERF3 smoothed seismicity model (figure 14A or B), with equal weight 

being given to each. While there was some preference for the UCERF3 smoothed seismicity

model, for reasons discussed above, preliminary hazard calculations showed it to imply 

significant hazard changes (discussed below). And so, given the remaining uncertainties on 

which smoothed seismicity map is most applicable for large damaging events in a long-term 

model, we ended up giving each equal weight. While there was also interest in applying the 

deformation-model based spatialPDF options (model-specific maps shown figure 9, or the 

average shown in figure 14C), we did not have time to do so. 

The subseismogenic MFD for each fault section is distributed among the grid cells that 

fall within the associated fault zone polygon, consistent with the smoothed seismicity rates used 

to derive the subseismogenic MFDs. Given the ad hoc choices used to construct fault zone 

polygons (fig. 4), the hazard implications of this methodology need to be understood. The 

primary influence of fault zone width is on the maximum magnitude for gridded seismicity near 

faults. Inside the polygons this maximum magnitude is defined by the minimum magnitude of 

supraseismogenic on-fault ruptures (6.3 on average), whereas outside the polygons it is specified 

by Mmax

off−fault, with UCERF3 logic-tree options of 7.3, 7.6, or 7.9. Therefore, changing the fault 

zone widths primarily changes the gridded seismicity maximum magnitudes near the outer edges 

of the polygon, which should have only a very small effect on UCERF3 hazard estimates 

because the hazard near faults is generally dominated by supraseismogenic, on-fault ruptures. 
Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time-Independent Model 

47

Gutenberg-Richter Branches

These branches represent the possibility that earthquakes on individual faults are 

governed by a Gutenberg-Richter magnitude-frequency distribution. This GR hypothesis 

conflicts with all previous WGCEP and NSHMP models, which assumed that ruptures on large, 

well-developed faults exhibit characteristic behavior. Imposing GR behavior on faults in the 

UCERF2 framework exacerbates the MFD “bulge” near M6.7, whereas the UCERF3 grand 

inversion reduces this problem by allowing multifault ruptures. Given the support the GR 

hypothesis has received in recent analyses (for example, Parsons and Geist, 2009), we tried to 

accommodate such a branch on the UCERF3 logic tree.

Figure 16. Graph showing magnitude-frequency distributions implied by the Gutenberg-Richter (GR) 

hypothesis. Total target GR (black line) satisfies the total regional rate (7.9 events/year for UCERF3) 

and the Mmax implied by the largest event in the fault system (8.25 for Shaw09mod magnitude-area 

relationship here). The total on-fault target (orange line) is the total target GR multiplied by the 

fraction of on-fault seismicity (58 percent here), and the truly off-fault (green line) MFD is the total 

target minus the total on-fault target, and then truncated at Mmax

off−fault=7.6. The GR-implied onfault curves (red and magenta lines) represent the MFDs implied by the GR hypothesis for two 

extreme branches (and with no off-fault seismicity being added), both of which fall well above the 

total on-fault target; results for all other GR branches with RM≥5

total = 7.6 fall between these endmembers. The GR-implied curves roll off at the highest magnitudes because not all fault sections 

participate in the largest events.
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The target MFDs for the GR case are simple to construct (fig. 16). The total regional 

target (black line in figure 16) is again specified by the choice of RM≥5

total and Mmax, and 

partitioned according to the fraction of seismicity that is on-fault (for example, 58 percent for 

UCERF3 smoothing), yielding the orange on-fault target MFD shown figure 16. The off-fault 

MFD (green line) is the different, truncated at the specified value of Mmax

off−fault. 

The GR hypothesis states that each fault section nucleates a GR distribution of 

earthquakes, with a b-value of 1.0 and a maximum magnitude defined by the largest rupture in 

which the section participates, including multifault ruptures. The rate of events, or the GR avalue, for each fault section can then be found by satisfying the section moment rate. Even 

before any inversion, we can sum all the consequent fault-section MFDs to obtain a total GRimplied on-fault MFD. Two examples are shown figure 16. The red curve, which represents the 

ABM Deformation Model paired with the Shaw09mod magnitude-area relationship, exceeds not 

only the on-fault target (orange) but also the total regional target (black). The magenta curve, 

which represents the Zeng Deformation Model pared with the HanksBakun08 magnitude-area 

relationship, is just below the total target, and well above the on-fault target. Results for all other 

GR branches fall between these two cases.

 This discrepancy can be quantified as an on-fault coupling coefficient, defined as the 

ratio of the total rate of the target on-fault MFD (orange line in figure 16) to the total rate of the 

GR-implied on-fault MFD (red or magenta curve figure 16). The implied coupling coefficients, 

listed in the U3_PreInversionAnalysisTable, range from 0.37 to 0.75 among all the GR branches 

figure 3 (slip rate reductions of 63 to 25 percent). One option for matching the target MFDs is to 

apply these implied coupling coefficients, which can be done via two of the “Fault Moment Rate 

Fix” options in the UCERF3 logic tree (fig. 3):

• Apply Implied Coupling Coefficient—reduce the slip rates on all fault sections by the 

implied coupling coefficient (same reduction on all faults).

• Do Nothing—let the inversion decide where to reduce slip rates in matching the target 

MFD.

The other two “Fault Moment Rate Fix” options listed figure 3, which include relaxing 

the regional MFD constraint all together, cannot be applied, because both violate the GR 

hypothesis. 

Not all fault sections participate in the largest events, causing the on-fault GR MFDs to 

roll off at high magnitudes (red and magenta curves figure 16). Hence, more moment has to be 

taken up by smaller earthquakes, which increases overall rate of events. The discrepancy would 

be reduced if all sections shared the same maximum magnitude, but this would require including 

many of the ruptures filtered out by our plausibility criteria, or adding many more faults 

throughout the region to increase connectivity (which would add moment as well). 

There is some evidence that faults might have a lower b-value than surrounding regions 

(Page and others, 2011). Assuming b=0.95 on faults reduces the discrepancy a little, but not 

enough to satisfy regional rates. The definition of fault zone polygons also has some influence in 

terms of the target on-fault rate, such that increasing their collective area would lessen the 

discrepancy. However, reasonable adjustments are not adequate. In fact, figure 16 implies that 

the fault zone polygons would have to encompass the entire region (because the red and magenta 

curves essentially match the total target). Doing so would also worsen existing problems with the 

implied off-fault coupling coefficients (U3_PreInversionAnalysisTable).

Other possible explanations are that the true total regional rate (RM≥5

total) is significantly 

higher than our existing branch options, that shear rigidity is considerably less than that assumed 
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(3.0×1010 Pa), or some combination of the possibilities discussed here. Any one of these GR 

corrections would have significant implications. For example, applying the implied coupling 

coefficients of 0.37 to 0.75 would reduce fault-based hazard by about 25 to 63 percent, whereas 

increasing the total regional rate would increase hazard by a similar amount.

An alternative is that the hypothesis is wrong; faults do not honor a GR nucleation MFD. 

In fact, this may be one of the most important UCERF3 findings. Either way, these branches 

would get very low relative weight given the extraordinary corrections needed to satisfy all data, 

leading us to abandon further pursuit for UCERF3, which was the advice of our SRP as well. 

Further details are therefore not provided here, although these branches remain fully 

implemented for those wishing to explore viability and (or) practical implications further. 

Gardner-Knopoff Aftershock Filter

The UCERF3 earthquake rate model includes aftershocks, whereas previous NSHMP 

models have removed such events using the Gardner-Knopoff declustering algorithm (Gardner 

and Knopoff, 1974). The definition of aftershocks implied by this type of declustering is out of 

date. For example, it implies that the fraction of aftershocks relative to main shocks is magnitude 

dependent, whereas recent aftershock studies do not support such dependence (for example, 

Felzer and others, 2004). 

Nevertheless, the Gardner-Knopoff definition is still used in formulating and applying 

hazard policies; for example, in current building codes that rely on the NSHMP models. To 

facilitate comparison and consistency with other earthquake hazard models, a procedure for 

removing Gardner-Knopoff aftershocks has been implemented in the UCERF3 framework. 

Gardner-Knopoff declustering typically reduces the b-value from about 1.0 (full catalog) 

to about 0.8 (declustered catalog). For this reason, the NSHMP has generally used a b-value of 

0.8 for modeling smaller events as gridded seismicity. The b-value difference can be combined 

with the fraction of M≥5 events designated as main shocks by the declustering model to 

construct a Gardner-Knopoff filter. According to UCERF2, appendix I (Felzer, 2008), the total 

number of M≥5 events per year in the UCERF region is 7.50 for the full catalog, compared with 

4.17 for a Gardner-Knopoff declustered catalog, which implies that 56 percent of these events 

are Gardner-Knopoff main shocks. The corresponding GR MFDs for both full and declustered 

catalogs are compared in figure 17A. The UCERF3 Gardner-Knopoff aftershock filter is simply 

the ratio of the decustered MFD to total MFD in figure 17A, capped at 1.0 above the point where 

the two MFDs cross over. This filter compares well with binned data values from table 16 in 

appendix L (this report), as shown here in figure 17B.

In applying this Gardner-Knopoff aftershock filter, the rate of each UCERF3 rupture can 

be scaled by the value on the red curve in figure 17B. This implicitly assumes that the fraction of 

aftershocks is location independent, which is consistent with past NSHMP applications. 

Observational evidence for a systematic spatial dependence is lacking, though the available data 

do not exclude that possibility. 

From a practical perspective, our approach is the same as applied in UCERF2 for gridded 

sources. For fault-based sources, however, the two applications are a bit different. In UCERF2, 

all fault-based sources were effectively reduced by 3 percent to account for aftershocks 

(independent of magnitude), whereas the fractional reduction is magnitude dependent using the 

Gardner-Knopoff filter. Below magnitude 6.7 (where our filter has a ~3-percent reduction) the 

new methodology reduces rates more than in UCERF2, and above 6.7 the new reduction is less 

(and zero above magnitude 6.75). While these differences are generally quite small compared to 
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other epistemic uncertainties in the model, there are situations where the differences may require 

further consideration. For example, about 30 percent of magnitude ~6 Parkfield earthquakes are 

aftershocks according to this new filter. 

To ensure maximum consistency with UCERF2 and past NSHMP practice, the GardnerKnopoff filter defined here is applied only to gridded-seismicity sources, whereas the rates of all 

supraseismogenic ruptures are reduced by 3 percent (again, the latter being the UCERF2 value). 

This means the Gardner-Knopoff filter is not applied for supraseismogenic ruptures. 

Figure 17. Plots showing application of the Gardner-Knopoff aftershock filter in UCERF3. A, A fullcatalog cumulative magnitude-frequency distribution (MFD; black line, with b-value=1.0 and 

normalized by the total rate of M≥5 events) together with the cumulative MFD implied by the 

Gardner-Knopoff aftershock declustering algorithm described in the text (blue line, with b-value=0.8 

and a relative total rate of 0.56, meaning 56 percent of M≥5 events are main shocks according to 

this algorithm). B, The UCERF3 Gardner-Knopoff aftershock filter (red curve), obtained by taking the 

ratio of incremental versions of the MFDs in A (blue divided by black) and capping values above 1.0 

at 1.0 (above the crossover magnitude, which is M6.8 for the incremental distributions). Also shown 

are data (black triangles) from table 16 of appendix L (this report).

Results

This section presents UCERF3 results, postponing important sensitivity tests to the 

section that follows, both because those tests depend on evaluation metrics introduced here, and 

because interpretations here are not influenced by the test results.
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Model Evaluation Challenges

One of the primary challenges in evaluating UCERF3 is the increased number of viable 

ruptures in the fault system—more than 250,000, compared to less than 8,000 mapped into our 

fault system by UCERF2. Furthermore, the rupture rates in UCERF2 were largely prescribed in 

terms of rupture extents and assumed MFDs, whereas these properties are derived in UCERF3 

from the system-level inversion. Interpretation of UCERF3 results is therefore much more 

challenging. For example, a 5-second visual examination of each UCERF3 rupture would take 

about 350 hours for just one of the 1,440 alternative logic tree branches. We therefore have to 

rely on aggregate evaluation metrics.

