Final Report: USGS NEHRP Project G17AP00010

Final Report: USGS NEHRP Project G17AP00010 Project Title: Automated fault mapping of the North America-Paciﬁc plate boundary using airborne laser swath mapping (ALSM) data George Hilley and Robert Sare Department of Geological Sciences Stanford University Stanford, CA 94305-2115 email:[email protected] voice: (650) 723-3782 fax: (650) 725-0979 Term of Award: January 1, 2017-December 30, 2019

Abstract Fault scarps and fault-related landforms provide important information about fault zone activity over timescales that are not captured by instrumental measurements or historic records. Semi-automated methods for delineating these landforms using topographic data from light detection and ranging (lidar) and spaceborne imaging systems offer the opportunity to charac- terize fault zones on a global scale. This project explored a computationally efficient method for extracting scarp-like landforms from high-resolution (≤ 2 m), regional-scale (≥ 100-km-long) digital topographic datasets. We identified fault-related landforms using a curvature template based on the diffusion model for scarp degradation and extract scarp heights and morphologic ages at each pixel. The method was applied to the GeoEarthScope Northern California dataset, an airborne lidar acquisition imaging nearly 2500 km2 of the northern San Andreas fault system, by adapting the algorithm to use cloud computing resources. Template results and fault trace mapping show spatial agreement in active fault zones with clear topographic expression, including detection of fault scarps, shutter ridges, and elongated drainages. Comparison of the method against field-based morphologic dating of scarps along the southern San Andreas re- veals a trade-off between template window size and morphologic age contrasts resolved between strike-slip fault scarps of different relative ages. Detection performance suggests that window size and orientation constraints may play a key role in improving the accuracy of methods for semi-automated fault zone mapping. As data availability grows, these methods could constrain key earthquake simulation parameters such as damage zone width or rupture length and improve fault maps worldwide. This project produced two peer-reviewed publications (from which much of this Final Report is derived; Sare et al., 2019a, b), as well as three conference abstracts: Sare, R. M., & Hilley, G. E. (2017). ESTIMATING FAULT ZONE MATURITY AT THE PLATE BOUNDARY SCALE USING TEMPLATE MATCHING FOR FAULT SCARP DE- TECTION AND MORPHOLOGIC DATING. Presented at the GSA Annual Meeting in Seattle, Washington, USA - 2017, Geological Society of America. https://doi.org/10.1130/abs/2017am- 308245 Sare, R., & Hilley, G. E. (2018). Scarplet: Cloud-based Template Matching for Detecting Earthquake-Related Landforms in Large Topographic Datasets. Scientific Python Conference 2019, Austin, TX. Sare, R., & Hilley, G. E. (2018). Faults in the cloud: Distributed topographic template matching of fault-related landforms in Shuttle Radar Topography Mission data using a cloud- based processing framework. In AGU Fall Meeting Abstracts.

A Introduction

The lateral extent of past earthquake surface ruptures is a primary input to seismic hazard assessment and earthquake rupture forecasts [Field et al., 2015]. Geomorphic indicators of faulting,

1 such as fault scarps and topographic lineaments, provide important evidence of fault zone extent, maturity, and activity beyond the observational timescales of instrumental or historical data (∼100 years). In particular, the height and curvature of fault scarps may encode information about the relative activity of a fault zone over millenia, the timing and extent of past earthquakes, or the amount of aseismic motion accrued along a creeping fault [e.g., Gilbert, 1909; Arrowsmith and Zielke, 2009; Zielke et al., 2015]. Observations by G. K. Gilbert following the 1906 M = 7.9 San Francisco Earthquake seeded the idea that offsets along tectonic structures create steep surface slopes that are then rounded by geomorphic processes [Gilbert, 1907; Lawson and Reid, 1908; Gilbert, 1909]. The fact that the San Andreas fault zone hosted a diversity of sub-parallel, apparently tectonically generated landforms of various stages of rounding led Gilbert [1909] to speculate that they encoded information about the temporal development of the fault zone. This idea was later codified by Hanks et al. [1984] and Andrews and Hanks [1985], which drew on existing geomorphic theory [Culling, 1960] to associate geomorphic degradation of scarps with diffusion-like transport. This led to the deployment of “diffusion dating” of scarps to provide calibrated estimates of the time at which geomorphic features might have formed in the past. These methods have since been applied extensively to tectonic and non-tectonic landforms, including normal fault scarps [Hanks and Schwartz, 1987; Avouac and Peltzer, 1993; Enzel et al., 1996; Hanks, 2000; Mattson and Bruhn, 2001; Kogan and Bendick, 2011], fault scarps resulting from strike-slip motion [Arrowsmith et al., 1998; DeLong et al., 2010; Hilley et al., 2010], wave-cut shorelines, [Hanks et al., 1984; Hanks and Wallace, 1985; Andrews and Bucknam, 1987; Pelletier et al., 2006], alluvial terrace scarps [Pierce and Colman, 1986; Clarke and Burbank, 2010], and gullies on alluvial fan surfaces [Hsu and Pelletier, 2004]. Early approaches to dating of scarp-like landforms used the slope at the midpoint of one or several scarp profiles to determine the relative or morphologic age of individual features [Bucknam and Anderson, 1979; Nash, 1980; Colman and Watson, 1983]. Later, quantitative methods based on solutions to the diffusion equation were developed for a variety of scarp-like initial conditions, such as multiple-event fault scarps or scarps cutting sloped fan surfaces [Andrews and Hanks, 1985; Andrews and Bucknam, 1987; Hanks and Andrews, 1989; Hanks, 2000]. Subsequent work used this approach to invert for initial offset and morphologic age using the full scarp profile [Avouac, 1993; Avouac and Peltzer, 1993; Arrowsmith et al., 1998]. Such profiles were often created manually by field surveys or hand-selected profiles from detailed contour maps. In contrast, recent innovations in laser-based ranging now provide < 0.5-m-resolution postings of the bare-ground surface across broad (> 100s of km2) areas [e.g., Prentice et al., 2009]. This large volume of data, some of which images entire fault systems, requires some semi-automated method of extracting scarp-like landforms for further targeted analysis. To this end, recent studies developed a template-based method for detection of fault-related landforms and morphologic dating of fault scarps in digital topographic data using a curvature template derived from the analytic solution for the elevation of a vertical scarp subject to diffusive degradation [Hilley et al., 2010]. Similar methods incorporating template matching, spectral transforms, or wavelet transforms have been developed to extract channel networks [Lashermes et al., 2007; Sangireddy et al., 2016; Isikdogan et al., 2017], map landslides [Booth et al., 2009], and model lateral moraine evolution [Doane et al., 2018] using topographic data. While large-scale results have been achieved in channel network extraction from topographic data [Isikdogan et al., 2017] and measuring the planform geometry of rivers in satellite imagery [Rowland et al., 2016; Schwenk et al., 2017], applications to other landforms have been limited to smaller areas of 1-100 km2. The size of high-resolution topographic datasets and the potentially large search space of morphologic ages, wavelet scales, or window sizes limit many existing spectral or template-based methods, which rely on serial implementations that scale poorly with problem size.

2 In this contribution, we apply a distributed template matching algorithm to a plate-boundary- scale topographic dataset along the northern San Andreas fault system (SAF). We evaluate the hypothesis that template-based feature detectability is related to the orientations and length scales of fault-related landforms, including scarps, elongated valleys, and topographic lineaments. Mor- phologic age estimates are compared to field-based morphologic dating of scarps on the southern San Andreas Fault. We find template morphologic ages to be biased towards lower values and that the discriminating power of age estimates declines with increasing template window size. We mea- sure template performance through comparison to regional fault mapping and detailed geomorphic mapping of individual fault zones. We find that changes in template window size and orientation constraints impact the fidelity of template-derived fault mapping in a range of topographic settings. Relationships between template parameter estimates and slip rate and time of latest fault activity are also explored. Drawing on these findings, we discuss improvements to increase the resolving power of semi-automated mapping methods, including supervised learning methods, and ameliorate the trade-off between window size and morphologic age discrimination.

B Data

B.1 Topographic datasets This study primarily uses the GeoEarthScope (GES) Northern California lidar dataset [NCAL, 2008] (Figure 1). Collected in 2007, it images the San Andreas Fault and other major fault zones in Northern California [Prentice et al., 2009]. Elevation data is provided as 3680 digital elevation model (DEM) tiles covering 1 km2 at 0.5 m resolution over a total survey area of 2448 km2 with an average point density of 5.17 points m−2. This study uses bare earth DEM tiles provided as a final survey data product; these were produced by kriging of ground-classified points using a linear variogram with nugget variance of 0.15 m and a search radius of 25 m [NCAL, 2008]. Each tile was resampled using the nearest-neighbor method to 2 m resolution prior to analysis. One validation site on the southern SAF on the Carrizo Plain was also processed. This site includes Wallace Creek, a Holocene channel complex offset by approximately 128 m along the SAF and a series of fault scarps with documented differences in morphologic age [Sieh and Jahns, 1984; Arrowsmith et al., 1998]. These data are derived from the B4 Project airborne lidar survey, which images the southern SAF with an average point density of 2.98 points m−2 [Bevis et al., 2005; B4 , 2006]. All data were downloaded as bare earth DEMs from OpenTopography (https://opentopography.org)[Krishnan et al., 2011]. A plot of TP rate and FP rate for varying threshold values defines the receiver operating characteristic (ROC) curve for a set of classifiers (Fawcett, 2006). Classifiers that plot along a one-to-one line in this space identify true and false positives in equal proportions, and classifiers above this line identify true positives at a higher rate than false positives. The performance of a classification method can be measured by the area under the ROC curve (AUC), which ranges from 0 to 1, with AUC = 0.5 describing an essentially random classifier and AUC = 1 describing an optimal classifier (Fawcett, 2006). ROC curves were constructed for the entire dataset, the North Coast segment of the San Andreas Fault, and the Green Valley Fault (Figure 2). In general, AUCs are less than or equal to 0.51 for the 100 m window size, unconstrained processing case at all sites, and the AUC is similarly low (0.49) for the entire dataset for this case. Unconstrained processing at a larger template window size yields higher AUC values for both individual sites (0.59-0.68) and the full dataset (0.58). Applying swath orientation constraints and increasing template window size improved the classification results for the North Coast and GVF sites, which have AUC ranges of 0.62-0.72 and 0.57-0.68 for these cases.

3 Figure 1: a) Location map, b) Map of major Northern California fault zones included in this study. F2: Location of Figure 6, North Coast segment of San Andreas Fault, F3: Location of Figure 11, Green Valley Fault, F4: Location of Figure 12, Hollister section of Calaveras Fault. Abbreviations: CF: Calaveras Fault, GVF: Green Valley Fault, HF: Hayward Fault, MF: Maacama Fault, NC: North Coast, RCF: Rodgers Creek Fault, SAF: San Andreas Fault, SCF: Southern Calaveras Fault.

4 1.0 a b c

0.5

100 m, NC (AUC = 0.49) 100 m, NC (AUC = 0.51) 100 m, NC (AUC = 0.50) 500 m, NC (AUC = 0.58) 500 m, NC (AUC = 0.68) 500 m, NC (AUC = 0.67) 1000 m, C (AUC = 0.63) 1000 m, C (AUC = 0.72) 1000 m, C (AUC = 0.67) 0.0

1.0 d e f True positive rate positive True

0.5

100 m, NC (AUC = 0.49) 100 m, NC (AUC = 0.43) 100 m, NC (AUC = 0.50) 500 m, NC (AUC = 0.62) 500 m, NC (AUC = 0.59) 500 m, NC (AUC = 0.65) 1000 m, C (AUC = 0.68) 1000 m, C (AUC = 0.61) 1000 m, C (AUC = 0.72) 0.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 False positive rate

Figure 2: Receiver operating characteristic curves for pixel classiﬁers applied to fault zone swaths using diﬀerent template window sizes and search constraints. a) Northern California dataset, b) North Coast swath, c) Rodgers Creek Fault swath, d) Green Valley Fault swath, e) Maacama Fault swath, f) Hollister area, southern Calaveras Fault swath. Constrained search refers to search using template orientations between −60◦ and 0◦. C: Constrained template search, NC: Template search with no orientation constraints, AUC: Area under ROC curve.

