U.S. Department of the Interior

U.S. Geological Survey

Incorporating Induced Seismicity in the 2014 United 

States National Seismic Hazard Model—Results of 

2014 Workshop and Sensitivity Studies

By Mark D. Petersen, Charles S. Mueller, Morgan P. Moschetti, Susan M. Hoover, Justin L. Rubinstein, Andrea L. 

Llenos, Andrew J. Michael, William L. Ellsworth, Arthur F. McGarr, Austin A. Holland, and John G. Anderson

Open-File Report 2015–1070 
ii

U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2015 

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

its natural and living resources, natural hazards, and the environment—visit

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visit http://www.usgs.gov/pubprod/.

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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.

Suggested citation:

Petersen, M.D., Mueller, C.S., Moschetti, M.P., Hoover, S.M., Rubinstein, J.L., Llenos, A.L., Michael, A.J., 

Ellsworth, W.L., McGarr, A.F., Holland, A.A., and Anderson, J.G., 2015, Incorporating induced seismicity in the 

2014 United States National Seismic Hazard Model—Results of 2014 workshop and sensitivity studies: U.S. 

Geological Survey Open-File Report 2015–1070, 69 p., http://dx.doi.org/10.3133/ofr20151070. 

ISSN 2331-1258 (online)
iii

Acknowledgments

We wish to thank the workshop participants who made valuable suggestions for revising the 

2014 U.S. Geological Survey (USGS) National Seismic Hazard Modeling Project maps and models to 

incorporate induced seismicity. We also thank the Oklahoma Geological Survey for cohosting the 

workshop with the USGS. We especially thank members of the National Seismic Hazard And Risk 

Assessment Steering Committee: Norm Abrahamson, Ken Campbell, Martin Chapman, Michael 

Hamburger, William Lettis, Nilesh Shome, Ray Weldon, Chris Wills, who reviewed the documentation, 

data, methods, and models, and provided excellent feedback that helped us to improve the quality of this 

product. We thank the National Earthquake Hazard Reduction Program (NEHRP) for funding the 

development of the maps. We also thank Teri Losano, Jill McCarthy, and Janet Slate for editing the 

manuscript. 
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Contents

Acknowledgments.......................................................................................................................................................iii

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

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

Hazard Models for Induced Seismicity........................................................................................................................ 9

Earthquake Catalog .............................................................................................................................................. 11

Delineate Areas with Potential Induced Earthquakes........................................................................................ 11

Declustering ...................................................................................................................................................... 13

Relation Between Small and Large Earthquakes—b-Value .............................................................................. 16

Magnitudes Used to Predict Future Earthquakes .............................................................................................. 18

Earthquake Rate Models....................................................................................................................................... 21

Earthquake Location Models................................................................................................................................. 23

Earthquake Maximum Magnitudes........................................................................................................................ 25

Earthquake Ground Motion Models....................................................................................................................... 27

Comparison of the 2014 NSHM Combined with Alternative Input Models............................................................. 29

Seismic Hazard Products Suggested at the Workshop............................................................................................. 36

USGS Research Agenda for Induced Seismicity Hazard Studies............................................................................. 39

Short-Term Hazard Agenda for Induced Earthquakes (2015–16)......................................................................... 39

Long-Term Research Directions for Understanding Hazard from Induced Earthquakes (2015–20) ..................... 40

Catalog.............................................................................................................................................................. 40

Rate Model........................................................................................................................................................ 41

Location Model (Smoothing).............................................................................................................................. 41

Maximum Magnitude ......................................................................................................................................... 42

Ground Motion Models ...................................................................................................................................... 42

Beyond the Logic Tree ...................................................................................................................................... 42

Conclusions .............................................................................................................................................................. 43

References Cited...................................................................................................................................................... 44

Appendix 1: Initial Likelihood Tests of Potential Seismicity-Rate Models for Induced Seismicity in Oklahoma, 

Southern Kansas and North-Central Texas .............................................................................................................. 49

Appendix 2: Recurrence Analysis in Recent (2001–14) Oklahoma Earthquakes ..................................................... 58

Appendix 3: Ratio Maps for Figures 13 through 17................................................................................................... 64

Figures

1. 2014 United States National Seismic Hazard Maps, 5-Hz spectral acceleration, 2-percent probability of 

exceedance in 50 years or 0.04-percent probability of exceedance in 1 year on firm rock site condition. 

Areas where suspected induced seismicity because of fluid injection, mining, and conventional oil and 

gas production have been intentionally removed from the hazard model, and are shown as polygons......... 3

2. Workshop participants' affiliations .................................................................................................................. 4

3. Polygons showing where potential induced earthquakes have been extracted for the following: 

A, Central and Eastern United States, B, Induced seismicity showing area near Oklahoma. C, Time 

histories of seismicity for 17 zones shown in in 3A........................................................................................ 5

4. Logic tree for induced seismicity showing alternative models...................................................................... 10

5. Sensitivity study comparing base model to declustered catalog model ....................................................... 15
v

6. Sensitivity study comparing a b-value (the slope of the curve that relates the numbers of small and 

large earthquakes) of 1.0 and 1.5................................................................................................................ 17

7. Sensitivity study comparing earthquake catalogs with minimum magnitude set at moment magnitude

(M) 2.5 and M2.7 ........................................................................................................................................ 19

8. Sensitivity study comparing earthquake catalogs with minimum magnitude set at moment magnitude 

(M) 2.5 and M3.0 ......................................................................................................................................... 20

9. Sensitivity study comparing hazard calculated from 2014 and 2013 catalogs. The 2014 catalog is from 

November 1, 2013, to October 31, 2014. The 2013 catalog is from November 1, 2012, to October 31,

2013............................................................................................................................................................. 22

10. Sensitivity study comparing earthquake location models based on smoothing parameters with 

5-kilometer (km) and 50-km width................................................................................................................ 24

11. Sensitivity study comparing the NSHM craton maximum magnitude (Mmax) model (mean moment 

magnitude [M] 7), and an M6.0 maximum magnitude.................................................................................. 26

12. Sensitivity study comparing low and high ground motion model.................................................................. 28

13. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This base case model uses a 2014 

nondeclustered catalog with magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 

1.0, 5 kilometers (km) smoothing, 8 National Seismic Hazard Model (NSHM) ground motion models 

(GMM), and NSHM craton maximum magnitude (Mmax) model (mean M7)............................................... 30

14. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 nondeclustered 

catalog with magnitudes greater than minimum magnitude (Mmin) 3.0, b-value equal to 1.0, 5 kilometers 

(km) smoothing, 8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM 

craton maximum magnitude (Mmax) model (mean M7) .............................................................................. 31

15. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 declustered catalog 

with magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 1.0, 5 kilometers (km) 

smoothing, 8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM craton 

maximum magnitude (Mmax) model (mean M7) ......................................................................................... 32

16. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 nondeclustered 

catalog with magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 1.5, 5 kilometers 

(km) smoothing, 8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM 

craton maximum magnitude (Mmax) model (mean M7) .............................................................................. 33

17. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 declustered catalog 

with magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 1.0, 50 km smoothing, 

8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM craton maximum 

magnitude (Mmax) model (mean M7).......................................................................................................... 34

18. Hazard curves for Fort Worth, Texas and Oklahoma City, Oklahoma for the 2014 National Seismic 

Hazard Model (black) and adding the induced seismicity component using the full nondeclustered or 

declustered catalogs with a b-value (the slope of the curve that relates the numbers of small and large 

earthquakes) of 1.0 or 1.5, and for smoothing parameters of 5 kilometers (km) or 50 km........................... 35
vi

Tables

1. Seventeen induced seismicity zones, Central and Eastern United States................................................... 13

2. Central and Eastern United States ground motion models and weights in the 2014 hazard models ........... 29

3. Median and 84th percentile ground motions for firm rock site condition (NEHRP BC) from Frankel and 

others (1996) ............................................................................................................................................... 36
1

Incorporating Induced Seismicity in the 2014 United 

States National Seismic Hazard Model—Results of 

2014 Workshop and Sensitivity Studies

By Mark D. Petersen, Charles S. Mueller, Morgan P. Moschetti, Susan M. Hoover, Justin L. Rubinstein, Andrea L. 

Llenos, Andrew J. Michael, William L. Ellsworth, Arthur F. McGarr, Austin A. Holland, and John G. Anderson

Abstract

The U.S. Geological Survey (USGS) National Seismic Hazard Model (NSHM) for the 

conterminous United States was updated in 2014 to account for new methods, input models, and data 

necessary for assessing the seismic ground shaking hazard from natural (tectonic) earthquakes. The 

USGS NSHM project uses probabilistic seismic hazard analysis to quantify the rate of exceedance for 

earthquake ground shaking (ground motion). For the 2014 NSHM assessment, the seismic hazard from 

potentially induced earthquakes was intentionally not considered because we had not determined how to 

properly treat these earthquakes for the seismic hazard analysis. The phrases “potentially induced” and 

“induced” are used interchangeably in this report, however it is acknowledged that this classification is 

based on circumstantial evidence and scientific judgment. For the 2014 NSHM update, the potentially 

induced earthquakes were removed from the NSHM’s earthquake catalog, and the documentation states 

that we would consider alternative models for including induced seismicity in a future version of the 

NSHM. As part of the process of incorporating induced seismicity into the seismic hazard model, we 

evaluate the sensitivity of the seismic hazard from induced seismicity to five parts of the hazard model: 

(1) the earthquake catalog, (2) earthquake rates, (3) earthquake locations, (4) earthquake Mmax 

(maximum magnitude), and (5) earthquake ground motions. We describe alternative input models for 

each of the five parts that represent differences in scientific opinions on induced seismicity

characteristics. In this report, however, we do not weight these input models to come up with a preferred 

final model. Instead, we present a sensitivity study showing uniform seismic hazard maps obtained by 

applying the alternative input models for induced seismicity. The final model will be released after 

further consideration of the reliability and scientific acceptability of each alternative input model. 

Forecasting the seismic hazard from induced earthquakes is fundamentally different from forecasting 

the seismic hazard for natural, tectonic earthquakes. This is because the spatio-temporal patterns of 

induced earthquakes are reliant on economic forces and public policy decisions regarding extraction and 

injection of fluids. As such, the rates of induced earthquakes are inherently variable and nonstationary. 

Therefore, we only make maps based on an annual rate of exceedance rather than the 50-year rates

calculated for previous USGS hazard maps. 

To discuss the latest research on induced seismic activity, and to obtain feedback on products 

that will be useful for decision makers, the USGS and the Oklahoma Geological Survey cohosted a 

workshop that included about 150 participants from academia, industry, and government on 17–19 

November 2014 in Midwest City, Oklahoma. In this report we summarize the discussions from this 
2

workshop, show alternative input models and corresponding uniform hazard maps, and describe a 

research agenda for improving future seismic hazard assessment products. Probabilistic ground motions 

are calculated at 1-percent and 0.04-percent probability of exceedance in 1 year. The annual frequencies 

of the 0.04-percent probability of exceedance in a 1-year uniform hazard map and the 2-percent 

probability of exceedance in a 50-year uniform hazard map are equivalent. The sensitivity studies are 

developed for peak horizontal ground acceleration, 5-Hertz (Hz), and 1-Hz spectral acceleration on a 

uniform firm rock site condition; only 5-Hz spectral acceleration ground motions are shown in the 

report. Preliminary results indicate very large changes in probabilistic ground motion depending on the 

following: range of earthquake magnitudes applied in the forecast model, whether or not clustered 

earthquakes (foreshocks, aftershocks, and swarms) are included, the slope (b-value) of the curve that 

relates the numbers of small and large earthquakes, efficacy of using seismicity from one year to predict 

the following year’s activity, degree of spatial smoothing, assumed maximum magnitude of future 

earthquakes, and the ground motion models applied in the analysis. Regardless of the choice of the 

alternative input models examined in this study, we find that potentially induced seismicity greatly 

increases the seismic hazard in Oklahoma and in the other induced seismicity zones compared to 

seismic hazard assessed for the 2014 update of the National Seismic Hazard Model. 

Introduction

During the past several decades, the U.S. Geological Survey (USGS) has provided the National 

Seismic Hazard Model (NSHM) which is applied in earthquake mitigation strategies, risk assessments,

insurance rate structures, and seismic-design regulations for buildings, bridges, highways, railroads, and 

other structures (Algermissen and Perkins, 1976; Frankel and others, 1996, 2002; Petersen and others, 

2008, 2012, 2014). The NSHM considers where future earthquakes will occur, how often they will 

occur, and how strong the ground shaking will be. The final model, for the contiguous 48 States, is

updated every 6 years based on new data, input models, and methods that have become available since 

the last update. The final probabilistic seismic hazard model is constructed using the best available 

science, allowing for variability in the input seismic model parameters and for alternative input models 

proposed by the scientific community. Products resulting from the model can be displayed as uniform 

probabilistic seismic hazard maps with a 2-percent probability of exceedance in 50 years (fig. 1), or as 

hazard curves that show the probability of exceedance in 50 years for each given ground shaking level. 