The grand inversion approach to UCERF3 would not be feasible without access to 

supercomputers. In addition to the large number of ruptures in each model, we also have to 

contend with a large number of alternative logic tree branches (1,440). Each simulated annealing 

run takes about 5 hours on a typical desktop computer (appendix N, this report). Furthermore, 

simulated annealing finds the optimum solution by sampling the solution space somewhat 

randomly (using a “smart” Monte Carlo procedure based on thermodynamics). For an 

overdetermined problem, it is guaranteed to find the global minimum if given infinite time 

(Granville and others, 1994). Our computation time is limited, however, so it is important to 

quantify the convergence properties by examining the spread of results from repeated runs of the 

same problem. Multiple runs are also needed to sample underdetermined parts of the solution 

space. Such convergence properties, as well as the influence of alternative equation set weights, 

are summarized in the “Sensitivity Tests” section, and some are discussed in more detail in 

appendix N (this report). For the results presented here, we ran 10 separate simulated annealing 

inversions for each branch, which will be shown to be more than adequate in terms of 

quantifying hazard. Multiplying 1,440 logic tree branches by 10 runs per branch, and then by 5 

hours compute time for each run, implies about 72,000 hours of total compute time (8.2 years). 

Consequently, most of the results presented here were computed on the Stampede cluster at the 

University of Texas, which can accommodate as many as 6,144 separate inversion runs at a time.

We have also made extensive use of the cluster at the Center for High-Performance Computing 

and Communication, University of Southern California, which can accommodate as many as 60 

inversions at a time.

Dealing with the large number of ruptures and logic tree branches has also necessitated 

the development of new evaluations metrics and visualization tools. Those currently available 

are listed in table 11, most of which are exemplified below, with most others being used in the 

appendixes (as noted below). 

Given the many differences between UCERF2 and UCERF3, a full, step-by-step 

accounting of the influence of each is not feasible, especially for every site of potential interest 

and for every evaluation metric. Our aim here, therefore, is to identify and explain important 

differences with respect to UCERF2, and to characterize the influence of different UCERF3 

logic tree branches as best we can.

Preliminary models (for example, UCERF3.0) included grand inversion results that used 

UCERF2 ingredients only (same deformation models, scaling relationships, and so forth), with 

the hope that this would indicate where differences are strictly methodological. Unfortunately 

this was not helpful, because whether or not methodological differences are important turns out 

to depend on which ingredients are chosen. Thus, the conclusions from such controlled 

experiments do not necessarily apply to the final UCERF3 model. We therefore do not present 

any such results here.
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Table 11. Evaluation metrics currently available in the UCERF3 framework.

Inversion data fits

Regional MFD plots

Slip rate plots (and misfits)

Paleo event rate plots (and misfits) 

Tabulation of equation-set residuals and pre-inversion metrics

Simulated annealing run diagnostics

Other data fits

Event correlation between paleoseismic sites

Fault jumping statistics

Variability of average slip per event at points on faults (slip COV)

Frequency of different rupture lengths statistics

General implications

Parent-section MFDs (also tabulated)

Subregion MFDs (for example, LA and SF Boxes)

Participation rate maps

Maps showing how often other fault sections participate with a particular section

Implied segmentation (for example, on SAF)

Hazard/loss metrics

Hazard curves at sites

Tornado diagrams (showing which logic tree branches are influential)

Hazard Maps (and their ratios to UCERF2)

Risk Targeted Ground Motion (RTGM) at sites (Luco and others, 2007) 

Statewide Loss Estimates (for example, Porter and others, 2012) 

SCEC VDO (3D visualizations) 

Model Fits To Data

Here we summarize how well final models fit the various data constraints; appendix N 

(this report) has further details.

Regional MFDs

Figure 18 compares the envelope of the UCERF3 branch MFDs with the mean MFDs for 

UCERF2 for the entire California region. The inversion successfully eliminates the apparent 

UCERF2 overprediction near M6.5. We also illustrate what happens if the UCERF2-like MFDs 

are applied strictly to all faults in UCERF3 (orange curve, obtained by giving equation set 7 

infinite weight). In this case the overprediction is even greater than in UCERF2, mostly because 

of the addition of new fault sections. Appendix N (this report) shows that the final MFDs for a 

given branch match the associated pre-inversion targets very well. Table 12 lists the cumulative 
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MFDs for both UCERF3 and UCERF2, averaged over all branches and including aftershocks. 

As expected, the rates have increased by ~42% for M≥5, gone down by ~23% at M≥6.7, and 

increased by ~37% for M≥8.

Figure 18. Magnitude-frequency 

distributions (MFDs) for the entire 

California region for all UCERF3 logic 

tree branches, with comparison to mean 

results from UCERF2. A, 

Supraseismogenic on-fault MFDs for 

UCERF3 are shown in blue, with the 

minimum and maximum among all 

branches being represented by the 

shaded region. The average result from 

UCERF2 is shown in red for comparison. 

B, Same as A, but for gridded seismicity 

(subseismogenic on-fault ruptures plus 

truly off-fault sources). C, Total MFDs, 

representing the sum of the MFDs in A

and B. The black lines in all plots 

represent reference Gutenberg-Richter 

distributions for the alternative values of 

the total regional M≥5 rate (RM≥5

total). Also 

shown with orange in A and C are 

UCERF3 MFDs obtained by applying the 

Fault Section MFD Constraint (equation 

set 7) with infinite weight, which reveals 

the overprediction of regional rates when 

one assumes UCERF2-like MFDs for 

each fault. Note that the gridded 

seismicity MFDs for UCERF2 have had 

aftershocks added back in by reversing 

the Gardner-Knopoff filter described in 

the text.
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Table 12. Average cumulative magnitude-frequency distributions for UCERF3 and UCERF2. [“Faults” refers to supraseismogenic on-fault ruptures; “Gridded” refers to the gridded seismicity, and “Total” 

includes both; each rate given in events per year. “U3/U2 Total Ratio” is the ratio of total values from UCERF3 and 

UCERF2. These rates include aftershocks, where those for the UCERF2 gridded seismicity were added using the 

Gardner-Knopoff filter described in the text. Note that UCERF2 on-fault values include aleatory variability of 

magnitude for given rupture area, whereas values for UCERF3 do not.]

Magnitude

UCERF3 UCERF2 U3/U2 total 

Total Faults Gridded Total Faults Gridded ratio

5.0 8.26E+00 4.59E-01 7.80E+00 5.80E+00 3.53E-01 5.45E+00 1.42

5.1 6.56E+00 4.59E-01 6.10E+00 4.66E+00 3.53E-01 4.31E+00 1.41

5.2 5.21E+00 4.59E-01 4.75E+00 3.76E+00 3.53E-01 3.41E+00 1.39

5.3 4.14E+00 4.59E-01 3.68E+00 3.04E+00 3.53E-01 2.69E+00 1.36

5.4 3.28E+00 4.59E-01 2.83E+00 2.46E+00 3.53E-01 2.11E+00 1.33

5.5 2.61E+00 4.59E-01 2.15E+00 2.01E+00 3.51E-01 1.66E+00 1.30

5.6 2.07E+00 4.59E-01 1.61E+00 1.64E+00 3.48E-01 1.29E+00 1.26

5.7 1.64E+00 4.59E-01 1.18E+00 1.34E+00 3.42E-01 1.00E+00 1.22

5.8 1.30E+00 4.58E-01 8.45E-01 1.10E+00 3.34E-01 7.71E-01 1.18

5.9 1.03E+00 4.54E-01 5.80E-01 9.11E-01 3.24E-01 5.87E-01 1.14

6.0 8.20E-01 4.12E-01 4.08E-01 7.55E-01 3.15E-01 4.40E-01 1.09

6.1 6.50E-01 3.54E-01 2.96E-01 6.31E-01 3.03E-01 3.27E-01 1.03

6.2 5.15E-01 3.03E-01 2.12E-01 5.30E-01 2.93E-01 2.37E-01 0.97

6.3 4.08E-01 2.58E-01 1.50E-01 4.48E-01 2.82E-01 1.65E-01 0.91

6.4 3.22E-01 2.18E-01 1.04E-01 3.79E-01 2.71E-01 1.08E-01 0.85

6.5 2.55E-01 1.82E-01 7.23E-02 3.20E-01 2.57E-01 6.30E-02 0.80

6.6 2.01E-01 1.51E-01 4.96E-02 2.56E-01 2.09E-01 4.76E-02 0.78

6.7 1.58E-01 1.25E-01 3.35E-02 2.06E-01 1.71E-01 3.52E-02 0.77

6.8 1.24E-01 1.02E-01 2.22E-02 1.62E-01 1.37E-01 2.51E-02 0.76

6.9 9.72E-02 8.29E-02 1.43E-02 1.26E-01 1.08E-01 1.71E-02 0.77

7.0 7.58E-02 6.69E-02 8.86E-03 9.40E-02 8.34E-02 1.06E-02 0.81

7.1 5.88E-02 5.36E-02 5.19E-03 7.02E-02 6.26E-02 7.56E-03 0.84

7.2 4.53E-02 4.25E-02 2.82E-03 5.16E-02 4.66E-02 5.03E-03 0.88

7.3 3.46E-02 3.32E-02 1.36E-03 3.72E-02 3.43E-02 2.92E-03 0.93

7.4 2.60E-02 2.54E-02 5.71E-04 2.68E-02 2.51E-02 1.75E-03 0.97

7.5 1.92E-02 1.90E-02 1.87E-04 1.90E-02 1.82E-02 7.87E-04 1.01

7.6 1.38E-02 1.37E-02 5.94E-05 1.32E-02 1.32E-02 0.00E+00 1.04

7.7 9.43E-03 9.40E-03 2.71E-05 9.35E-03 9.35E-03 0.00E+00 1.01

7.8 5.97E-03 5.95E-03 1.21E-05 6.08E-03 6.08E-03 0.00E+00 0.98

7.9 3.30E-03 3.30E-03 0.00E+00 3.35E-03 3.35E-03 0.00E+00 0.98

8.0 2.01E-03 2.01E-03 0.00E+00 1.47E-03 1.47E-03 0.00E+00 1.37

8.1 1.07E-03 1.07E-03 0.00E+00 5.09E-04 5.09E-04 0.00E+00 2.09

8.2 4.20E-04 4.20E-04 0.00E+00 9.99E-05 9.99E-05 0.00E+00 4.21

8.3 4.55E-05 4.55E-05 0.00E+00 7.26E-06 7.26E-06 0.00E+00 6.27

8.4 4.68E-06 4.68E-06 0.00E+00 1.08E-06 1.08E-06 0.00E+00 4.34

8.5 1.56E-06 1.56E-06 0.00E+00 0.00E+00 0.00E+00 0.00E+00 Inf
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Slip Rates

The final slip rate misfits (solution over target, branch-averaged) are listed for each fault 

section in the “AveSolSlipRates” sheet of the U3_FaultSectionData file given in the “Data and 

Resources” section. Figure 19 shows these misfits for FM 3.1, together with an equivalent plot 

for UCERF2. In general, the UCERF3 fits are better than for UCERF2, which tends to 

overpredict slip rates near the centers of fault sections and underpredict those near the ends. This 

is caused by the UCERF2 “floating” ruptures being given a uniform probability along strike, and 

partly by the tapered-slip distribution.

There are two prominent overprediction (red) outliers for UCERF3 (fig. 19). The 

southernmost represents the Elsinore-Glen Ivy fault section. Here the solution slip rate is pulled 

above the target, by a factor of 1.54, in fitting the paleoseismic event rate constraint on this 

section (table 7), which is underpredicted by a factor of 0.73; improving the match to one 

worsens the fit to the other, illustrating data inconsistency. The other red outlier, in central 

California, is in the center of the Creeping Section of the San Andreas Fault (SAF), where the 

mean slip rate is reduced by 80 percent to 5 mm/yr to account for creep. The inversion is unable 

to match this rapid slip rate change, giving a high value of 10 mm/yr. All other UCERF3 slip rate 

overpredictions are within 20 percent of the targets, and virtually all those greater than 10 

percent can be explained by fitting relatively high paloeseismic event rates.

Overall, UCERF3 underpredicts slip rates more than it overpredicts them, particularly in 

southern California (where many faults are slightly blue in figure 19). On average, total on-fault 

solution moment rates are 4 percent below the targets, primarily because of limitations on total 

event rates by the regional MFD constraint. Although some fault sections have slip rate 

reductions of as much as a factor of two, all can be explained by either the paleoseismic rate

constraint being incompatible with the slip rate constraint (for example, the Whittier alt 1 fault 

section) or by the regional MFD constraint coupled with a lack of fault connectivity needed to 

produce larger events (for example, the Santa Susana East (connector) fault section). Only six 

fault sections have final branch-averaged slip rates that fall outside the range defined by the 

alternative deformation models, and all of these cases fall within the Geologic bounds. 

