Electronic Supplement to
Fault Displacement Hazard for Strike-Slip Faults

by Mark D. Petersen, Timothy E. Dawson, Rui Chen, Tianqing Cao, Christopher J. Wills, David P. Schwartz, and Arthur D. Frankel

This electronic supplement is divided into five sections:

• Section 1: Compilation of Displacement Data along Strike-Slip Faults for on-Fault Displacements
• Section 2: Assessment of Distributed Ruptures for Fault Rupture Hazard along Strike-Slip Faults
• Section 3: Assessment of Distributed Displacements for Fault Rupture Hazard along Strike-Slip Faults
• Section 4: Assessment of Mapping Accuracy for Fault Rupture Hazard along Strike-Slip Faults
• Section 5: Summary of Regression Statistics

A brief explanation is provided at the beginning of each section.

Compilation of Displacement Data along Strike-Slip Faults for on-Fault Displacements

The displacement data used for the regressions of on-fault displacements have been compiled into a Microsoft Excel workbook that is available for download. Included in the spreadsheet are the compilations of displacements normalized by average displacement (D/AD) from the end of the fault, referred to on the spreadsheet as x/L (folded). The same data are also presented as displacements normalized by the maximum displacement observed during each particular earthquake (D/MD). Also included in the spreadsheet are the digitized measurements for each of the nine earthquakes that we compiled in a GIS for this study, presented as a function of distance along the rupture, as well as percent of the rupture. For some earthquakes, we have column for net amount of slip, using both the strike-slip and vertical component, and assumes a 90-degree fault dip. We did not utilize this column in our regressions because 1.) The actual fault dip was not known or well-constrained at the surface and 2.) It was unclear from the data if the vertical component of slip was representative of the fault as a whole, or if it was a reflection of a local change in geometry. This column has been left in the spreadsheet for completeness. Finally, we have augmented our database with thirteen additional strike-slip earthquakes compiled from the data presented by Wesnousky (2008).

The spreadsheet can be accessed here:

Download: PFDHA_Displacements.xls [Microsoft Excel Workbook; 1.2 MB]

Assessment of Distributed Ruptures for Fault Rupture Hazard along Strike-Slip Faults

We adapt the methods of Youngs et al. (2003) to quantify the occurrence of distributed ruptures that surround a principal fault trace. The term principal faulting refers to coseismic surface rupture that occurs along the fault or faults responsible for the release of seismic energy during an earthquake (Coppersmith and Youngs, 2000). Principal faulting is commonly expressed at the surface as a narrow zone of faulting a few meters to tens of meters wide as a mostly continuous fault trace that is the manifestation of fault slip at the earth’s surface.

In contrast to principal fault rupture, we define the term distributed faulting as surface ruptures that occurs along faults off of the principal fault trace and in response to an earthquake along the principal fault. Distributed ruptures can occur from tens of meters to many kilometers away from the principal fault trace, are often discontinuous, and can occur on a variety of structures either related to the principal fault that ruptures during an earthquake, or along separate structures with no direct connection to the principal fault either at the surface or at depth. Such structures include parallel to sub-parallel faults, splay faults that branch away from the principal fault trace, as well as regional faults that are structurally unrelated to the principal fault that produced the earthquake Unlike the hazard presented by the principal fault trace, where the location is usually known from geologic mapping, distributed ruptures and their associated displacements can be along faults and structures that are unrecognized or are too small to be considered an independent seismogenic source.

Figure S1. Maps of surface ruptures used in this compilation.

Figure S1. Maps of surface ruptures used in this compilation.

In general, there are three categories of distributed ruptures: 1.) Ruptures located on distinct faults other than the one that produced the earthquake, 2.) Rupture along faults that splay off of the principal fault trace, and 3.) Rupture along faults that are parallel and sub-parallel to the principal rupture. This third category of ruptures presents a conundrum in that if there are parallel fault strands, it may be difficult to distinguish between distributed ruptures from two or more faults that are simply partitioning slip between the faults, where both fault strands could be considered principal traces. In this case, we employ the criteria that if surface faulting splits into two or more fault strands, it must reconstitute into a single trace after some distance in order for the multiple traces to be considered principal traces. Furthermore, the traces must be more or less continuous from the point where they split into multiple traces to the point where they rejoin into a single trace. Additionally, slip along the multiple traces must be partitioned more or less equally between the multiple traces. If the fault trace meets these criteria, then the ruptures are categorized as principal, rather than distributed ruptures.

Our study expands on the methods of Coppersmith and Youngs (2000) and Youngs and others (2003) using a worldwide data set of strike-slip faulting earthquakes. The probability of surface rupture at a distance from a fault is calculated by comparing the number of raster cells classified as distributed ruptures divided by the total number of cells within the faulting area which gives a measure of the frequency of occurrence of distributed rupture. The analysis of Youngs and others (2003) was done using a dataset of Basin and Range normal faulting surface ruptures that were digitized and converted to a raster image, using a 0.5 km x 0.5 km pixel size. In contrast to the Youngs and others (2002) approach, we selected a variety of cell sizes in order to analyze the rupture potential for different footprint sizes. This was done because one would expect that as the footprint size (which is the cell size that is selected when converting from the vector-based file to the raster-based data) decreases, there should be a corresponding decrease in the probability of rupture. Footprint sizes in this analysis were set at 25 x 25 m, 50 x 50 m, 100 x 100 m, and 200 x 200 m cells in the GIS.