5 In addition to the classification metrics defined in the text, the F1 score is often used to evaluate classifier performance. It is an average of the precision and the true positive rate of the classifier,

Precision + TPR F = 2 (1) 1 Precision × TPR

The changes of these classiﬁcation metrics and the F1 score with increasing signal-to-noise thresh- olds is presented in Figures 3–5.

B.2 Validation data B.2.1 Regional mapping Compiled by the United States Geological Survey (USGS), the USGS Quaternary faults and fold database (Q-faults; https://earthquake.usgs.gov/hazards/qfaults/) contains mapped faults thought to be sources for moderate to large earthquakes (M > 6) during the Quaternary (1.6 Ma to present) based on mapping of at least 1:24,000 scale [USGS, 2006]. Attributes such as time of most recent activity, estimated slip rate, mapped location quality and scale of mapping are provided for each fault trace. To create a regional-scale validation dataset, Q-faults features were rasterized to generate co-registered grids of mapped pixels at the resolution of the template parameter grids. Linear features were buffered by a 100 m circular buffer to capture the extent of each mapped fault zone. The time of most recent prehistoric activity, slip rate, and mapping confidence level associated with each mapped feature were also extracted. Examples of validation data and detected features are provided in Figures 6-12 and Figures 7 and 8.

B.2.2 Detailed fault trace mapping Mapped indicators of fault expression, such as individual scarps, other fault-related landforms, or tonal contrasts identified in aerial photographs, are documented in miscellaneous field studies and fault evaluation reports at sites throughout California. We selected the North Coast segment of the SAF and the Green Valley Fault as detailed validation sites due to availability of high-quality fault trace mapping (Figure 1). Geomorphic features identified in USGS and CGS maps were digitized to assess the fidelity with which the scarp template detected specific groups of mapped landforms. The North Coast segment of the SAF has been mapped in detail by Koehler et al. [2005], which used a 2003 NASA-USGS airborne lidar dataset [NSAF , 2005] to delineate the fault zone and precisely locate fault-related landforms in addition to extensive field mapping. Fault-trace mapping is also provided with confidence levels designated for concealed and clearly visible features. This dataset is not published electronically, but maps included in this report were used for qualitative assessment of these results. The Green Valley Fault was mapped by Frizzell Jr. and Brown Jr. [1976] using topographic base maps and aerial photography. Landforms such as scarps, historical offsets, sag ponds, and pressure ridges are indicated by trace mapping and leaderlines denoting small-scale features. Labeled landforms indicated by leaderlines in Frizzell Jr. and Brown Jr. [1976] were manually digitized as point features. The northern section of this swath is occupied by the Berryessa Fault, which was recently mapped by Lienkaemper [2012] based on lidar and air photo interpretation with field verification of features, including detailed field notes and geomorphic descriptions for each mapped feature. Both Frizzell Jr. and Brown Jr. [1976] and Lienkaemper [2012] document indicators of faulting, such as vegetation lineaments, springs, and tonal contrasts in soil or vegetation. These mapped features are important evidence for fault zone location that would not necessarily be detected by methods based on topographic data alone.

6 Accuracy Precision F1 score Kappa % Negative Median SNR a Maximum b Maximum c Maximum 1.0 Accuracy 0.77 Accuracy 0.69 Accuracy 0.70 Precision 0.19 Precision 0.32 Precision 0.26 F1 0.31 F1 0.47 F1 0.40 Kappa 0.01 Kappa 0.02 Kappa 0.02 0.8

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d Maximum e Maximum f Maximum 1.0 Accuracy 0.77 Accuracy 0.81 Accuracy 0.72 Precision 0.22 Precision 0.16 Precision 0.26 F1 0.36 F1 0.27 F1 0.39 Kappa 0.00 Kappa 0.00 Kappa 0.04 0.8

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0 125 250 0 125 250 0 125 250 Signal-to-noise threshold

Figure 3: Classiﬁcation metrics for classiﬁers developed by thresholding 100 m, unconstrained template results. a) Northern California dataset, b) North Coast swath, c) Rodgers Creek Fault swath, d) Green Valley Fault swath, e) Maacama Fault swath, f) Hollister area, southern Calaveras Fault swath. Inverted triangle shows median SNR for swath.

7 Accuracy Precision F1 score Kappa % Negative Median SNR a Maximum b Maximum c Maximum 1.0 Accuracy 0.75 Accuracy 0.70 Accuracy 0.72 Precision 0.23 Precision 0.59 Precision 0.39 F1 0.34 F1 0.52 F1 0.45 Kappa 0.08 Kappa 0.24 Kappa 0.19 0.8

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d Maximum e Maximum f Maximum 1.0 Accuracy 0.77 Accuracy 0.79 Accuracy 0.73 Precision 0.36 Precision 0.19 Precision 0.35 F1 0.39 F1 0.30 F1 0.43 Kappa 0.15 Kappa 0.07 Kappa 0.16 0.8

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0 125 250 0 125 250 0 125 250 Signal-to-noise threshold

Figure 4: Classiﬁcation metrics for classiﬁers developed by thresholding 500 m, unconstrained template results. a) Northern California dataset, b) North Coast swath, c) Rodgers Creek Fault swath, d) Green Valley Fault swath, e) Maacama Fault swath, f) Hollister area, southern Calaveras Fault swath. Inverted triangle shows median SNR for swath.

8 Accuracy Precision F1 score Kappa % Negative Median SNR a Maximum b Maximum c Maximum 1.0 Accuracy 0.81 Accuracy 0.72 Accuracy 0.75 Precision 0.35 Precision 0.67 Precision 0.52 F1 0.35 F1 0.56 F1 0.45 Kappa 0.13 Kappa 0.31 Kappa 0.21 0.8

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d Maximum e Maximum f Maximum 1.0 Accuracy 0.78 Accuracy 0.83 Accuracy 0.76 Precision 0.46 Precision 0.21 Precision 0.44 F1 0.44 F1 0.31 F1 0.46 Kappa 0.24 Kappa 0.10 Kappa 0.22 0.8

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0 125 250 0 125 250 0 125 250 Signal-to-noise threshold

Figure 5: Classiﬁcation metrics for classiﬁers developed by thresholding 1000 m, constrained template results. a) Northern California dataset, b) North Coast swath, c) Rodgers Creek Fault swath, d) Green Valley Fault swath, e) Maacama Fault swath, f) Hollister area, southern Calaveras Fault swath. Inverted triangle shows median SNR for swath.

9 Figure 6: Results of template matching along North Coast segment of the San Andreas Fault. a) Color relief hillshade with Q-faults trace mapping, b) Feature amplitudes, c) Feature morphologic ages, d) Feature orientations, e) Signal-to-noise ratios. Layer transparency is set by signal-to-noise ratio, with all pixels below SNR = 100 fully transparent. Template search constrained to orientations between −60◦ and 0◦. Template window size of 1000 m. SAF: San Andreas Fault, D1, D2: linear drainages, SR: shutter ridge, TS: ﬂuvial terrace scarps.

10 Figure 7: Example of true and false positives deﬁned by masking of trace mapping. a) Annotated hillshade, b) Validation data derived from mapping, c) Signal-to-noise ratio from 1000 m template with validation overlay.

11 Figure 8: Examples of validation data for Green Valley Fault. a) Hillshade, b) Validation data derived from line mapping, c) Validation data derived from point features digitized from Frizzell Jr. and Brown Jr., 1976, c) Signal-to-noise ratio from 1000 m template.

12 C Study areas

The San Andreas fault system defines the western edge of the North America-Pacific plate boundary, spanning over 1000 km. This study presents regional template matching results from the Northern California section of the SAF (Figure 1). The plate boundary in this area is defined by a series of sub-parallel, strike-slip fault zones that take up various portions of the total plate-boundary motion. We performed detailed case studies of five portions of these fault zones (North Coast segment of the SAF, the Maacama Fault, the Rodgers Creek Fault, the Green Valley Fault, and the southern Calaveras Fault) to understand factors that allow for, or obfuscate fault-scarp detection using the template matching approach. These areas were selected to minimize urban modification, while spanning a range of long-term slip rates (104 − 105 years). The North Coast segment of the SAF (NC) spans nearly 200 km between Point Arena and the outlet of the San Francisco Bay. It last ruptured in the 1906 earthquake, with sections experienc- ing up to 5 meters of surface displacement, as documented in Lawson and Reid [1908]. Geodetic estimates indicate a slip rate of about 17.5 mm yr−1 on the northern San Andreas [Freymueller et al., 1999]. Restoration of a buried Holocene channel supports a maximum slip rate of 25.5 mm yr−1 for the NC at Point Arena [Prentice, 1989], and a similar Holocene slip rate estimate of 24 mm yr−1 is reported from trenching across the southern section of the NC near Olema [Niemi and Hall, 1992]. The northern part of NC between Point Arena and Fort Ross is distinguished by a series of northwest-oriented valleys and deflected drainages, including the Gualala and Garcia basins. Brown Jr. and Wolfe [1972] and Koehler et al. [2005] document a series of fault scarps, linear valleys, deflected drainages and a shutter ridge that define the fault zone between Gualala River and Voorhees Grove (Figure 6 and Figure 7). The Maacama Fault (MF) lies to the east of the northern-most NC segment (Figure 1). It displays surface creep, seismicity, and geodetic displacement, and has been mapped in detail near Willits, CA and in the Little Lake Valley area [Prentice et al., 2014]. A ML = 4.8 earthquake occurred on the Willits section of the MF, followed by aftershocks on the MF and its Rocktree Valley strand [Warren et al., 1985]. Together, the NC segment and MF accommodate approximately 45% and 35% of the total plate boundary motion of 39.6 mm yr−1 in this area, with a geodetic slip rate estimate of about 13.9 mm yr−1 for the MF [Freymueller et al., 1999]. Several prominent geomorphic features, including a pressure ridge and abandoned channels in the Willits area were mapped by [Prentice et al., 2014], and a trench study at the Haehl Creek site provides evidence for multiple prehistoric earthquakes in the area [Prentice et al., 2014]. Near Little Lake Valley, Prentice et al. [2014] used the 2009 GeoEarthScope dataset to map a series of lineations, slope breaks, and deflected drainages that define the East Willits Fault (Figure 9). The Rodgers Creek Fault (RCF) lies to the south of the Maacama Fault (Figure 1). It crosses the city of Santa Rosa and forms the southwestern topographic boundary of Sonoma Mountain to the north of San Pablo Bay [Hecker et al., 2016; Watt et al., 2016]. Two magnitude 5.6 and 5.7 earthquakes on the RCF produced significant shaking and building damage in Santa Rosa and the San Francisco Bay Area in 1969 [Cloud et al., 1970; Hecker et al., 2016]. At this latitude, InSAR observations of the Rodgers Creek Fault indicate shallow creep at rates of 3-6 mm yr−1, and theodolite measurements of creep rates along the Green Valley Fault range from 1.0 to 3.5 mm yr−1 [Funning et al., 2007; McFarland et al., 2009]. Slip rates of 6.6 and 7.0 mm yr−1, respectively, have been estimated by block modeling of geodetic data [d’Alessio et al., 2005]. The RCF has been mapped in detail in the Santa Rosa area by Hecker et al. [2016], which delineates a pull-apart basin within a right-stepping bend in the fault from mapping based on the GES dataset, interpretation of prominent anomalies in several geophysical datasets, and geotechnical testing (Figure 10). The Green Valley Fault (GVF) spans the area between Suisun Bay and Lake Berryessa (Figure

13 Figure 9: Results of template matching along the Maacama Fault. a) Annotated hillshade. Red box shows Haehl Creek trench site of Prentice, et al., 2014. b) Signal-to-noise ratios for 100 m template, c) Signal-to-noise ratios for 500 m template. Layer transparency is set by signal-to-noise ratio, with all pixels below SNR = 100 fully transparent. Template search not constrained.