Paleo Event Rate Data

UCERF3 paleoseismic event rate misfits are also listed in the U3_FaultSectionData file 

given in the “Data and Resources” section (sheets labeled “PaleoEventRateFits” and 

“ProxyEventRateFits”). Results for paleoseismic sites along the SAF are compared with 

UCERF2 results in figure 20 with slip rate fits, to clarify why rates vary along strike. All 

UCERF3 data are fit well, given uncertainties, and are generally fit better than in UCERF2.

Misfits on the North Coast, Santa Cruz, Big Bend, and Mojave North sections are 

dominated by inconsistencies between paleoevent rate and slip rate constraints. The average slip 

rate discrepancy for Parkfield, which reflects the a priori constraint on the 25-year recurrence 

interval of historical ~M6 events, is at odds with other inversion constraints, possibly a result of

deficiencies in modeling the aseismic processes on this fault.

Average slip rates on the Cholame, Carrizo, and Coachella sections are also 

underpredicted. Paleoseismic event rates are also underpredicted on the latter two, which raises

the question of why the inversion does not simply add more events to satisfy these data. Owing 

to the regional MFD constraint, adding earthquakes there requires subtracting such events from 

other areas, which degrades the slip rate fits. Both slip rates and event rates can be fit well on 
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56

these sections if the MFD constraint is removed altogether, but this leads to a significant 

overprediction of the regional event rates near M7. 

Figure 19. Maps showing average subsection slip rate misfits for both UCERF3 (Fault Model 3.1) and 

UCERF2 (Fault Model 2.1), shown as ratios of final implied slip rates divided by deformation model 

slip rates, and averaged over all logic tree branches. Equivalent plots for each deformation model 

(branch subsets) are given in appendix N (this report). The distribution of subsection slip rate misfits 

is shown for UCERF2 and UCERF2 at the upper right.

Removing the MFD constraint also puts a high rate of smaller events at the northern end 

of the Cholame section. These events fill in the precipitous drop in modeled slip rates toward the 

north (fig. 20), as required by the Parkfield a priori constraint (appendix N, this report). This 

issue is also apparent in the UCERF2 results. From a hazard perspective, it is more important to 

get the total rate of events correct than to satisfy slip rates exactly, so we kept the regional MFD 

constraint to prevent the inflation of total event rates. 

UCERF3 event rates on the southern SAF average about 25 percent below our best 

paleoseismic estimates (table 7). The worst case is Carrizo, where the mean model rate (an 

observable paleoevent every 193 years) is 40 percent below the best paleo-rate estimate (one 

every 115 years). In UCERF2, the average paleo constraint for Carrizo was an event every 225 

years (fig. 20), so the paleo estimate has been revised by almost a factor of two. The average 

UCERF3 model rate is relatively consistent with the UCERF2 model average (one every 193 

year versus one every 185 years, respectively); therefore, the hazard change in UCERF3 is 

minimal. Hazard-ratio maps, discussed later, will show that this is generally true of the entire 

SAF.

The misfits on the southern SAF nevertheless point to some possible inconsistencies that 

we should strive to understand and resolve in the future. Until we do so, however, minimizing 
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changes with respect to UCERF2 is appropriate, especially since matching the paleoseismic data 

better will increase hazard. Nevertheless, the uncertainties reflected in figure 20 indicate general 

agreement, as well as the existence of some UCERF3 branches that do fit the southern SAF data 

better (meaning these branches could be given higher weight if users could justify doing so). 

None of the UCERF3 model rates at the 31 paleoseismic sites are outside of the 95-

percent confidence bounds on the data, and the reduced chi-squared value for the UCERF3 event 

rate fit is 0.72, indicating that, on the whole, UCERF3 over-fits the paleoseismic event rate data 

(appendix N, this report). Although the model systematically underpredicts event rates on the 

southern SAF, these sites do not represent independent data because the sites are seeing the same 

period of time and many of the same events. UCERF2 rates, for comparison, are outside of the 

(UCERF3) 95-percent confidence bounds at five of the sites. 

Plots like figure 20 are available for all the faults that have paleoseismic constraints 

(Plots of Paleoseismic Data Fits Along Faults; see the files that end with "_combined.png," for 

which the legend is the same as in figure 20). The data fits on these faults are generally better

than on the SAF, with discrepancies in the mean model being attributable to conflicts between 

slip rate and paleoevent rate constraints.

A Posteriori Model Evaluation

Each inversion run provides quantitative metrics on how well the final model fits each 

data constraint (see appendix N, this report). In principal, these data could be used to adjust logic 

tree branch weights a posteriori (for example, using Bayes theorem with the a priori branch 

weights listed in figure 3). Likewise, some of the pre-inversion metrics, such as the implied offfault coupling coefficients discussed above, could be used to rank models. We have not 

attempted any such branch-weight modifications here, however, because doing so will require

more careful analysis in terms of avoiding cases where a good fit to data is actually the result of

two “wrong” components canceling each other. 

Fits to Data Not Used in the Inversion

One type of observation not included in the inversion is the extent to which 

paleoseismically inferred events are observed to corupture neighboring trench sites 

simultaneously (event correlation, or lack thereof). For example, such inferences are an 

important component of the “stringing pearls” methodology of Biasi and Weldon (2009). 

Appendix N (this report) demonstrates that currently available correlation data not only agree 

well with UCERF3 results, but also generally agree better than those implied by UCERF2. The 

interpretive uncertainties are admittedly large with respect to these correlation data because 

samples are limited, and correlation does not necessarily mean rupture in the same event because 

of uncertainty in the event dates. 

Appendix N also compares UCERF3 results to a couple of different multifault rupture 

statistics, such as how often ruptures involve fault sections with different names and how many 

times ruptures jump across fault steps of various distance thresholds. Even considering data 

uncertainties and interpretive assumptions, the analysis implies that, if anything, UCERF3 has 

too few multifault ruptures, not too many. 
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Figure 20. Latitudinal plots showing slip rate and paleoseismic data fits for the southern San Andreas 

Fault, for both UCERF3 (top) and UCERF2 (bottom). The paleoseismic data on the UCERF2 plot 

are those used in that study, whereas the version of this figure in appendix N (this report) compares 

UCERF2 results to UCERF3 data. 
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Wells (2013) presented a preliminary update to the Wells and Coppersmith (1994) global 

database, including a list of magnitude, area, length, and average slip for a number of historical 

ruptures. Figure 21 compares the histogram of observed rupture lengths based on 258 events in 

the dataset with the frequency of rupture lengths predicted by the UCERF3 branch-averaged 

model, which agrees quite well. Again, if anything UCERF3 underpredicts the rate of the longest 

events.

Figure 21. Histogram of observed rupture lengths from a global data compilation of 258 earthquakes 

(Wells, 2013), compared to the distribution implied by UCERF3 (thicker black line represents 

branch-averaged values, and thin lines represent the min and max among all branches). Curves 

have been normalized to density functions (values sum to 1) for comparison purposes.

The above analyses indicate that UCERF3 is quite reasonable with respect to multifault 

rupture statistics, and that our exclusion of the improbability constraint (equation set 4) seems to 

be justified. Good statewide statistics do not, however, guarantee that the data for individual 

faults are also well fit. The fault-by-fault review meetings (table 3) did not reveal egregious 

problems. To allow users to judge for themselves, we have generated participation rate maps that 

show the frequency with which other fault sections corupture (or participate) with any given 

section (http://pubs.usgs.gov/of/2013/1165/data/UCERF3_SupplementalFiles/UCERF3.3/

Model/FaultParticipation/), as exemplified for the Cucamonga Fault in figure 22. Note that this 

figure does not show a rupture, but rather the combined sum of many different ruptures that 

connect with Cucamona in different ways. 

Noda and Lapusta (2013) recently presented a “plausible physical mechanism” for 

ruptures passing completely through the creeping section of the SAF, which had zero probability 

of occurrence in UCERF2. Branch-averaged recurrence intervals for UCERF3 are as follows: 

150,000 years between the center of the Offshore and Coachella sections; 2,500 years between 

the center of the North Coast and Mojave sections, and 900 years between the Parkfield and 

Santa Cruz sections. While these recurrence intervals are certainly reasonable, we caution that 

they have high uncertainties due to several modeling assumptions. 
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Figure 22. Map showing the rate at which the Cucamonga Fault coruptures (participates) with other 

fault sections for the branch-averaged UCERF3 model (for Fault Model 3.1). Such plots for other 

fault sections were also prepared (available at http://pubs.usgs.gov/of/2013/1165/data/

UCERF3_SupplementalFiles/UCERF3.3/Model/FaultParticipation/).

Another evaluation metric is the coefficient of variation (COV) for slip at a site, 

computed as the standard deviation of paleo-observable slip per event divided by the mean. 

Figure 23 shows a histogram of subsection COVs for the reference logic tree branch. The center 

of the peak is about 0.42, which is a central value among alternative scaling relationships;

EllsworthB produces the smallest value, about 0.33, and HanksBakun08 produces the largest, 

0.47. These results are only a bit less than the values of 0.45 to 0.5 inferred by Hecker and others 

(2013) from a global paleoseismic data compilation. However, the latter includes intraevent 

variability (along-strike variability within a given observed rupture), whereas our values only 

include the amount of that captured by our average Tapered slip model for Dsr (or none for the 

equally weighted Boxcar branches). Our values are therefore roughly consistent. However, 

evaluation of this will be more relevant for any future GR logic tree branches, as the Hecker and 

others (2013) study concluded that their observed COVs are incompatible with a GR model.
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Figure 23. Histogram of the coefficient of variation (COV) for average slip per event, where each 

sample is the standard deviation of slip on a subsection divided by the mean slip, taken among all 

subsections for the reference logic-tree branch inversion. The rates of each rupture and the 

probability of paleoseismic observance (Pr

paleo−slip−proxy) have been accounted for in generating 

this plot.

Hazard Related Metrics

This section presents evaluation metrics that are particularly relevant to hazard 

implications.

Total Regional Moment Rates

Figure 24 shows the regional moment rate distributions implied by the UCERF3 logic 

tree branches, as well as the deformation model targets listed table 4. The solution on-fault 

values are in general agreement with the targets, but the off-fault rates are well below 

deformation model values. As discussed above, the off-fault moment rates are not explicitly used 

in UCERF3, whereas the model values are implied by the choice of total regional earthquake 

rate, maximum magnitude off fault, and other branch choices. The reason for this off-fault 

discrepancy remains unresolved, although it may be associated with assumptions made in 

calculating the deformation model values (appendix C, this report). We also note that the 

coupling coefficients implied by geodetic deformation in broad regions are subject to 

considerable uncertainty, with values between 20 and 100 percent being cited in the literature 

(for example, Ward, 1998; Kagan, 2002a,b; Jenny and others, 2004; Masson and others, 2005; 

Pancha and others, 2006; Rontogianni, 2010). The total moment rate implied by the earthquake 

catalog is 2.29×1019 N⋅m/yr, in good agreement with the average model values of both UCERF3 

(2.15×1019N⋅m/yr) and UCERF2 (2.27×1019 N⋅m/yr).
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Figure 24. Graphs showing the distribution of regional moment rates implied by UCERF3 logic tree

branches (including their weights), where blue represents total on-fault (including subseismogenic 

ruptures), gray is the off-fault, and black is the total combined rate. The vertical lines represent the 

various model targets as listed in table 4 and as labeled at the bottom, where dotted is for off-fault 

and dashed is for on-fault values at the top.

Fault Section Participation MFDs

Hazard at a site is often dominated by one or more nearby faults, so a particularly 

important metric is the participation MFD, which quantifies the rate at which ruptures occur on 

each fault section (even if they nucleate elsewhere). While these MFDs were prescribed in 

UCERF2, UCERF3 derives them by finding the range of models that fit the data. The 

characteristic MFD nucleation constraint (equation set 7) overdetermines the inversion for fault 
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section MFDs, so the remaining concerns are whether simulated annealing can find the global 

minimum and whether the results are robust with respect to equation-set weights (both of which 

are quantified below).

Because it is not practical to look at the participation MFDs for all ~2,600 fault 

subsections, we aggregate results back onto the 350 main fault sections, which also aids in 

making meaningful comparisons to UCERF2. Results were produced for all fault sections 

(available at http://pubs.usgs.gov/of/2013/1165/data/UCERF3_SupplementalFiles/

UCERF3.3/Model/FaultMFDs/); see the appropriate subdirectories for nucleation versus 

participation, and incremental versus cumulative MFDs), with figure 25 providing a few 

representative examples. Participation MFDs for the two SAF sections (Peninsula and Mojave S) 

are very consistent between UCERF2 and UCERF3. For the two other San Francisco Bay area 

faults (Calaveras N and Hayward N), UCERF3 has a wider range of magnitudes and lower total 

rates of supraseismogenic ruptures. Of the two Los Angeles region examples (San Cayetano and 

Cucamonga), both have lower total UCERF3 rates because they participate in larger magnitudes. 