The NSHM affects economic and safety decisions across the United States.
3

Figure 1. 2014 United States National Seismic Hazard Maps, 5-Hz spectral acceleration, 2-percent probability of 

exceedance in 50 years or 0.04-percent probability of exceedance in 1 year on firm rock site condition. Areas 

where suspected induced seismicity because of fluid injection, mining, and conventional oil and gas production 

have been intentionally removed from the hazard model, and are shown as polygons. Three of the polygons 

contain seismicity associated with coal production (one zone is near Paonia, Colorado, and two zones are related 

to coal fields in central Utah). 

Nontectonic earthquakes were deleted in earlier National Seismic Hazard Model versions, either 

because the causative industrial process had been suspended or because the earthquakes did not appear 

to pose a significant hazard. However, dramatic increases in seismicity rates have been observed in the 

Central United States in the past 5 to 7 years. This increase is reported to be stimulated by injection of 

wastewater or other fluids in deep disposal wells (Healy and others, 1968; Raleigh and others, 1976; 
4

Seeber and others, 2004; Frohlich and others, 2011; Horton, 2012; Ellsworth, 2013; Keranen and others, 

2013; Llenos and Michael, 2013; Block and others, 2014; Rubinstein and others, 2014a, b; Sumy and 

others, 2014). In addition, scientists studying the 2011 MW (moment magnitude) 5.6 Prague, Oklahoma 

earthquake suggested that deep injection of wastewater could trigger earthquakes with enough strength 

to damage nearby structures (Keranen and others, 2013). The increased rate of earthquakes (including 

potentially induced earthquakes) translates into an increased earthquake hazard. The phrases 

“potentially induced seismicity,” “induced seismicity,” “potentially induced earthquakes” or “induced 

earthquakes” are used interchangeably in this report, and indicate that the seismicity in a given region 

has shown an increased earthquake rate that can be attributed to human activities, such as fluid injection 

or extraction. We acknowledge that this classification is based on circumstantial evidence and scientific 

judgment. Difficulties in assessing seismic hazard arise from a lack of relevant technical information on 

human industrial activity (that is, pumping data for injection wells). Thus, in this report we do not 

explore the causes of the increased seismicity, but rather try to find a way to quantify the associated 

hazard. Also, this report does not address the seismic hazard from induced earthquakes because of 

mining activities, for example, rock bursts or coal bumps. 

For the 2014 hazard models (Petersen and others, 2014) we delineated and removed suspected 

induced seismicity. We advised users that the seismic hazard would be higher in these areas from the 

additional induced seismicity than the seismic hazard depicted on the 2014 NSHM. To better assess the 

seismic hazard contributed by these induced earthquakes, the USGS and the Oklahoma Geological 

Survey cohosted a workshop focused on the seismic hazard from induced seismicity November 17–19, 

2014 in Midwest City, Oklahoma. The purpose of the workshop was to seek feedback from the 

scientific and user communities on how to best assess the hazard and what products would be most 

useful for those who need to make business and public safety decisions. The workshop included about 

150 in-person and webcast participants from academia, government, and industry (fig. 2), including the 

USGS National Seismic Hazard and Risk Assessment Steering Committee. The Steering Committee

provides external advice, guidance, and review of the data, input models, and methods used in the 

seismic hazard analysis.

Figure 2. Workshop participants’ affiliations. 
5

Conclusions of the workshop and meeting indicated that induced earthquakes are difficult to 

include in probabilistic seismic hazard analysis because the hazard is (1) highly variable spatially and 

temporally, (2) dependent on human economic or societal decisions regarding when to initiate or 

terminate wastewater disposal and how much fluid (volume) would be injected or extracted, (3) 

conditional on understanding differences between source and ground shaking characteristics of induced 

and natural earthquakes, and (4) dependent on the length and depth extent of the causative faults, which 

are generally unknown. For this 2015 sensitivity study, we redefine the 2014 zones based on locations 

of earthquakes that have been attributed to human activities such as wastewater injection and hydraulic

fracturing.

Induced seismicity patterns and rates vary across the Central United States. The locations and 

rates of earthquakes for the past 50 years at each of the 17 induced seismicity zones are shown in figure 

3. Patterns of increased seismicity vary considerably between the different areas. Some areas show 

pulses of increased activity interspersed between periods with little or no activity (for example, Cogdell, 

Texas, and Rangely, Colorado). Other areas (such as central Oklahoma and southern Kansas) show 

exponential growth patterns of seismicity that are continuing today (2015). In a few places, seismic 

activity increased as pumping began but diminished or ceased when the pumping stopped, sometimes 

with a lag time before the earthquake activity terminated (for example, Rocky Mountain Arsenal, 

Colorado). It is important to recognize that the induced seismicity behavior differs substantially between 

zones, so these rate characteristics need to be evaluated for each zone separately. 

Figure 3. Polygons showing where potential induced earthquakes have been extracted for the following: 

A, Central and Eastern United States, B, Induced seismicity showing area near Oklahoma. For 3A and 3B 
6

Red = 2014 nondeclustered catalog, Green = 2013 nondeclustered catalog, Blue = 2012 and previous using a 

declustered catalog. C, Time histories of seismicity for 17 zones shown in in 3A, blue lines represent 

nondeclustered catalog and red lines represent declustered catalog. The minimum magnitude (Mmin) used in 

these plots is M2.7.

Figure 3. Polygons showing where potential induced earthquakes have been extracted for the following: 

A, Central and Eastern United States, B, Induced seismicity showing area near Oklahoma. For 3A and 3B Red = 

2014 nondeclustered catalog, Green = 2013 nondeclustered catalog, Blue = 2012 and previous using a 

declustered catalog. C, Time histories of seismicity for 17 zones shown in in 3A, blue lines represent 

nondeclustered catalog and red lines represent declustered catalog. The minimum magnitude (Mmin) used in 

these plots is M2.7.—Continued
7
8

Figure 3. Polygons showing where potential induced earthquakes have been extracted for the following: 

A, Central and Eastern United States, B, Induced seismicity showing area near Oklahoma. For 3A and 3B Red = 

2014 nondeclustered catalog, Green = 2013 nondeclustered catalog, Blue = 2012 and previous using a 

declustered catalog. C, Time histories of seismicity for 17 zones shown in in 3A, blue lines represent 

nondeclustered catalog and red lines represent declustered catalog. The minimum magnitude (Mmin) used in 

these plots is M2.7.—Previous page
9

In this report, we describe the workshop discussions pertaining to the inputs necessary for 

seismic hazard evaluation, show how the hazard varies depending on different modeling choices within 

17 areas of increased seismic activity, and submit a research agenda that will be critical for developing 

new input models that consider this activity. The main objective of this report is to show results from 

sensitivity studies that will guide future model development. This report is organized into three primary 

sections. First, technical suggestions from participants are discussed and results of the sensitivity tests 

are presented in the section “Hazard Models for Induced Seismicity.” Second, product suggestions and 

attendee questions are outlined in the section on “Seismic Hazard Products Suggested at the Workshop.” 

Finally, potential research directions are described at the end of the report in a section entitled “USGS 

Research Agenda for Induced Seismicity Hazard Studies.” Three appendices also are included that 

describe the results of studies on induced seismic hazard. 

Hazard Models for Induced Seismicity

Seismic hazard analyses provide information about the expected ground shaking from future, 

damaging earthquakes. Probabilistic Seismic Hazard Analysis (PSHA) (Cornell, 1968) provides the 

framework for computing the rate of exceeding a particular ground shaking level caused by these 

earthquakes. The analysis is based on where and how often future earthquakes will occur and how 

strongly the ground will shake. While there are many hazards associated with earthquakes, including 

liquefaction, tsunamis, and landslides, for the purpose of this report, we only address one: the ground 

shaking (or ground motion). As such, the induced seismicity PSHA sensitivity tests that we carry out for 

this report provide rates of exceeding a set of ground motion at sites across the United States. We use 

the standard assumption of Poissonian earthquake occurrences, P(λ,t) = 1 − e−λt to compute 

probabilities of exceedance, P, from rates of exceedance, λ, within specified time periods, t. This 

distribution implies that the probabilities are time-independent. 

In this report, we refer to the probabilities or rates of exceedance as the ‘hazard’ or as the 

‘hazard level,’ and we refer to the ground motions as the ‘probabilistic ground motions,’ indicating that 

the computed ground motions are derived from a probabilistic distribution. The sensitivity results 

presented in this report examine the impact of the probabilistic ground motions at a fixed hazard level to 

the seismic source and ground motion models developed for the induced seismicity. 

The hazard calculations depend on five inputs that are well established in the probabilistic 

hazard methodology: the earthquake catalog, the earthquake rate model, the earthquake location model, 

the maximum magnitude model, and the ground motion model. The earthquake catalog is used to

statistically assess where and how often future earthquakes may occur. We use M or MW to represent 

moment magnitude in this report. The earthquake rate model assumes that the rate of smaller 

earthquakes near a site can be used to predict the rate of larger earthquakes (by assuming that 

earthquake magnitude follows a truncated exponential distribution). The earthquake location model 

assumes that future moderate to large earthquakes will occur in the vicinity of past smaller earthquakes. 

The maximum magnitude model assumes alternatives for the magnitude at which the probability density 

function of earthquake magnitude is truncated. The ground motion model relates earthquake magnitudes 

and distances to the strength of ground shaking at a site. We implement these five inputs using a logic 

tree approach (Petersen and others, 2014) that formally accounts for a range of alternative

interpretations of data, models, and methods. A logic tree for the induced seismicity portion of the 

hazard is shown in figure 4. In the text that follows, we discuss each branch of the logic tree and the 

sensitivity of hazard models to the different input choices. 
10

Figure 4. Logic tree for induced seismicity showing alternative models. M is moment magnitude, b-value is the 

slope of the curve that relates the numbers of small and large earthquakes, km is kilometers, NSHMP is National 

Seismic Hazard Modeling Project, FEA is Frankel and others (1996), TORO is Toro and others (1997) and Toro 

(2002), SILVA is Silva and others (2002), CAMP is Campbell (2003), PEZ is Tavakoli and Pezeshk (2005), A08 is 

Atkinson (2008), AB06 is Atkinson and Boore (2006), and PEZ11 is Pezeshk and others (2011). 

For the sensitivity study, we use the parameters that were favored by many participants at the 

workshop. These choices, however, do not constitute our final model, and impacts and science are still 

being analyzed. For the base model, which is used to compare all the alternative models, we consider

the 17 areas and associated seismicity catalogs shown in figure 3. For this model we incorporate the 

nondeclustered catalog (which contains some statistically dependent events), we extrapolate from small 

to large earthquakes using a slope (b-value) of 1.0, we use earthquakes greater than M2.5 minimum 

magnitude (Mmin) to predict larger earthquakes, we apply a 1-year catalog (11/1/2013 to 10/31/2014) to 

predict the activity for the following year, we apply a 5-kilometer (km) fixed length smoothing 

parameter to assess the locations of future earthquakes, we model earthquakes from magnitude 4.7 to as 

much as the maximum magnitudes considered in the 2014 NSHM (with a mean of M7, but with a 

distribution extending down to M6.5 and as much as M7.9), and we apply the 8 ground motion models 

that were considered in the 2014 NSHMs. Each of these decisions will be reevaluated in developing the 

final models. Primary results of the sensitivity studies are presented as uniform hazard maps and 

difference maps with respect to the base model. Probabilistic ground motions are calculated at 1-percent

and 0.04-percent probability of exceedance in 1 year (rather than the typical 50-year period) for 5-Hz 

spectral acceleration, on a uniform firm rock site. The ground motion models have been modified from 

the hard-rock site condition (soil type A) to the firm-rock site condition (BC, which is the boundary 

between soil types B and C). For this study, we apply a National Earthquake Hazards Reduction 

Program (NEHRP, Building Seismic Safety Council, 2009) shear wave velocity (time-average) in the 

upper 30 meters (VS30) of 760 meters per second (m/s). In this report we focus on the 5-Hz spectral 

acceleration ground motions, but have calculated peak horizontal ground acceleration (PGA) and 1-Hz 

spectral accelerations that are typically lower than the 5-Hz motions by factors of 1.7 and 3.4, 

respectively.
11

Earthquake Catalog

The earthquake catalog contains the locations and magnitudes of recorded past earthquakes and

can be used to assess rates and locations of future earthquakes (appendix 1). The earthquake catalog 

used in this analysis is based on the USGS Advanced National Seismic System (ANSS) Comprehensive 

Catalog (ComCat: http://earthquake.usgs.gov/earthquakes/map/doc_aboutdata.php), which should 

include all of the Central and Eastern United States earthquakes greater than or equal to moment 

magnitude (M) 3.0 since the year 2000

(http://earthquake.usgs.gov/monitoring/anss/docs/ANSS_Perf_Standards.pdf). Various magnitude types 

are reported by ComCat, thus for our purposes, all earthquake magnitudes are converted to a moment 

magnitude (M) as is consistent practice with the 2014 NSHMs catalog. 

For a given region, the Gutenberg-Richter magnitude-frequency relation, logN=a-bM provides a 

good fit to the magnitude distribution, where N is the number or earthquakes above a certain magnitude, 

M; a is the parameter that defines the rate of earthquakes; b (b-value) is a parameter that defines the 

slope of the distribution. This relation depends on a magnitude of completeness (Mc) for which all 

earthquakes above that level are considered completely represented in the catalog. A more accurate Mc

increases the likelihood of determining the actual b-value of the distribution. 