14 Hecker, et al., 2016

PR R

Template window size 100 m WS

Template window size LR 500 m

Figure 10: Results of template matching along the Rodgers Creek Fault. a) Hillshade of Lytton- Geyserville section of swath, b) Signal-to-noise ratios for 100 m template, c) Signal-to-noise ratios for 500 m template, d) Hillshade of Santa Rosa section of swath, Red box shows extent of detailed mapping in Hecker, et al., 2016. e) Signal-to-noise ratios for 100 m template, Labels show major features described in Hecker, et al., 2016, f) Signal-to-noise ratios for 500 m template. Layer transparency is set by signal-to-noise ratio, with all pixels below SNR = 100 fully transparent. Template search not constrained. LD: linear drainage, LR: linear ridge, PR: Pressure ridge, R: fault bounded ridge, WS: West facing escarpment

1). Surface creep rates of 1.0-3.5 mm yr−1 have been measured along the GVF [McFarland et al., 2009], and block modeling of geodetic measurements supports a slip rate of about 7.0 mm yr−1. Several large, surface-rupturing earthquakes have been documented at trench sites on the southern GVF, with the most recent events occurring at times from about 1610 to the present [Lienkaem- per et al., 2013]. Many distinctive fault-related landforms were documented by Frizzell Jr. and Brown Jr. [1976] at the southern end of the GVF, including prominent linear ridges, lineaments, east-facing scarps, and historic oﬀsets near Cordelia and Green Valley (Figure 11). The central section of the GVF is characterized by linear valleys and ridges, and landslide deposits modify the fault zone north of Wooden Valley [Frizzell Jr. and Brown Jr., 1976; Lienkaemper, 2012]. The northern section, referred to as the Berryessa Fault, is charactered by oriented drainages, discontinuous scarps, and linear features between areas of landslide terrain as documented in Lienkaemper [2012]. The southern section of the Calaveras Fault (CF) transects the westernmost Diablo range between San Jose and Hollister (Figure 1). It ruptured in the 1979 M 5.7 Coyote Lake earthquake [Armstrong, 1979], and interseismic creep was observed after the 1984 M 6.2 Morgan Hill earthquake [Hoose, 1987]. Block modeling of geodetic data give estimated slip rate of about 12.7 mm yr−1 for the southern and central CF [d’Alessio et al., 2005]. South of its junction with the Hayward Fault, surface creep rates of 10.2 mm yr−1 have been measured along the southern CF [Lienkaemper et al., 2014]. Numerous small fault scarps, shutter ridges, and extensional features have been mapped along the southern Calaveras Fault between Coyote Lake and Hollister, CA [Radbruch, 1974]. These landforms are visible in topographic data as high slope contrasts with the low-relief basin which hosts the fault in this area (Figure 12).

15 Figure 11: Results of template matching along the Green Valley Fault near Cordelia, CA. a) Color relief hillshade with Q-faults trace mapping, b) Feature amplitudes, c) Feature morphologic ages, d) Feature orientations, e) Signal-to-noise ratios. Layer transparency is set by signal-to-noise ratio, with all pixels below SNR = 100 fully transparent. Template search constrained to orientations between −60◦ and 0◦. Template window size of 1000 m. GVF: Green Valley Fault, GV: Green Valley, CR: curvilinear ridge, R: ridge, S: scarps.

16 Figure 12: Results of template matching along the Calaveras Fault north of Hollister, CA. a) Color relief hillshade with Q-faults trace mapping, b) Feature amplitudes, c) Feature morphologic ages, d) Feature orientations, e) Signal-to-noise ratios. Layer transparency is set by signal-to-noise ratio, with all pixels below SNR = 100 fully transparent. Template search constrained to orientations between −60◦ and 0◦. Template window size of 1000 m. SCF: Southern Calaveras Fault, ES1, ES2: East-facing scarps, DS: Deﬂected stream, SP1, SP2: Sag ponds.

17 D Methods

D.1 Template matching of fault scarps based on linear diffusion Fault scarp expression arises from the fact that dip-slip, oblique-slip, and strike-slip faulting may produce topographic steps by vertical displacement of the ground surface or juxtaposition of high and low topography. Over time, turbation transports mass rapidly in areas of high slope and generally deposits material in low-slope portions of the scarp [Carson and Kirkby, 1972]. Diffusive transport is due to a number of processes including soil creep, soil wash, and rainsplash operating over a range of length- and timescales and transport rates [Kirkby, 1971; Carson and Kirkby, 1972]. The net effect of this activity is to reduce scarp curvatures over time, if no further rejuvenating events revisit the feature. For the case of vertical offset, this process of tectonic sharpening and geomorphic rounding has been well-characterized, leading to the idea that the evolution of a fault scarp profile can be modeled as a step function that decays according to the one-dimensional linear diffusion equation

∂z ∂2z = κ (2) ∂t ∂x2 in which x [L] is distance in the across-scarp direction, z [L] is elevation, t [T] is time since scarp formation, and κ [L2T−1] is a diffusivity constant [Hanks et al., 1984]. This assumes that mass is conserved and the flux of material across the scarp obeys a linear slope-dependent transport law [Culling, 1960, 1963]. The solution to the diffusion equation gives the expected topographic profile of the scarp as a function of time in the form of an error function [Hanks et al., 1984; Hanks, 2000]

x z(x, t) = a erf √ + bx (3) 2 κt where a is the scarp slope, b is the regional slope, and erf denotes the error function. The product κt [L2] is referred to as the morphologic age of the landform, and measures the amount of material transported across the scarp profile since its formation. Solutions to the scarp diffusion equation have been derived for scarps produced by faults of varying initial dip cutting sloped surfaces [Hanks, 2000]. Hilley et al. [2010] derived a curvature template function for a vertical scarp by differentiating Equation 3 twice and normalizing the result. This yields a function describing scarp curvature in the across-profile direction over time

∂2z −ax x2 √ 2 = exp − (4) ∂x template,θ 2κt πκt 4κt where x is the across-profile direction at orientation angle θ. A two-dimensional, windowed template can be formed by duplicating this template function in the out-of-plane direction. The across-scarp length of the template window is determined by the template morphologic age, and the out-of-plane width of the window (referred to as “template window size”) is specified, producing a rectangular template window. The template window is convolved with the directional curvature of the topography with a stride of one pixel. The curvature is calculated by a second-order central finite difference approximation in the orientation direction (Figures 13 and 14). This convolution yields an estimate of scarp amplitude (A, L) at each DEM pixel location, defined as

∂2z A = 2 ∗ W (5) ∂x data,θ

18 Figure 13: a) Map of directional curvature (orientation 0◦) for a synthetic scarp. Scarp is oriented at 0◦ with a morphologic age of 10 m2 and amplitude of 1 m, and noised with Gaussian noise with σn = 0.001 m. Red square shows location of sample pixel. b) Contours of misﬁt for sample pixel as a function of orientation and morphologic age. White star shows maximum signal-to-noise ratio parameters, which coincides with a local minimum of the misﬁt function. Template window size of 10 m.

h ∂2z i where 2 is the directional curvature at orientation θ, W is the normalized version of ∂x data,θ Equation 4, and ∗ denotes convolution. The template misﬁt E is deﬁned as

2 Z ∞ Z ∞ 2 ! 2 1 ∂ z E (x0, y0) = 2 (x, y)M(x − x0, y − y0) − A(x0, y0)W (x − x0, y − y0) n −∞ −∞ ∂x data,θ (6) where x0, y0 are the coordinates of the window center and M is a binary indicator function that takes a value of 1 at points where the template curvature W is nonzero, and n is the number of nonzero points. The discrete version of Equation 6 is used to calculate the misfit at each pixel. Misfit contours are shown in Figures 13 and 14. The ratio of squared amplitude to the `2 norm of the template misfit (E) defines the signal-to- noise ratio (SNR) at each pixel

A2 SNR(x0, y0) = 2 (7) E(x0, y0) For a fixed template window size, best-fit template parameters are determined by a forward search over the template morphologic ages and the orientations which retains the parameters that maximize SNR. The final output of this algorithm is a set of co-registered grids of best-fit amplitude, morphologic age, orientation, and the corresponding signal-to-noise ratios at each pixel. The reader is referred to Hilley et al. [2010] and Sare and Hilley [2018] for full details of this method and an open-source implementation. Many topographic edges are detected by the scarp template. These include true positive detections of fault scarps, other scarp-like landforms, or larger-scale landforms such as rangefront

19 Figure 14: a) Map of directional curvature (orientation 0◦) for the Wallace Creek site. Red square shows location of sample pixel. Contours of b) misfit and c) signal-to-noise ratio for pixel as a function of orientation and morphologic age. White star shows maximum signal-to-noise ratio parameters, which does not correspond to a minimum of the misfit function. Template window size of 10 m. escarpments, fault-parallel ridges, and linear valleys, as well as false positives such as channel banks or roads. While tectonic landforms such as fault-parallel ridges are not direct evidence of past earthquake surface rupture or aseismic motion, and cannot be morphologically dated, elongated or fault-parallel landforms are often used as indirect evidence of fault zone location and kinematics [e.g., Lawson and Reid, 1908; DeLong et al., 2010]. Detection of tectonic landforms other than scarps offers useful information about the prevalence, orientations, and length scales of these non-scarp features.