Figure S1 shows the rupture traces of the earthquakes included in this analysis. The earthquake rupture maps were selected on the basis of the availability of large-scale maps that could be worked with in a Geographic Information System (GIS). Three earthquake ruptures, including the 1987 Superstition Hills – Elmore Ranch earthquake sequence, 1992 Landers, and 1999 Hector Mine earthquakes were available as digitized GIS files from the California Geological Survey. The remaining earthquake rupture maps, including the 1968 Borrego Mountain, 1979 Imperial Valley, 1995 Kobe, and 1999 Izmit earthquakes were digitized from published paper maps. With the exception of the 1:50,000 scale Kobe rupture map, all source maps were at a scale greater than 1:25,000. In order to calculate the frequency of occurrence of rupture along and surrounding the principal trace of the fault, the shapefiles were converted to a raster (pixel-based) format. The data compiled was then compiled in Microsoft Excel for further analysis

The results of the distributed rupture analysis for the 40,000 m2, 10,000 m2, 2500 m2, and 625 m2 cell sizes are compiled into a Microsoft Excel workbook and can be accessed here:

Download: PFDHA_Distributed_ruptures.xls [Microsoft Excel Workbook; 254 KB]

Assessment of Distributed Displacements for Fault Rupture Hazard along Strike-slip Faults

Figure S2. Example of how distributed displacement observations are related to the distance from principal fault along the 1999 Hector Mine earthquake surface rupture. Red lines are rupture traces. Green dots are slip measurements. Grey lines represent measurements. SS is lateral component of slip, V is vertical component of slip in centimeters.

Figure S2. Example of how distributed displacement observations are related to the distance from principal fault along the 1999 Hector Mine earthquake surface rupture. Red lines are rupture traces. Green dots are slip measurements. Grey lines represent measurements. SS is lateral component of slip, V is vertical component of slip in centimeters.

In this study, we have also compiled data on displacements that occur off of the principal fault trace. Fault slip that is measured on the distributed ruptures are referred to here as distributed displacements. For this study, we have digitized the surface ruptures and displacement values in a GIS for eight historical strike-slip earthquakes with large-scale (≥1:50,000) maps and measurements of fault displacements. These earthquakes include the 1968 Borrego Mountain earthquake, 1979 Imperial Valley earthquake, 1987 Superstition Hills, 1992 Landers earthquake, 1995 Kobe and the 1999 Izmit, Turkey, 1999 Hector Mine, and 1999 Duzce, Turkey earthquakes. These earthquakes were selected for their detailed mapping and where we believe that the post-earthquake investigation was able to identify most distributed ruptures and displacements that occurred as a result of the earthquake.

In this analysis, we relate a distributed displacement measurement to the principal fault by distance, measured from the location of the distributed displacement measurement to the principal fault, orthogonal to the local trend of principal fault. Figure S2 is an example from the 1999 Hector Mine surface rupture showing how distributed displacement slip measurements are measured as a function of distance from the principal fault trace. The individual lengths of all of the lines are then calculated in the GIS. The collection of these measurements forms the basis of the regressions that define the probability density function for distributed displacements in the assessment of fault rupture hazard.

These measurements have been compiled into a Microsoft Excel workbook and can be accessed here:

Download: PFDHA_Distributed_displacements.xls [Microsoft Excel Workbook; 229 KB]

Assessment of Mapping Accuracy for Fault Rupture Hazard along Strike-slip Faults

In this analysis, we compare fault maps prepared before surface-rupturing earthquakes with maps of surface rupture following the earthquakes. Although there are multiple examples of mapped faults that have subsequently experienced surface rupture (e.g., 1976 Motagua fault, portions of the 2002 Denali fault rupture), very few of these faults have been mapped at a large enough scale both prior and following a surface rupturing earthquake and in sufficient detail to allow for a detailed comparison between the two maps. In order to assess how well faults have been mapped prior to a surface rupturing earthquake, we have compiled pre- and post-earthquake fault maps for the earthquakes where large-scale (≥1:24,000 scale) mapping exists. This dataset includes the 1979 Imperial Valley, 1987 Superstition Hills, 1992 Landers, and 1999 Hector Mine earthquakes.

Pre-earthquake surface fault mapping for these four earthquakes are compiled from a variety of sources. For the 1979 Imperial Valley earthquake, we use 1:24,000 scale pre-earthquake fault maps published by Sharp et al (1977a, 1977b). These original source maps were compiled using a combination of aerial photo analysis, mapping of triggered slip along the Imperial fault following the 1968 Borrego Mountain earthquake, and comparison to the 1940 Imperial Valley rupture trace from historical aerial photography and field notes. Rupture traces resulting from the 1979 Imperial Valley earthquake are from Sharp and others (1982).