Four tasks are required to develop the seismicity model from an earthquake catalog: (1) delineate 

areas with potentially induced seismicity using information available in scientific publications, 

seismicity patterns, and information on industrial activity; (2) determine whether or not to decluster the 

catalog, which removes foreshocks, aftershocks, and swarm events leaving only independent events; 

(3) assess the annual parameters of the exponential magnitude-frequency (Gutenberg and Richter, 1944) 

distribution that relates the number or rate of small and large earthquakes (b-value); and (4) evaluate the 

minimum magnitudes (Mmin) of the earthquakes in the catalog that will best predict the future large 

earthquakes, considering local completeness levels of the catalog. 

Delineate Areas with Potential Induced Earthquakes

In developing the 2014 National Seismic Hazard Models (Petersen and others, 2014), we 

initially identified 14 areas in the Central and Eastern United States (fig. 1) that contained seismicity 

that was suspected to have been induced by fluid injection or fluid removal. Three additional areas 

outlined in figure 1 will not be addressed in this report. These three additional areas contain nontectonic 

seismicity associated with coal production. One zone is near Paonia, Colorado, and two zones are 

related to coal fields in central Utah.

At the workshop, participants recommended that we update the catalog through October 2014 to 

include activity since 2012 that was not included in the previous model. We updated the catalog and

identified three new areas of enhanced seismicity (Oklahoma–north and Kansas–south; Greeley, 

Colorado; and Azle, Texas). Seismicity maps and time histories of the 17 regions are shown in figure 3. 

Table 1 shows the names and seismicity parameters (location, largest associated earthquake, and time 

window) for each of the zones that are discussed in this report. For this update, we also expanded the 

zone boundaries shown on the NSHM in places where recent (2013 and 2014) seismicity was located 

outside the earlier boundaries (Fashing, Texas; Dallas – Fort Worth, Texas; Oklahoma; Raton Basin

(Raton in figures), New Mexico – Colorado; Youngstown, Ohio; and Timpson, Texas). We 

acknowledge that natural earthquakes could occur within the defined zones during the stated time 

windows; however, we treat the seismicity as induced for this study because the earthquakes are all 

located near deep fluid injection wells or other industrial activities capable of inducing earthquakes. 
12

Scientific publications also proved useful for suggesting causal relations between industrial activities 

and seismicity (table 1). 

The Guy-Greenbrier, Arkansas zone was established for the 2014 NSHM (Petersen and others, 

2014) and took into account seismicity through 2012. Indeed, the injection wells that were considered to 

be the cause of the Guy-Greenbrier earthquakes stopped injecting in March 2011, and the seismicity 

decayed to background levels not long thereafter. However, during 2013 and 2014 about 25 earthquakes 

between M2.7 and M3.8 occurred in an area just outside of the defined Guy-Greenbrier zone. The area 

of seismicity for 2013 and 2014 is about 20 kilometers by 60 km, and extends to the north and to the 

west of the defined Guy-Greenbrier zone; no earthquakes of this size occurred within the zone. Experts 

believe that the 2013 and 2014 seismicity in central Arkansas includes natural clusters and induced 

clusters (Horton and others, 2013). At this time we do not define this seismicity in 2013 and 2014 to be

induced because the clusters do not occur exclusively near the well locations, and the experts believe 

that there are natural clusters in close proximity to the potentially induced clusters (Horton and others, 

2013). Hence, for this study, we do not expand the Guy-Greenbrier zone to include this recent 

seismicity. This example near Guy-Greenbrier illustrates the complexity of the task at hand and 

highlights one of the main challenges to developing separate hazard models for natural and induced 

seismicity, especially in regions where both types of earthquakes have been detected. Whereas for 

earthquakes induced by mining and oil and gas production from conventional reservoirs the relation

between the earthquakes and the causative industrial operation is reasonably obvious, this is often not 

the case in areas where there are many injection wells and broadly distributed seismicity. 

Relating earthquakes to specific injection activities can be difficult, partly because, given enough 

time, the pore pressure perturbations caused by injection may have traveled substantial distances from 

the injection site. 
13

Table 1. Seventeen induced seismicity zones, Central and Eastern United States. 

Induced Seismicity Zone

(this report) Location

Largest 

Earthquake

(moment 

magnitude)

Time Window Reference

Rocky Mountain Arsenal Environs of Denver, Colorado 4.8, Aug. 1967 1962–1979 Evans (1966), Healy and others (1968)

Rangely Northwestern Colorado 4.3, Apr. 1970 1957–2014 Raleigh and others (1976) 

Paradox Southwestern Colorado 3.9, Jan. 2013 1991–2014 Ake and others (2005), Block and others (2014)

Greeley In the Denver Basin, Colorado 3.2, Jun. 2014 2013-2014 Yeck and others (2014)

Raton Basin New Mexico-Colorado border 5.2 Aug. 2011 2001-2014 Meremonte and others (2001), Rubinstein and 

others (2014a)

Dagger Draw Southeastern New Mexico 4.1, Dec. 2005 1998–2014 Sanford and others (2006), Pursley and others 

(2013)

Guy-Greenbrier Central Arkansas 4.7, Feb. 2011 2009–2014 Horton (2012)

Oklahoma Central Oklahoma 5.6, Nov. 2011 2006–2014 Keranen and others (2013, 2014) 

Oklahoma-N; Kansas-S Oklahoma-Kansas border 4.8, Nov. 2014 2013-2014 Rubinstein and others (2014b)

Cogdell West-central Texas 4.5, Jun. 1978 1976–2014 Davis and Pennington (1989)

Fashing Conventional natural gas field in 

southern Texas

4.6, Oct. 2011 1973–2014 Pennington and others (1986)

Timpson Eastern Texas 4.8, May 2012 2011–2014 Brown and Frohlich (2013)

Dallas-Fort Worth Near Dallas-Fort Worth, Texas 3.2, Jun. 2012 2008–2014 Frohlich and others (2011)

Azle Northwest of Fort Worth, Texas 3.4, Nov. 2013 2013-2014 DeShon and others (2014)

Ashtabula Northeastern Ohio 3.9, Jan. 2001 1987–2007 Seeber and others (2004)

Youngstown Northeastern Ohio 3.7, Dec. 2011 2010–2014 Kim (2013)

Brewton Alabama-Florida border 4.9, Oct. 1997 1997–2014 Gomberg and Wolf (1999)

Declustering

Hazard analysis is usually computed using declustered earthquake catalogs to remove 

statistically dependent events such as foreshocks and aftershocks (Petersen and others, 2014). This is

because the statistical model commonly used in probabilistic seismic hazard assessment assumes that 

the earthquakes are independent. The 2014 NSHM used the Gardner and Knopoff (1974) declustering 

method to remove dependent earthquakes. Declustering, however, can remove earthquakes that may not 

be dependent events. For example, for about 9 months following the M5.6 Prague earthquake, 

declustering removes dependent earthquakes within about a 50-km radius. We know, however, that

independent earthquakes (not aftershocks or foreshocks) occurred before and after this 9-month 

window, and we might expect some to occur during this time interval. Another example is the 2010 

Guy-Greenbrier sequence in Arkansas, in which approximately 90 percent of the earthquakes in the 

sequence are removed by standard Gardner-Knopoff declustering (fig. 3C). This issue was discussed at 

the workshop, and the general consensus was that the hazard from all of the induced earthquakes 

(independent and dependent) should be included by using catalogs for the induced seismicity that are 

not declustered. Nevertheless, use of the declustered catalog is more consistent with standard practice in 

hazard analysis (Petersen and others, 2014). Participants recommended that more research be done to 

develop new models for declustering induced seismicity. Recent research focusing on several 
14

earthquake sequences in Oklahoma indicates that induced earthquake sequences tend to die out faster 

than typical decay patterns from natural earthquakes, however the aftershocks are distributed spatially

across a larger area than would be expected (McNamara and others, 2015). For this sensitivity analysis, 

we calculated the hazard using the declustered and nondeclustered catalogs to show the effect of this 

decision. Figure 5 shows that ground motions can be 0.5 to 1.0 g (acceleration of gravity) greater when 

using the nondeclustered catalog (corresponding ratios over a broad region of the Central United States

can be more than a factor of 2 larger). Appendix 1 shows a preliminary analysis of how declustering

influences the predictive power of the model. 
15

Figure 5. Sensitivity study comparing base model to declustered catalog model. Five-hertz (0.2 seconds) spectral 

accelerations and differences are in units of g (acceleration of gravity).
16

Relation Between Small and Large Earthquakes—b-Value

Typically, we use the rate of small earthquakes included in the earthquake catalog to extrapolate 

the rate of potential large earthquakes. The Gutenberg and Richter (1944) exponential equation is used 

to quantify this rate. The b-value in this equation represents the slope of the exponential distribution and

relates the number or rate of small and large earthquakes. A b-value of 1.0 is determined to be consistent 

with most declustered global earthquake catalogs. We also determined this b-value of 1.0 to be a 

reasonable estimate for declustered natural earthquakes in the Central and Eastern United States, and 

this value was applied in the 2014 NSHM. Our preliminary analysis of earthquakes within induced 

seismicity zones, using the nondeclustered catalog, indicates that for some regions the b-value may be 

either about 1.0 or may be larger (b=1.2–1.5), implying that the proportion of small-to-large earthquakes 

is greater in regions of induced seismicity than the global average (appendix 2). The relation between an 

elevated b-value and fluid injection rates has been studied for enhanced geothermal systems (Bachmann 

and others, 2011); the b-value can exceed 1.5 during periods of active fluid injection. Figure 6 compares

the uniform hazard maps that result from using a b-value of 1.0 and a b-value of 1.5. As expected, the 

probabilistic ground motions calculated for b=1.5 are lower than the ground motions calculated for b=1 

because the former model forecasts relatively fewer large earthquakes. 
17

Figure 6. Sensitivity study comparing a b-value (the slope of the curve that relates the numbers of small and large 

earthquakes) of 1.0 and 1.5. Five-hertz (0.2 seconds) spectral accelerations and differences are in units of g 

(acceleration of gravity).
18

Magnitudes Used to Predict Future Earthquakes

In a well-instrumented region moderate earthquakes will be recorded and cataloged, but small 

earthquakes below some magnitude completeness threshold can be missed. Completeness levels vary in 

space and time, and seismicity models, which estimate the rates and locations of large earthquakes by 

extrapolating from the smaller earthquakes, must account for these variations. Due to the exponential 

magnitude distribution, there are many more M2.5 earthquakes than M3.0 earthquakes. The lower 

magnitudes can provide more detailed information on the locations of future earthquakes; therefore, it is 

advantageous to use the lowest magnitude for which the catalog is complete to assess the hazard. For the 

2014 maps (Petersen and others, 2014), we used earthquakes through 2012 with MW greater than or 

equal to 2.7. For this analysis, we compare the uniform hazard maps, which show the ground motions at 

annual hazard levels of 1 percent and 0.04 percent using catalogs with magnitude thresholds (Mmin) of 

M2.5, 2.7, and 3.0 to forecast the locations and rates of large earthquakes. Figures 7 and 8 show 

comparisons of the uniform hazard maps based on these three catalogs. The M2.5 catalog may be 

deficient in the number of small earthquakes, as it is close to the completeness of the earthquake catalog 

for many areas; the result of this deficiency will be an under-prediction of the true seismicity rate.
19

Figure 7. Sensitivity study comparing earthquake catalogs with minimum magnitude set at moment magnitude 

(M) 2.5 and M2.7. Five-hertz (0.2 seconds) spectral accelerations and differences are in units of g (acceleration of 

gravity).
20

Figure 8. Sensitivity study comparing earthquake catalogs with minimum magnitude set at moment magnitude 

(M) 2.5 and M3.0. Five-hertz (0.2 seconds) spectral accelerations and differences are in units of g (acceleration of 

gravity).
21

Earthquake Rate Models

The earthquake rate model is based on the assumption that we can forecast the future rates of 

induced seismic activity based on information contained in the earthquake catalog. In the workshop, there 

were many comments suggesting that the current year’s seismicity rate is the best predictor of the next

year, but it is difficult to project these rates much further in the future than a year or two. For example, 

prior to 2012, there was virtually no earthquake activity in southern Kansas and northern Oklahoma, but in 

2013 and especially in 2014, the number of earthquakes in that region increased dramatically with several 

hundred earthquakes being recorded (fig. 3). In this region, the 2013 catalog is not a perfect predictor of 

the 2014 activity—but certainly better than a catalog based on pre-2012 activity. 

For this sensitivity study, we have considered two different time intervals: November 1, 2012, to 

October 31, 2013 (referred to hereinafter as the 2013 catalog), and November 1, 2013, to October 31, 

2014 (2014 catalog), to compare changes in seismicity rates and locations. During 2014, no earthquakes 

greater than M2.5 occurred in 8 zones (Brewton, Dagger Draw, Rangely, Rocky Mountain Arsenal, 

Greeley, Paradox, Ashtabula, and Guy-Greenbrier; table 1), and only one earthquake occurred in 2 

zones (Timpson and Fashing; table 1). Therefore, more than half of the zones experienced little or no 

seismicity during 2014, and this year’s seismicity may or may or may not be a good predictor of next 

year’s activity. If fluid injection has ceased, then this model might be a good predictor. However, if 

injection is resumed, we could jump back to the previously observed levels or some other level based on 

the amount and rate of fluid disposal. We may want to account for the possibility that induced activity 

could resume, especially if we do not have any updated information on the injection rates. 

