Fault zone structure from topography: Signatures of en echelon fault …pangea.stanford.edu/~hilley/REPRINTS/Delongetal... · 2011. 2. 19. · Fault zone structure from topography:

Fault zone structure from topography: Signatures of en echelonfault slip at Mustang Ridge on the San Andreas Fault,Monterey County, California

Stephen B. DeLong,1 George E. Hilley,2 Michael J. Rymer,1 and Carol Prentice1

Received 20 January 2010; revised 1 June 2010; accepted 9 June 2010; published 2 September 2010.

[1] We used high‐resolution topography to quantifythe spatial distribution of scarps, linear valleys, topo-graphic sinks, and oversteepened stream channelsformed along an extensional step over on the SanAndreas Fault (SAF) at Mustang Ridge, California.This location provides detail of both creeping faultlandform development and complex fault zone kine-matics. Here, the SAF creeps 10–14 mm/yr slowerthan at locations ∼20 km along the fault in either direc-tion. This spatial change in creep rate is coincidentwith a series of en echelon oblique‐normal faults thatstrike obliquely to the SAF and may accommodatethe missing deformation. This study presents a suiteof analyses that are helpful for proper mapping offaults in locations where high‐resolution topographicdata are available. Furthermore, our analyses indicatethat two large subsidiary faults near the center of thestep over zone appear to carry significant distributeddeformation based on their large apparent vertical off-sets, the presence of associated sag ponds and fluvialknickpoints, and the observation that they are rotatinga segment of the main SAF. Several subsidiary faultsin the southeastern portion of Mustang Ridge are likelyless active; they have few associated sag ponds andhave older scarp morphologic ages and subdued chan-nel knickpoints. Several faults in the northwestern partof Mustang Ridge, though relatively small, are likelyalso actively accommodating active fault slip basedon their young morphologic ages and the presence ofassociated sag ponds. Citation: DeLong, S. B., G. E. Hilley,M. J. Rymer, and C. Prentice (2010), Fault zone structure fromtopography: Signatures of en echelon fault slip at Mustang Ridgeon the San Andreas Fault, Monterey County, California, Tectonics,29, TC5003, doi:10.1029/2010TC002673.

1. Introduction[2] Conspicuous surface features along the ∼1300 km

length of the San Andreas Fault (SAF) have long been

exploited to interpret local fault zone structure and kine-matics. Gilbert’s observations (in the work by Lawson[1908]) of the tectonic geomorphology and 1906 earth-quake effects in Olema Valley, California stand as an earlyrigorous example of this, and have been followed by manyothers [e.g., Sieh, 1978;Weldon et al., 2002;McCalpin, 2009,and references therein]. Mapping these features in the pasthas relied principally on aerial photograph interpretationand direct field observation. However, such data cannotimage the fault zone structure in areas that are heavilyvegetated, and rely on a specific configuration of lighting toshade the topographic features of interest [Oskin et al., 2007].In 2007, high‐resolution topographic data were collectedusing airborne light detection and ranging (lidar) surveysalong the principal faults zones of California. These data wereacquired with the intention of quantifying the location ofindividual, recently active fault strands and inferring thetemporal development of the fault zone at an unprecedentedresolution and along regions that previously could not beaccessed, as well as to provide baseline topographic data priorto the next great earthquake [Prentice et al., 2009]. Suchsurveys allow visualization of meter‐scale landforms evenwhere dense vegetation exists. Shaded‐relief models of thesevegetation‐filtered digital elevation models (DEMs) canreveal features not clearly visible in the field or on air photosand have enhanced mapping of tectonic features along activefault zones [Arrowsmith and Zielke, 2009; Prentice et al.,2009]. Such lidar surveys have been collected over othertectonically active areas (e.g., Puget Sound [Haugerud et al.,2003]), and continuing efforts strive to achieve statewideand even countrywide lidar coverage. Thus, comprehensiveimaging of plate boundary topography will likely aid effortsto quantify seismic hazard [e.g., Sherrod et al., 2004;Cunningham et al., 2006], to understand the kinematics ofplate boundary deformation over long time‐scales, and toelucidate the mechanical development of the principle faultzones over time [e.g., Hilley et al., 2010].[3] As these high‐resolution (≤1 m pixel spacing) data