In fact, Cucamonga represents the biggest rate change that is due primarily to methodological 

differences (the inclusion of multifault ruptures, as depicted in figure 22). Both of these cases 

were viewed as an improvement by participants of the fault-by-fault review meetings table 2), 

and the Cucamonga multifault ruptures are supported by the static and dynamic stress modeling 

of Anderson and others (2003). 

Note that UCERF2 fault section MFDs are generally smoother than those for UCERF3, 

which is only because the former have aleatory variability in magnitude for a given rupture area 

(a Gaussian magnitude PDF applied to each characteristic rupture, with a standard deviation of 

0.12 and truncated at ±2 standard deviations). For example, there are only 10 different 

magnitudes for all characteristic model events on the northern SAF in UCERF2, so without this 

aleatory variability UCEF2 results would be spikier than those of UCERF3. Whether or not to 

apply such aleatory variability in UCERF3 is a hazard modeling question not addressed in this 

report, except to note that the option exists for users that want it. The point here is that UCERF2 

fault section MFDs are not really any smoother than those of UCERF3. 

Subregion MFDs

Figure 26 shows the mean and range of nucleation MFDs, for both UCERF2 and 

UCERF3, in rectangular regions surrounding San Francisco (SF), Los Angeles (LA), and in the 

vicinity of the Northridge Fault. These box regions are mapped in figure 27, which also shows 

the ratio of off-fault spatial seis PDFs (SpatialPDF) between UCERF2 and UCERF3, as well as 

the ratio of branch-averaged, on-fault moment rates. Note that the MFDs shown in figure 26 are 

cumulative, and that aftershocks have been added back in for UCERF2 (by reversing the 

Gardner-Knopoff filter described above). Table 13 lists the number of fault sections, the moment 

rate, and various event rates inside each of these regions.
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Figure 25. Graphs showing example fault-section participation magnitude-frequency distributions 

(MFDs) averaged over all logic tree branches, and weighted accordingly. UCERF3 results are in 

blue and UCERF2 are in red. The corresponding faults sections are as labeled. The darker colored 

lines are cumulative distributions, and the lighter colored lines are incremental. The black/gray 

curves are UCERF3 MFDs with subseismogenic rupture added (total on-fault MFD). The thinner 

lines represent cumulative-distribution minimum and maximum among all logic tree branches. It is 

important to understand that “participation” includes all ruptures that touch any part of the parent 

fault section (even if a large rupture extends only a couple of subsections in at one end). For this 

reason, participation MFDs at a point on the fault (for example, a peleoseismic trench) will be less 

than or equal to those shown here. Results were also obtained for other fault sections (http://pubs.

usgs.gov/of/2013/1165/data/UCERF3_SupplementalFiles/UCERF3.3/Model/FaultMFDs/).
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Figure 26. Plots showing cumulative magnitude-frequency distributions (MFDs) for selected regions. 

A, Total branch-averaged cumulative MFD for the Los Angeles region depicted in figure 27. Blue is 

for UCERF3, red is for UCERF2, and the thin lines represent the minimum and maximum over all 

branches. Note that aftershocks have been added back in for UCERF2 by reversing the GardnerKnopoff filter described above. B and C are equivalent plots for the San Francisco and Northridge 

regions depicted in figure 27.
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The UCERF3 MFDs for the Los Angeles region are more consistent with a GR 

distribution, with lower mean rates from M6.0 to M7.7 and higher mean rates above, as expected

from the inclusion of multifault ruptures. The range of MFDs from the respective logic trees 

generally overlaps, except between M6.5 and M7.0 and just barely at M5. The UCERF3 rate of 

M≥5 is about 58 percent greater than for UCERF2 (table 13), which is consistent with the 

branch-averaged 43 percent increase in RM≥5

total discussed above. The total rate of M≥6.7 events 

has gone down by a factor of two in UCERF3 because of the inclusion of multifault ruptures. 

Note also that while 40 new fault sections were added to the Los Angeles region in UCERF3, the 

new deformation models actually lowered the average total moment rate by about 7 percent 

(table 13).

The UCERF2 and UCERF3 MFDs for the San Francisco region are much more 

consistent. The rate of M≥5 events has increased by 39 percent in UCERF3, which also is 

generally consistent with the effective 43 percent increase in RM≥5

total. The rate of M≥6.7 events is 

essentially unchanged, while the rates of M≥7.5 are about 48 percent higher, which reflects a 

tradeoff between the inclusion of multifault ruptures and a ~7-percent increase in moment rate 

from the addition of 33 new fault sections (table 13).

Table 13. Number of fault sections, total moment rate (in units of 1018 N⋅m/year), and event rates 

(per year) inside the three subregion boxes shown in figure 27.

[“U3” corresponds to UCERF3, and “U2” corresponds to UCERF2, both averaged over all logic tree branches. More 

rates and (or) lists of fault sections inside the regions are available upon request. Aftershocks are included as 

described in the figure 26 caption] 

LA region SF region Northridge region

U3 U2 U3 U2 U3 U2

Number of fault sections 102 62 67 34 18 11

On-fault moment rate 4.18 4.51 3.12 2.91 0.43 0.36

Total rate M≥5 0.736 0.465 0.780 0.561 0.091 0.040

Total rate M≥6.7 0.025 0.053 0.035 0.037 0.0036 0.011

The UCERF3 MFD for the Northridge box (fig. 26C) is much more GR than that of 

UCERF2. In fact, we included this region here precisely because the strongly characteristic 

UCERF2 MFD was found to produce runaway aftershock sequences in preliminary Northridge 

earthquake ETAS simulations (Field, 2012). The inclusion of multifault ruptures has cut the 

average rate of M≥6.7 events by a factor of three, even though UCERF3 has a 19 percent 

moment rate increase in this area (table 13). This change represents a significant improvement 

over UCERF2. 
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Figure 27. Maps showing ratios of UCERF2 and UCERF3 results. A, Ratio of the average UCERF3 to 

UCERF2 off-fault spatial seis PDF (equal to 0.5(U2sm+U3sm)/U2sm, where U2sm is the UCERF2 

smoothed seismicity map fig.14A) and U3sm is the UCERF3 smoothed seismicity map (fig. 14B). 

This ratio does not include the overall regional rate increase for RM≥5

total. B, Ratio of branchaveraged, on-fault moment rates between UCERF3 and UCERF2, where infinite values are shown 

in black (a result of new faults being added where none existed in UCERF2).

Participation Rate Maps

Figure 28 compares the mean UCERF3 participation rate maps for various magnitude 

thresholds with those for UCERF2. The ratio for M≥5 is generally high owing to the increase in 

RM≥5

total, although there are some low areas near faults. The ratios for M≥6.7 are more extreme, 

including low areas near the UCERF2 Type C zones in northeastern California, high areas where 

new faults have been added (for example, offshore San Diego), and some low values on 

preexisting faults, reflecting lowered rates owing to the inclusion of multifault ruptures. More 

areas are capable of M≥7.7 events in UCERF3 because of an increase in Mmax

off−fault, and more 

areas generate M≥8 events because of multifault ruptures. Such events on Elsinore and Death 

Valley are seen in UCERF2 but not UCERF3, because the former includes aleatory magnitudearea variability. 
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Figure 28. Branch-averaged participation rate maps for UCERF3 and UCERF2, and for the ratio of 

the two (UCERF3/UCERF2). For the ratios, zero values are white, values above the color scale 

maximum (103) are black, and infinite values are white (where the UCERF2 denominator is zero).

These plots have had aftershocks removed in order to make the comparison to UCERF2.
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Implied Segmentation

Figure 29 (from appendix N, this report) shows model-implied segmentation along the 

SAF for both UCERF3 and UCERF2. As expected, segmentation is much less pronounced in the 

new model, which can significantly influence hazard. For example, in a strictly segmented 

model, a site on a segment boundary has twice as many events at zero distance, on average, than 

a site halfway down a segment, which is a potential factor of two difference in hazard. The effect 

is less when both single and multisegment ruptures are included, as with UCERF2 type A faults, 

but strict segmentation was effectively applied to adjacent type B faults in UCERF2. This effect 

partially explains a hazard reduction identified for the city of Oakland below. 

Figure 29. Latitudinal plots showing average model-implied segmentation on the San Andreas Fault

system for UCERF2 (top) and UCERF3 (bottom). The right side includes all supraseismogenic 

ruptures, whereas the left side is for only M≥7 events. The Brawley and Imperial Faults were not 

included in UCERF2 (and are therefore not shown for this model). Red points show the rate at which

neighboring subsections do not rupture together, normalized by the total rate of ruptures involving 

those two subsections. Thus, when the red line reaches 1, there is strict segmentation and no 

ruptures break through that location.
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Hazard Curves and Maps

Perhaps the most important questions for UCERF3 are: how and why have hazard 

estimates changed relative to UCERF2; and what are the most influential UCERF3 logic tree 

branches? This section addresses these questions, concluding that the dominant factors are 

deformation models (slip rates) and the new smoothed seismicity model, with methodological 

differences (multifault ruptures) being important in some places. 

A seismic hazard curve gives, for a site, the probability of exceeding various earthquakeshaking levels over a specified period of time period (typically 50 years for building codes). The 

type of shaking is referred to as the ground motion parameter, or intensity measure type, with the 

most widely used including peak ground acceleration (PGA) and spectral acceleration (SA) at 3-

second, 1-Hz, and 5-Hz (3s SA, 1Hz SA, and 5Hz SA, respectively). For example, the seismic 

design provisions recommended by the Building Seismic Safety Council (2009) use 1Hz and 

5Hz SA. To support engineering design and building codes, the USGS NSHMP publishes 

probabilistic ground motion maps, which show the shaking levels that have a certain probability 

of being exceeded over a given time period (the hazard-curve x-axis value corresponding to 

some y-axis level, with the latter typically being the 2-percent- or 10-percent-in-50-years 

exceedance probability; see figure 30 for an example).

To understand UCERF3 implications, a wide variety of hazard curves and maps have 

been generated using OpenSHA (www.OpenSHA.org), which was the only PSHA code that 

could accommodate UCERF3 (at least at that time). Doing so, however, required considerable 

effort in terms of implementing and verifying details needed for a precise replication of official 

2008 NSHMP values (based on the NSHMP FORTRAN Code). Documentation of such 

implementation details will be provided in a forthcoming report, but results for all UCERF3 

hazard calculations are currently available, with explanations, at http://pubs.usgs.gov/of/

2013/1165/data/UCERF3_SupplementalFiles/UCERF3.3/Hazard/.

The results cited below come from this database. To ensure meaningful comparisons, the 

same set of ground motion models employed by NSHMP-2008 (for crustal faults) has been used. 

Although a wide array of hazard metrics are available at the above website, including the risk 

targeted ground motions now being considered by the BSSC (Luco and others, 2007), we focus 

only on those needed to make important points here. 

Table 14 lists a number of sites where hazard curves have been computed, along with 

various UCERF3/UCERF2 hazard ratios (or more precisely, ratios of ground motions that have a 

certain probability of exceedance). The first 21 “NEHRP” sites are those used by the Building 

Seismic Safety Council (BSSC) when considering updates to seismic design provisions, and 

those listed as “Other” have been of particular interest to the WGCEP (for example, added 

during review). The full hazard-curve results for all these sites, from which the data in table 14

were obtained, are available at http://pubs.usgs.gov/of/2013/1165/data/UCERF3_

SupplementalFiles/UCERF3.3/Hazard/HazardCurves/. To complement these test-site 

calculations, we computed a variety of probabilistic ground motion maps. Figure 31 shows the 

UCERF3/UCERF2 ratio map for 2-percent-in-50-year PGA (abbreviated as “2in50 PGA” 

hereafter).