D.2 Distributed implementation For this work, the template matching algorithm is implemented using a task-based model similar to the popular MapReduce framework for distributed computing [Dean and Ghemawat, 2008; Kr- ishnan et al., 2010]. In this framework, worker nodes receive tasks for matching a template defined by orientation (θ) and morphologic age (κt) to the input data (Figure 17). The worker nodes syn- chronously process tasks and save intermediate results as grids of template amplitude, morphologic age, orientation, and SNR. As intermediate results are emitted, reducer nodes compare template fits and save the best-fitting template parameters. Performance benchmarks are presented in Figure 15 and Table D.2. All benchmark tests search over template orientations θ between −90◦ and 90◦ with a spacing of 1◦, and morphologic ages κt with logarithmically spaced points with log10(κt) between 0 and 3.5 with a spacing of 0.1. The processing time for the main dataset used in this study (Section 2) was approximately 25 hours using a 100 m window size. The serial implementation was benchmarked on a single user session on one node of a high- performance computer cluster with two 2.26 GHz processors (Intel Nehalem) with four cores and 24 GB RAM under MATLAB R2013a. The distributed Python implementation was run and benchmarked using Amazon Elastic Compute Cloud (EC2) services. Each node was deployed on an EC2 virtual machine, or instance, with 35 c4.xlarge instances deployed as worker nodes and a single t2.medium instance acting as a reducer node. The c4.xlarge instance class provides the equivalent of a dedicated 2.9 GHz processor with four cores (Intel Xeon E5-2666 v3) and 7.5 GB RAM. The

20 x 106

Figure 15: Performance of distributed template matching algorithm (dashed line) compared to serial implementation in Hilley, et al., 2010 (solid line). Test case results given in Table S1. t2.medium instance class provides the equivalent of a dual-core 3.3 GHz processor (Intel Xeon) for periodic use (referred to as a “burstable” CPU) and 4 GB RAM. Data was re-gridded at 2 m resolution for template matching. Each tile was pre-processed by padding the boundaries of the tile with a width of twice the out-of-plane window size of the template. Outside of swath boundaries, no data areas were filled by local interpolation using inverse distance weighted interpolation with a search radius of 100 pixels. Template matching results were post-processed to remove major sources of false detections in urban areas, such as roads and building footprints, and edge effects due to data gaps outside ALSM swath boundaries. For the classifier analysis (Section 5), built-up urban areas were removed by masking out urban area footprints provided in the California Adjusted Urban Areas boundary dataset (http://dot.ca.gov/hq/tsip/hseb/urban.html). A map of this data mask is shown in Figure 16. Fault zones such as the Hayward Fault, the northern Calaveras Fault, and parts of the Calaveras Fault (CF) are excluded by this mask (Figure 1). No urban masking is applied for the detailed validation cases (Section 6), as the North Coast segment does not intersect any major urban areas and there is significant fault zone expression in the Cordelia-Green Valley urban corridor that would be excluded by masking. Maps for individual fault zones do not include urban masking. Interpolation of swath edges in no data areas outside of swath boundaries produces vertical and horizontal edge effects. Topographic steps resulting from interpolation of swath edge pixels are detected as discrete features with high SNR and low morphologic age with widths of one pixel and lengths proportional to the out-of-plane window size of the template. These artifacts were removed by masking out all features within one degree of vertical or horizontal orientation (θ = 0◦ or θ = 90◦) and re-interpolating the results using an inverse distance weighted interpolation algorithm (Figure 18).

21 Figure 16: Location map of EarthScope Northern California lidar swath boundaries (red) and Northern California urban areas (grey).

22 Figure 17: Diagram of distributed template matching algorithm.

23 Implementation Test case Grid dimensions (pixels) Time (s) Serial Synthetic 100 × 100 36 Synthetic 500 × 500 515 Carrizo Plain 505 × 4169 5269 NC ES DEM tile 2000 × 2000 7436 Distributed Synthetic 100 × 100 22 Synthetic 500 × 500 13 NC ES DEM tile 2000 × 2000 624

Table 1: Performance benchmarks for template matching algorithm implementations. Times are running times measured for a single test. The distributed implementation does not include ini- tialization time for the matcher and reducer nodes. “Carrizo Plain” benchmark data is from the B4 Project lidar dataset, downloaded from OpenTopography (www.opentopography.org) at 2 m resolution. “NC ES DEM tile” test case refers to a single DEM tile from the Northern California EarthScope lidar dataset, 1 × 1 km at 0.5 m resolution.

Figure 18: Examples of swath edge artifacts in template matching results. a) Tile showing artifacts near swath boundary before post-processing. Box shows 1 km2 tile extent. b) Results after post- processing described in text. Red colormap indicates signal-to-noise ratio of detected features.

24 E Pixel-based landform classiﬁcation

E.1 Defining and evaluating landform classifiers Binary classification schemes can be constructed from scores or probabilities by applying a threshold for accepting a feature as belonging to a particular class [Fawcett, 2006]. The template matching algorithm can be used to define an unsupervised binary classifier for scarp-like landforms by applying a threshold to one or more template parameters, such as the signal-to-noise ratio and accepting or rejecting pixels that fall above or below the threshold (Figure 7). For consistency, this SNR threshold is defined for each fault zone as the median SNR observed in that fault zone, which varies from 30.04 to 89.62 (Table 1). Given a fault map, the true positive (TP) rate and false positive (FP) rate of a classifier are defined as

Number of tectonic pixels classiﬁed as positive TP TP rate = = (8) Total number of tectonic pixels P and

Number of non-tectonic pixels classified as positive FP FP rate = = (9) Total number of non-tectonic pixels N In this case, “tectonic pixels” refers to pixels in areas mapped as faults, and “non-tectonic pixels” refers to pixels not in areas mapped as faults or fault zones (Figure 7). The true and false negative rates (TNR and FNR) are defined in a similar way. Buffered fault zone trace mapping is used to provide pixel labels, and this dataset is discussed in Section B.2. Many metrics are used to assess the performance of a classifier, including accuracy and classification error [Hastie et al., 2009]. The accuracy of a binary classifier is defined as

TP + TN Accuracy = (10) P + N where TN is the number of pixels correctly classified in the negative category, that is, not within the mapped a fault zone. Accuracy varies from 0 to 1, with 1 denoting that all labeled pixels have been correctly classified. For classifier evaluation, accuracy is often discussed with context from other metrics, such as classifier precision or Cohen’s kappa [Fawcett, 2006]. These metrics compare the ability of a classifier to correctly identify relevant features with its false positive detection rate. Precision is defined as

TP Precision = (11) TP + FP Precision varies from 0 to 1, where 1 indicates that all positive classifications are correct. However, these metrics can be affected by class imbalances, which can lead to uninformative classifiers with high accuracy or precision that place all pixels in a single class [Fawcett, 2006; Hastie et al., 2009]. For the case study swaths, as many as 85% of the swath pixels are not mapped and up to 31% are mapped as fault zone pixels in the buffered Q-faults database (Table 1). Cohen’s kappa is a classification metric that accounts for the expected accuracy of a classifier by chance [Cohen, 1960]. It is defined as

Accuracy − Accuracy κ = Ex (12) 1 − AccuracyEx

25 Accuracy Precision Kappa % Negative Median SNR a b c 1.0

0.5

0 125 250 0 125 250 0 125 250 Signal-to-noise threshold

Figure 19: Classiﬁcation metrics for North Coast swath using a) 100 m, unconstrained, b) 500 m, unconstrained, and c) 1000 m, constrained template results. Horizontal line shows the proportion of negative (non-tectonic) pixels in the North Coast Quaternary faults dataset, which represents the maximum accuracy of a classiﬁer that places every pixel in the negative class. Inverted triangle shows the median signal-to-noise ratio in the swath (Table 3).

where Accuracy is the accuracy (Equation 10), and AccuracyEx is the expected accuracy. The expected accuracy is the accuracy expected if the classiﬁer agrees with the correct labels by chance, deﬁned as

P TP + FP N TN + FN Accuracy = + , (13) Ex P + N P + N P + N P + N in which each term is the product of the proportion of pixels labelled as a particular class, and the proportion of pixels receiving that classification. Expected accuracy and Cohen’s kappa can be defined using a ground-truth labelling and a set of classifier results, as they are in this work, or using results from two classifiers. Cohen’s kappa varies from -1 to 1, where 1 indicates that the correct labels and classifier agree exactly, 0 indicates that the expected accuracy has been achieved, and -1 indicates that the classifier performs worse than the expected accuracy [Cohen, 1960]. Precision, Cohen’s kappa, and AUC values are provided for each test case in Table 1. Changes in these metrics with SNR threshold are shown in Figure 19 and Figures 3–5). Finally, receiver operating characteristic (ROC) curves, or plots of TP rate and FP rate for varying threshold values, are used to assess the performance of a set of classifiers [Fawcett, 2006; Hastie et al., 2009]. Classifiers that plot along a one-to-one line identify true and false positives in equal proportions, and classifiers above this line identify true positives at a higher rate (Figure 20a). The performance of a classification method can be measured by the area under the ROC curve

26 a b

Figure 20: Receiver operating characteristics curves. a) Schematic ROC curve showing area under the curve (AUC) metric for uninformative classifier, b) ROC curves for North Coast swath. Each point corresponds to the true positive rate and false positive rate for a pixel classifier using a single SNR cutoff. NC: Not constrained, C: constrained. Numbers refer to template window sizes.

(AUC), which ranges from 0 to 1, with AUC = 0.5 describing an essentially random classifier and AUC = 1 an optimal classifier [Fawcett, 2006]. ROC curves produced from classification of the North Coast swath and other fault zones are shown in Figure 20 and Figure 2. For validation of the method’s spatial performance, both regional and detailed fault zone mapping were used to provide comprehensive active fault trace mapping of the North Coast segment of the SAF and Green Valley fault zone (Section B.2). Landform-scale validation data were created by buffering the point and line features documented in each study with a 20 m circular buffer. The resulting feature masks were used to extract template parameters within the buffered neighborhood of each set of features (Figures 7 and 8).

F Results

F.1 Validation at Wallace Creek section of San Andreas Fault We attempted to validate the template-matching algorithm in an area where forward modelling of the upper crest of scarp profiles constrains the morphologic age of a series of scarps with systematically varying morphologic ages [Arrowsmith et al., 1998]. The previous work was performed within the northern portion of the Carrizo Plain, CA, south of Wallace Creek, where the progressive uplift and offset of a fan surface has created a scarp that displays systematically lower curvatures with distance southeast of Wallace Creek. Two template window sizes were tested: 10 m window size was selected to capture approximately the same features as the swath profile data analyzed by Arrowsmith et al. [1998], and a 100 m window size for comparison to results from this study. The template orientation was constrained to within 15◦ of the fault zone orientation to avoid bias from curved channel banks. The distribution of best-fitting morphologic ages and amplitudes from the template method and Arrowsmith et al. [1998] are plotted in Figure 21 and maps of the scarp locations are given in

27 a Scarps Maximum SNR

Figure 21: Comparison of morphologic ages at Wallace Creek, CA using template window size of 100 m. a) Map with approximate location of profiles used in Arrowsmith et al. [1998]. Red points show location of maximum signal-to-noise ratio detected by template. b) Along-strike distribution of best-fitting morphologic ages (red points) and 90th and 10th percentiles of ages at that location (shaded area). Morphologic ages and 1σ uncertainty determined by Arrowsmith et al. [1998] shown with black squares. y-axis in logarithmic scale. c) Along-strike distribution of best-fitting scarp amplitudes (red points) and 90th and 10th percentiles of amplitudes at that location (shaded area). Vertical offsets determined by Arrowsmith et al. [1998] shown with black squares. Reported uncertainties are smaller than symbol sizes where error bars are not visible.

Figure 21a and Figure 4 of Arrowsmith et al. [1998]. In general, the morphologic ages determined by the template approximately increase from scarp A to scarp I, as reported by Arrowsmith et al. [1998], but the template ages are lower than the profile ages by an order of magnitude. The best- fitting amplitude estimates of the 100 m template are within 1-2 m of the vertical offsets reported by Arrowsmith et al. [1998]. Decreasing the template window size to 10 m increases the variability of along-strike distributions of both parameters, but the relative differences between the field and template ages are similar (Table 2).