become available, it is necessary to develop and evaluatenew tools to analyze the large volume of data in a mannerthat goes beyond viewing and mapping landforms on shadedrelief and other derivative products of the topographic data.Here we evaluate several of these analyses on a particularlycomplex part of the San Andreas fault zone at MustangRidge to identify those that provide detailed informationabout geologic structure and relative rates of tectonic activity.This area serves as a case study for methods development, butthe methods discussed here can be applied to a range oflandscapes for which high resolution topographic data are

1U.S. Geological Survey, Menlo Park, California, USA.2Department of Geological and Environmental Sciences, Stanford

University, Stanford, California, USA.

Copyright 2010 by the American Geophysical Union.0278‐7407/10/2010TC002673

TECTONICS, VOL. 29, TC5003, doi:10.1029/2010TC002673, 2010

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http://dx.doi.org/10.1029/2010TC002673

available. This area (Figure 1) has been previously mapped indetail by Rymer [1981] using field and aerial photographicmethods. We exploit this existing database to test analyses oflidar DEMs in a complex area that has existing ground truth.We compare lidar‐derived landscape metrics to the mappeddistribution of surface faults to identify the metrics that bestilluminate the structure and kinematics of this area. Specifi-cally, we present shaded relief, slope, aspect, curvature andtopographic sink maps that provide detailed representationsof local topography. We analyze fault scarp morphology todetermine which subsidiary faults may be more active thanothers. We also identify and interpret the spectral sig-natures of en echelon landforms atMustang Ridge using two‐dimensional discrete Fourier transforms and DEM filtering.Additionally, we analyze the longitudinal profile of smallchannels that cross subsidiary faults to look for signatures ofactive tectonic process. These analyses allow us to proposerefinements to the mapped surface expression of faults atMustang Ridge and to interpret specific subsidiary faults thatappear to have higher relative rates of surface deformation.[4] This study provides not only insight into the local faults

along Mustang Ridge, but provides a set of tools that may beof use to other workers that map fault zones that have asso-ciated high resolution topographic data. These relativelysimple methods are applicable to other locations along theSAF and other active fault zones worldwide. Complementarytools such as Hilley et al.’s [2010] 2D scarp template methodcan also be added to a workflow that will allow geologiststo not only map fault locations but assess relative rates offault activity in a quantitative way.[5] This study focuses on a portion of the creeping seg-

ment of the SAF. Recent work in this area has begun tounravel the physical causes of creep and the importance oftalc‐bearing serpentinite in particular [Moore and Rymer,

2007]. That work pointed toward presence of silica‐richhydrothermal fluids and serpentinite as a primary control onfault creep. This suggests a strong link between materialsand fault zone kinematics which further motivates ourefforts to quantify fault zone activity along Mustang Ridge,where serpentinite‐bearing Franciscan rocks are the primarylithology.

2. Study Area[6] We focused on the SAF where it traverses Mustang

Ridge in middle of the creeping segment of the fault(Figure 1). The majority of Mustang Ridge is underlain bycentral belt Franciscan mélange that includes chert, green-stone, serpentinite, meta‐greywacke, mudstones and lime-stones [Rymer, 1981]. As the SAF passes from the SE end ofMustang Ridge to the NW end, it has a right‐sense step overof approximately 1 km.[7] We suggest that the creeping segment has particularly

