Global Surface Displacement Data for Assessing Variability 

of Displacement at a Point on a Fault

By Suzanne Hecker, Robert Sickler, Leah Feigelson, Norman Abrahamson, Will Hassett, Carla Rosa, and

Anne Sanquini

Open-File Report 2013–1305

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2014

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Suggested citation:

Hecker, Suzanne, Sickler, Robert, Feigelson, Leah, Abrahamson, Norman, Hassett, Will, Rosa, Carla, and Sanquini, 

Anne, 2014, Global surface displacement data for assessing variability of displacement at a point on a fault: U.S. 

Geological Survey Open-File Report 2013-1305, 28 p., http://dx.doi.org/10.3133/ofr20131305.

ISSN 2331-1258 (online)

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iii

Contents

Introduction.................................................................................................................................................................... 1

Compilation Criteria and Data Uncertainties.................................................................................................................. 1

Analysis and Results ..................................................................................................................................................... 2

Summary ....................................................................................................................................................................... 6

References Cited........................................................................................................................................................... 7

Figures

Figure 1. Graph showing distribution of sites by the number of events at a site ........................................................... 3

Figure 2. Graph showing distribution of sites by fault style. .......................................................................................... 4

Tables

Table 1. Global Compilation of Surface Displacement at a Point on a Fault ................................................................. 1

Table 2. Computed coefficient of variation (CV) and standard error of the estimate for subsets of data....................... 6
iv

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1

Global Surface Displacement Data for Assessing 

Variability of Displacement at a Point on a Fault

By Suzanne Hecker, Robert Sickler, Leah Feigelson, Norman Abrahamson, Will Hassett, Carla Rosa, and Anne

Sanquini

Introduction

This report presents a global dataset of site-specific surface-displacement data on faults (table 1). 

We have compiled estimates of successive displacements attributed to individual earthquakes, mainly 

paleoearthquakes, at sites where two or more events have been documented, as a basis for analyzing 

inter-event variability in surface displacement on continental faults. 

An earlier version of this composite dataset was used in a recent study relating the variability of 

surface displacement at a point to the magnitude-frequency distribution of earthquakes on faults, and to 

hazard from fault rupture (Hecker and others, 2013). The purpose of this follow-on report is to provide 

potential data users with an updated comprehensive dataset, largely complete through 2010 for studies 

in English-language publications, as well as in some unpublished reports and abstract volumes.

Table 1. Global Compilation of Surface Displacement at a Point on a Fault. 

[Table 1 is a Microsoft© Excel file and can be downloaded at http://pubs.usgs.gov/of/2013/1305/.]

Compilation Criteria and Data Uncertainties

For this compilation effort, we have included no more than one study site per section of fault (for 

faults that have been segmented or otherwise subdivided), both to reduce the correlation of displacement 

values between sites, and to make our task more manageable. For sections of fault with more than one 

set of observations, we selected the dataset with the best quality and the most events. Where we had a 

choice, we minimized the influence of along-strike variability by minimizing the distance between

observations. However, some types of data necessarily involve observations at more than one location, 

such as records of accruing lateral displacements along strike-slip faults. 

Ideally, displacement estimates should represent the net or the main component of displacement 

across the entire zone of faulting at a site. However, studies of distributed faulting commonly include 

only part of the zone, and observations for many strike-slip and oblique-slip faults consist only of the 

local vertical component of displacement. For these cases, any intra-event variation in the distribution of 

displacement across strike, or in the ratio of horizontal to vertical displacement at the site, would

contribute to the variability of the displacements sampled. Studies of faults that have blind ruptures but 

produce surface or near-surface fault-related fold scarps also are included in this compilation.
2

Sources of uncertainty affecting observed displacement variability are further discussed in 

Hecker and others (2013). That article includes, as an electronic supplement, a checklist of issues that 

can affect the accuracy of displacement measurements, recognition of events, or overall utility of

results. Hecker and others (2013) developed and used this list as a guide for evaluating the quality of the 

datasets in their compilation. For the larger, updated compilation, we have excluded a formal evaluation 

of data quality because of the difficulty in consistency applying a subjective rating scheme among a 

group of compilers with varied backgrounds.

Analysis and Results

We have compiled 860 surface-displacement observations from 292 sites on faults in 34 

countries (table 1). For almost one-half of these countries, the earliest studies date from 2000 or later, 

probably reflecting the global expansion of paleoseismology. Slightly more than one-half of the sampled 

faults are in the United States; one-third of the United States faults are in California.

The number of observations per site averages about three, although about 50 percent of the sites 

have only two documented displacements, and only 12 percent have more than four (fig. 1). This data 

distribution is essentially unchanged from the data distribution presented in Hecker and others (2013) 

for an earlier version of the compilation that contains 505 observations from 171 sites, primarily from 

studies available prior to 2000. The limited number of observations per site probably reflects a persistent 

difficulty worldwide in obtaining long records of paleoseismic displacements on individual faults. 