F.2 Features detected in major fault zones of Northern California The template matching algorithm was applied to the GES dataset at template window sizes of 100 m and 500 m with a search over all template orientations from -90◦ to 90◦. To assess the impact of fault zone orientation, two areas were processed with a constrained search with orientations between -60◦ to 0◦, representing deviations of 30◦ from the average swath and fault zone orientation. These sites, NC and GVF, were processed using template window sizes of 100 m and 500 m with unconstrained and constrained searches and 1000 m with a constrained search. The full GES dataset was also

28 Arrowsmith, Template (10 m) Template (100 m) et al., 1998 Scarp κt [m2] ∆κt Minimum RMSE [m] Amplitude [m] κt [m2] Misﬁt E [m] Amplitude [m] κt [m2] Amplitude [m] Misﬁt E [m] A 179.00 25.00 7.50 0.11 21.00 8.06 0.87 31.00 7.72 0.54 B 151.00 24.00 7.40 0.14 31.00 13.12 1.12 21.00 6.90 0.31 C 325.00 97.00 6.40 0.33 11.00 4.95 0.58 21.00 5.46 0.29 D 115.00 34.00 3.80 0.17 61.00 8.67 0.93 21.00 3.98 0.24 29 E 152.00 50.00 2.80 0.17 91.00 8.96 1.05 31.00 3.07 0.21 F 353.00 123.00 3.40 0.23 1.00 0.13 0.02 51.00 3.19 0.25 G 530.00 159.00 4.10 0.28 61.00 5.27 0.69 61.00 4.45 0.29 H 553.00 285.00 4.80 0.23 91.00 8.97 1.05 61.00 5.62 0.27 I 592.00 212.00 4.50 0.18 61.00 7.73 0.75 71.00 5.30 0.31

Table 2: Morphologic ages and amplitudes measured by 10 m and 100 m templates.“∆κt” refers to the maximum error reported by Arrowsmith, et al., 1998. processed with a constrained search using a 1000 m template to assess performance on larger-scale topographic features. All sites are covered by mapping included in the Q-faults database, and classification metrics were computed using Q-faults validation data and a median SNR threshold at each site (Table 1). Changes in classification metrics with increasing SNR threshold are shown in Figure 19 and Figures 3–5. The sites are presented as three groups with similar maximum Cohen’s kappa values reflecting moderate (≥ 0.2), fair (≥ 0.18), and poor (0.1) performance. Maximum TP rate varied from 0.73 (NC) to 0.66 (MF) with corresponding FP rate of 0.44 and 0.47. Classification accuracy for the full dataset ranged from 0.48 to 0.51, with corresponding precisions of 0.22 and 0.23. The minimum Cohen’s kappa values were -0.01 (full GES dataset) and -0.02 (MF), and the maximum was 0.29 (NC). Maximum kappa values of 0.2 or above were observed for NC and SCF. AUC values are reported in Table 1; classification of the NC and SCF results gave the highest AUC values (0.72), and NC, GVF, and SCF show increasing AUC with increasing template window size and orientation constraints. In these cases, the improvements in AUC between 100 and 500 m are greater than those between the 500 m and 1000 m cases, which suggests that classification performance will peak at an optimal intermediate window size instead of increasing monotonically (Figure 2). RCF and MF have lower maximum AUC values (0.61 and 0.67) and show small or no changes in AUC for a constrained search (Figure 2).

F.2.1 Sites with Cohen’s kappa ≥ 0.20 North Coast segment, San Andreas Fault Classification results in the NC area change as template constraints are varied. Accuracy values for classifiers applied to the NC swath increase from 0.51 using an unconstrained template with window size of 100 m to 0.71 using a constrained template search with window size of 500 m (Table 1). The maximum TPR of 0.73 (FPR 0.40) is achieved using a constrained template search with window size of 1000 m. Higher true positive rates are observed for template configurations with relatively large window sizes and orientation constraints, which is reflected in an increase in Cohen’s kappa from 0.01 to 0.29, and AUC values from 0.51 to 0.72. Quaternary fault mapping in this area is focused on landforms in the central valley of the NC segment. Sub-parallel scarps, oriented channels, and elongated valleys aligned with the trend of the primary fault valley are mapped as predominately well-constrained and moderately constrained features. Where alluvial material obscures fault scarps, the Quaternary fault database includes inferred, lower confidence trace mapping. The highest SNR template results are broadly consistent with the major features mapped along the valley axis and off-axis elongated valleys (Figure 6 and 22). Detailed geomorphic mapping is also available for the NC segment. Many features mapped by Koehler et al. [2005] are resolved by the fault scarp template at 100 m, 500 m, and 1000 m window sizes. For example, scarps hosted in fluvial terraces (TS in Figure 6) are identified as morphologically young features with high signal-to-noise ratios. These are among the highest confidence mapped features reported by Koehler et al. [2005] in that area. Similarly, the prominent elongated drainages that bound the large shutter ridge mapped by Brown Jr. and Wolfe [1972] and Koehler et al. [2005] (D1, D2, and SR in Figure 6) and the topographic lineaments and scarps to the north of Log Cabin Creek (Figure 7) are identified with high signal-to-noise ratios. Hollister area, Southern Calaveras Fault The Hollister area contains obvious, mapped fault scarps, but suffers from many false positive agricultural features. The maximum TPR of 0.71 (FPR 0.43) is achieved with a constrained

30 Figure 22: Examples of fault trace mapping referenced in text. a) North Coast section of SAF, mapping from Quaternary faults and folds database with major landforms identiﬁed by Koehler, et al., 2005 indicated by leaderlines. b) Shutter ridge SR in Figure 1, c) Example of valley-bounding escarpment and linear valley south of linear drainage D2 (Figure 1), d) Gualala-Garcia river junction containing terrace scarps TS (Figure 1). Map data by Google, provided as shaded relief based on Shuttle Radar Topography Mission dataset.

31 Proportion Proportion Test case Conﬁguration Median SNR TPR FPR TNR FNR Accuracy Precision Kappa AUC Positive Negative GES 100 m, NC 0.18 0.82 74.72 0.48 0.50 0.50 0.52 0.50 0.18 -0.01 0.49 500 m, NC 89.62 0.70 0.56 0.44 0.30 0.48 0.22 0.07 0.58 1000 m, C 53.72 0.72 0.54 0.46 0.28 0.51 0.23 0.10 0.63 NC 100 m, NC 0.31 0.69 65.32 0.51 0.50 0.50 0.49 0.51 0.31 0.01 0.51 500 m, NC 86.14 0.68 0.42 0.58 0.32 0.61 0.42 0.22 0.68 100 m, C 39.42 0.61 0.45 0.55 0.39 0.57 0.38 0.14 0.62 500 m, C 57.23 0.70 0.41 0.59 0.30 0.62 0.43 0.25 0.70 1000 m, C 61.45 0.73 0.40 0.60 0.27 0.64 0.45 0.29 0.72 GVF 100 m, NC 0.22 0.78 55.47 0.52 0.50 0.50 0.48 0.51 0.21 0.01 0.49 500 m, NC 80.59 0.65 0.46 0.54 0.35 0.56 0.26 0.12 0.62 100 m, C 30.04 0.58 0.48 0.52 0.42 0.53 0.25 0.07 0.57 500 m, C 48.26 0.67 0.45 0.55 0.33 0.57 0.29 0.15 0.65

32 1000 m, C 52.66 0.72 0.44 0.56 0.28 0.59 0.31 0.19 0.68 MF 100 m, NC 0.15 0.85 65.14 0.46 0.51 0.49 0.54 0.49 0.13 -0.02 0.43 500 m, NC 87.44 0.63 0.48 0.52 0.37 0.54 0.18 0.07 0.59 1000 m, C 66.45 0.66 0.47 0.53 0.34 0.55 0.20 0.10 0.61 RCF 100 m, NC 0.25 0.75 34.84 0.60 0.47 0.53 0.40 0.54 0.26 0.09 0.50 500 m, NC 46.50 0.63 0.46 0.54 0.37 0.56 0.27 0.11 0.67 1000 m, C 76.03 0.68 0.44 0.56 0.32 0.59 0.34 0.18 0.67 SCF 100 m, NC 0.24 0.76 42.80 0.58 0.48 0.52 0.42 0.53 0.25 0.07 0.50 500 m, NC 64.59 0.65 0.46 0.54 0.35 0.56 0.28 0.13 0.65 1000 m, C 65.91 0.71 0.43 0.57 0.29 0.60 0.34 0.20 0.72

Table 3: Classification metrics for binary classifiers applied to Northern California fault zones. GES: GeoEarthScope dataset, test case abbreviations as in Figure 1. SNR threshold is median SNR; pixels above median SNR are designated as positive “fault zone” classifications, negative otherwise. “Proportion Positive” and “Proportion Negative” refer to the proportion of positive (tectonic) and negative pixels in the Quaternary faults validation dataset. C: constrained test case, NC: test case with no orientation constraints. SNR: signal-to-noise ratio, TPR: true positive rate, FPR: false positive rate, TNR: true negative rate, FNR: false negative rate, AUC: Area under ROC curve. template search using 1000 m window size (Table 3). Increasing template window size increases Cohen’s kappa by a factor of nearly two, from 0.07 (100 m template) to 0.13 (500 m template). The maximum kappa of 0.20 was observed in the 100 m, constrained results. Accuracies for the Hollis- ter area range from 0.51 (100 m template, unconstrained) to 0.60 (1000 m template, constrained). The trends in AUC values for the SCF are similar to the NC and GVF swaths, with a minimum AUC of 0.50 for the 100 m, unconstrained template configuration, and a maximum of 0.72 for the constrained, 1000 m template. The Q-faults database in this area largely reflects the mapping of Radbruch [1974] and subsequent work. The highest SNR features in this area are located in a zone of distributed faulting northwest of Tequisquita Slough, including successful detection of a large sag pond (SP1) and a deflected drainage (DS), all landforms mapped by Radbruch [1974] (Figure 12). In low relief areas, several small, east-facing scarps near the center of the swath are not detected (ES1 and ES2, Figure 12). North of Hollister, sag ponds and the slough coincide with slightly higher relief sections of the fault zone, resulting in higher SNR detections in this area (SP2, Figure 12). A network of rural roads and agricultural channels is the primary source of false positive detections in the area that appear as high SNR, morphologically young features off the main fault zone trace.

F.2.2 Sites with Cohen’s kappa 0.18–0.19 Green Valley Fault Like the North Coast segment, GVF scarp pixel classification performance improves as window size increases and search constraints are added (Table 1). The maximum TPR of 0.72 (FPR 0.44) is obtained with a constrained template search using a 1000 m window size. Adding constraints increased Cohen’s kappa by 0.06 in the 100 m case, and 0.03 in the 500 m case. The highest kappa value, 0.19, was achieved using the 1000 m, constrained template. A minimum accuracy of 0.46 was achieved using the unconstrained, 500 m template. A maximum accuracy of 0.73 was achieved using the same window size but with swath constraints. The AUC values range from a minimum of 0.49 for the 100 m, unconstrained case and a maximum of 0.68 for the 1000 m, constrained case. The Q-faults database incorporates mapping from Frizzell Jr. and Brown Jr. [1976] and is consistent with Lienkaemper [2012] north of Green Valley. Fault expression was clearly resolved by the template in the southern and central sections of the fault zone, particularly along escarpments south of Cordelia (S) and linear valleys north of the town of Green Valley (GV, Figure 11). Land- forms such as scarps (S), a large linear ridge (R), and a curvilinear ridge (CR, Figure 11) mapped by Frizzell Jr. and Brown Jr. [1976] were detected with relatively high SNR at template window sizes of 100 m, 500 m, and 1000 m (Figure 11 and 23). Rodgers Creek Fault Performance along the RCF swath is mixed, with significant true positive detections south of Santa Rosa, and along the range front between Santa Rosa and Lytton, and generally poor performance in Santa Rosa and the south flank of Sonoma Mountain (Figure 10). This is reflected in a minimum accuracy of 0.50 in the unconstrained, 100 m template case. Performance improves to an accuracy of 0.60 at 500 m template window size; several topographic lineaments are detected at this scale but not using a 100 m template (Table 1). Cohen’s kappa for the RCF varies by a factor of two from 0.09 (100 m) to 0.18 (1000 m, constrained). The maximum TPR of 0.70 (FPR 0.43) is obtained with an unconstrained template search using a window size of 500 m. Increasing the template window size to 1000 m and applying orientation constraints decreases both TPR and accuracy, to 0.68 and 0.59, respectively. The AUC values are equal for the 500 m and 1000 m constrained template configurations, which yield constants AUCs of 0.67, unlike other test cases for which AUC increases with increasing window size.