distinct fault‐related landforms because surface offset isongoing as plate boundary strain is accommodated in fre-quent microearthquakes, and that Mustang Ridge may beparticularly structurally complex due to the dominant weakFransiscan lithology. Within the creeping segment of theSAF, surface creep rate increases monotonically from zeroat the NW end in San Juan Bautista, California, for ∼80 km,peaks around 28–32 mm/yr along the middle ∼55 km por-tion of the fault segment, and decreases monotonically tozero along the southeastern ∼60 km to Parkfield, California[Burford and Harsh, 1980]. These rates are principally derivedfrom creepmeters and alignment array surveys that measurecreep rates over apertures of meters to several tens of metersacross the creeping fault [Burford and Harsh, 1980; Schulzet al., 1982; Titus et al., 2005] and intermediate‐scale distancemeasurements across hundreds of meters [Lisowski andPrescott, 1981]. Far‐field measurements from Geodolitesurveys and continuous GPS indicate a similar spatial distri-bution of slip rates across apertures of >1 km. The highestfar‐field rates are somewhat higher at 33 ± 2 mm/yr and donot reduce to zero at San Juan Bautista but rather declineonly slightly to the northwest. At the broadest scale, plateboundary motion proceeds at 39 ± 2 mm/yr [Argus andGordon, 2001; Titus et al., 2006].[8] It is unclear how the maximum shallow creep rate is

related to deeper creep rates, fault zone structure, rates ofdistributed deformation, and accumulation of elastic strainwithin the larger plate boundary [Burford and Harsh, 1980;Titus et al., 2006; Ryder and Bürgmann, 2008; Rolandoneet al., 2008]. However, narrow aperture (≤100 m) surfacecreep rates vary systematically with position along the fault.The most notable exception to this is along Mustang Ridgeeast of King City, California (Figure 1), where near‐field(<100 m) surface creep rates are 14–18 mm/yr [Burford andHarsh, 1980; Titus et al., 2006] on a part of the SAF wherelarge‐aperture (>10 m) deformation measurements suggestthat creep rates should be at least 28 mm/yr. The fact thatintermediate (∼1 km) and large (several km) aperture mea-surements of creep [Lisowski and Prescott, 1981; Ryder andBürgmann, 2008] approach the expected rate of ∼28 mm/yrsuggests that slip is accommodated within a several‐km wide

Figure 1. Location of study area in central California. SanJuan Bautista (SJB) and Parkfield are approximate boundsof the creeping section of the San Andreas Fault. Inset atbottom left shows trace of SAF in study area. Dashed linesindicate projections of straight segments of SAF to illustrate∼1 km right step.

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zone in this area. Rymer et al. [1984] concluded this apparentslip‐rate anomaly could be explained by the presence of anetwork of subsidiary faults that accommodate this off‐faultdeformation. These interpretations were based on detailedmapping that located appropriately oriented faults based ontopographic features, offset lithologies, presence of sag ponds,springs, aligned vegetation, linear gullies, and linear scarps[Rymer, 1981]. This mapping indicated that the main faultzone here is ∼1 kmwide, which is nearly the width of the low‐relief ∼700 m elevation ridge top at Mustang Ridge. Thisridge is flanked on either side by steep landslide‐prone slopes.

3. Methods[9] We analyzed high‐resolution topographic data and

performed limited fieldwork that included reconnaissancemapping and measurement of Monarch Peak alignmentarray. Most of our analyses are derived from 1‐m‐resolutionbare‐earth digital elevation data, though for the spectralanalyses we sub‐sampled the data to 2‐m resolution andfor curvature analysis we dropped elevation values to achieve4‐m resolution. Details about data collection, processingbare‐earth extraction are available in the metadata at www.opentopography.org. We used the preprocessed bare earthDEMs and explored shaded relief, slope, aspect, and curva-ture mapping; hydrologic analysis for extraction of sagponds; channel profile analysis; fault scarp morphologicalanalysis; and two‐dimensional spectral analyses and filtering(Figure 2). We also measured the Monarch Peak alignmentarray following the methods of Burford and Harsh [1980]which involve repeated measurement of angles betweenalignment array endpoint across the fault perpendicular to afault‐parallel reference line. We used a Leica TCR‐803 with ahorizontal angle measurement accuracy of 3 mgon (0.0027°).This had not been done since 1977. Titus et al. [2006]reoccupied the site with GPS, but their analysis used slightlydifferent methods that instead relied on projecting best fitlines through monuments on either side of the fault back tothe fault.