We have computed the hazard for several models that apply alternative rates: (1) 2014 rate, 

(2) 2013 rate, (3) rate during period of enhanced seismicity, (4) long-term rate—averaged since 1960, 

and (5) a very low or zero rate after earthquakes have diminished as injection is discontinued. One 

participant at the workshop suggested that it would be most reasonable to disregard the short-term 

increase in earthquake rates when injection ceases. One written comment suggested that another logic 

tree branch should be added to represent a proactive approach to managing hazard. For this branch, a 

program of monitoring (and perhaps disclosure) would allow regulators to require changes to injection 

based on the appearance of seismicity on, for example, well-oriented faults of substantial size. With an 

approach such as this, there would be a rationale for reducing the likelihood of large induced events and

would have the merit of giving industry some measure of control over managing the seismic hazard and 

risk (G. Beroza, written commun., 2014). 

A comparison of the uniform hazard maps that result from using the 2013 and 2014 catalogs is 

shown in figure 9. Probabilistic ground motions based on the 2014 catalog is much higher in central to 

north-central Oklahoma and south-central Kansas during 2014 compared to the probabilistic ground 

motions calculated using the 2013 and previous catalogs. The 2014 map shows substantial increases in 

probabilistic ground motions for the zones associated with Raton Basin, Greeley, Oklahoma, Kansas, 

Azle, Cogdell, Fashing, Timpson, and Youngstown (locations shown in Fig. 3A). The 2013 map shows 

substantial increases in probabilistic ground motions for the Raton Basin, Paradox, Oklahoma, Kansas, 

Dallas – Ft. Worth, Cogdell, and Timpson. Activity in Oklahoma, southern Kansas, Azle, Cogdell, and 

Youngstown is much higher in the 2014 catalog than in the 2013 catalog; hence the probabilistic ground 

motion is higher when using the 2014 catalog. The activity was higher in 2013 for Paradox, southern 

Oklahoma, Dallas – Ft. Worth, and Timpson compared to 2014, and thus the probabilistic ground 

motion is higher for these areas using the 2013 catalog. In general, the probabilistic ground motion can 

differ by more than a factor of two when applying the 2013 compared to the 2014 catalog. Testing the 

predictions of these two models with current activity would help us to understand how to improve the 

models for future iterations. 
22

Figure 9. Sensitivity study comparing hazard calculated from 2014 and 2013 catalogs. The 2014 catalog is from 

November 1, 2013, to October 31, 2014. The 2013 catalog is from November 1, 2012, to October 31, 2013. Fivehertz (0.2 seconds) spectral accelerations and differences are in units of g (acceleration of gravity).
23

Earthquake Location Models

The 2014 NSHM used fixed kernel and adaptive smoothing kernel distances to predict the 

locations of future earthquakes. In previous models, we applied a 50-km correlation length (35-km 

standard deviation length) distance parameter for the fixed kernel model. At the workshop, it was 

suggested that a smaller smoothing length might be more appropriate for estimating the locations of 

seismicity in a 1-year period. This shorter length would reflect better earthquake locations and tighter 

clusters. For our sensitivity study, we compare the uniform hazard maps generated using a fixed 

correlation length of 5 km and 50 km to assess the effect of the smoothing distance. The comparison of 

alternative smoothing distances in estimating locations of future earthquakes is shown in figure 10. 

Differences in the probabilistic ground motions from using these two smoothing parameters are quite 

high. The larger smoothing distances result in an increased probabilistic ground motion at larger 

distances from the induced seismicity zones. This is represented as a halo in the difference map. 

Appendix 1 shows a preliminary analysis to assess the predictive power of seismicity models in 

predicting future earthquakes.
24

Figure 10. Sensitivity study comparing earthquake location models based on smoothing parameters with 

5-kilometer (km) and 50-km width. Five-hertz (0.2 seconds) spectral accelerations and differences are in units 

of g (acceleration of gravity).
25

Earthquake Maximum Magnitudes

The maximum magnitude that can be generated by induced seismicity is not easy to assess

because we can only rely on the largest observed earthquake, global analogs, or physical principles. The 

maximum magnitude should be larger than the magnitude of the largest observed injection induced 

earthquake because we only have a short observation period. McGarr (2014) argues that the maximum 

potential magnitude of an injection induced earthquake is limited by the total injected volume, whereby 

the largest earthquake possible increases in magnitude with increased injection volume. The largest

United States induced earthquake to date has been the 2011 M5.6 Prague, Oklahoma earthquake 

(Keranen and others, 2013); however, earthquakes greater than M6 or M7 also have been generated near 

impounded dams or near sites of gas withdrawal. For example, Gupta (2002) indicates that the 1967 

Koyna M6.3 (India) was the largest and most damaging reservoir-triggered earthquake. Simpson and 

Leith (1985) suggested that the 1984 M7.0 Gazli (Uzbekistan) earthquake may have been induced by 

gas withdrawal. There is also some debate about whether the 2008 M7.9 Wenchuan (China) earthquake 

was induced by reservoir impoundment (Kerr and Stone, 2009; Deng and others, 2010; Gahalaut and 

Gahalaut, 2010). Alternatively, the induced seismicity may trigger tectonic earthquakes on adjacent 

fault structures, as suggested by Keranen and others (2014). Participants at the workshop felt that the 

USGS induced seismicity models should consider the possibility of triggering large regional 

earthquakes and should consider the same maximum magnitude distribution as was used for the tectonic 

earthquakes in the NSHM model which has a mean of 7.0 but extends from M6.5 to M7.95 with low 

weights at the ends of the distribution. For the sensitivity study, we also considered a model with 

maximum magnitude of M6.0, close to that which we have observed. The uniform hazard maps for 

these two cases are shown in figure 11. The difference in probabilistic ground motions is significant and 

varies by about 25 percent, but causes much less of an effect than many of the other factors that are 

being considered in the logic tree. 
26

Figure 11. Sensitivity study comparing the NSHM craton maximum magnitude (Mmax) model (mean moment 

magnitude [M] 7), and an M6.0 maximum magnitude. Five-hertz (0.2 seconds) spectral accelerations and 

differences are in units of g (acceleration of gravity).
27

Earthquake Ground Motion Models

Ground motions have been recorded from many suspected induced earthquakes. These ground 

motions provide information on the earthquake source and ground shaking characteristics. In general, 

comparisons shown at the workshop indicate that the ground motions are quite similar between induced 

and natural earthquakes, especially for long period ground shaking. However, other studies indicate that 

induced earthquake ground motions may differ from natural ground motions (McGarr and Fletcher, 

2005; Hough, 2014). The main difference may be the depth, which is typically less than 5 km in the case 

of induced seismicity. Regrettably, none of the 8 equations that were applied in the 2014 NSHM have a 

depth term (table 2). Therefore, it is difficult to account for this difference in the hazard calculations at 

this time. New ground motion models are being developed as part of the NGA-East project 

(http://peer.berkeley.edu/ngaeast/), and these equations will allow for consideration of depth in 

calculating the ground shaking. Once these new equations are published, it will be possible to account 

for the shallower depths of the induced earthquakes in the hazard models. 

At this time, we have made comparisons using the highest and lowest ground motion models to 

show the span of ground motions that are considered in the current equations. A comparison between 

one of the highest and lowest equations considered in the analysis is shown in figure 12. This 

comparison shows that the probabilistic ground motions for the highest ground motion model are nearly 

a factor of two higher than the lowest ground motion model leading to a large epistemic uncertainty. 

This large uncertainty is not unique to induced earthquakes. Additional research on the source (for 

example, stress drops) and the ground shaking characteristics of induced earthquakes could reduce the 

epistemic uncertainty in the hazard models.
28

Figure 12. Sensitivity study comparing low and high ground motion model. Five-hertz (0.2 seconds) spectral 

accelerations and differences are in units of g (acceleration of gravity).
29

Table 2. Central and Eastern United States ground motion models and weights in the 2014 hazard models. 

2014 Ground motion models Abbreviation Type Weight

Frankel and others (1996) FEA-96 Single corner 0.06

Toro and others (1997), Toro (2002) T0RO-02 Single corner 0.13

Silva and others (2002) SILVA-02 Single corner 0.06

Campbell (2003) CAMP- 03 Hybrid 0.13

Tavakoli and Pezeshk (2005) PEZ-05 Hybrid 0.13

Atkinson and Boore (2006) AB06’ Dynamic corner 0.25

Pezeshk and others (2011) PEZ11 Hybrid 0.16

Atkinson (2008) A08’ Reference empirical 0.08

Comparison of the 2014 NSHM Combined with Alternative Input Models

We have combined the 2014 NSHM with the induced seismicity input models to develop 

1-percent and 0.04-percent probability of exceedance in 1-year maps, for 5-Hz spectral acceleration and 

a uniform firm rock site condition. The 0.04-percent annual probability of exceedance uniform hazard 

maps are based on the same rate of exceedance as the final 2014 maps for 2-percent probability of 

exceedance in 50 years. We compare the new maps with the 2014 maps for which the suspected induced 

earthquakes were deleted. Results for the base case model are shown in figure 13: nondeclustered 

catalog with earthquakes down to M2.5, b=1.0, 5-km smoothing, Mmax from NSHM, and 8 ground 

motion models. Figure 14 shows the same parameters for the base case but considers the minimum 

magnitude (Mmin) of M3.0 in the catalog instead of M2.5 to calculate earthquake rates (for both cases, 

earthquakes from magnitude 4.7 to the maximum magnitudes are used to calculate probabilistic seismic 

ground shaking hazard). For figures 15 and 16, we also use the same parameters but consider a 

declustered rather than a nondeclustered catalog and a b-value of 1.5 rather than 1.0, respectively. 

Figure 17 shows the base case parameters with two variations: a declustered catalog and 50-km 

smoothing. All of these models indicate that, for both of these probability levels, the Oklahoma induced 

seismicity is a major contributor to the seismic ground shaking hazard. Probabilistic ground motions are 

highest with the following parameter choices: nondeclustered catalog, 2014 rates, NSHM maximum 

magnitude, and a b-value of 1.0. Probabilistic ground motions are lower when applying the steeper 

b-value and the declustered catalog. Appendix 3 shows ratios of the sensitivity study models combined 

with the 2014 NSHM for which induced seismicity was extracted.
30

Figure 13. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This base case model uses a 2014 nondeclustered 

catalog with magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 1.0, 5 kilometers (km)

smoothing, 8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM craton maximum 

magnitude (Mmax) model (mean M7). Five-hertz (5-Hz, 0.2 seconds) spectral accelerations are in units of 

acceleration of gravity (g).
31

Figure 14. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 nondeclustered catalog with 

magnitudes greater than minimum magnitude (Mmin) 3.0, b-value equal to 1.0, 5 kilometers (km) smoothing, 

8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM craton maximum magnitude

(Mmax) model (mean M7). Five-hertz (5-Hz, 0.2 seconds) spectral accelerations are in units of acceleration of 

gravity (g).
32

Figure 15. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 declustered catalog with 

magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 1.0, 5 kilometers (km) smoothing, 

8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM craton maximum magnitude 

(Mmax) model (mean M7). Five-hertz (5-Hz, 0.2 seconds) spectral accelerations are in units of acceleration of 

gravity (g).
33

Figure 16. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 nondeclustered catalog with 

magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 1.5, 5 kilometers (km) smoothing, 

8 National Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM craton maximum magnitude 

(Mmax) model (mean M7). Five-hertz (5-Hz, 0.2 seconds) spectral accelerations are in units of acceleration of 

gravity (g).
34

Figure 17. 2014 NSHM combined with induced seismicity hazard. Uniform hazard maps for 1-percent (top) and 

0.04-percent (bottom) probability of exceedance in 1 year. This model uses a 2014 declustered catalog with 

magnitudes greater than minimum magnitude (Mmin) 2.5, b-value equal to 1.0, 50 km smoothing, 8 National 

Seismic Hazard Model (NSHM) ground motion models (GMM), and NSHM craton maximum magnitude (Mmax) 

model (mean M7). Five-hertz (5-Hz, 0.2 seconds) spectral accelerations are in units of acceleration of gravity (g).
35

The differences and ratios of the new models compared to the 2014 NSHM are so large that we 

need to consider several important modeling issues when developing the final model: (1) Is the 

methodology appropriate for this spatio-temporal clustering behavior of induced seismicity? (2) Should 

we consider truncation of ground motion model or the aleatory distribution of the ground motion at 

levels that are very high? (3) What source input parameters are most appropriate for consideration of 

this very high seismic activity rate? 

Hazard curves shown in figure 18 represent the rate of exceedance for different ground motion 

levels. The curves show very marked differences in the hazard (annual rate of exceedance) close to a 

factor of 100 for a wide range of ground motion values for Oklahoma City. This increase is consistent 

with the new earthquake rates that are more than a factor of 100 greater in some active areas than those 

considered in the 2014 models (Petersen and others, 2014). 