One goal has been to understand and justify all “important” hazard differences between 

UCERF3 and UCERF2, which we define as greater than ten percent changes in probabilistic 

ground motion. Sites with such discrepancies are color coded in table 14 and shown as nonyellow areas in figure 31. Although considerable effort has been put into understanding all such 

cases, we focus here on the more discrepant and informative examples.
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The biggest change listed in table 14 is a factor of 2.32 increase for 2in50 PGA at the 

Redding site, the location of which is plotted in figure 31B. The hazard curve for Redding is 

shown in figure 30, together with a tornado diagram and histogram revealing the influence of 

alternative logic tree branches, relative to a median branch. The SpatialSeisPDF logic tree branch 

is clearly most influential at this site; the two options (UCERF2 versus UCERF3 Smoothed Seis) 

create a strong bimodal distribution of ground-motion levels. This is because Redding is situated 

near a high seismicity area that is clearly visible in the UCERF3 Smoothed Seis model, but 

spreads into other regions in the UCERF2 Smoothed Seis model. Adding the new 

SpatialSeisPDF option has therefore increased the hazard at Redding, as well as at other sites 

indicated in figure 31B (which represents areas of correlation between figure 27A and figure 

31A). However, the more focused smoothing kernels have also reduced the hazard at areas 

further from the seismicity clusters.

San Diego has a factor of 1.37 increase for 10in50 PGA, which is the largest change 

among the National Earthquake Hazards Reduction Program (NEHRP) sites in table 14. This 

increase is clearly attributable to the addition of new offshore faults, including those shown as 

black in figure 27: Carlsbad, Thirty Mile Bank, San Clemente, San Diego Trough north, San 

Diego Trough south, Oceanside, and half of Coronado Bank (the latter was used in only one of 

two UCERF2 fault models). Figure 31C highlights this and other areas influenced by the 

addition of faults, or by changes in average fault moment rates.

Cucamonga exhibits the biggest decrease among all sites in table 14, with a factor of 0.53 

reduction for 2in50 PGA, which can also be seen in the ratio map in figure 31D. As noted 

previously in the context of figure 25, the rate of M≥6.7 events on the Cucamonga Fault has 

dropped by a factor of three, due entirely to the inclusion of multifault ruptures (going from 

~M6.7 single-segment ruptures in UCERF2 to also participating in events up to ~M8 in 

UCERF3). Therefore, this fault also represents the biggest methodological change with respect to 

hazard. Another example is the San Cayetano Fault section, as indicated in figure 31D and also 

shown in figure 25. We reiterate that both these cases were deemed a significant improvement at 

the fault-by-fault review meetings (table 2).

The Oakland site shows the largest reduction amongst NEHRP sites in table 14, a drop of 

22 percent for 10in50 5Hz SA, which is more challenging in terms of parsing influences. The 

hazard in Oakland is dominated by the nearby North fault section, which actually had a 90 

percent increase in the average moment rate. This increase is apparently countered by its now 

participating in more multifault ruptures; for example, the 10,000-year event has gone from 

~M7.3 in UCERF2 to ~M7.7 in UCERF3 (fig. 25). Another significant factor, revealed by highresolution hazard maps, is that Oakland is situated near a UCERF2 segment boundary, which 

gives it a higher rate of events in close proximity than at other locations along the fault. 

Removing the strong influence of this segment boundary in UCERF3 therefore contributed to 

reducing the hazard in Oakland (another methodological influence). 

Other cites of interest include Los Angeles, which has only a minor reduction (<10 

percent) for the location in table 14, and San Francisco, which also shows minor differences in 

table 14. An exception for the San Francisco site is 10in50 1Hz SA, which dropped by 11 

percent. Evaluation of the tornado diagram for this location (available at http://pubs.usgs.gov

/of/2013/1165/data/UCERF3_SupplementalFiles/UCERF3.3/Hazard/HazardCurves/Sites/sites/S

AN_FRANCISCO/10in50_1Hz.pdf) implies that average slip-rate changes are responsible. 

Sacramento, another site of interest, exhibits an 11 percent increase for 2in50 PGA. 
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The associated tornado diagram (http://pubs.usgs.gov/of/2013/1165/data/UCERF3_

SupplementalFiles/UCERF3.3/Hazard/HazardCurves/Sites/sites/SACRAMENTO/2in50_PGA.pdf

) indicates that gridded seismicity is most influential, so the change can be attributed to the total 

regional rate increase for UCERF3.

To summarize, the following are generally found to be most influential in terms of 

UCERF2 to UCERF3 hazard changes (listed in descending order of importance, although this 

has a heavy spatial dependence):

• Addition of new faults and average moment rate changes on existing faults 

• Addition of the UCERF3 Smoothed Seis option 

• Inclusion of multifault ruptures in UCERF3 

• The effective 43 percent increase in the total rate of M≥5 events

This conclusion generally applies to all ground motion parameters and probability levels 

examined.
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Figure 30. Graphs illustrating the hazard-curve example for PGA at the Redding site listed in table 13. 

Top, Comparison of UCERF3 and UCERF2 hazard curves. The blue and red lines mark the 

weighted mean hazard curve across all UCERF3 and UCERF2 (time-independent) logic tree 

branches, respectively. The light blue shaded region delineates the minimum and maximum hazard 

values among all UCERF3 branches, and the dashed red lines are the same for UCERF2 (just 

barely visible to the left). The horizontal grey line marks the 2-percent-in-50-year probability of 

exceedance level. The vertical lines mark the mean (solid) and minimum and maximum (dashed) 2-

percent-in-50-year ground-motion values. Bottom left, Distribution of 2-percent-in-50-year ground 

motions across the UCERF3 logic tree (considering branch weights). Color coding of the vertical 

lines is the same as at the top. Bottom right, Tornado diagram (see, for example, Porter and others, 

2012), indicating the influence of each UCERF3 logic tree branch on the overall uncertainty. The 

“swings” away from the thin vertical line represent the influence of changing each branch option, 

one at a time, relative to the branch corresponding to the median, and ignoring branch weights.
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Table 14. Ratios of UCERF3 to UCERF2 ground motion exceedance values for varios sites, intensity measures, and return periods*.

Site Lat Lon Group 2% in 50 years 10% in 50 years RTGM Average

PGA 5Hz SA 1Hz SA 4sec SA PGA 5Hz SA 1Hz SA 4sec SA 5Hz 1Hz

Century City 34.05 -118.40 NEHRP 1.07 1.07 1.04 1.04 1.07 1.05 1.02 1.00 1.06 1.02 1.04

Concord 37.95 -122.00 NEHRP 1.02 0.98 1.01 1.09 0.96 0.93 0.94 1.01 0.97 0.98 0.99

Irvine 33.65 -117.80 NEHRP 0.91 0.91 0.90 0.98 0.98 0.98 0.92 0.90 0.94 0.91 0.93

Long Beach 33.80 -118.20 NEHRP 1.15 1.13 1.11 1.06 1.13 1.11 1.04 1.00 1.12 1.07 1.09

Los Angeles 34.05 -118.25 NEHRP 0.94 0.93 0.95 1.09 0.94 0.93 0.91 0.96 0.93 0.93 0.95

Monterey 36.60 -121.90 NEHRP 0.96 0.94 0.96 0.99 0.93 0.93 0.96 0.99 0.97 0.98 0.96

Northridge 34.20 -118.55 NEHRP 1.20 1.18 1.16 1.20 1.15 1.13 1.06 1.03 1.15 1.09 1.14

Oakland 37.80 -122.25 NEHRP 0.85 0.83 0.87 0.99 0.81 0.78 0.80 0.90 0.81 0.83 0.85

Riverside 33.95 -117.40 NEHRP 1.03 1.02 0.97 1.02 0.98 0.97 0.88 0.85 0.99 0.91 0.96

Sacramento 38.60 -121.50 NEHRP 1.11 1.10 1.07 1.10 1.04 1.02 1.02 1.06 1.05 1.03 1.06

San 

Bernardino 34.10 -117.30 NEHRP 0.90 0.89 0.88 1.03 0.89 0.86 0.79 0.81 0.88 0.83 0.88

San Diego 32.70 -117.15 NEHRP 1.18 1.19 1.12 1.00 1.37 1.36 1.23 1.06 1.21 1.12 1.19

San 

Francisco 37.75 -122.40 NEHRP 0.94 0.93 0.91 0.92 0.92 0.90 0.89 0.90 0.91 0.90 0.91

San Jose 37.35 -121.90 NEHRP 1.07 1.07 1.12 1.20 1.05 1.04 1.08 1.18 1.04 1.09 1.09

San Luis 

Obispo 35.30 -120.65 NEHRP 1.09 1.08 1.07 1.09 1.03 1.02 1.00 0.99 1.06 1.04 1.05

San Mateo 37.55 -122.30 NEHRP 0.96 0.95 0.95 0.96 0.96 0.96 0.95 0.96 0.95 0.95 0.95

Santa 

Barbara 34.45 -119.70 NEHRP 0.91 0.88 0.93 1.00 0.83 0.81 0.81 0.89 0.86 0.89 0.88

Santa Cruz 36.95 -122.05 NEHRP 1.03 1.03 1.04 1.07 1.03 1.03 1.05 1.06 1.04 1.05 1.04

Santa Rosa 38.45 -122.70 NEHRP 0.88 0.88 0.87 0.93 0.87 0.85 0.82 0.85 0.88 0.86 0.87

Vallejo 38.10 -122.25 NEHRP 1.28 1.23 1.26 1.25 1.13 1.10 1.12 1.12 1.13 1.16 1.18

Ventura 34.30 -119.30 NEHRP 0.94 0.94 0.96 1.08 0.94 0.92 0.89 0.94 0.91 0.92 0.95

Bakersfield 35.35 -119.00 Other 1.06 1.06 1.06 1.07 1.02 1.02 0.99 0.97 1.04 1.01 1.03

Big Sur 36.25 -121.75 Other 1.26 1.22 1.24 1.17 0.94 0.94 0.96 0.95 1.13 1.17 1.10

Brawley 33.00 -115.55 Other 1.09 1.08 1.14 1.38 1.10 1.08 1.08 1.12 1.08 1.09 1.12

Brookings 42.05 -124.25 Other 2.06 2.12 1.98 1.81 1.67 1.66 1.52 1.54 1.91 1.80 1.81

Carson City 39.15 -119.75 Other 1.19 1.26 1.19 0.98 1.18 1.22 1.15 1.00 1.22 1.16 1.16
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Site Lat Lon Group 2% in 50 years 10% in 50 years RTGM Average

PGA 5Hz SA 1Hz SA 4sec SA PGA 5Hz SA 1Hz SA 4sec SA 5Hz 1Hz

Coalinga 36.15 -120.40 Other 1.03 1.03 0.98 1.02 1.06 1.05 0.97 0.95 1.05 0.98 1.01

Cucamonga 34.20 -117.55 Other 0.53 0.53 0.67 0.98 0.57 0.57 0.60 0.77 0.57 0.64 0.64

Death 

Valley 36.35 -116.85 Other 0.58 0.56 0.60 0.73 0.57 0.58 0.58 0.61 0.58 0.62 0.60

Diablo 

Canyon 35.20 -120.85 Other 0.90 0.85 0.84 0.92 0.88 0.87 0.88 0.89 0.88 0.88 0.88

Eureka 40.80 -124.20 Other 1.05 1.02 1.07 1.04 1.17 1.16 1.10 1.02 1.06 1.08 1.08

Fresno 36.75 -119.75 Other 1.22 1.22 1.14 1.09 1.15 1.15 1.08 1.06 1.17 1.11 1.14

Malibu West 34.05 -118.95 Other 0.73 0.68 0.71 0.95 0.89 0.86 0.83 0.91 0.77 0.78 0.81

Morgan Hill 37.15 -121.65 Other 0.94 0.93 1.05 1.24 0.94 0.94 1.01 1.19 0.96 1.03 1.02

Palm 

Springs 33.85 -116.55 Other 0.93 0.90 0.90 0.94 0.91 0.91 0.88 0.89 0.91 0.88 0.91

Palmdale 34.50 -118.00 Other 0.95 0.93 0.93 0.97 0.92 0.92 0.87 0.86 0.93 0.91 0.92

Pasadena 34.15 -118.15 Other 0.86 0.85 0.91 1.09 0.78 0.76 0.79 0.91 0.82 0.86 0.86

Redding 40.60 -122.40 Other 2.32 2.29 1.67 1.18 2.21 2.19 1.42 1.12 2.15 1.55 1.81

Reno 39.55 -119.80 Other 0.93 0.94 0.84 0.71 1.00 1.02 0.93 0.82 0.99 0.89 0.91

San Onofre 33.40 -117.55 Other 1.05 1.04 1.03 1.02 0.99 0.99 0.95 0.92 1.04 0.99 1.00