3.1. GIS Analyses

[10] Many GIS packages have spatial analysis tools thatare functional with little user interaction. These include slope,slope‐aspect, curvature, and automatic extractions of hydro-logical internal topographic sinks. Slope is calculated by fit-ting a plane to a 3 by 3 cell neighborhood and calculating

maximum slope [Burrough and McDonnell, 1998]. Slope‐aspect is defined as the azimuthal direction of this maximumslope (1–360°). Curvature is calculated by fitting a fourth‐order polynomial to the 3 × 3 cell calculation area, andcalculating the second derivative of that surface. Profile cur-vature is the spatial rate of change of the slope in the directionof the maximum slope [Zevenbergen and Thorne, 1987;Moore et al., 1991]. The sign of a grid cell’s curvature isindicative of its convexity (negative) or concavity (positive)and themagnitude indicates how rapidly the slope is changingat that cell. For curvature analysis, we first gridded thetopographic data to 4‐m resolution using bilinear interpo-lation to focus on landforms over a several meter analysisdomain. This step reduces the noise that results from subtlesurface roughness that is unrelated to the tectonic land-forms of interest.[11] Because topographic sinks are common along active

fault zones, we extracted them automatically using hydro-logical tools that assign a flow direction to each cell basedon elevation of adjacent cells, then identifies cells or groupsof cells at which no neighboring cells have lower elevation.This extracts sinks of any origin, including tectonic sag ponds,data errors, small depressions not caused by tectonics, andanthropogenic (or anthropogenically enhanced) depressions,most commonly earthen‐dammed cattle “tanks.”

3.2. Scarp Profile Analyses

[12] Under conditions of slope‐dependent sediment fluxand conservation of mass according to a continuity equation,the evolution of a 1D hillslope profile can be approximatedby the diffusion equation:

@h

@t¼ �

@2h

@x2

� �; ð1Þ

in which h is the elevation (m), t is time (kyr), x is horizontaldistance (m) and � is the diffusivity coefficient (m2/ky), whichdepends on slope material properties, regional environmentalfactors, vegetation, and microclimatic factors [Hanks et al.,1984; Hanks, 2000]. This type of hillslope diffusion modelis applicable to slopes that evolve by slope dependent pro-cesses that include creep, sheet flow, rain splash, bioturba-tion, but are not subjected to significant mass wasting orfluvial erosion after an early rapid decay to a mechanicallymore stable slope angle. The faults at Mustang Ridge cutweak Franciscan bedrock that is soil‐mantled nearly every-

Figure 2. (a) A 1‐m resolution shaded relief map created from digital elevation model, which was generated from a fil-tered lidar point cloud. Most vegetation is removed during the filtering process though brushy vegetation results in sometexturing of land surface. Hill shades with two different lighting azimuths are available via http://www.opentopography.org/for interactive viewing in Google Earth. (b) Slope map on shaded relief. Slope values are binned according to likely geo-morphic process zones: 0°–2° is stable to diffusion‐dominated on slopes and fluvial in channel, 2°–5° is often mixed debrisflow and fluvial in channels and diffusion dominated on slopes, 5°–10° is debris flow dominated in channels, 10–30° isdiffusion dominated on hillslopes, 30°–60° is mass wasting dominated, and > 60° is often competent bedrock or mass wast-ing headwall. (c) Slope‐aspect map. (d) Profile curvature map derived from 4‐m DEM. Blue pixels are convex up, and redare concave up. Intensity of color is proportional to magnitude of curvature. (e) Automatically extracted sag pond featureson shaded relief map. Only sag features larger than 5 m across are shown on this map. (f) Results from targeted scarp mor-phology analyses. Bold number is �t (morphologic age) (m2) assuming a linear diffusion model, minimum RMS error ofmodel fit to profile (m) is given in parentheses. Dh is the apparent vertical offset (m).