Pre-earthquake mapping for the 1987 Superstition Hills earthquake is taken from mapping by Allen and others (1972). This fault map is unique in our data set in that the location of the Superstition Hills fault was mapped based on triggered slip produced by the 1968 Borrego Mountain earthquake. The surface rupture fault traces are compiled from the Sharp et al. (1989) map of the 1987 Superstition Hills earthquake fault rupture.

For both the 1992 Landers and 1999 Hector Mine earthquakes, the pre-earthquake mapping is compiled from California Geological Survey (CGS) Alquist-Priolo Earthquake Fault Zone (A-P EFZ) maps. For the 1992 Landers earthquake, the surface rupture mapping is compiled from the A-P EFZ maps, which were updated with surface rupture mapping following the 1992 earthquake. The source of surface rupture map produced by the 1999 Hector Mine earthquake is taken from Treiman and others (2002).

Methods

Using pre-earthquake fault mapping and maps of surface rupture, mapping accuracy can be quantified by measuring the distance from the mapped fault trace, orthogonal to the local trend of the fault, to the rupture fault trace at a series of points along the mapped trace. We use the term mapped trace to refer to faults mapped prior to an earthquake that produces surface rupture. The term rupture trace refers to those faults that experience coseismic surface rupture and subsequently mapped following an earthquake.

Figure S3. Example of mapping accuracy measurements.

Figure S3. Example of mapping accuracy measurements.

Figure 3 is an example of how the difference between the location of the mapped trace and rupture trace is measured, where the blue lines represent the deviation of the rupture trace from the mapped trace labeled as a distance, labeled “d”.

Mapping accuracy can be taken a step further to include uncertainties in the mapped fault trace location. We adopt the location uncertainty nomenclature used by the A-P EFZ maps, which categorizes the fault location uncertainty into the following categories: accurately located, approximately located, inferred, and concealed. Although the definitions of each category may vary between different fault maps, the location uncertainties are generally defined as follows: Accurately located faults are typically those faults that are expressed geomorphically either as scarps, aligned offset features, linear features, or are locations of previously known fault ruptures. Similar to accurately-located faults, approximately-located faults are defined much in the same way, but have been judged by a geologist to have a greater uncertainty in their location, possibly due to erosion or deposition across the fault trace. Inferred traces are those that have less obvious evidence of recent movement and poorly expressed at the earth’s surface, but likely a fault. Concealed traces are fault traces that are not expressed at the surface, usually due to being covered by surficial deposits that are younger than the most recent movement along the fault, obscured by vegetation, or anthropological activity. By measuring the deviation of the rupture trace from the mapped fault trace and recording what type of location uncertainty the mapped traced is categorized as, we can assess whether or not accurately mapped fault traces are better located than traces where the fault traces have a greater uncertainty as to their location, such as concealed or inferred faults.

The pre-earthquake and post-earthquake fault maps were either compiled from existing digital data, or were digitized from existing paper copies of the maps. We used ESRI ArcGIS 8.3 as our GIS software and the mapping accuracy measurements were compiled as ESRI shapefiles and exported to Microsoft Excel for further analysis.

Sampling

Initially, we choose to sample along each mapped fault at fixed intervals of every 0.5 km along strike. Upon inspection, we realized that this sampling interval may not be adequate to provide a robust number of observations. One problem is that the mapped faults are often not mapped as continuous faults, but instead are often short discontinuous segments. Therefore, sampling at evenly spaced intervals along strike often results without an observation because the interval lacks a mapped fault trace. Although sampling at smaller intervals could alleviate this problem, many mapped individual fault traces on the source maps are less than 100 m in length and would also be missed unless sampled at very short intervals.

An alternate sampling strategy that includes all of the mapped traces without having to sample at extremely small intervals is to sample each fault trace at the middle of the mapped fault segment. Furthermore, one might suspect that the location uncertainty of a mapped fault might be greater at the ends of a fault strand, where the geomorphic evidence might be less evident than in the middle. For this reason, we also took measurements for each mapped trace along the endpoints and midpoints of the line segment in the GIS.

Finally, each measurement along a concealed or inferred mapped fault trace was also qualitatively characterized by fault complexity For our purposes, fault complexities are features such as fault terminations, bends, and stepovers This characterization is done based on the pre-earthquake fault map, without the hindsight provided by the post-earthquake surface rupture map.

The results of our GIS analysis have been compiled into a Microsoft Excel workbook that can be accessed here:

Download: PFDHA_Mapping Accuracy.xls [Microsoft Excel Workbook; 365 KB]

Summary of Regression Statistics

All regressions were performed using Microsoft Excel. Summary statistics for all of the regressions performed in this study are compiled in a Microsoft Excel workbook for those who might be interested.

The file can be accessed here:

Download: Regression_Statistics.xls [Microsoft Excel Workbook; 37 KB]

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