AC01 34.42 -118.10 PBR 0.98 0.97 0.98 1.02 0.95 0.94 0.93 0.94 0.95 0.95 0.96

ACTN 34.46 -118.18 PBR 0.97 0.96 0.98 1.02 0.94 0.92 0.92 0.93 0.94 0.94 0.95

BKBU 34.56 -117.73 PBR 0.98 0.99 0.98 1.00 0.98 1.00 0.94 0.89 0.99 0.95 0.97

GLBT 33.96 -117.38 PBR 1.03 1.01 0.97 1.02 0.97 0.96 0.87 0.84 0.98 0.90 0.96

GOPH 33.90 -117.36 PBR 1.02 1.01 0.96 1.00 0.97 0.96 0.88 0.84 0.98 0.91 0.95

GV03 34.28 -117.23 PBR 0.67 0.66 0.69 0.86 0.71 0.70 0.67 0.74 0.70 0.68 0.71

LBUT2 34.59 -117.81 PBR 0.98 0.99 0.98 1.01 0.98 0.99 0.94 0.90 0.99 0.95 0.97

LMAT 33.79 -117.40 PBR 1.10 1.11 1.03 0.96 1.13 1.14 1.03 0.92 1.11 1.02 1.05

LPER 33.89 -117.16 PBR 0.82 0.78 0.77 0.88 0.77 0.76 0.68 0.68 0.79 0.74 0.77

MKBD 33.88 -117.39 PBR 1.03 1.03 0.97 1.00 0.99 0.99 0.90 0.86 1.00 0.93 0.97

MRVY 33.93 -117.17 PBR 0.83 0.80 0.82 0.95 0.76 0.74 0.66 0.69 0.79 0.75 0.78

NUEVO 33.78 -117.15 PBR 0.93 0.90 0.88 0.94 0.87 0.86 0.80 0.78 0.89 0.84 0.87

PACI2 34.39 -118.05 PBR 0.99 0.98 0.99 1.03 0.95 0.94 0.93 0.94 0.95 0.95 0.97
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Site Lat Lon Group 2% in 50 years 10% in 50 years RTGM Average

PGA 5Hz SA 1Hz SA 4sec SA PGA 5Hz SA 1Hz SA 4sec SA 5Hz 1Hz

PBWL 34.41 -117.86 PBR 1.00 1.00 0.95 0.98 1.02 1.03 0.96 0.88 1.03 0.96 0.98

PEDLEY1 33.99 -117.46 PBR 1.04 1.03 0.99 1.02 0.99 0.98 0.90 0.87 0.99 0.92 0.97

PERR2 33.79 -117.24 PBR 0.97 0.95 0.91 0.96 0.93 0.93 0.86 0.83 0.95 0.89 0.92

PERRM 33.80 -117.25 PBR 0.96 0.95 0.91 0.96 0.93 0.92 0.86 0.83 0.95 0.89 0.92

PIBU 34.65 -117.85 PBR 0.99 1.00 0.99 1.01 0.98 0.99 0.94 0.91 0.99 0.95 0.98

SW01 34.30 -117.34 PBR 0.79 0.78 0.81 0.95 0.77 0.75 0.72 0.78 0.77 0.76 0.79

UCR 33.96 -117.32 PBR 0.99 0.96 0.92 1.01 0.94 0.92 0.82 0.80 0.94 0.86 0.92

 *In the “Group” column, “NEHRP” sites are from table C11.4-1 of the Recommended Seismic Provisions for New Buildings and Other Structures (2009). 

Those listed as “Other” are WGCEP-chosen sites, and those listed as “PBR” are locations of precariously balanced rocks (James Brune, written commun., 2012). 

The “RTGM” column gives ratios of the Risk Targeted Ground Motions, as described by Luco and others (2007). A digital version (Microsoft Excel file format 

xlsx) of this table is available here. 
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To help quantify the influence of UCERF3 epistemic uncertainties, 2in50 PGA maps 

were computed for all 1,440 logic tree branches. We then averaged over the options on each 

branch separately, and normalized by the total average, to reveal the influence of each. The 

process is illustrated in figure 32 for Deformation Models, where each option is represented by 

an average over the associated subset of maps (360 given the four branch options in this 

example) divided by the average over all 1,440 maps. Figure 32 reveals a strong influence from 

the block boundaries used in the ABM model (red areas), which was the basis for downweighting this model (because some of these areas may be model artifacts).

The resultant branch ratio maps for all UCERF3 epistemic uncertainties are available as 

links in table 15. The most influential choices in descending order of overall importance are:

deformation models, UCERF2 versus UCERF3 smoothed seis, and scaling relationships. Fault 

models and total M≥5 event rate have some influence in specific areas, while Mmax

off−fault and 

slip along rupture (Dsr) have very little influence. These conclusions are generally applicable to 

other return periods and ground motion parameters, although we reemphasize the spatial 

dependence of such conclusions. 

Table 15. Influence of different logic-tree branches.

[Clicking on the links in this table will show the relative influence of different logic tree branches (as labeled) for 2-

percent-in-50-year peak ground acceleration. These are subdirectories of

http://pubs.usgs.gov/of/2013/1165/data/UCERF3_SupplementalFiles/UCERF3.3/Hazard/BranchRatios/

Branch Ratio Maps for Logic tree Subsets

Fault Model 3.1 versus 3.2

Deformation models

Scaling relationships

Tapered versus boxcar slip along rupture (Dsr)

Total M≥5 event rate

Off-fault Mmax

Off-fault spatial seis PDF (UCERF2 vs UCERF3 smoothed seismicity)

Total M≥5 event rate and off-fault Mmax
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Figure 31. Comparison of UCERF2 and UCERF3 for 2-percent-in-50-year PGA. A, Ratio of UCERF3

2-percent-in-50 year PGA map divided by that for UCERF2. The attenuation relationships used for 

these calculations are the same ones used in the NSHMP 2008 maps. In B–D, ovals show areas 

where discrepancies can be explained by (B) addition of the UCERF3 Smoothed Seism option, (C)

addition of new faults or average moment-rate changes on existing faults, and (D) methodological 

changes in terms of including multifault ruptures.
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Figure 32. Branch ratio maps showing the influence of each deformation model on 2-percent-in-50 

year peak ground acceleration. These ratios are obtained by averaging results over deformationmodel subset branches, and then dividing by the total average. Numbers in blue indicate the 

weights each model is given in UCERF3.
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Sensitivity Tests

Simulated Annealing Convergence and Nonuniqueness

We first consider how well the simulated annealing algorithm converges, which depends 

on the problem and how long the inversion algorithm is run. We also consider the problem of 

nonuniqueness, in particular how the simulated annealing samples the null space. Given that 

there can be an infinite, yet bounded, number of viable models in this situation, the more 

appropriate question is how many runs are needed to get stable averages of individual solutions. 

We refer to both of these issues as convergence because the convergence and nonuniqueness 

problems cannot be separated in our tests. 

Whether the inversion is over-, under-, or mixed-determined depends on the evaluation 

metric of interested. We are solving for more than 250,000 unknown rupture rates (fr) with about 

37,000 equality constraints (appendix N, this report), so clearly individual solutions are not 

unique. But what about metrics that are more relevant to seismic hazard, such as fault section 

participation MFDs and hazard curves? And what about branch-averaged results versus what is 

resolved on individual branches? We quantify sensitivity to each of these here, and conclude that 

convergence is not an issue for hazard-related metrics.

Individual Logic Tree Branches

To test convergence for individual branches, we ran 200 simulated annealing inversions 

for the reference model (bold typeface options in figure 3). About 10,000 nonzero-rate (or abovewater-level) ruptures are needed to “fit” the data on a single run, which is only ~4 percent of all 

ruptures. Figure 33 shows how this number varies as a function of the number of runs averaged. 

For example, averaging 10 runs, as done for each branch in UCERF3, increases the number to 

~38,000 (~15 percent of ruptures), and averaging 200 runs increases the number to ~115,000 

(~46 percent). This indicates that each solution samples a different set of ruptures in satisfying 

the data, as expected for an underdetermined problem. The roll off in figure 33 suggests that an 

infinite number of runs would yield 50 to 60 percent ruptures above water level, implying that 

half the ruptures are excluded on this particular branch. 

We attempted to quantify the number of runs needed to resolve mean rupture rates to 

some level of precision. However, interpretations were complicated by the fact that most rates 

are at water level (producing a bimodal distribution with a relatively high spike at the water 

level). Therefore the mean rupture rates are difficult to resolve on individual branches, although 

we did find that those with higher rates are also better resolved. 
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Figure 33. Graph showing number of above-water-level ruptures as a function of the number of 

simulated annealing runs averaged (for the reference branch). The maximum value on the y-axis is 

the total number of ruptures (~250,000 = 2.5×105 = 2.5E5).

Fault section participation MFDs represents a more appropriate metric for hazard. For a 

given magnitude event, standard PSHA for a site is relatively insensitive to rupture-endpoint 

differences, and completely so if the closest point to the rupture surface is the same. Figure 34

shows three participation MFDs obtained from the 200 reference branch runs. In terms of M>6.7 

rate variability among the 200 solutions, defined as the sample standard deviation (s) divided by 

the sample mean (μ), these represent the worst, median, and best cases among all fault sections. 

The number of inversion runs (N) needed to get “well resolved” average estimates (those with 

the upper 95-percent confidence bound (μ + 1.96s/√N) within 10 percent of the mean) is:

μ + 1.96s/√N ≤ 1.1μ

where s/√N is the sample standard deviation of the mean. Solving for N we obtain: 

N = (19.6s/μ)2

With the sample statistics shown in figure 34, the implied number of runs needed for 

well-resolved M≥6.7 event rates is 1,294 for the worst case (Richfield), 9 for the median case 

(Puente Hills), and 1 for the best case (San Jacinto-Anza). The median is near the number of runs 

chosen for each branch in UCERF3 (10), which implies that roughly half our fault sections have 

“well resolved” rates on individual branches. The worst case implies that, for some fault 

sections, many more runs would be needed to get well-resolved rates on individual branches. 

However, these turn out to be the least hazardous faults, because there is anticorrelation between 

variability and mean rate. For example, the worst case in figure 34 also has the lowest rate of 

M≥6.7 events among all fault sections (with an average repeat time exceeding 1,000,000 years). 

All fault sections that have average M≥6.7 repeat times less than 1,000 years are well resolved, 
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and the mean fractional uncertainty for all faults, weighted by the mean rate of each section, is 

1.04. 

We have also conducted this same analysis with respect to hazard curves. Specifically, 

from the 200 reference branch runs, and for all test locations in table 14, we computed sample 

means and standard deviations for 2in50 and 1in100 ground motion levels for PGA, 5Hz SA, 

1Hz SA, and 4sec SA. Note that the 1in100 case, representing a 10,000-year return period, and 

4-sec SA were added to test more extreme circumstances (where more uncertainty might be 

expected). In terms of variability (s/μ), the worst case is 2in50 5Hz SA at Brookings (located just 

north of California on the Oregon coast). The fractional uncertainty for this worst case, (μ +

1.96s/√N)/μ, is 1.03 for N=10, meaning the upper 95- percent confidence bound is 3 percent 

above the mean with 10 runs. The median and best cases among this test had fractional 

uncertainties of 1.004 and 1.0001. These results imply that all customary hazard metrics are well 

resolved on individual branches given the 10 simulated annealing runs on each in UCERF3. The 

same conclusions can be drawn by examining the mean and range of hazard curves obtained 

among the 200 reference branch runs, which are available for each site at 

http://pubs.usgs.gov/of/2013/1165/data/UCERF3_SupplementalFiles/UCERF3.3/Hazard/Inversi

onTests/Convergence/ (note that the range plotted is the minimum and maximum among all 

branches, not a standard-deviation-based confidence or range, which would require very thin 

lines to discern from the mean). 

Figure 34. Graphs showing cumulative participation magnitude-frequency distribution statistics for 

200 simulated annealing runs on the reference branch. The fault-section examples shown here 

represent the worst case (Richfield), median case (Puente Hils), and best case (San Jacinto-Anza) 

in terms of fractional uncertainty described in the test (which is proportional to the standard 

deviation divided by the mean).

Branch-Averaged Results

The 1,440 different logic tree branches provide a great deal of additional averaging with 

respect to mean hazard, and we can use the 10 different runs for each branch to quantify how 

well such metrics are resolved for branch-averaged results. Figure 35 shows the number of 

ruptures above water level for branch-averaged results, as a function of how many runs on each 

branch are included. If only one simulated annealing run is used for each branch, about 176,000 

events (76 percent) are above water level in the branch-averaged model. After averaging over all 

10 runs, the full UCERF3 branch-averaged model has about 236,000 ruptures above water level 
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(94 percent). Mean rupture rates are also much better resolved, but they are still difficult to 

interpret given bimodal distributions with respect to water levels.