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Figure 2


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where. This observation supports the use of a diffusionmodel and diminishes the importance of lithologic vari-ability because it suggests that soil production outpaceserosion across Mustang Ridge and on the subsidiary faultscarps in particular. The proximity of small channels andsag ponds to the base of scarps at Mustang Ridge must alsobe acknowledged. These highly ephemeral systems (meanannual precipitation is less than 50 cm) may affect scarpsvia fluvial erosion or sag pond deposition on the lower partof the scarps. We tried to avoid area where this is evidentwhen we extracted topographic profiles.[13] By fitting model profiles to topographic profiles, we

estimated values for �t and best fit vertical fault offsetmagnitude Dh following methods similar to those employedby Arrowsmith et al. [1998] and the full‐scarp methods ofPelletier et al. [2006]. In our analyses we assumed that thescarps evolved to 35° rapidly after offset began, and that anoriginally horizontal surfacewas offset by faulting. The initialangle and single‐event assumptions oversimplify the likelyongoing slip history of these scarps, and the values of �tare sensitive to the initial angle [Hsu and Pelletier, 2004],but the method is nevertheless a robust means of calcu-lating relative differences in scarp morphology. In order toimplement a continuous‐slip model of fault development,we would have to parameterize slip rate and � independentlyto solve for morphologic age. This more highly parameterizedmodel does not help us determine relativemorphology among

faults in an improved manner over the single‐event model.Our approach leads us to caution against attempting tounravel � and t from our results, because not only is � locallyuncalibrated, but the absolute value of �t is likely to belower when calculated with the single event model than whencalculated with a continuous slip model due to the ongoingrejuvenation of the scarp slope in the continuous slip model.Numerical experiments beyond the scope of this paper sug-gests that this relationship is linear and approximately a factorof two.[14] We extracted topographic profiles from the 1‐m lidar

DEM from several scarps on Mustang Ridge that showedminimal evidence for disturbance by fluvial or mass wastingprocesses. Using these topographic profiles, we minimizedthe misfit between measured and modeled topographic formsusing an L‐2 norm misfit criterion. We report apparent ver-tical fault offset, single event �t, and the minimum RMSerror between topographic and model profiles used to cal-culate the reported �t. We provide figures of the topographicand model profiles in the auxiliary material.1

3.3. Channel Profile Analyses

[15] Bedrock river channel longitudinal profiles can recordzones of active tectonic process. Locally steep sections

Figure 2. (continued)

1Auxiliary materials are available in the HTML. doi:10.1029/2010TC002673.


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(knickpoints) may occur where a river crosses an activefault if the upstream channel reach is on a more rapidlyuplifting block. Alternatively, if fault activity has juxtaposedrocks of differing hardness, or on a nontectonic lithologiccontact or fault line scarp is present, a knickpoint may notindicate a locus of active faulting. Since we cannot unravelthe possible causes for knickpoints with certainty, theirpresence cannot be used in isolation as an indicator of activefaulting. We extracted channel profiles from DEMs in loca-tions where channels crossed mapped fault traces to locateexisting knickpoints.

3.4. Spectral Analyses

[16] If a two‐dimensional surface contains periodic fea-tures, it can be described quantitatively using the discreteFourier transform (DFT) of the data. This analysis decom-poses the original topographic signal into its constituentwaveforms, such that the topography can be transformedinto a complex function in wave number space. The squareof the resulting amplitudes provides a measure of spectralpower, which can be used to identify the amplitude and phaseof periodic topographic features as a function of orientationand wavelength. Perron et al. [2008] provided general pro-cedures for applying the two‐dimensional DFT to topographicdata. They used this technique to identify characteristic ridge‐valley spacing in two topographic settings. We use thismethod to evaluate the location, amplitude, wavelength, ori-entation, and statistical significance of periodic fault scarps,ridges and valleys at Mustang Ridge.[17] Detailed descriptions of data processing and analyses