33 Figure 23: Distributions of signal-to-noise ratio for geomorphic features mapped by Frizzell, Jr. and Brown, Jr, 1976 in Green Valley fault zone. Horizontal lines indicate minimum, median, and maximum SNR for each feature type. “Line” category includes all mapped features designated as linear, such as linear valleys, topographic lineaments, or tonal lineaments. “Not mapped” category aggregates all pixels in GVF swath not captured by digitized point features. Template window size of 1000 m.

34 Q-faults mapping of the RCF identifies the active trace of the fault zone along the southwestern front of Sonoma Mountain. It is mapped as a well-constrained to moderately-constrained feature through Taylor Mountain and the Santa Rosa area, and its trace is almost entirely well constrained as it follows the range front and ridgelines from Santa Rosa to Lytton [USGS, 2006]. Virtually none of the fault scarps identified in Hecker et al. [2016] were detected by the fault scarp template, which primarily detected roads and building footprints in the city of Santa Rosa (Figure 10). In particular, a significant west-facing scarp and two ridges are mapped at the scale of the template (PR, R, and WS, Figure 10), but these landforms cross channel banks and urban features that disrupt their continuity (see Figures 5 and 7 of Hecker et al. [2016]). Large ridges and linear features outside of the Santa Rosa and Healdsburg areas were identified with high SNR, including a ridge-bounding lineament on Taylor Mountain south of the study area of Hecker et al. [2016] (LD) and a prominent linear ridge near Lytton Creek north of Healdsburg (LR, Figure 10). Few features were detected along the relatively seismically quiescent segment of the RCF south of Sonoma Mountain, where rough topography obscures fault expression [Budding et al., 1991] (Figure 10).

F.2.3 Site with Cohen’s kappa of 0.10 Willits area, Maacama Fault The Maacama Fault contains shutter ridges, deflected drainages, and oriented slope breaks along its northern section near Willits (Figure 9), as well as rugged, complex terrain to the south and at its northern terminus in the Mendocino Highlands. The maximum TPR of 0.66 (FPR 0.47) is obtained with constrained template search using a 1000 m window size. Notably, the Cohen’s kappa values for the MF, -0.02, 0.07, and 0.10, were the most similar to the range in Cohen’s kappa determined from the full GES dataset (-0.01 to 0.10). Accuracies for the MF range from 0.47 (100 m, unconstrained) to 0.55 (1000 m, constrained). There is only moderate improvement in classification performance as measured by AUC, with minimum and maximum AUC values of 0.43 and 0.61 for the MF swath for the 100 m and 1000 m, constrained configurations, respectively. Regional-scale Quaternary mapping of the Maacama Fault is restricted to the western strand of the fault zone; the East Willits section proposed in Prentice et al. [2014] is not included in the Quaternary faults and folds database. The mapped fault zone follows a series of oriented ridges, slope breaks, and a shutter ridge in the Willits area (Figure 9). Few tectonic features along the Maacama Fault were identified at any template window size, including slope breaks mapped by Prentice et al. [2014] along the East Willits Fault near Berry Canyon (Figure 9). Many of these landforms are curvilinear and modified by channels that drain nearby high topography, complicating their detection by a linear scarp template. The most significant detections at these sites include slope breaks and an isolated ridge south of Berry Canyon, which was detected with high SNR at both 100 m and 500 m template window sizes, and a northwest-trending topographic lineation north of Willits, which was detected with high SNR using a 500 m template (Figure 9). The small pressure ridge north of the Prentice et al. [2014] trench site was detected with a relatively low SNR of about 100 at both template window sizes (Figure 9, and Figure 4 of Prentice et al. [2014]), and few fault-related features were detected in the town of Willits. At both template window sizes, urban features such as roads, building footprints, and U.S. Highway 101 were detected as false positives in the Willits area.

F.3 Relationship with fault activity and slip rate The Quaternary faults and folds database includes four non-exclusive categories for time of most recent fault activity and provides slip rate estimates for faults in three categories between less

35 Figure 24: Normalized histograms of template amplitudes (a, b) and morphologic ages (c, d) for mapped features of diﬀerent slip rates. a) and c) show 100 m template results, b) and d) show 500 m template results. Results from features detected in full Northern California dataset. SNR threshold of 100. Amplitude threshold of 0.1 m. than 1 mm yr−1 and over 5 mm yr−1. Distributions of template parameters as a function of these categories are shown in Figures 24 and 25. Small diﬀerences in the mean amplitude for the high (over 5 mm yr−1 and 1-5 mm yr−1) and low (0.2-1.0 mm yr−1) slip rate categories are observed in the results from 500 m template window size, but otherwise the amplitude and morphologic age distributions for all mapped categories are similar.

G Discussion

These findings indicate that fault zones can be mapped using a scarp template with reasonable confidence in areas of high degrees of fault zone expression and limited modification by channels or other human-induced land surface changes. Testing shows that there is a trade off between the effective range of morphologic ages estimated by this method and the spatial accuracy of detected features, and that template age estimates fall below geomorphic estimates. In most cases, classifier performance is better at window sizes of 500 and 1000 m, as can be seen from the development of distinct maxima in Cohen’s kappa values for the North Coast swath (Figure 19) and all other cases except the Maacama fault (Figures 3–5). The optimal window size for classification purposes is likely to be an intermediate window size that captures the dominant length scales in a fault zone

36 a b

c d

Figure 25: Normalized histograms of template amplitudes (a, b) and morphologic ages (c, d) for mapped features with diﬀerent timing of most recent fault activity. a) and c) show 100 m template results, b) and d) show 500 m template results. Results from features detected in full Northern California dataset. SNR threshold of 100. Amplitude threshold of 0.1 m.

37 determined by tectonic activity, fault zone maturity, and host landscape characteristics such as maximum hillslope and channel lengths.

G.1 Comparison to field-based morphologic dating Arrowsmith et al. [1998] fit a version of Equation 3 to individual scarp profiles using elevation data from a 0.3 m contour map of the Wallace Creek area using only the upper crest and slope of the scarp. A constant elevation boundary condition was imposed on the upper boundary of the scarp profile and a constant lowering rate was prescribed at the lower profile boundary [Arrowsmith et al., 1998]. The best-fitting morphologic age was determined by choosing the value of κtˆ that resulted in the lowest root-mean square error between the predicted elevation profile and actual upper scarp profile. By contrast, the morphologic age estimated by the curvature template represents the diffusion age determined by fitting a single-offset curvature template to the topographic curvature in a rectangular window around the scarp. Morphologic ages determined with a large window represent an along-strike average age (Figure 21), whereas using a smaller template window size of 10 m captures along-strike variability, for example, where channels reduce scarp curvature (Figure 26). Nevertheless, the template age is sensitive to along-scarp variability in scarp curvature within this swath, unlike an age determined from a single profile. Constraining template orientation may alleviate this effect in some cases, where scarp-perpendicular channel banks are fit with higher SNR than scarps, but a constrained template will still be influenced by curvature variability due to modification of the scarp itself. The minimum misfit of each method at the scarp locations reflect this difference (Table 2). The misfits of the 10 m template are generally larger than the minimum RMSEs reported by Arrowsmith et al. [1998] for each scarp in all cases except scarp F (0.02 m and 0.13 m). The misfits of the 100 m template are lower than the 10 m estimates, but they exceed the profile-based misfits in all cases except scarp C (0.29 m and 0.33 m). This trend is consistent with the fact that the curvature template is fit to the full scarp form, leading to higher misfits for asymmetric scarp profiles like those at the Wallace Creek site.

G.2 Evaluating semi-automated fault zone mapping When it is used to locate a potential fault zone within a lidar swath, the template matching method performs reasonably well in fault zones with clear topographic expression, such as the NC and GVF sites. This is reflected in the magnitude and trends in kappa and AUC values for these areas when compared to baseline performance over the GES dataset. (Table 1). When distinguishing individual mapped landforms, the curvature template appears to identify many mapped features with higher signal-to-noise ratio than non-tectonic areas (Figure 23), but discontinuous or smaller-scale features may go undetected. Landforms mapped at a smaller scales, such as the topographic benches and fault scarps of Frizzell Jr. and Brown Jr. [1976], are difficult to identify in the topographic data. They also exhibit a large range of signal-to-noise ratios (11 to 453), and have median SNRs comparable to those of non-tectonic pixels (Figure 23). Alternatively, the high median SNRs of mapped features such as trenches and depressions could be a consequence of these landforms being hosted in or near detectable landforms, such as ridges and valleys. This is consistent with the high median SNRs of the largest mapped features. Detection failures can be divided into three categories: 1. failure due to lack of topographic fault expression, 2. failure due to modification of fault-related landforms, and 3. failure due to faulting of complex pre-existing topography. The success of the template along the North Coast segment and the southern Green Valley Fault is partly attributable to high levels of fault-related landform

38 a b

c d

Figure 26: Normalized histograms of template amplitudes and morphologic ages for individual fault zone test cases. a) Amplitude, 100 m template, b) Amplitude, 500 m template, c) Morphologic age, 100 m template, d) Morphologic age, 500 m template. Dashed lines indicate fault zones with documented creep. SNR threshold of 100, and features with amplitude ¡ 0.1 m are excluded. NC: North Coast segment, GVF: Green Valley Fault, SCF: Southern Calaveras Fault, SB: San Benito segment of SAF, LP: Loma Prieta segment of SAF, MF: Maacama Fault.

39 expression and preservation in these areas. In the North Coast case, fault scarps are established in fluvial terraces, and these and other valley-bounding scarps and slope breaks are oriented with the dominant northwest-southeast direction of sediment transport in the Gualala river system. These features are consistently detected by the scarp template (TS, Figure 6 and Figure 8). By contrast, notable detection failures in this swath coincide with unfaulted terrace cover, for example, the fault trace near Elk Prairie, where Koehler et al. [2005] describe a poorly located fault trace covered by terrace sedimentation and flood deposits where the North Fork of the Gualala River drains into the Gualala River valley (Figure 8). The major sources of false positive detections vary between faults zones. All of the case studies shown here include channel banks or terrace risers detected as false positives and some include agricultural roads and canals that are detected as high SNR features. Many of these features could be excluded by postprocessing with channel network or infrastructure maps. Fault-related slope breaks in low relief areas are typically detected as high SNR features at the center of the break in slope, but high SNR values appear on either side of most of these features. This is due to low misfits with a nonzero template function at high curvature points near the upper and lower edges of the scarp-like landform. Localization of these features could be improved by applying non-maximum suppression or other common filtering operations as post-processing steps.