Figure 18. Hazard curves for Fort Worth, Texas and Oklahoma City, Oklahoma, for the 2014 National Seismic 

Hazard Model (black) and adding the induced seismicity component using the full nondeclustered or declustered 

catalogs with a b-value (the slope of the curve that relates the numbers of small and large earthquakes) of 1.0 or

1.5, and for smoothing parameters of 5 kilometers (km) or 50 km. Five-hertz (5-Hz, 0.2 seconds) spectral 

accelerations (SA) are in units of acceleration of gravity (g). TX is Texas, OK is Oklahoma.
36

The probabilistic ground motions calculated in the sensitivity tests are quite high near zones of 

intense induced seismicity and often are a factor of more than two higher than the 2014 NSHM across 

broad areas (appendix 3). To put these probabilistic ground motions in context, we compared the 

deterministic (scenario) ground shaking from the Frankel and others (1996) ground motion model. 

Results are shown in table 3. Ground motions (median and 84th percentile) for 5-Hz spectral 

acceleration also exceed 2 g (acceleration of gravity) at short distances (less than10 km). Near-source, 

peak ground accelerations recorded from the 2011 Prague M5.6 earthquake ranged between 0.34 and 

0.65 g (acceleration of gravity), which correspond to Modified Mercalli Intensity (MMI) VIII. MMI 

VIII represents the following: severe shaking; damage slight in specially designed structures; 

considerable damage in ordinary substantial buildings with partial collapse; damage great in poorly built 

structures; fall of chimneys, factory stacks, columns, monuments, and walls; and heavy furniture 

overturned. The probabilistic ground shaking assessments near zones of induced seismicity are typically 

greater than the median predicted ground shaking. The ground motion models developed from empirical 

and synthetic data vary by about a factor of 2 at one standard deviation (aleatory variability). 

Table 3. Median and 84th percentile ground motions for firm rock site condition (NEHRP BC) from Frankel and 

others (1996). 

[Firm rock site condition is NEHRP BC (National Earthquake Hazards Reduction Program shear wave velocity [time-average] in the upper 

30 meters of 760 meters per second), g is acceleration of gravity, R is hypocentral distance in kilometers (km), PGA is peak ground 

acceleration, and Hz is hertz. 84th percentile motions are set equal to median times a factor of 2.0, assuming sigma= 0.3 common log units 

or 0.7 natural log units] 

Ground

motion

Median (g) 84th percentile (g) 

R= 10 km R= 25 km R= 10 km R= 25 km

Moment magnitude = 5

PGA 0.36 0.10 0.72 0.20

5-Hz 0.45 0.15 0.90 0.30

1-Hz 0.03 0.01 0.06 0.02

Moment magnitude = 6

PGA 0.85 0.27 1.70 0.54

5-Hz 1.26 0.45 2.52 0.90

1-Hz 0.22 0.08 0.44 0.16

Moment magnitude = 7

PGA 1.78 0.60 3.56 1.20

5-Hz 2.88 1.05 5.76 2.10

1-Hz 0.71 0.27 1.42 0.54

Seismic Hazard Products Suggested at the Workshop 

It is clear that the established, 6-year update schedule for the NSHM is not ideal to address 

induced seismicity. Annual or even more frequent updates of the hazard model and other products could 

account for rapid changes in induced seismicity. Workshop participants agreed that creating a short-term 

(for example, 1 year) hazard model that incorporates induced seismicity would be beneficial. Although 

this report offers a general idea of how induced seismicity might affect the NSHM, several questions 

must be answered before a preferred model is put forward. This section contains suggested hazard 

products and possible research directions discussed at the workshop. 
37

Although it was not unanimous, the general consensus at the workshop was that the current 

method of declustering is too severe, and should not be used if the seismic hazard model takes into 

account a 1-year catalog or less. Workshop participants suggested that a workshop on declustering 

methods to discuss the appropriate declustering methods (such as the optimal distance and time 

windows) be held. Also, participants wanted to understand what b-value, catalog, magnitude (minimum 

magnitude for the catalog [Mmin]), and smooth-seismicity distance (correlation length) should be used 

to predict future seismicity. Statistical tests should be used to maximize the predictive power of the 

short-term hazard models. It was also suggested that change-point analysis could be used to assess 

short-term (annual) seismicity rate fluctuations.

Ground motion models are a key contributor to seismic hazard assessments and participants at 

the workshop had several comments regarding these important models. They wondered what ground 

motion models are most appropriate for induced earthquakes. Currently, none of the 2014 NSHM 

ground motion equations takes depth into account (Petersen and others, 2014). Induced seismicity 

depths are generally shallower and tend to have lower stress drop than natural earthquakes. It is 

necessary to incorporate a ground motion model that can properly characterize the shallow depth typical 

of induced seismicity. Truncation could be appropriate for induced seismicity hazard models. Two 

options that were discussed are truncating the ground motion models at the 84th percentile level (similar 

to truncations applied to faults), or at the median value.

Workshop participants had several specific comments about the input hazard parameters. More 

seismic stations and VS30 measurements would be helpful to better locate and quantify induced 

seismicity. Also, workshop attendees would like an earthquake catalog that differentiates natural 

earthquakes from induced earthquakes caused by fluid injection, hydraulic fracturing, and other manmade causes. It would be interesting to distinguish the induced earthquakes that are directly caused by 

hydraulic fracturing (as opposed to the other forms of induced seismicity). This would likely require 

shared information from the oil and gas industry. Also, attendees wondered how to quantify the 

optimum minimum magnitude of the probabilistic hazard calculation and maximum magnitude (Mmax)

applied in the seismic hazard analysis. Currently M4.7 is the minimum magnitude for the 2014 NSHM 

hazard calculation. It was suggested at the workshop that a smaller value could be appropriate for the 

hazard calculation’s minimum magnitude to account for nuisance shaking. Also, workshop attendees 

would like to know if magnitude-area scaling differs between natural and induced earthquakes. We will 

need to determine the optimum weights to use for the alternative models in the logic tree. How should 

seismic source characterization models reflect local differences in induced seismicity? The uncertainties 

associated with seismic source characterization for induced earthquakes should be properly quantified or 

reduced. Researching the Enola, Arkansas earthquake swarm, or the swarm near Reno, Nevada, could 

help us understand how tectonic swarms differ from induced seismicity. 

Building officials need products that can inform their decisions. Participants also wanted to 

know how building, bridges, roads, and so on should be designed to withstand induced earthquakes. 

Also, after a particular size of earthquake occurs, what distance measure should be used to inspect 

buildings and infrastructure? At the workshop, it was suggested that a parallel could be drawn to surface 

mining and the setback distance that is used to control ground shaking during operation. Ideally, if 

induced seismicity could be kept below an established nuisance level, it would be tolerable. However, 

relatively small earthquakes can cause damage and earthquakes as small as M1.8 can be felt. It was 

reported at the workshop that an M3.4 earthquake in Oklahoma caused damage to residences (cracked 

bricks, door frames off center, shattered window, and chimney collapse). Damage from earthquakes, as 

low as mid-M3, could also affect the well systems, such as casing and pipes. Communities experiencing 
38

elevated levels of induced seismicity (which includes the citizens, local governments, and industries) are 

looking to the USGS to understand the associated ground shaking hazard and earthquake risk to society. 

To help the engineering community determine if the building standards should be modified, or if a 

reevaluation of industrial practices would be preferable, a probability gain map could be used to show how 

the annual seismic hazard has increased because of induced seismicity. One comment from the 

workshop’s regulatory panel was that engineers could determine a reasonable range of ground motions to 

consider in design by comparing the building code hazard curves with hazard curves that include induced 

seismicity. To help the community as a whole (citizens and professionals) understand the potential effect

of the larger predicted ground motions because of induced seismicity, it would be helpful to compare the 

new seismic loads to the wind loads, which is a significant building design factor in Oklahoma. A risk 

matrix could be used to show the probability of a specific MMI and the consequence for the population 

and structures, ideally taking into account the existing building stock. This matrix might be similar to the 

type applied in safety of dams. 

Communities would also benefit from summary statistics (for example, the probability of 

exceeding building codes) for the specific cities and towns experiencing such activity, and a map

showing the predicted number of felt earthquakes. A cumulative shake map could be produced for areas 

that have reported significant levels of induced seismicity, such as Oklahoma. This map would display 

the maximum intensity observed at any location over a given past time-interval based on Did You Feel 

It? (DYFI?, http://earthquake.usgs.gov/earthquakes/dyfi/) public responses. Also, felt earthquakes from 

DYFI? could be used to create an empirical hazard curve to compare with the calculated hazard curve.

Deterministic earthquake scenarios could be produced for the areas reporting induced seismicity. 

Compared to probabilistic seismic hazard, scenarios are straightforward and easier for the general public 

to appreciate. It was suggested at the workshop that creating scenarios for M6 earthquakes could 

illustrate the effect of a strong earthquake. The ground shaking could be represented in several ways: 

peak horizontal ground acceleration (PGA), 1-Hz spectral acceleration, 5-Hz spectral acceleration, and 

Modified Mercalli Intensity (MMI). MMI describes the level of shaking and damage experienced by an 

observer. We have already developed a table of scenario ground motions for M6 earthquakes (table 3). 

Prompt Assessment of Global Earthquakes for Response (PAGER) is a USGS feature that uses

shaking estimates from real-time earthquakes (ShakeMap) and then incorporates information on 

populations and structures to provide a ballpark range of potential human impacts and economic losses. 

For our purposes, PAGER could be used to estimate the potential risk associated with a particular 

deterministic earthquake scenario. A PAGER scenario could be produced for several areas reporting 

induced seismicity. The messaging associated with a PAGER scenario is important. It must be clearly 

stated that this is a theoretical earthquake (not a prediction), and that the associated losses could vary 

greatly from the estimates if an earthquake occurred with a drastically a different hypocenter, 

magnitude, or rupture characteristics. 

Operational Earthquake Forecasts provide estimates of aftershock rates or changes in rates and 

can be automated and updated frequently, on a daily or hourly basis. At the workshop, regulators said 

that they would like the ability to identify new areas of induced seismicity and to determine when 

seismicity rates and patterns have changed. Operational Earthquake Forecasts can provide this type of

information at a much faster pace than the NSHM. 

Participants at the workshop requested advice regarding reasonable guidelines for when to shut 

down and when to restart injection. This is a difficult problem because it is unknown why induced 

seismicity occurs near some fluid injection wells and not at others; in some cases seismicity tracks 

injection, and in other cases seismicity lags. A helpful first step would be to compile a common format 

(and publicly accessible) database for wastewater injection operations that can be used to compare 
39

observed seismicity with exploration activities. This would also encourage the information exchange 

between industry and scientists. 

USGS Research Agenda for Induced Seismicity Hazard Studies

The Documentation for the 2014 Update of the United States National Seismic Hazard Maps 

states: “We will consider alternative models for including potentially induced seismicity in future 

versions of the map. Users of the current hazard information should consider that hazard might be 

higher in these zones of potentially induced seismicity than are presently shown on the map.” (Petersen 

and others, 2014, page 22-23). The USGS and Oklahoma Geological Survey workshop held in 

Oklahoma and this Open File Report address the need to delineate areas with increased rates of 

seismicity near sites of hydrocarbon production or wastewater disposal. Our first priority is to develop a 

short-term (annual based) seismic hazard model that could be updated annually to incorporate the 

seismic hazard from natural and induced earthquakes. Other priorities are to develop a process-based 

understanding of induced earthquakes and the seismic hazard they pose, and to work with government, 

industry, and academia to acquire data and to develop products that will provide information on how to 

better assess and deal with such seismicity. 

Short-Term Hazard Agenda for Induced Earthquakes (2015–16)

Our first priority is to develop a seismic hazard model for induced seismicity that can be used to 

show where future earthquakes might occur, how often, and how strong the ground could shake from 

those earthquakes. The 2014 model did not directly consider the ground shaking hazard from induced 

seismicity but included seismic zones to indicate where such activity had been identified. To account for 

this increased seismicity in the new models, scientists need to develop consensus-based models on the 

following: (1) seismic catalogs, (2) models for assessing short-term rates, (3) models for assessing how 

to account for future earthquake locations, (4) models for the size of future induced earthquakes, and 

(5) models for how strong the ground will shake from induced earthquakes. Each of these models 

requires analysis from a broad group of scientists who are experts in physics of earthquakes, modeling 

of earthquake recurrence, and modeling of ground shaking. 