Figure 35. Number of above-water-level ruptures for branch-averaged solutions as a function of the 

number of simulated annealing runs on each branch (for Fault Model 3.1). The maximum value on 

the y-axis is the total number of ruptures (~250,000=2.5×105 =2.5E5).

Fault-section-participation MFDs are also much better resolved for branch average 

results. Sample means and standard deviations were computed from the 10 different sets, and 

fractional uncertainties for M≥6.7 event rates were computed for all fault sections. The worst 

case found is the Fitzhugh Creek section, which has a fractional uncertainty of 1.07 (meaning the 

upper 95-percent confidence bound is 7 percent above the mean and not visually discernable as 

plotted in figure 34. The median case implies that half the fault sections have upper 95-percent 

confidence bounds that are less than 0.5 percent above the mean. This implies that branchaveraged participation MFDs are well resolved on all fault sections in UCERF3. 

Hazard metrics are extremely well resolved for branch averages. We generated a 2in50 

PGA map for each of the 10 branch-averaged models, computed a sample mean and standard 

deviation from these 10, and then computed the fractional mean uncertainty at each map 

location. We then repeated this process for 1in100 PGA, 2in50 3-sec SA, and 1in100 3-secHz 

SA. Among all the map sites, probability levels and ground motion parameters, the largest 

fractional uncertainty found was 1.004 (for a site near the northwest corner of California). This 

implies that for branch-averaged probabilistic ground motion maps, including all those released 

by the USGS NSHMP, inversion nonuniqueness is negligible, and even one simulated annealing 

run on each branch would be adequate (because the 1,440 logic tree branches provide sufficient 

averaging on their own). 
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These conclusions apply not only to mean hazard, but to logic tree-implied percentiles as 

well. For each site listed in table 14, we computed 2-, 16-, 84-, and 98-percent fractiles among 

the 10 sets of runs, for both PGA and 3-sec SA, and for 2in50 and 1in100 probability levels. The 

worst case found was a fractional uncertainty of 1.006, meaning an upper 95-percent confidence 

bound that is just 0.6 percent above the mean percentile. 

Equation-Set Weights 

A thorough discussion of how the inversion equation-set weights were applied is given in 

appendix N (this report), which includes sensitivity tests conducted on the reference branch, 

where each equation-set weight was scaled up and down by a factor of 10. It is important to note 

that this range of weights is considered extreme in that fits to the other data are generally 

degraded to the point of model rejection. Example hazard curves from these tests are shown in 

figure 36 (and more results are available at http://pubs.usgs.gov/of/2013/1165/data/

UCERF3_SupplementalFiles/UCERF3.3/Hazard/InversionTests/EquationSetWeights/), where it 

can be seen that the range of values from alternative equation-set weights is small compared to 

that implied by alternative logic tree branches. We therefore conclude that accommodating a 

range of equation-set weights for each branch, which would need to be narrower than that tested, 

would not significantly change UCERF3 results.

Figure 36. Peak ground acceleration (PGA) hazard curves for the Los Angeles and San Francisco 

sites listed in table 14, obtained by varying equation-set weights on the UCERF3 reference branch, 

as summarized in the main text and detailed in appendix N (this report). The minimum and 

maximum curves among these tests are plotted with the red dashed lines, which can be compared 

with the range implied by alternative logic tree branches (blue shaded region). The difference 

between the mean curves (red and blue solid lines) is not meaningful in this comparison. Results for 

other sites are available here.

Discussion

We begin this section with a summary of UCERF3 advantages (relative to UCERF2) and 

then discuss model limitations, both of which are important from a user’s perspective. Table 15
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lists some of the key assumptions underlying UCERF3, and we finish this section with possible 

future improvements. 

Improvements Over UCERF2

The UCERF3 long-term model appears largely successful in terms of the original project 

goals—relaxing segmentation assumptions; incorporating multifault ruptures; fitting a broader 

range of data better; and sampling a wider range of epistemic uncertainties. This has been 

accomplished by implementing a system-level, “grand inversion” framework, which has the 

following advantages over previous approaches: 

• The rate of all earthquakes is solved for simultaneously 

• A wider range of viable solutions is provided (all those consistent with data) 

• The inversion is conceptually simple (summarized in table 5) 

• Results are relatively reproducible (in terms of the influence of expert opinion) 

• The framework is extensible (other constraints can easily be added)

UCERF2 and previous models were largely prescriptive in terms of making assumptions 

about magnitude-frequency distributions and in treating different seismic sources separately (for 

example, via segmentation assumptions). Although elegantly simple, this approach produces an 

overprediction of regional M6.5-7 event rates and ignores the potential influence of multifault 

ruptures. The UCERF3 approach, in contrast, is more derivative in that fault MFDs are not 

assumed, but rather derived from a system-level inversion. 

Results from the derivative approach are more difficult to understand, especially given a 

large increase in the number of possible fault-based ruptures (form ~8,000 to 250,000). Whereas 

previous efforts had only to verify that assumed MFDs and rupture extents were correctly

implemented, the grand inversion required the development of new tools for exploring the nature 

of solutions and their implications. UCERF3 also posed considerable computational challenges 

with respect to solving the large inverse problem thousands of times, and extensive hazard 

calculations were required to understand the potential influence of solution nonuniqueness. All 

of these challenges were new to UCERF3, and not fully appreciated at the beginning of the 

project.

Although the grand-inversion approach is not free of subjectivity, it does provide a more 

comprehensive framework for checking overall consistency between, and therefore balancing the 

influence of, different experts. Opinions of the latter were solicited through an unprecedented set 

of technical, consensus-building workshops (table 2), with a particularly good example being the 

series of fault-by-fault review meetings. These not only provided an important reality check for 

individual faults (not needed in the prescriptive approach taken previously), but also allowed 

comparisons with new, unpublished data and provided a record of faults needing further scrutiny 

in future efforts (see the “ReviewComments” sheet of the U3_FaultSectionData file given in the 

“Data and Resources” section).

UCERF3 also constitutes an improvement in terms of epistemic uncertainty 

representation. For example, UCERF2 had only a single logic tree branch in areas dominated by

gridded seismicity (for example, Sacramento). UCERF3 now has 18 such branches given the 

new alternatives for off-fault maximum magnitude, the spatial distribution of seismicity, and the 

total regional rate of events. Epistemic uncertainties have also been added for fault-based 

ruptures, including a wider range of slip rates (deformation models), new scaling relationships 

that represent the possibility that larger ruptures extend below the depth of microseismicity, and 

alternatives for how average slip varies along strike.
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The geologic databases have been substantially revised and expanded, including 

statewide fault models (appendix A, this report), geologic slip data (appendix B), and 

paleoseismic recurrence rates (appendix G). Fault polygons have been introduced to associate 

fault surfaces with deformation volumes (appendix O). New datasets have been compiled, 

including GPS velocities (appendix C) and displacement-per-event data (appendix R). Geologic 

and geodetic data have been jointly inverted for a suite of statewide deformation models 

(appendix C). 

The data on fault creep rates have been greatly enlarged using InSAR measurements, and 

a new approach has been introduced for extrapolating surface creep rates to average creep rates 

across the fault surface (appendix D, this report). The probability of detecting ground ruptures at 

paleoseismic sites has been estimated (appendix I), and the interpretation of paleoseismic

interevent times has been updated (appendix H). A revised earthquake catalog (appendix K) has 

been used to constrain magnitude-frequency distributions (appendix L), to develop a new model 

of smoothed seismicity (appendix M), and to reconsider the issue of empirically adjusted 

seismicity rates (appendix Q). Scaling relationships for magnitude and depth of rupture have 

been reexamined (appendix E), and a dataset relating rupture length to displacement has been 

developed (appendix F). 

The new deformation models are particularly noteworthy. In addition to a relatively pure 

geologic model (appendix B, this report), we have three that are based on kinematically 

consistent inversions of geodetic and geologic data (appendix C). This is in contrast to the 

previous approach, which relied on expert opinion to broker discrepancies between geologic and 

geodetic observations. The geodetic signal is persistently "flat" across the southern SAF system, 

causing models that use these data to seek slip in places other than the SAF. The signal expected 

from geology and paleoseismology, on the other hand, would have a sharper change in observed 

velocity across the southern SAF (as it is in northern California, although the signal is muted 

compared to geology there too). This is a data-driven result, but we do not know how well the 

short-term GPS data reflect the long-term slip rates; the geologic and paleoseismic constraints 

suggest that they may not be representative of 103

 to 105 year time scales. Finally, the 

kinematically consistent deformation models have also provided estimates of off-fault 

deformation, allowing us to retire the less refined type C zones used in previous models. 

Observations have been compiled to constrain fault-to-fault rupture probabilities 

(appendix J, this report), which not only guided the development of our rupture plausibility filter 

(appendix T) but will also constitute an important resource for further testing of, and improving 

upon, UCERF3. With respect to the grand inversion, appendix N documents the simulated 

annealing algorithm, including parallelization; sensitivity tests, including some based on 

synthetic datasets; the tuning and testing of final constraint weights; and how well each type of 

data is fit by final models. Appendix N also provides additional implementation details, such as 

the treatment of creep and how multifault rupture statistics compare with various types of 

observations. 

The system-level aspect of the grand inversion makes it well suited for hypothesis testing. 

Perhaps the best and most important example of this is with respect to the Gutenberg-Richter 

(GR) branches, where the hypothesis that each fault nucleates such a distribution of events 

cannot match all data—not even close. The inversion implies that doing so would require one or 

more of the following to fall outside the current bounds of consensus-level acceptability: (1) a 

higher degree of creep both on and off faults; (2) higher long-term rate of earthquakes over the 
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whole region (and significant temporal variability on faults such as the SAF); (3) more fault 

connectivity throughout the state (for example, ~M8 anywhere); and (or) (4) lower shear rigidity.

The obvious alternative is that the GR hypothesis does not apply at the local scale of 

individual faults, which would make reports of the death of the Characteristic Model (Kagan and 

others, 2012) greatly exaggerated. Either way, the GR hypothesis is clearly inconsistent with the 

current UCERF3 modeling framework, which is why it was given zero weight on the logic tree. 

If the GR hypothesis turns out to be correct, then the explanation for current discrepancies will 

be equally profound scientifically, and quite consequential with respect to hazard. The main 

point here is that the grand inversion provides an ideal framework for testing this and other such 

hypotheses, which will not only further our scientific understanding, but will also allow us to 

identify and focus resources on the questions that matter. Eliminating model options will also 

reduce epistemic uncertainties, and thereby improve hazard and loss assessments.

Finally, the entire UCERF3 development has been followed closely by a participatory 

scientific review panel, from reviewing original project plans, attending the various meetings and 

workshops (table 2), reviewing all appendixes (table 1), and scrutinizing four different versions 

of UCERF3. We also hosted two workshops where results were presented to the broader 

scientific and engineering communities (table 2). Furthermore, UCERF3 was evaluated by an 

NSHMP steering committee, which recommended that it be used in the 2014 national maps. 

Model Limitations

In spite of improvements, UCERF3 is still an approximation of the system. For example, 

we continue to divide between “on-fault” and “off-fault” ruptures, whereas nature will surely 

violate these model boundaries. Our plausibility filter for multifault ruptures also has arbitrary 

cutoffs, such as the 5-km jumping threshold between faults, and we currently lack any 

improbability constraint. These limitations, coupled with the fact that the relative geometry of 

neighboring faults is poorly known at depth, imply we have most certainly included some 

unlikely ruptures, and excluded some that are plausible. In addition, the multifault rupture rates 

coming out of the grand inversion depend both on how average slip is distributed along such 

ruptures (Dsr), and how slip rates transition between faults, neither of which is well known. 

Some reviewers expressed dissatisfaction with the nonuniqueness of UCERF3 solutions, 

exemplified by the fact that single inversions leave only about 4 percent of ruptures above waterlevel rates. In an attempt to remedy this, we tried applying an additional constraint to, in essence, 

make the rate of similar ruptures equal. However, doing so effectively made the inversion 

nonlinear and therefore prohibitively slow in comparison to simply averaging more inversion 

runs. Each simulated annealing solution can be thought of as one sample among an infinite 

population of viable models, or even as a realization of events for some time period. We do not 

see this as a problem, but rather an improvement in terms of acknowledging nonuniqueness and 

sampling a wider range of models; the problem is inherently underdetermined unless you impose 

segmentation. Fortunately, solution nonuniqueness has a negligible impact on hazard estimates, 

because results depend more on the participation MFD of faults, and much less so on ruptureendpoint details. 