G.3 Factors affecting template misfit Smaller-scale features, such as slope breaks on the scarp face, often represent the highest SNR features in the neighborhood of a larger scarp. In these cases, morphologic ages estimated by the template are biased towards low values because higher curvature subsidiary slope breaks are identified with low misfit by the template search. These secondary features appear as morphologically young local detections within areas of elevated SNR and morphologic age around the full scarp face (Figure 26). An alternative approach, the scarp dating method of Avouac [1993], accounts for local sources of error and differing crest and basal curvatures through use of a weighted misfit function which can be defined using sample spacing for nonuniform data, or set to zero to emphasize one part of a landform, like a scarp crest. It is possible to weight the topographic curvature within the windowed area of the template to provide analogous functionality using a curvature template, but determination of weight values for each template configuration is likely to be computationally inefficient. The template window size used to determine individual scarp ages at Wallace Creek is signif- icantly smaller than the window sizes used to process the Northern California dataset. Template window size selection introduces a trade-off between the accuracy of scarp detection and the level of detail of individual scarp measurements. In the case of Wallace Creek, the template window size of 100 m yields a less variable morphologic age distribution across the individual scarps modeled in Arrowsmith et al. [1998] (Figure 21). Similarly, choosing a smaller template window size of 10 m results in more variable age and amplitude measurements for each scarp (Figure 21 and Figure 26). However, decreasing the template window size also introduces more false positives, degrading the regional accuracy of template-based fault zone mapping. Finally, the fault scarps and scarp-like landforms that appear in the Northern California dataset may violate key assumptions of the linear diffusion model. Early morphologic dating studies ex- amined pluvial shoreline scarps [Hanks and Wallace, 1985; Andrews and Bucknam, 1987], alluvial terrace edges [Pierce and Colman, 1986], and fault scarps established in unconsolidated alluvium and conglomerates [Avouac and Peltzer, 1993; Arrowsmith et al., 1998]. Many scarp-like features in the Northern California dataset are hosted in basin sediments or weakly consolidated soils, but other detected slope breaks include valley-bounding escarpments and topographic lineaments

40 formed in cohesive sediments or other bedrock material (Figures 6 and 11). That is, diffusivity (κ) varies between, and in some cases within, the study sites. Similarly, many scarps, especially young scarps and scarps in cohesive material are subject to non-diffusive processes, such as slump- ing or gravitational collapse, that are not accounted for by the linear diffusion template. Models of scarp degradation incorporating gravitational collapse, such as Kogan and Bendick [2011], have been shown to provide more accurate morphologic age estimates in these cases, but these more sophisticated models cannot be used to derive a simple curvature template function.

G.4 Limitations of validation data Unlike labelled images used in other image classiﬁcation or object detection contexts, the validation data produced for this study do not represent perfect ground truth locations of fault scarp pixels. For instance, fault zone maps may exclude features below the scale of mapping, and earthquakes may rupture the ground surface where no fault scarps previously existed, or experts may disagree about whether certain topographic or hydrologic features are the result of fault motion. Similarly, erroneously detected features, like channel bank false positives, may coincide with mapped areas, incorrectly deﬁning them as true positives. The validation data presented in this study represent a minimal set of mapped faults or fault-related landforms in each study area based on mapping with topographic basemaps or air photos, geophysical interpretation, or other sources of evidence such as seismicity, geodetic displacements, or creep measurements.

G.5 Future work While this work has focused on a strike-slip fault system, the template matching approach could also be applied to normal fault scarps formed in historic earthquakes [Kogan and Bendick, 2011] or rangefront scarps of the Basin and Range. In these cases, consideration of the far field slope of the scarp is important, possibly requiring an asymmetric template function [Hanks and Andrews, 1989]. Feature detection could also improve mapping of extensional steps in strike-slip faults [e.g., DeLong et al., 2010]. For both of these settings, using a range of informative template window sizes in a multi-scale analysis would be appropriate for detailed fault scarp identification or dating. Likewise, this method could be used to make detailed scarp measurements using very high resolution, small footprint photogrammetric datasets from drone, kite or other survey methods [e.g., Bemis et al., 2014; Johnson et al., 2014]. Using this implementation, orientation constraints from user input and tiled data processing would allow for efficient analysis of large datasets of decimeter to centimeter resolution. Modern supervised or semi-supervised machine learning methods, including convolutional neu- ral networks (CNNs), are also natural choices for landform detection problems. Compared to other common edge detection or object detection problems, fault scarp detection is a challenging problem requiring identification of a range of forms within diverse classes of scarp-like and non-tectonic landforms. The work presented here highlights the complex nature of the training, testing, or validation datasets that would need to be produced to train and test a machine learning method focused on fault-related landforms. If fault scarp mapping were approached as a supervised learning problem, issues such as intraclass variability and training data quality would have to be addressed given the range of landforms used as evidence for faulting and the lack of standardized, regional-scale geomorphic mapping in many tectonically active areas. For example, producing fault scarp image chips, a common method for generating training data for CNN-based object detection in satellite imagery, would be subject to the vagaries of fault zone expression and limited by available mapping.

41 H Conclusions

The GeoEarthScope Northern California dataset, a major plate boundary-scale lidar acquisition, was processed using a distributed template matching algorithm to detect fault scarps and other tectonic landforms. Performance was assessed at several well-mapped fault zones in Northern California and the San Francisco Bay Area. The morphologic ages estimated using the template matching algorithm were compared to field-based morphologic dating of fault scarps, showing that template estimates are generally lower than those from field dating. The spatial accuracy of the method was evaluated at several template window sizes using a pixel classification scheme applied to results from fault zones capturing a range of geodetic slip rates, documented historic and pre-historic earthquakes, and varied topographic complexity. The changes in classification performance and performance variability across different fault zones documented in this study highlight several points for future work:

1. Orientation constraints reduce the false positive rate for fault-related landform classiﬁers. These constraints could be provided by lidar swath orientation or derived from multi-scale analysis of the dominant landform orientations using lower-resolution data or other landscape metrics.

2. The resolving power of template-based methods is related to template window size and the scales of landscape features, especially in the case of tectonic landforms that may be coherent features at multiple scales.

3. Many landform detection methods using only topographic data may fail in areas of rough topography or depositional settings where the target landforms are poorly preserved.

4. Incorporating independent datasets, such as satellite imagery and derivatives that capture hydrologic, vegetative, or pedological evidence for faulting, may be useful where fault-related topography is subtle or absent.

42 Acknowledgement of Support and Disclaimer This material is based upon work supported by the U. S. Geological Survey under Grant No. G17AP00010. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the opinions or policies of the U.S. Geological Survey. Mention of trade names or commercial products does not constitute their endorsement by the U.S. Geological Survey. Data Availability

Source code for the template matching application described in this paper can be found at https://github.com/rmsare/scarplet. Data are publicly available at the following link: https://doi.org/10.25740/jb798nz9559.

Publications

Publications arising from this work include: Refereed publications

1. Sare, R., Hilley, G. E., and DeLong, S. B. (2019). Regional-Scale Detection of Fault Scarps and Other Tectonic Landforms: Examples From Northern California, Journal of Geophysical Research, Solid Earth, 124, doi: 10.1029/2018JB016886.

2. Sare, R., and Hilley, G. E. (2018). Scarplet: A Python package for topographic template matching and diﬀusion dating, Journal of Open Source Software, 3, 1066, doi:10.21105/joss.01066.

Conference Abstracts

1. Sare, R. M., & Hilley, G. E. (2017). ESTIMATING FAULT ZONE MATURITY AT THE PLATE BOUNDARY SCALE USING TEMPLATE MATCHING FOR FAULT SCARP DETECTION AND MORPHOLOGIC DATING. Presented at the GSA An- nual Meeting in Seattle, Washington, USA - 2017, Geological Society of America. https://doi.org/10.1130/abs/2017am-308245

2. Sare, R., & Hilley, G. E. (2018). Scarplet: Cloud-based Template Matching for Detecting Earthquake-Related Landforms in Large Topographic Datasets. Scientiﬁc Python Conference 2019, Austin, TX.

3. Sare, R., & Hilley, G. E. (2018). Faults in the cloud: Distributed topographic template matching of fault-related landforms in Shuttle Radar Topography Mission data using a cloud-based processing framework. In AGU Fall Meeting Abstracts.

43 References

Andrews, D., and R. C. Bucknam, Fitting degradation of shoreline scarps by a nonlinear diffusion model, Journal of Geophysical Research: Solid Earth, 92 (B12), 12,857–12,867, 1987. Andrews, D., and T. Hanks, Scarp degraded by linear diffusion: Inverse solution for age, Journal of Geophysical Research: Solid Earth, 90 (B12), 10,193–10,208, 1985. Armstrong, C. F., Coyote Lake earthquake, August 6, 1979, California Geology, 32 (11), 248–25, 1979. Arrowsmith, J. R., and O. Zielke, Tectonic geomorphology of the san andreas fault zone from high resolution topography: An example from the cholame segment, Geomorphology, 113 (1-2), 70– 81, 2009. Arrowsmith, J. R., D. D. Rhodes, and D. D. Pollard, Morphologic dating of scarps formed by repeated slip events along the San Andreas Fault, Carrizo Plain, California, Journal of Geophysical Research: Solid Earth, 103 (B5), 10,141–10,160, 1998. Avouac, J.-P., Analysis of scarp profiles: evaluation of errors in morphologic dating, Journal of Geo- physical Research: Solid Earth, 98 (B4), 6745–6754, 1993. Avouac, J.-P., and G. Peltzer, Active tectonics in southern xinjiang, china: Analysis of terrace riser and normal fault scarp degradation along the hotan-qira fault system, Journal of Geophysical Research: Solid Earth, 98 (B12), 21,773–21,807, 1993. B4, B4 Project - Southern San Andreas and San Jacinto Faults lidar dataset. Ohio State University and National Center for Airborne Laser Mapping (NCALM), distributed by OpenTopography, doi:10.5069/g97p8w9t, 2006. Bemis, S. P., S. Micklethwaite, D. Turner, M. R. James, S. Akciz, S. T. Thiele, and H. A. Bangash, Ground-based and uav-based photogrammetry: A multi-scale, high-resolution mapping tool for structural geology and paleoseismology, Journal of Structural Geology, 69, 163–178, 2014. Bevis, M., et al., The B4 project: scanning the San Andreas and San Jacinto fault zones, in AGU Fall Meeting Abstracts, 2005. Booth, A. M., J. J. Roering, and J. T. Perron, Automated landslide mapping using spectral analysis and high-resolution topographic data: Puget Sound lowlands, Washington, and Portland Hills, Oregon, Geomorphology, 109 (3-4), 132–147, 2009. Brown Jr., R., and E. W. Wolfe, Map showing recently active breaks along the San Andreas fault between Point Delgada and Bolinas Bay, California, U. S. Geological Survey Numbered Series Map 692, 1972. Bucknam, R., and R. Anderson, Estimation of fault-scarp ages from a scarp-height–slope-angle relationship, Geology, 7 (1), 11–14, 1979. Budding, K. E., D. P. Schwartz, and D. H. Oppenheimer, Slip rate, earthquake recurrence, and seismo- genic potential of the Rodgers Creek fault zone, northern California: Initial results, Geophysical Research Letters, 18 (3), 447–450, 1991. Carson, M., and M. Kirkby, Hillslope: form and process, Cambridge geographical studies, University Press, 1972. Clarke, B. A., and D. W. Burbank, Evaluating hillslope diffusion and terrace riser degradation in New Zealand and Idaho, Journal of Geophysical Research: Earth Surface, 115 (F2), 2010. Cloud, W., et al., The Santa Rosa earthquakes of October, 1969, Mineral Information Service, 23, 43–63, 1970.