The seismic catalogs include natural and induced seismicity. They also include dependent 

(foreshocks and aftershocks) and independent earthquakes. To develop a hazard model, we may need to 

distinguish between natural and induced seismicity where these different types of earthquakes have 

different hazard metrics. To accomplish this we will need to understand how the statistical properties of 

the catalogs (Gutenberg-Richter b-values and magnitude completeness) vary between the 17 regions of 

induced seismicity and natural earthquake swarms. In addition, hazard methodologies conventionally 

require assessing rates of earthquakes from a catalog containing independent earthquakes. We need to 

establish new ways to assess which earthquakes are dependent and independent. The current 

declustering model uses a simple formula to separate these events based on magnitude and distance 

windows. However, the 2011 Prague earthquake declustering process resulted in earthquakes being 

removed from the hazard analysis that were smaller than M5.6 for about three-quarters of a year and 

within about 50 km of the earthquake. This catalog reduction may not be appropriate for swarm activity 

or when earthquake rates are increasing. Alternative seismic declustering models, such as the UCERF3 

cluster model (Field, 2014), which was applied in California, allows for more complexity than in the 

model considered in the 2014 NSHM for the Central and Eastern United States, and may be more 

appropriate for assessing the seismic hazard in these areas. We may need to test alternative models for 

declustering or develop a new model based on these induced earthquakes. 
40

Several statistical models for assessing short-term (annual) rates and future earthquake locations 

have been considered in this report. It is difficult to assess future earthquake rates since the earthquakes 

vary rapidly in space and time, and may also depend on economic decisions and regulatory actions. 

Appendix 1 shows a preliminary example of a likelihood test that can be used to assess the optimal 

parameters for assessing earthquake rates and locations. Additional testing is needed to determine the 

optimal earthquake catalog (for example, the duration and minimum magnitude), and the length scale of 

the smoothing kernels.

At the workshop, we proposed using maximum magnitudes of M6 and M7 (with a distribution 

obtained from the 2014 NSHM). Alternative maximum magnitude models were not proposed; therefore, 

it does not seem that there is short-term research that needs to be completed on this input parameter 

during the next year. 

The ground motion models are key inputs for the hazard assessment. New models will allow for 

a depth parameter that will be helpful in assessing seismic hazard from induced seismicity, as it is 

typically shallower than the full depth range of many natural earthquakes. To improve these ground 

motion models, and our assessment of seismic hazard, we need to assess the ground shaking parameters 

from the hundreds of seismograms that have been collected over the past several years. It is very 

important to examine the statistical measures of these shaking records, and then to use these records to 

make an empirical hazard model. This empirical model can be compared with the hazard model 

obtained using NGA-East models and standard probabilistic hazard methodologies. In addition, 

estimates of ground properties are needed to forecast ground shaking. These activities will help users 

gain confidence in the forecasted shaking levels.

Long-Term Research Directions for Understanding Hazard from Induced Earthquakes (2015–20)

The short-term research agenda addresses the most pressing issues identified through the 

sensitivity tests of the logic tree (figs. 4–18). The USGS will work with other state and federal 

government agencies, academia and industry to collect new data that will improve the accuracy and 

timeliness of the hazard model. A multiyear effort would enable us to develop and validate new 

findings, and integrate them into future versions of the hazard model. Long-term research activities 

targeting reduction of epistemic uncertainty in the logic tree (fig. 4) are described in greater detail here.

Catalog

A more comprehensive catalog of induced earthquakes requires lowering the magnitude 

detection threshold on a national scale and on the scale of the areas where oil and gas production is 

taking place, especially from unconventional reservoirs. Because the industrial activities that induce 

earthquakes change with time, depending on various circumstances, it is necessary to be able to detect at 

an early stage, the development of a previously unrecognized site of induced seismicity. To do this 

requires reducing the detection threshold of the national network from its current threshold of about 

M3 to at least M2, or, ideally, even lower. This improvement of the national network would be 

invaluable for guiding the deployment of local networks where they are needed to monitor in a timely 

way detailed behavior of the induced earthquakes. 

Local networks must be capable of recording ground motion with wide dynamic range and broad 

bandwidth with sufficient station coverage for precise hypocentral locations. Magnitude detection 

thresholds in the range of 0 to 1 are probably achievable, at least in reasonably quiet locations. With 

location precision of 100 m, or less, the low magnitude thresholds will enable images of previously 

unmapped structures to be resolved from the well-located hypocenters, although considerable work will 
41

also need to be done on reducing absolute location uncertainty. Similarly, earthquake focal mechanisms, 

or better yet, moment tensors, can lead to a better understanding of how the earthquakes are related to 

the geologic structures and fluid injection activities. Seismic stress drop and radiated seismic energy 

estimates can yield additional insights regarding the induced earthquakes and their ground motion. 

Although most fluid-induced earthquakes that are large enough to be felt are the result of 

wastewater disposal by deep injection, there are an increasing number of reports of felt earthquakes 

caused by hydraulic fracturing (Holland, 2011). A low-magnitude threshold will increase the likelihood 

of detecting these events and gaining insights as to the factors that give rise to them. Gathering data on 

the timing and location of hydraulic fracturing treatments will also be very valuable to the development 

of induced seismic hazard models, since the seismic hazard associated with hydraulic-fracture-induced 

earthquakes terminates with the completion of the hydraulic fracture treatment, and these events may be 

removed from the earthquake catalog. By identifying earthquakes induced by hydraulic fracturing, we 

may remove potential bias in the hazard calculation.

Sun and Hartzell (2014) recently demonstrated that local and regional seismic data can be used 

successfully to develop finite fault models of induced earthquakes. (Extending this capability to lower 

magnitudes by taking advantage of improved network data could provide some very useful insights 

concerning the behavior and causes of fluid-induced earthquakes. 

Rate Model

Topics that require additional research include determining the appropriate b-value to use in 

regions of induced seismicity and fine-tuning declustering methods for induced earthquakes, including 

regional variability. Evidence suggests that reoccurrence and clustering behavior of induced earthquakes 

may differ from natural earthquakes (Llenos and Michael, 2013; McNamara and others, 2015).

Therefore, identifying alternative ways of quantifying earthquake occurrence rates that are more 

appropriate for induced seismicity could be used to differentiate induced earthquakes from natural ones. 

Another issue is how to determine an appropriate time window over which to estimate seismicity 

rates. At the Midwest City workshop, it was suggested that the current year’s seismicity is a sufficient 

predictor for the next year’s seismicity; however, in Oklahoma, the seismicity rate changed dramatically 

over the course of one year between 2013 and 2014. Furthermore, how to model seismicity rates in an 

area if injection suddenly starts and after injection has stopped also needs to be addressed. This requires 

further research into how external processes such as fluid injection drive earthquake rates, and how 

earthquake rate models may be able to incorporate available fluid injection data to improve rate 

estimates.

Future research could also consider the development of seismic hazard assessment methods that 

do not require the use of stationary Poisson earthquake rates and would vary in time. As the case in 

Oklahoma shows, earthquake rates can vary significantly in space and time. Developing short-term 

time-dependent probabilistic seismic hazard assessments can help eliminate the need for declustering, as 

well as determining what time windows over which to estimate rates. 

Location Model (Smoothing)

Research to explore how to select an optimal spatial smooth kernel would be beneficial. The 

strong effect that the width of the smoothing kernels has on probabilistic ground motion is demonstrated 

by figure 10. A large smoothing kernel, such as 50 km, can reduce the probabilistic ground motion in 

the area of the seismicity and increase the effect of the ground shaking hazard farther from the initial 

area of the seismicity. Given that induced seismicity is likely going to be limited to areas affected by 
42

fluid injection, we might expect that a narrower smoothing kernel would be valuable for estimating the 

seismic hazard. How to select this kernel is complex, though, as sometimes we see earthquake triggering 

limited to an area very close to an injection well (Kim, 2013) and in others cases we see earthquake 

triggering extending to tens of kilometers beyond injection wells (Keranen and others, 2014). Analysis 

of a number of areas of induced earthquakes with quality locations and wastewater injection wells could 

be analyzed and modeled to better understand the range of distances that are characteristic of induced 

earthquakes.

Research into the interaction of induced seismicity with known faults is important for 

understanding future induced earthquake locations. As presented at the workshop, M. Zoback suggested 

that we forecast the likelihood of whether an area will have induced earthquakes based upon the 

orientation of faults and stress fields. The development of fault and stress databases could help forecast 

seismic hazard in areas of seismicity associated with oil and gas production. 

Maximum Magnitude

Research has been completed to discuss whether the maximum magnitude of an induced 

earthquake correlates with the total volume of fluids injected (Hallo and others, 2014; McGarr, 2014; 

Zoller and Holschneider, 2014). Additional research in these areas would be helpful as well as research 

to determine if the maximum induced earthquake size is the same as the maximum natural earthquake 

size for the region. Numerical modeling and observational studies of Mmax are needed to better 

understand whether Mmax varies with time. For example as injection increases, does Mmax increase as 

well? Whether observed faults and faults inferred from seismicity can be used to estimate Mmax is 

another research question. In many areas, we see lineations of seismicity that are 10 or more kilometers 

long, but none of these areas have to date reported an earthquake that ruptures a large fraction of the 

lineation.

Ground Motion Models

Several studies have indicated that ground motions from induced earthquakes may differ from 

their counterparts for natural earthquakes (McGarr and Fletcher, 2005; Hough, 2014). The differences 

could be related to the shallow depths of induced earthquakes, usually located in the shallow crystalline

basement, or to stress drops that appear to be lower than those for natural events, or some combination 

of these two factors. In any case, induced earthquake ground motion prediction equations could be 

developed in the course of determining useful hazard models. There are already numerous datasets 

available for developing ground motion prediction equations for induced earthquakes, including 

recorded ground motion and intensities. More comprehensive network coverage will give rise to 

considerably more data to constrain these equations. Ground motion data recorded by local networks 

and regional stations out to epicentral distances of 100 km are ideally suited to developing the required 

ground motion models. In addition to magnitude and hypocentral distance, the ground motion models 

probably need to account for hypocentral depth, site response and, perhaps, stress drop and basin 

effects. Where adequate velocity models have been developed, synthetic seismograms may prove useful 

for interpreting the observed ground motion. 

Beyond the Logic Tree

Seismic hazard models that incorporate a process-based understanding of injection-induced 

seismicity would be useful to assess probabilistic seismic hazard. By combining information on the state 
43

of stress, hydrologic properties of injection formations and the basement, and the locations and 

orientations of faults with injection data, we have the possibility of building predictive models that 

anticipate the seismic potential of an area based on its past history. As shown at the workshop, the 

initiation of seismicity in the Mississippi Lime Play of north-central Oklahoma and south-central 

Kansas followed the development of the field with a lag of months to a year. Investigations of this type 

are needed elsewhere to understand where and when this could be a useful tool to forecast if the seismic 

hazard will change based on the expansion of activities in a particular field.

Developing methodologies would enable rapid updates of the hazard model as the underlying 

parameters of the seismic hazard change. The seismic hazard may go up or down, depending on 

specifics of the situation, and our hazard products need to be current at all times. Operational 

Earthquake Forecasting (OEF) is a developing capability that uses rigorously tested statistical models of 

earthquake sequences to continuously update the seismic hazard estimates (Jordan and others, 2014). 

Operational earthquake forecasting for induced earthquakes could also be informed by physical models 

that incorporate hydrogeology, fluid pressure diffusion and forecasts produced by physics-based 

earthquake simulators. All of these extensions to the hazard model should improve significantly the 

reliability and performance of industry “traffic light” systems for managing the seismic hazard posed by 

injection-induced earthquakes. 

Conclusions

Modeling induced seismicity in probabilistic seismic hazard analysis is very difficult, since we 

do not understand some of the fundamental differences between natural and induced earthquakes, and 

because the seismic activity can change based on changes in human activity. Predicting when and where 

induced seismicity will occur in the future is challenging. For example, induced seismicity does not 

occur near every disposal well, so it is important that we continue to study and learn more about how 

these earthquakes are generated, so we can better assess future patterns and trends. In Oklahoma, 

activity rates have varied exponentially, and earthquakes have migrated several tens of kilometers over a 

year or two. These changes may be related to oil and gas exploration activity but they also may depend 

on physical processes, which are poorly understood. Many decisions are critical for the analysis, 

including modeling decisions about earthquake catalogs, rates, locations, maximum magnitudes, and 

ground motions. Many questions remain, and additional research would enable us to better characterize 

data, models, and methods. Likelihood testing can be used to evaluate which models and parameters are 

optimal in forecasting future earthquakes. Our preliminary analysis (appendix 1) supports the use of the 

recent part of the earthquake catalog, though we may want to consider the use of shorter time periods 

than one year for developing the smoothed seismicity models. Such analyses will guide our 

implementation of the logic tree in developing final models.

The sensitivity studies we present here indicate very high probabilistic ground motions that 

differ considerably from previous hazard products that excluded induced earthquakes. The high and 

variable probabilistic ground motions contained in this report may be difficult for users to implement; 

working together with regulators and industry will enable us to determine how to better portray the 

seismic hazard in regions where induced seismicity is active. Possible future directions include seismic

hazard models that are updated annually, as operational earthquake forecasts that provide daily or 

hourly updates, or as shake maps that show how the ground shakes or how it could shake. Workshop 

participants felt that these kinds of products may be useful for public agencies or industry groups that 

need to make decisions on economics and public safety. 
44

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49

Appendix 1: Initial Likelihood Tests of Potential Seismicity-Rate Models for 

Induced Seismicity in Oklahoma, Southern Kansas and North-Central Texas

By Morgan P. Moschetti and Susan M. Hoover

We investigate the effects of smoothing parameters, catalog type and catalog duration on 

likelihood parameters to guide future research and the selection of seismicity rate models for seismic 

hazard calculations. Based on input received at the workshop and observed variations in the seismicity 

in Oklahoma, southern Kansas and north-central Texas (OK–KS–TX), we develop various smoothedseismicity models and test the ability of these models to predict the spatial distributions of earthquakes 

that occurred May 2014 through October 2014 (2014.2, fig. 1-1). We test the smoothed-seismicity 

models using the data-consistency in likelihood space method (Schorlemmer and others, 2007), which 

we describe below. 