Organizing the data by style of faulting (fig. 2) shows that 50 percent of the sites are from normal or 

normal-oblique faults, 33 percent are from faults with dominantly strike-slip movement, and about 17

percent are from faults with a reverse sense of slip.
3

Figure 1. Graph showing distribution of sites by the number of events at a site.
4

Figure 2. Graph showing distribution of sites by fault style. Eleven sites on oblique-slip faults having subequal 

components of horizontal and vertical slip are double-counted. N=normal slip; R=Reverse slip; S=strike slip.
5

To analyze inter-event variability in surface displacement at a point on a fault, Hecker and others

(2013) created a composite dataset by normalizing the displacement values by the mean displacement at 

each site. Combining data from different sites requires making the assumption that the coefficient of 

variation (CV) of the displacement, given by the ratio of the standard deviation to the mean, is constant 

for observations at all sites, or for a selected subset of sites. Then,

, (1)

in which Dij is the jth displacement at site i, Ni is the number of displacements for the ith site, Nsite is 

the number of sites, and Ndispl is the total number of displacements observed at all sites. The accuracy 

of the computed CV is characterized by the standard error (SE) of the estimate and is approximated by

. (2)

There are two main sampling issues that may bias the CV of our dataset: the small number of 

observations per site and the presence of events smaller than the limit of detectable displacement in the 

geologic record. Although addressing these issues is beyond the scope of this report, Hecker and others

(2013) used a forward modeling approach to formally consider how factors such as these may affect the 

observed CV.

Using equations (1) and (2), we have estimated the CV for the data presented in Table 1, for the 

entire dataset and for subsets of the data based on faulting style. Following the procedure outlined in 

Hecker and others (2013), we compute the CV both with and without the uncertainty of the measured 

displacement (table 2). Some displacements include stated measurement error or interpretive uncertainty 

(recorded as minimum and maximum values in table 1); for displacements that did not include stated 

measurement error or interpretive uncertainty, we estimated the uncertainty of the observed 

displacement using a maximum-to-minimum displacement ratio of 1.5, as determined from the subset of

values with reported uncertainty in Hecker and others (2013).

Including the uncertainty of the measured displacement leads to a small increase in the estimated 

CV (table 2); in the following, we refer to the CV values that account for this uncertainty. Considering 

the standard error of the estimates, the CV of data grouped by sense of fault slip does not vary 

significantly (table 2). For the entire dataset, we compute a CV of 0.53±0.02. This value is the same as 

that computed from the smaller dataset (171 sites; CV = 0.53±0.03) used in Hecker and others (2013), 

indicating that this degree of variability is a stable feature of paleoseismic observations.
6

Table 2. Computed coefficient of variation (CV) and standard error of the estimate for subsets of data.

[CV (w/o unc): Uses preferred values of displacement from table 1. For displacements reported as a range, mid-point is 

used as preferred displacement; for displacements reported as a minimum or maximum value, a scale factor of 1.25 is used to 

derive the preferred displacement (after Hecker and others, 2013). CV (w/unc): Incorporates range of uncertainty in 

estimates (minimum and maximum values, table 1). For estimates without stated uncertainty, a scale factor of 1.25 is applied 

to the preferred value to derive a range. Abbreviations: Unc, uncertainty in the measured displacement values; w/, with; 

w/o, without]

Dataset Nsite Ndispl CV (w/o unc) CV (w/ unc)

All data 292 860 0.46±0.01 0.53±0.02

Strike slip1 100 285 0.44±0.02 0.51±0.03

Normal slip1 153 461 0.48±0.02 0.54±0.03

Reverse slip1 50 132 0.41±0.03 0.51±0.04

1

A total of 11 sites on oblique-slip faults having subequal components of lateral and vertical slip are double counted for this 

analysis.

Summary

In this report, we present a global compilation of earthquake surface-displacement data at sites 

where two or more events have been documented, as a basis for analyzing the intra-event variability in 

surface displacement at a point on crustal faults. The dataset, representing studies available through 

2010, comprises 860 surface-displacement observations from 292 sites. About 50 percent of the sites 

have only two documented displacements, reflecting the difficulty in recovering long paleoseismic 

displacement records.

To analyze inter-event variability in displacement at a point, we construct a composite dataset by 

normalizing the observed displacement values by the mean displacement at each site (effectively 

substituting space for time), and compute the coefficient of variation (CV), given by the ratio of the 

standard deviation to the mean. For the entire dataset (and including uncertainty in the measured 

displacement values), we compute a CV of 0.53±0.02. This value is essentially identical to the CV 

computed from an earlier version of the dataset for a study relating the variability of surface 

displacement at a point to the magnitude-frequency distribution of earthquakes and to hazard from fault 

rupture.
7

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