Concerns were voiced regularly that our large number of fault-based ruptures was going 

to be a problem in terms of PSHA computation time. Not only have those concerns turned out to 

be unfounded (OpenSHA calculation time is about the same as it was for UCERF2, in part 

because of the increased speed of computers), but our analysis also demonstrates that use of a 

single inversion solution might be a legitimate way of down-sampling the entire event set. Doing 
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so properly, however, will vary between different types of hazard and loss studies, so we do not 

attempt any generic down-sampling advice here.

Another concern raised during review is whether relaxing segmentation has reduced 

epistemic uncertainty. For example, the Cucamonga Fault section has gone from a relatively high 

rate of moderate sized events (~M6.7) to a lower and relatively uniform rate of events out to M8 

(fig. 25). Technically speaking, this has not reduced epistemic uncertainty, but rather changed the 

behavior from one extreme to perhaps another. And while all such cases that have had a 

perceptible influence on hazard were deemed an improvement at our fault-by-fault review 

meetings, we acknowledge that there may be some areas where UCERF3 lacks an adequate 

characteristic alternative. For example, and in spite of the theoretical modeling of Anderson and 

others (2003), it is possible that Cucamonga never ruptures with neighboring faults. 

To address this possibility, we were asked to explore an inversion that imposes UCERF2 

segmentation throughout the system. While we know this would not be correct everywhere, it 

might be more correct on certain faults. BSSC deadlines prevented us from doing this for 

UCERF3. Furthermore, one does not need the grand inversion to implement a characteristic 

model (that would be overkill), and there is no guarantee that UCERF2 is correct with respect to 

segmentation details anyway. Potential cases like Cucamonga should therefore be handled on a 

case-by-case basis (for example, through site-specific analysis). That being said, figure 21

implies that we are not grossly overpredicting the rate of multifault ruptures (see also the 

multifault evaluation metrics in appendix N (this report), so we believe UCERF3 is doing better 

overall, and that UCERF2 is a relatively poor approximation in more areas of California. 

There is also the possibility that UCERF3 lacks connectivity in areas where it exists, 

which is another form of epistemic uncertainty left out of the model. Given all these limitations 

and assumptions, one might deem the grand inversion overly sophisticated or premature. 

However, we currently lack any alternative for relaxing segmentation and including multifault 

ruptures. Physics-based earthquake simulators (Ward, 2000; Rundle and others, 2006; Dieterich 

and Richards-Dinger, 2010; Tullis and others, 2012) are a promising solution. However, they 

currently suffer even more from some uncertainties, such as the unknown proximity of faults at 

depth. Simulator tuning procedures are also needed to match data (for example, paleoseismic 

event rates; fault-jumping statistics), and the propagation of epistemic uncertainties poses 

considerable computational challenges.

We also emphasize that UCERF3 is heavily weighted toward UCERF2, most notably in 

terms of the characteristic Fault Section MFD Constraint, but also in terms of the various limits 

on multifault ruptures. For example, both slip along rupture (Dsr) models put high amounts of 

slip at the mid-point along strike, as compared to the characteristic-slip model (Working Group 

on California Earthquake Probabilities, 1995), so rupture rates are consequently more limited by 

the slip rate constraint. These impositions explain why UCERF3 underestimates the observed 

frequency of multifault ruptures. Analysis in appendix N (this report) also implies that we are 

overfitting much of our data (as did UCERF2 and previous models). All of these factors further 

limit the range of UCERF3 models.

A final UCERF3 limitation is with respect to fitting some of the paleoseismic data and 

slip rates on the southern SAF (fig. 20). As noted, these constraints can be fit perfectly well if the 

regional MFD constraint is relaxed. Doing so, however, brings back the overprediction of 

moderate event rates. This tradeoff exemplifies the potential long reach of inversion constraints, 

where the rate in one location can be influenced by conditions far away. While some reviewers 

regarded this as physically problematic, others saw it as an appropriate way to achieve system-
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level balance. With respect to the SAF, some branches do fit the data better, but on average our 

rates are about 25 percent low compared to paleoseismic rates. Therefore, while the hazard 

implied by the SAF has changed little since UCERF2, it is currently underestimated if the latest 

paleoseismic interpretations are correct.

Table 16. Key assumptions made in UCERF3, most of which have at least implicit or partial 

representation on our logic tree.

Key Assumptions

1. Simplified faults models derived from synthesized data (for example, geologic 

mapping, microseismicity, well logs) provide an adequate approximation of fault 

structure and connectivity at depth.

2. Approximate 20-year GPS observations reflect long-term deformation rates.

3. Model-based transient corrections made to GPS data for past earthquakes and seasonal 

hydrologic processes are correct, and apparent outliers removed represent 

measurement error and not real signals.

4. “Backslip” methods used in deformation models (Zeng, ABM) are adequate.

5. Faults that lack slip rate constraints can reliably be assigned a categorical value based 

on recency of activity.

6. Depth extent of large ruptures is appropriately modeled by our scaling relationships.

7. Surface slip observations can be used to estimate slip at depth.

8. Surface creep mostly manifests as a seismogenic area reduction (rather than slip rate 

reduction)

9. Tapered and (or) boxcar models of Dsr represents average slip along rupture, even for 

multifault events.

10. A generic model for the probability of seeing events in a paleoseismic trench applies to 

all sites (as opposed to site-specific models).

11. Large regions honor the Gutenberg-Richter magnitude-frequency distribution.

12. Magnitude completeness thresholds as function of time, space, and magnitude have 

been correctly estimated.

13. Seismicity rates vary with time over the course of historical and instrumental 

observations.

14. Higher-resolution smoothed seismicity maps are applicable to large, damaging 

earthquakes and for approximately 50-year time periods.

15. Our plausibility filter provides an adequate set of ruptures in terms of quantifying 

hazard and risk at all locations.

Future Improvements

The extensibility of the grand-inversion platform will lend itself to several potential 

improvements. For example, quantification of multifault rupture statistics via observations, 

dynamic rupture modeling, and physics-based simulations could allow us to improve upon the 

UCERF3 plausibility filter, both in terms of representing epistemic uncertainties and the addition 

of improbability constraints. Some other possible improvements include the following (in no 

particular order):

• Apply deformation-model based options for off-fault spatial seis PDF.

• Explore inversions with UCERF2 segmentation imposed. 

• Explore a wider range of models by relaxing the UCERF2 fault section MFD constraint. 

• Explore a wider range of models by not over-fitting data as much.

• Explore use of inversion data fits for a posteriori adjustment of logic tree branch weights.

• Try to implement an inversion constraint that will achieve more equality among rupture 

rates (fewer water level ruptures).
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• Further explore possibility that points on faults nucleate a Gutenberg-Richter distribution 

of events. 

• Apply more customized/targeted inversion-constraint weights in order to fit certain data 

better (for example, on the southern SAF). 

• Investigate the discrepancy between off-fault moment rates predicted by the deformation 

models and those implied by the grand-inversion models. 

• Address issues identified for particular faults at the fault-by-fault review meetings (see 

the “ReviewComments” sheet of the U3_FaultSectionData file given in the “Data and 

Resources” section).

• Study creep manifestation and implications further, especially given the discrepancy 

between off-fault seismic moment rates between UCERF3 and those predicted by the 

deformation models (fig. 24).

• Coordinate/integrate fault zone polygon definitions with future deformation model 

developments. 

• Investigate how the characteristic slip model (for example, Hecker and others, 2013) 

could be incorporated into the inversion framework given we lack observed estimates on 

most faults.

• Explore model-based inferences that average slip, for a given length rupture, goes down 

with increasing number of fault-to-fault jumps (appendix F, this report) 

• Develop and use site-specific models for the probability of seeing events in a 

paleoseismic trench.

• Explore the applicability of recent seismicity to 50-year forecasts.

• Explore the applicability of different smoothed seismicity algorithms in forecasting large, 

damaging events and for different forecast durations.

Conclusions and Recommendations

We believe UCERF3 represents a considerable improvement over UCERF2. In addition 

to the methodological enhancements represented by the grand inversion, we have expanded the 

range of epistemic uncertainty representation. Hazard calculations allow us to conclude that the 

most influential uncertainties are deformation models (slip rates), the smoothed seismicity 

algorithm, the total regional rate of events, and scaling relationships. All of these new branches 

have produced significant and important changes in mean hazard estimates. New faults have also 

been added to the model, which produce some of the biggest hazard differences relative to 

UCERF2. The apparent overprediction of M6.5-7 event rates in UCERF2 has been removed, and 

UCERF3 includes multifault ruptures like those seen in nature. 

The added epistemic uncertainties are generally more influential than the inclusion of 

multifault ruptures, with at least two notable exceptions identified. However, these conclusions 

are with respect to traditional NSHMP hazard metrics, and may not apply to, for example, 

statewide loss estimates (where large, rare events may be more influential). It will therefore be 

important that practitioners carefully assess the applicability of this model in the context of their 

particular applications, as results may be sensitive to aspects of the model that differ from the 

influential factors inferred here. This is particularly true for site-specific studies, where the 

nearby influential fault(s) may not have adequate epistemic uncertainty representation in 

UCERF3.
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91

While the addition of epistemic uncertainties in UCERF3 is mentioned as an 

accomplishment, this also means we have not yet reached the point where further study is 

reducing the range of viable models. In fact, we have argued that UCERF3 may still be too 

limited, implying that a broader range of models could be forthcoming. That this conclusion is 

being made for one of the most data-rich areas on Earth implies that epistemic uncertainties are 

likely underestimated elsewhere.

Although the inversion is conceptually simple and extensible, the overall framework and 

implementation is far more involved than for previous models. UCERF3 relies on an extensive 

object-oriented programming framework, versus an Excel spreadsheet for Working Group on 

California Earthquake Probabilities (1995). However, this will be true of any system-level 

model, and the only consolation we can provide is the fact that everything is open-source and 

freely available.

The grand inversion has proven to be a powerful tool for quantifying the influence and 

consistency of various constraints, for exploring a range of models, and for testing hypotheses. 

There is considerable interactive complexity in the system, however, and further study will be 

needed to fully understand tradeoffs between the various inversion constraints. Such analyses 

may support applying a posteriori weights to UCERF3 branches in the future. 

Acknowledgments

The UCERF3 Scientific Review Panel (SRP), which was convened at the beginning of 

this project, thoughtfully reviewed the many model components and several cycles of WGCEP 

reports, including this final report and its appendices. We are especially indebted to the SRP 

chair, William Ellsworth, who provided WGCEP with outstanding scientific advice throughout 

the study, and to SRP member, Art Frankel, whose reviews and critiques of the methodology 

were particularly important in model verification. Bob Anderson and Badie Rowshandel 

provided very valuable feedback on behalf of the California Earthquake Authority. Helpful 

reviews were also provided by Mark Petersen and the USGS National Seismic Hazard Mapping 

Program's Steering Committee, chaired by John Anderson, as well as the California and National 

Earthquake Prediction Evaluation Councils (CEPEC and NEPEC). We thank many workshop 

participants for their contributions to the project and their support as UCERF3 came into focus. 

We are very grateful to Tran Huynh for her substantial efforts in organizing WGCEP 

activities and in editing the UCERF reports and appendices, and to John McRaney for his 

financial management of the project. The Management Oversight Committee helped WGCEP 

with project guidance and requisite resources, and Keith Knudson shepherded the main report 

and appendices through the USGS publication process. The SCEC Community Modeling 

Environment, USC Center for High-Performance Computing and Communications, and the 

Texas Advanced Computing Center provided access to the high-performance computing 

resources critical to the Grand Inversion and hazard calculations. We thank Jane Ciener for her 

thorough policy review of UCERF3, and the USGS publications group for their expeditious 

efforts.

This study was sponsored by the California Earthquake Authority, the USGS, the 

California Geological Survey, and the Southern California Earthquake Center. SCEC is 

supported in part by the National Science Foundation under Cooperative Agreement EAR1033462 and the USGS under Cooperative Agreement G12AC20038. This report is USGS 

Open-File Report 2013–1165, SCEC contribution number 1792, and California Geological 

Survey publication number 228. 
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92

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Data and Resources 

U3_FaultSectionData:

http://pubs.usgs.gov/of/2013/1165/data/ofr2013-1165_FaultSectionData.xlsx (800 KB)

U3_PreInversionAnalysisTable:

http://pubs.usgs.gov/of/2013/1165/data/ofr2013-1165_PreInversionAnalysisTable.xlsx (810 KB)

U3 Supplementary Figures:

http://pubs.usgs.gov/of/2013/1165/data/UCERF3_SupplementalFiles/