Figure 1-1. Earthquake catalog of potentially induced seismicity in Oklahoma, southern Kansas and north-central 

Texas. The polygon and earthquake catalogs are the ones described in the main text of this open-file report. The 

legend indicates the occurrence time of the earthquakes used in this study. Years and fractional years (for 

example, 2014.2) are defined in table 1-1. 

This appendix describes the construction of smoothed-seismicity models, the likelihood testing 

method, and our preliminary likelihood results. We examine the ability of 20 smoothed-seismicity 

models to predict the spatial distributions of earthquakes from the most recent part of the earthquake 

catalog by varying 3 parameters in the construction of the models: (1) the time period for selecting 
50

earthquakes from the catalog; (2) whether we use the full (nondeclustered) or declustered earthquake 

catalog; and (3) the smoothing distance. 

Time Periods for Smoothed-Seismicity Models

We calculate smoothed-seismicity models using earthquakes from five different time periods 

from an updated version of the Central and Eastern United States earthquake catalog, originally 

developed for the 2014 NSHM (Petersen and others, 2014). Because variations in seismicity rates from 

induced seismicity are inherently time-dependent, but the smoothed-seismicity models are treated in a 

time-independent manner, we test the effect of smoothed-seismicity models developed from earthquake 

catalogs as short as 6 months. However, the earthquake catalogs that we use in this study range from 6 

months to 5 years in duration. The starting and ending dates of the time periods used in this study are 

summarized in table 1-1; note that earthquakes from the time periods named 2013 and 2014 (for 

example, 2013.1) do not always fall within their respective calendar years. We refer to the time periods 

as (1) 2008-12 (5 years); (2) 2013.1 (6 months); (3) 2013.2 (6 months); (4) 2013 (1 year); (5) 2014.1 (6 

months); and (6) 2014.2 (6 months). Time periods 1–5 are used to develop smoothed-seismicity models, 

and time period 6 (2014.2) is used in testing the smoothed-seismicity models, as described below. 

Table 1-1. Time periods and abbreviations used in development of smoothed seismicity models for likelihood 

testing. Starting and ending dates are given in MM/DD/YY format.

Time period

number

Time period 

abbreviation Start End

(1) 2008–12 01/01/08 12/31/12

(2) 2013.1 11/01/12 04/30/13

(3) 2013.2 05/01/13 10/31/13

(4) 2013 11/01/12 10/31/13

(5) 2014.1 11/01/13 04/30/14

(6) 2014.2 05/01/14 10/31/14

The number of earthquakes greater than or equal to (≥) moment magnitude (M) 2.5 in the 

earthquake catalogs of time periods 1–5 suggests significant variations in the seismicity rate in the OK–

KS–TX region. We compute annual earthquake rates from the earthquake catalogs with durations 

ranging from 6 months to 5 years to make direct comparisons between the apparent rates of the five time 

periods (table 1-2). A significant increase in seismicity rate since 2008 is shown in table 1-2. Although 

the numbers of earthquakes in the declustered catalogs from time periods 5 (2014.1) and 6 (2014.2) are 

similar, there are substantial differences in the numbers from the full (nondeclustered) catalogs from 

these time periods.
51

Table 1-2. Comparison of earthquake (greater than or equal to moment magnitude [M] 2.5) numbers and 

calculated annual earthquake rates from the full (nondeclustered) and decl (declustered) catalogs used in 

developing (forecast catalog) and likelihood testing (test catalog) the smoothed-seismicity models.

[M≥2.5 is moment magnitude greater than or equal to 2.5, # eqs is number of earthquakes, /yr is per year, decl is declustered. 

Column headings are defined in table 1-1] 

Forecast catalog (M≥2.5) Test catalog

2008–12 2013.1 2013.2 2013 2014.1 2014.2

# eqs, full 393 61 103 163 581 984

# eqs/yr, full 78.6 122 206 163 1162 1968

# eqs, decl 120 19 32 51 56 61

# eqs/yr, decl 24 38 64 51 112 122

Smoothed-Seismicity Models

All smoothed-seismicity models for this analysis assume the Gutenberg-Richter (GR) 

magnitude-frequency relation (Ishimoto and Iida, 1939; Gutenberg and Richter, 1944): 

 log10 N(m) = a − bm (1)

where N(m) is the number of earthquakes with M≥m, and a and b are the GR parameters controlling the 

seismicity rate and the relative proportion of earthquakes with different magnitudes. We use two bvalues in the calculation of smoothed-seismicity models for potential induced seismicity, following the 

results on earthquake recurrence presented in appendix 2. For the smoothed-seismicity models 

computed from the full (nondeclustered) earthquake catalog for time periods 2–5 (2013.1, 2013.2, 2013, 

and 2014.1), we use b=1.6, because preliminary calculations show that a higher b-value might be more 

appropriate for induced seismicity in OK-KS-TX (appendix 2). For the smoothed-seismicity models 

computed from the declustered earthquake catalog, and for the smoothed-seismicity model computed 

from the full (nondeclustered) catalog and time period 1 (2008–12), we use b=1.0 in consistent practice 

with the 2014 NSHM which addresses declustered seismicity for 2012 and previous years (Petersen and 

others, 2014). For all models, we assume a minimum magnitude of completeness (Mc) of M2.5 in 

calculating the a-values; however, recent results, including those presented in appendix 2 suggest that 

this Mc may be too low for this region, and consequently, our computed seismicity rates may 

underestimate the true seismicity rate.

All smoothed-seismicity models are developed with the use of isotropic, Gaussian functions for 

the smoothing kernels: 

Kσj ��rj − ri�, σj� = C�σj�exp �

−�rj−ri�

2σj

2 � (2)

where C�σj� is a normalization coefficient and σj is the smoothing distance. For this study, we 

investigate the effect of two smoothing distances: 3.54 km (5-km correlation length) and 35.4 km 

(50-km correlation length). 
52

Likelihood Testing

We test all smoothed-seismicity models using the data-consistency in likelihood space (L-test) 

(Schorlemmer and others, 2007), which is one of the likelihood parameters employed by the RELM and 

CSEP projects (Schorlemmer and Gerstenberger, 2007; Zechar and others, 2010). The likelihood 

parameter for the L-test assumes that the probability of earthquake occurrence is given by the Poisson 

probability: 

 p(μi, ni) = �μi

∗�

ni

e−μi

∗

ni! (3)

where μi and ni are the predicted and observed number of earthquakes in the ith cell, respectively. 

Predicted earthquake numbers are calculated from the smoothed-seismicity models by specifying a time 

window of interest. We adopt the seismicity-rate-normalization scheme described by others (for 

example, Werner and others, 2011), which has the effect of equalizing the number of modeled and 

observed earthquakes for the likelihood testing: 

 μi

∗ = μiNtest

∑ μii

 (4)

where Ntest is the number of earthquakes in the testing catalog. By normalizing the observed and 

predicted earthquake counts, the effect of the aggregated seismicity rate is ignored and the L-test 

examines only the spatial distribution of earthquake occurrence. 

Likelihood calculations use the logarithm of equation 3 to give the log-likelihood associated 

with a smoothed-seismicity model, m: 

 LLm = ∑ log(p(μi, ni i )) (5)

 LLm = ∑ nii log μi

∗ − ∑ nilog ni − ∑ μi∗ i i (6)

To make comparisons between the smoothed-seismicity models developed in this study, we used 

the information gain parameter, Gm, which describes the probability gain per earthquake from using the 

smoothed-seismicity model, m, relative to the use of a seismicity rate model with a reference uniform 

rate in all cells, LLref. 

 Gm = exp �

LLm−LLref

Ntest

� (7)

Initial Likelihood Results

To compute the likelihood from the L-test, we compute smoothed-seismicity from the full 

(nondeclustered) and declustered earthquake catalogs in the time periods 1–5 (2008-12, 2013.1, 2013.2, 

2013, 2014.1) and test the models against the earthquakes that occurred in time period 6 (2014.2). 

Smoothed-seismicity models are developed using correlation lengths of 5 km and 50 km. All 

combinations of earthquake catalogs and smoothing parameters are used for a total of 20 smoothedseismicity models—2 options for the full (nondeclustered) and declustered catalogs, 5 catalog time 

periods, and 2 correlation lengths.
53

Information gain values (equation 7) from all 20 models are tested with M≥2.5 and M≥3.5 

earthquake catalogs from time period 6 (2014.2). The gain values from the M≥2.5 catalog are plotted in 

figure 1-2; gain values from the M≥3.5 testing catalog are not presented but show similar trends. Higher

information gains result from the use of the more recent earthquake catalogs (2013, 2013.2, 2014.1). 

Information gains from the smoothed-seismicity model derived from the declustered catalog are slightly 

better than the gains from the full (nondeclustered) catalog. However, the differences between the 

information gains resulting from the different correlation lengths (5 km and 50 km) are far more 

pronounced. The smoothed-seismicity models generated with 50-km correlation lengths show far better 

predictive power for characterizing the spatial distribution of earthquakes from time period 6 (2014.2) 

than do the models developed with 5-km correlation lengths. 

Figure 1-2. Information gain (Gm) from the 20 smoothed-seismicity rate models computed using a testing catalog 

of moment magnitude (M) greater than or equal to 2.5 earthquakes from time period 6 (2014.2). Time periods for 

the forecast catalogs are defined in table 1-1. Shape and color of the plotting symbols differentiate between the full 

(nondeclustered) and decl. (declustered) catalogs and the correlation lengths used in the smoothed seismicity 

models, as described by the legend. Note that because they yield similar information gains, the symbol for the full 

(nondeclustered) catalog using an R (correlation length) equal to 5 kilometers (km) is eclipsed by the symbol for the 

declustered catalog. Similarly, the symbols for the full (nondeclustered) catalog using R equal to 50 km during the 

catalog periods 2013.1 and 2013 are blocked because they plot at the same point as the declustered catalog.

Plots of the smoothed-seismicity rates and earthquake epicenter locations from time period 6 

(2014.2) testing catalog are highly informative for understanding the information gain results. Figure 

1-3 depicts the smoothed-seismicity models constructed from the declustered catalogs for earthquakes in 

time period 5 (2014.1) using correlation lengths of 5 km (fig. 1-3A) and 50 km (fig. 1-3B), overlain by 

the epicentral locations of M≥2.5 earthquakes in the testing catalog. Of the 61 earthquakes in the testing 

catalog, 25 earthquakes occur in cells where the rates of the 5-km smoothed-seismicity model are higher 

than the rates the 50-km smoothed-seismicity model; in comparison, 32 earthquakes occur in cells 

where the 50-km smoothed-seismicity model has higher rates. However, 36 earthquakes occur where 
54

the rates of the 5-km smoothed-seismicity model are lower than the rates of the reference, uniform 

model, whereas only 7 earthquakes occur where the rates of the 50-km smoothed-seismicity model are 

lower than the reference, uniform rate. 

Figure 1-3. Comparison of smoothed-seismicity models using correlation lengths of: A, 5 km and B, 50 km. Both 

smoothed-seismicity models use earthquakes from the declustered catalog, for time period 5 (2014.1); the color bar 

indicates number of earthquakes for time period 5 (2014.1) with a moment magnitude greater than or equal to (≥) 

0, using 0.1 by 0.1 degree grid cells. Epicenters from M≥2.5 earthquakes from the testing catalog (time period 6, 

2014.2) are plotted as black circles.
55

Figure 1-3. Comparison of smoothed-seismicity models using correlation lengths of: A, 5 km and B, 50 km. Both 

smoothed-seismicity models use earthquakes from the declustered catalog, for time period 5 (2014.1); the color bar 

indicates number of earthquakes for time period 5 (2014.1) with a moment magnitude greater than or equal to (≥) 

0, using 0.1 by 0.1 degree grid cells. Epicenters from M≥2.5 earthquakes from the testing catalog (time period 6, 

2014.2) are plotted as black circles.—Continued

Figure 4 presents summary comparisons of the first term of the log-likelihood expression 

(equation 6) for all cells containing earthquakes. Comparison of these per-cell log-likelihoods (fig. 

1-4A) shows the large number of earthquakes occurring in cells with low rates for the 5-km smoothedseismicity model. Binned log-rate terms (fig. 1-4B) for the 5-km smoothed-seismicity model show a 

bimodal distribution; many earthquakes occur where the 5-km smoothed-seismicity rates are high, but 
56

many earthquakes also occur where the 5-km smoothed-seismicity rates are low. By comparison, most 

earthquakes occur where the 50-km smoothed-seismicity rates are relatively high. Use of intermediate 

correlation lengths (between 5 km and 50 km) may give higher likelihood values than we have 

calculated here.