44 Cohen, J., A coefficient of agreement for nominal scales, Educational and psychological measurement, 20 (1), 37–46, 1960. Colman, S. M., and K. Watson, Ages estimated from a diffusion equation model for scarp degradation, Science, 221 (4607), 263–265, 1983. Culling, W., Analytical theory of erosion, The Journal of Geology, 68 (3), 336–344, 1960. Culling, W., Soil creep and the development of hillside slopes, The Journal of Geology, 71 (2), 127–161, 1963. d’Alessio, M., I. Johanson, R. Bürgmann,D. Schmidt, and M. Murray, Slicing up the San Francisco Bay area: Block kinematics and fault slip rates from GPS-derived surface velocities, Journal of Geophysical Research: Solid Earth, 110 (B6), 2005. Dean, J., and S. Ghemawat, MapReduce: simplified data processing on large clusters, Communications of the ACM, 51 (1), 107–113, 2008. DeLong, S. B., G. E. Hilley, M. J. Rymer, and C. Prentice, Fault zone structure from topography: Signatures of en echelon fault slip at Mustang Ridge on the San Andreas Fault, Monterey County, California, Tectonics, 29 (5), 2010. Doane, T. H., D. J. Furbish, J. J. Roering, R. Schumer, and D. J. Morgan, Nonlocal Sediment Transport on Steep Lateral Moraines, Eastern Sierra Nevada, California, USA, Journal of Geophysical Research: Earth Surface, 123 (1), 187–208, 2018. Enzel, Y., R. Amit, N. Porat, E. Zilberman, and B. J. Harrison, Estimating the ages of fault scarps in the Arava, Israel, Tectonophysics, 253 (3-4), 305–317, 1996. Fawcett, T., An introduction to ROC analysis, Pattern Recognition Letters, 27 (8), 861–874, 2006. Field, E. H., et al., Long-term time-dependent probabilities for the third Uniform California Earth- quake Rupture Forecast (UCERF3), Bulletin of the Seismological Society of America, 105 (2A), 511–543, 2015. Freymueller, J. T., M. H. Murray, P. Segall, and D. Castillo, Kinematics of the Pacific-North Amer- ica plate boundary zone, northern California, Journal of Geophysical Research: Solid Earth, 104 (B4), 7419–7441, 1999. Frizzell Jr., V., and R. Brown Jr., Map showing recently active breaks along the Green Valley fault, U. S. Geological Survey Miscellaneous Field Studies Map MF-743, 1976. Funning, G. J., R. Bürgmann,A. Ferretti, F. Novali, and A. Fumagalli, Creep on the Rodgers Creek fault, northern San Francisco Bay area from a 10 year PS-InSAR dataset, Geophysical Research Letters, 34 (19), 2007. Gilbert, G. K., The San Francisco earthquake and fire of April 18, 1906, and their effects on structures and structural materials, 324, US Government Printing Office, 1907. Gilbert, G. K., Earthquake forecasts, Science, 29 (734), 121–138, 1909. Hanks, T. C., The age of scarplike landforms from diffusion-equation analysis, Quaternary Geochronol- ogy: Methods and Applications, pp. 313–338, 2000. Hanks, T. C., and D. Andrews, Effect of far-field slope on morphologic dating of scarplike landforms, Journal of Geophysical Research: Solid Earth, 94 (B1), 565–573, 1989. Hanks, T. C., and D. P. Schwartz, Morphologic dating of the pre-1983 fault scarp on the Lost River fault at Doublespring Pass Road, Custer County, Idaho, Bulletin of the Seismological Society of America, 77 (3), 837–846, 1987.

45 Hanks, T. C., and R. E. Wallace, Morphological analysis of the Lake Lahontan shoreline and beachfront fault scarps, Pershing County, Nevada, Bulletin of the Seismological Society of America, 75 (3), 835–846, 1985. Hanks, T. C., R. C. Bucknam, K. R. Lajoie, and R. E. Wallace, Modification of wave-cut and faulting- controlled landforms, Journal of Geophysical Research: Solid Earth, 89 (B7), 5771–5790, 1984. Hastie, T., R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Infer- ence, and Prediction, Second Edition, Springer Series in Statistics, Springer, 2009. Hecker, S., V. Langenheim, R. Williams, C. Hitchcock, and S. DeLong, Detailed mapping and rupture implications of the 1 km releasing bend in the Rodgers Creek Fault at Santa Rosa, Northern California, Bulletin of the Seismological Society of America, 2016. Hilley, G., S. DeLong, C. Prentice, K. Blisniuk, and J. Arrowsmith, Morphologic dating of fault scarps using airborne laser swath mapping (ALSM) data, Geophysical Research Letters, 37 (4), 2010. Hoose, S. N., The Morgan Hill, California, earthquake of April 24, 1984, U. S. Geological Survey Bulletin, 1639, 1987. Hsu, L., and J. D. Pelletier, Correlation and dating of quaternary alluvial-fan surfaces using scarp diffusion, Geomorphology, 60 (3-4), 319–335, 2004. Isikdogan, F., A. Bovik, and P. Passalacqua, RivaMap: An automated river analysis and mapping engine, Remote Sensing of Environment, 202, 88–97, 2017. Johnson, K., E. Nissen, S. Saripalli, J. R. Arrowsmith, P. McGarey, K. Scharer, P. Williams, and K. Blisniuk, Rapid mapping of ultrafine fault zone topography with structure from motion, Geosphere, 10 (5), 969–986, 2014. Kirkby, M., Hillslope process-response models based on the continuity equation, Inst. Br. Geogr. Spec. Publ, 3 (1), 5–30, 1971. Koehler, R. D., J. N. Baldwin, C. S. Prentice, J. Pearce, and W. Lettis, Holocene Geologic Char- acterization of the Northern San Andreas Fault, Gualala, California, Final Technical Report to U.S. Geological Survey, National Earthquake Hazard Reduction Program, Award Number 03HQGR0045, 2005. Kogan, L., and R. Bendick, A mass failure model for the initial degradation of fault scarps, with application to the 1959 scarps at Hebgen Lake, Montana, Bulletin of the Seismological Society of America, 101 (1), 68–78, 2011. Krishnan, S., C. Baru, and C. Crosby, Evaluation of MapReduce for gridding lidar data, in 2010 IEEE Second International Conference on Cloud Computing Technology and Science, pp. 33– 40, IEEE, 2010. Krishnan, S., C. Crosby, V. Nandigam, M. Phan, C. Cowart, C. Baru, and R. Arrowsmith, Open- Topography: a services oriented architecture for community access to LIDAR topography, in Proceedings of the 2nd International Conference on Computing for Geospatial Research & Ap- plications, p. 7, ACM, 2011. Lashermes, B., E. Foufoula-Georgiou, and W. E. Dietrich, Channel network extraction from high resolution topography using wavelets, Geophysical Research Letters, 34 (23), 2007. Lawson, A. C., and H. F. Reid, The California Earthquake of April 18, 1906: Report of the State Earthquake Investigation Commission, 87, Carnegie Institution of Washington, 1908. Lienkaemper, J. J., Recently active traces of the Berryessa section and adjacent sections of the Green Valley Fault Zone, California a digital database, U. S. Geological Survey Data Series, 710, 12, 2012.

46 Lienkaemper, J. J., J. N. Baldwin, R. Turner, R. R. Sickler, and J. Brown, A record of large earthquakes during the past two millennia on the southern Green Valley fault, California, Bulletin of the Seismological Society of America, 103 (4), 2386–2403, 2013. Lienkaemper, J. J., F. S. McFarland, R. W. Simpson, and S. J. Caskey, Using Surface Creep Rate to Infer Fraction Locked for Sections of the San Andreas Fault System in Northern California from Alignment Array and GPS Data, Bulletin of the Seismological Society of America, 104 (6), 3094, doi:10.1785/0120140117, 2014. Mattson, A., and R. L. Bruhn, Fault slip rates and initiation age based on diffusion equation modeling: Wasatch fault zone and eastern Great Basin, Journal of Geophysical Research: Solid Earth, 106 (B7), 13,739–13,750, 2001. McFarland, F. S., J. J. Lienkaemper, S. J. Caskey, and K. Grove, Data from theodolite measurements of creep rates on San Francisco Bay region faults, California, 1979-2009, 1119, U.S. Geological Survey, 2009. Nash, D. B., Morphologic dating of degraded normal fault scarps, The Journal of Geology, pp. 353–360, 1980. NCAL, EarthScope Northern California lidar dataset. National Center for Airborne Laser Mapping (NCALM), distributed by OpenTopography, doi:10.5069/g9057cv2, 2008. Niemi, T. M., and N. T. Hall, Late Holocene slip rate and recurrence of great earthquakes on the San Andreas fault in northern California, Geology, 20 (3), 195–198, 1992. NSAF, Northern San Andreas Fault, CA lidar dataset. Terrapoint, distributed by OpenTopography, doi:10.5069/g9mw2f2h, 2005. Pelletier, J., S. DeLong, A. Al-Suwaidi, M. Cline, Y. Lewis, J. Psillas, and B. Yanites, Evolution of the Bonneville shoreline scarp in west-central Utah: Comparison of scarp-analysis methods and implications for the diffusion model of hillslope evolution, Geomorphology, 74 (1), 257–270, 2006. Pierce, K. L., and S. M. Colman, Effect of height and orientation (microclimate) on geomorphic degradation rates and processes, late-glacial terrace scarps in central Idaho, Geological Society of America Bulletin, 97 (7), 869–885, 1986. Prentice, C. S., Earthquake geology of the northern San Andreas fault near Point Arena, California, Ph.D. thesis, California Institute of Technology, 1989. Prentice, C. S., C. J. Crosby, C. S. Whitehill, J. R. Arrowsmith, K. P. Furlong, and D. A. Phillips, Illuminating Northern California’s active faults, Eos, Transactions AGU, 90 (7), 55, 2009. Prentice, C. S., M. C. Larsen, H. M. Kelsey, and J. Zachariasen, Late Holocene slip rate and ages of prehistoric earthquakes along the Maacama Fault near Willits, Mendocino County, northern California, Bulletin of the Seismological Society of America, 104 (6), 2966–2984, 2014. Radbruch, D., Map showing recently active breaks along the Hayward fault zone and the southern part of the Calaveras fault zone, California, U.S. Geological Survey Miscellaneous Investigation Series, Map 813, 1974. Rowland, J. C., E. Shelef, P. A. Pope, J. Muss, C. Gangodagamage, S. P. Brumby, and C. J. Wilson, A morphology independent methodology for quantifying planview river change and characteristics from remotely sensed imagery, Remote Sensing of Environment, 184, 212–228, 2016. Sangireddy, H., C. P. Stark, A. Kladzyk, and P. Passalacqua, GeoNet: An open source software for the automatic and objective extraction of channel heads, channel network, and channel morphology from high resolution topography data, Environmental Modelling & Software, 83, 58–73, 2016.

47 Sare, R., and G. E. Hilley, scarplet: A Python package for topographic template matching and diﬀusion dating, Journal of Open Source Software, 3 (31), 1066, doi:10.21105/joss.01066, 2018. Schwenk, J., A. Khandelwal, M. Fratkin, V. Kumar, and E. Foufoula-Georgiou, High spatiotemporal resolution of river planform dynamics from landsat: The rivmap toolbox and results from the ucayali river, Earth and Space Science, 4 (2), 46–75, 2017. Sieh, K. E., and R. H. Jahns, Holocene activity of the San Andreas fault at Wallace creek, California, Geological Society of America Bulletin, 95 (8), 883–896, 1984. USGS, Quaternary fault and fold database for the United States, 2006. Warren, D. H., C. Scoﬁeld, and C. G. Bufe, Aftershocks of the 22 November 1977 earthquake at Willits, California: Activity in the Maacama fault zone, Bulletin of the Seismological Society of America, 75 (2), 507, 1985. Watt, J., D. Ponce, T. Parsons, and P. Hart, Missing link between the Hayward and Rodgers Creek faults, Science Advances, 2 (10), 2016. Zielke, O., Y. Klinger, and J. R. Arrowsmith, Fault slip and earthquake recurrence along strike-slip faults – Contributions of high-resolution geomorphic data, Tectonophysics, 638, 43–62, 2015.