Figure 1-4. Summary plots of log-likelihood contributions from smoothed-seismicity models with 5-kilometer (km) 

and 50-km correlation lengths. Smoothed-seismicity models were developed from time period 5 (2014.1) and the 

declustered catalog. A, Comparison of the first term of the log-likelihood (Equation 6), ni log μi

∗

, from models 

developed from 5 km (ni log μi,5

∗ ) and 50 km (

ni log μi,50

∗ ) correlation lengths. The solid line has unit slope and 

zero intercept for reference; symbols above the line are indicate a better prediction of the spatial pattern of time 

period 6 (2014.2) seismicity by the 50-km-smoothed model, and values below the line indicate better prediction by 

the 5-km-smoothed model. B, Binned earthquake counts of the first term of the log-likelihood (equation 6), 

ni log μi

∗

, indicating the large fraction of cells containing earthquakes from the 50-km-smoothed model that 

predicted very low log-seismicity rates (log(μi

∗

)<-9).

References Cited

Gutenberg, B., and Richter, C.F., 1944, Frequency of earthquakes in California: Bulletin of the 

Seismological Society of America, v. 34, no. 4, p.185–188. 

Ishimoto, M., and Iida, K., 1939, Observations of earthquakes registered with the microseismograph 

constructed recently: Bulletin of the Earthquake Research Institute, v. 17, p. 443–478. 

Petersen, M.D., Moschetti, M.P., Powers, P.M., Mueller, C.S., Haller, K.M., Frankel, A.D., Zeng, 

Yuehua, Rezaeian, Sanaz, Harmsen, S.C., Boyd, O.S., Field, Ned, Chen, Rui, Rukstales, K.S., Luco, 

Nico, Wheeler, R.L., Williams, R.A., and Olsen, A.H., 2014, Documentation for the 2014 update of 

the United States national seismic hazard maps: U.S. Geological Survey Open-File Report 2014–

1091, 210 p. 

Schorlemmer, Danijel, and Gerstenberger, M.C., 2007, RELM testing center: Seismological Research 

Letters, v. 78, no. 1, p. 30–36. 

Schorlemmer, Danijel, Gerstenberger, M.C., Wiemer, S., Jackson, D.D., and Rhoades, D.A., 2007, 

Earthquake likelihood model testing: Seismological Research Letters, v. 78, no. 1, p. 17–29. 
57

Werner, M.J., Helmstetter, A., Jackson, D.D., and Kagan, Y.Y., 2011, High-resolution long-term and 

short-term earthquake forecasts for California: Bulletin of the Seismological Society of America, 

v. 101, no. 4, p. 1630–1648. 

Zechar, J.D., Schorlemmer, Danijel, Liukis, Maria, Yu, John, Euchner, Fabian, Maechling, P.J., and

Jordan, T.H., 2010, The collaboratory for the study of earthquake predictability perspective on 

computational earthquake science: Concurrency and Computation—Practice and Experience, v. 22, 

no. 12, p. 1836–1847. 
58

Appendix 2: Recurrence Analysis in Recent (2001–14) Oklahoma Earthquakes 

There are sufficient numbers of earthquakes in the full (nondeclustered) subcatalogs from the 

Oklahoma-south and Oklahoma-north zones to analyze completeness levels and magnitude-frequency 

distributions. To estimate b-values (the slope of the curve that relates the numbers of small and large 

earthquakes), we apply Weichert’s (1980) method that accounts for variable completeness. Consistent 

with the 2014 national maps (Petersen and others, 2014), we show results for moment magnitude (M)

greater than or equal to M2.7. 

The Oklahoma-south catalog is mapped in figure 2-1A, and earthquake counts in 0.5-magnitude 

unit and 2-year bins are listed in table 2-1. For the analysis, we assume completeness levels of M2.7 

since 2013 and M4.7 since 2011. Binned, incremental, annual earthquake rates, and the b-value estimate 

of 1.26 ± 0.05 are plotted in figure 2-1B. 

Figure 2-1. A, Seismicity in Oklahoma-south zone. The full (nondeclustered) earthquake catalog is shown with the 

years 1700–2012 as red, and 2013–2014 as green. B, b-value analysis for the Oklahoma-south full 

(nondeclustered) catalog. We assume completeness levels of M2.7 since 2013 and M4.7 since 2011. Eq/ Yr is the 

number of earthquakes in each 0.5-magnitude unit bin per year, and Mw is moment magnitude. 
59

Figure 2-1. A, Seismicity in Oklahoma-south zone. The full (nondeclustered) earthquake catalog is shown with the 

years 1700–2012 as red, and 2013–2014 as green. B, b-value analysis for the Oklahoma-south full 

(nondeclustered) catalog. We assume completeness levels of M2.7 since 2013 and M4.7 since 2011. Eq/ Yr is the 

number of earthquakes in each 0.5-magnitude unit bin per year, and Mw is moment magnitude.—Continued

Table 2-1. Earthquake counts in magnitude-time bins for Oklahoma-south nondeclustered catalog. 

2.7–3.2 3.2–3.7 3.7–4.2 4.2–4.7 4.7–5.2 5.2–5.7 5.7–6.2

2001-2002 3 0 0 0 0 0 0 

2003–2004 6 0 0 0 0 0 0 

2005–2006 8 0 0 0 0 0 0 

2007–2008 14 3 0 0 0 0 0 

2009–2010 115 10 3 1 0 0 0 

2011–2012 148 56 6 1 1 1 0 

2013–2014 598 186 20 8 0 0 0 
60

The Oklahoma-north catalog is mapped in figure 2-2A, and earthquake counts in 0.5-magnitude 

unit and 2-year bins are listed in table 2-2. For the analysis we assume a completeness level of M2.7 

since 2013. Binned, incremental, annual earthquake rates and the b-value estimate of 1.44 +/- 0.05 are 

plotted in figure 2-2B. 

Figure 2-2. A, Seismicity in Oklahoma-north zone. The full (nondeclustered) earthquake catalog is shown with the 

years 1700–2012 as red, and 2013–2014 as green. B, b-value analysis for the Oklahoma-north full 

(nondeclustered) catalog. We assume completeness levels of M2.7 since 2013. Eq/ Yr is the number of 

earthquakes in each 0.5-magnitude unit bin per year, and Mw is moment magnitude. C, Comparison of the model 

and observed annual rate of earthquakes for Oklahoma-north full (nondeclustered) catalog. M is moment 

magnitude.
61

Figure 2-2. A, Seismicity in Oklahoma-north zone. The full (nondeclustered) earthquake catalog is shown with the 

years 1700–2012 as red, and 2013–2014 as green. B, b-value analysis for the Oklahoma-north full 

(nondeclustered) catalog. We assume completeness levels of M2.7 since 2013. Eq/ Yr is the number of 

earthquakes in each 0.5-magnitude unit bin per year, and Mw is moment magnitude. C, Comparison of the model 

and observed annual rate of earthquakes for Oklahoma-north full (nondeclustered) catalog. M is moment 

magnitude.—Continued
62

Figure 2-2. A, Seismicity in Oklahoma-north zone. The full (nondeclustered) earthquake catalog is shown with the 

years 1700–2012 as red, and 2013–2014 as green. B, b-value analysis for the Oklahoma-north full 

(nondeclustered) catalog. We assume completeness levels of M2.7 since 2013. Eq/ Yr is the number of 

earthquakes in each 0.5-magnitude unit bin per year, and Mw is moment magnitude. C, Comparison of the model 

and observed annual rate of earthquakes for Oklahoma-north full (nondeclustered) catalog. M is moment 

magnitude.—Continued
63

Table 2-2. Earthquake counts in magnitude-time bins for Oklahoma-north nondeclustered catalog. 

2.7–3.2 3.2–3.7 3.7–4.2 4.2–4.7 4.7–5.2 5.2–5.7 5.7–6.2

2001–2002 0 0 0 0 0 0 0 

2003–2004 0 0 0 0 0 0 0 

2005–2006 1 0 0 0 0 0 0 

2007–2008 1 0 0 0 0 0 0 

2009–2010 1 1 0 0 0 0 0 

2011–2012 2 0 0 0 0 0 0 

2013–2014 754 179 18 2 1 0 0 

The analysis shows that b-values in the range 1.2–1.5 may be appropriate for recurrence models 

for recent (2001-14) seismicity in Oklahoma, using the full (nondeclustered) catalogs and depending on 

completeness assumptions. The Oklahoma-south and Oklahoma-north subcatalogs show evidence of 

incompleteness for magnitudes smaller than 2.7. Analysis of magnitudes 3.0 and greater with the full 

(nondeclustered) catalogs yields even larger b-values, in the range 1.5–2.0. Declustered Oklahoma 

catalogs yield b-values close to 1.0 for magnitudes 3.0 and greater, but uncertainties are large because of

the smaller earthquake counts. A similar analysis for the full (nondeclustered) catalog for potentially 

induced earthquakes associated with the Raton Basin (as described in the main text and table 1 of this 

open-file report) yields a b-value close to 1.0, so it may not be appropriate to simply project the 

Oklahoma recurrence results into other cases of potential injection-related seismicity. A comparison of 

the model (using a b-value of 1.5) and observed rate of earthquakes in the Oklahoma-north zone is 

shown in figure 2-2C. The model is comparable to the observed rates for this zone. Magnitude 7 

earthquakes recur about once every 3,300 years in this model. 

References Cited

Petersen, M.D., Moschetti, M.P., Powers, P.M., Mueller, C.S., Haller, K.M., Frankel, A.D., Zeng, 

Yuehua, Rezaeian, Sanaz, Harmsen, S.C., Boyd, O.S., Field, Ned, Chen, Rui, Rukstales, K.S., Luco, 

Nico, Wheeler, R.L., Williams, R.A., and Olsen, A.H., 2014, Documentation for the 2014 update of 

the United States national seismic hazard maps: U.S. Geological Survey Open-File Report 2014–

1091, 210 p. 

Weichert, D.H., 1980, Estimation of the earthquake recurrence parameters for unequal observation 

periods for different magnitudes: Bulletin of the Seismological Society of America, v. 70, no. 4, 

p. 1337–1346. 
64

Appendix 3: Ratio Maps for Figures 13 through 17

In this appendix, we show the ratios of the sensitivity study maps (report figs. 13–17) and the 

2014 National Seismic Hazard Models (Petersen and others, 2014). The 2014 map for 5-Hz spectral 

acceleration and a 2-percent probability of exceedance in 50 years (equivalent to a 0.04 percent per 

year) on a firm rock (shear wave velocity [time-average] in the upper 30 meters [VS30] of 760 meters per 

second [m/s]) uniform site condition is shown in figure 3-1. In the following figures (figs. 3-2–3-6), the

ratio maps are generated for 5-Hz spectral acceleration at a 0.04-percent annual probability of 

exceedance on a firm rock site condition. The ratios are calculated by combining the induced seismicity 

hazard layer with the 2014 hazard (that excludes the induced seismicity), and then dividing this 

combined hazard by the 2014 hazard. Figure 3-2 shows the ratio of the base case **sensitivity study. 

Figure 3-3 shows the ratios for the base case but using a catalog with the minimum magnitude of 

moment magnitude (M) 3.0 rather than M2.5. Figure 3-4 shows the ratio for the base case but using a 

declustered catalog rather than the full (nondeclustered) catalog. Figure 3-5 shows the ratio of the base 

case but applies a b-value (the slope of the curve that relates the numbers of small and large 

earthquakes) of 1.5 rather than a b-value of 1.0 in the seismicity model. Figure 3-6 shows the base case

but applies a declustered catalog and uses a 50-kilometer (km) smoothing length rather than the 5-km 

smoothing length applied in the base case. These maps all show ratios exceeding a factor of 3.0 over a 

broad region of Kansas, Oklahoma, and Texas and in smaller regions across portions of other states. On 

the plots, some ground motions may exceed ratios of 3.0 but are not distinguished in these figures. 

Figure 3-1. 2014 NSHM provided for reference.
65

Figure 3-2. The base case combined with the 2014 NSHM (fig. 13) divided by the 2014 NSHM.
66

Figure 3-3. The base case modified by using moment magnitude (M) 3 minimum magnitude (Mmin) combined with 

the 2014 NSHM (fig. 14) divided by the 2014 NSHM.
67

Figure 3-4. The base case modified by using the declustered catalog combined with the 2014 NSHM (fig. 15) 

divided by the 2014 NSHM.
68

Figure 3-5. The base case modified by using b-value (the slope of the curve that relates the numbers of small and 

large earthquakes) equal to 1.5 combined with the 2014 NSHM (fig. 15) divided by the 2014 NSHM.
69

Figure 3-6. The base case modified by using the declustered catalog and 50-kilometer (km) smoothing combined 

with the 2014 NSHM (fig. 15) divided by the 2014 NSHM.

References Cited

Petersen, M.D., Moschetti, M.P., Powers, P.M., Mueller, C.S., Haller, K.M., Frankel, A.D., Zeng, 

Yuehua, Rezaeian, Sanaz, Harmsen, S.C., Boyd, O.S., Field, Ned, Chen, Rui, Rukstales, K.S., Luco, 

Nico, Wheeler, R.L., Williams, R.A., and Olsen, A.H., 2014, Documentation for the 2014 update of 

the United States national seismic hazard maps: U.S. Geological Survey Open-File Report 2014–

1091, 210 p.