are given byPerron et al. [2008].We performed these analyseson a subset of lidar data with a horizontal resolution of 2 m.Subsampling from the original 1‐m DEM has the effect ofsmoothing features that may have spectral power at a wavenumbers approaching grid resolution, but increases compu-tational efficiency. In this setting, those features are likely tobe fluvial scarps, legacy features from vegetation filtering,data errors, and small tectonic scarps.[18] Following Perron et al. [2008], we normalized the

spectral power to that expected from 1000 randomly gen-erated fractal topographies in which spectral power is notconcentrated in any particular wave number. This allows us toidentify those wave numbers in the landscape that are sta-tistically distinct (normalized power > 5.1 [Perron et al.,2008]) from such fractal topography. It highlights wave-lengths at which significant spectral power exists and theorientation of these features. For this analysis, the originalDEM was rotated so that the SAF is oriented parallel to thex axis during subsampling. Following Perron et al. [2008],we designed two‐dimensional spectral filters that allowed usto isolate landforms corresponding to areas of high spectralpower. Since these isotropic filters also pass topography withstatistically significant wavelengths but ignores orientationof those features, we also designed anisotropic filters that passonly landscape features with significant spectral power inwavelength and orientation. This was done in two ways: first,we generated an automatic filter that passes all topographywith spectral power above a 99% confidence level basedon orientation and wavelength; second, we developed filters

that isolate parts of the two‐dimensional periodogram, so thatspecific wavelengths and orientations can be extracted fromthe topography.

4. Results[19] We measured the Monarch Peak alignment array at

Mustang Ridge following the procedures of Burford andHarsh [1980]. This measurement allowed calculation ofoffset of the endpoints of the full alignment array (97.2 maperture) over a period of 41.35 yr. Over this time periodthe fault creep rate is 17.9 ± 0.05 mm/yr (error based on2 mm measurement error following Titus et al. [2006]),which is similar to Titus et al.’s [2006] rate of 17.4 mm/yrusing best fit projection of alignment arrays to the faulttrace but not using the fault parallel reference lines.[20] Shaded relief, slope, slope aspect, profile curvature,

topographic sinks and scarp morphology are displayed inFigures 2a–2f. The shaded relief slope map shown inFigure 2b was manually binned to highlight ranges of slopesthat often correlate with surface processes. Draping the par-tially transparent slope map onto the shaded relief map servesto mediate the undesirable effect that lighting direction hason scarps obscured in shaded areas in a shaded relief map.The profile curvature map shown in Figure 2d was classi-fied first into areas of convex and concave slope, and alsoclassified by magnitude of curvature. We also present resultsfrom several targeted scarp profile analyses in Figure 2f andin the auxiliary material.


[21] The two‐dimensional periodogram is presented inFigure 3. Figure 3 displays wavelengths and normalizedspectral power of significant nonfractal topographic featuresin the landscape. The highest peak in spectral power occursat a wavelength of 769 ± 181

64 m, which approaches the widthof Mustang ridge as a topographic feature, as well as thewidth of the topographic swath used. A second major peakoccurs at 357 ± 87

231 m that is oblique 23° to the strike of theSAF.[22] In Figure 4, we show the power spectrum of the study

area without regard for the orientation of the periodic fea-tures. In this one‐dimensional periodogram, several peaksare apparent in between 100 and 1000 m. A peak occursat 600–900 m, as does a broad peak spanning 150–500 m.At shorter wavelengths, spectral power is significant, butdecreases with decreasing wavelength.

4.2. Two‐Dimensional Isotropic Filtering

[23] Topography was first filtered to isolate the dominantwavelengths in the Mustang Ridge topography. FollowingPerron et al. [2008], we perform an inverse DFT on thosewavelengths of the DFT of the DEM that showed statisticalsignificance to isolate these components of the landscape.The two‐dimensional isotropic filters were constructed fromvisual inspection of the normalized one‐dimensional peri-odogram (Figure 4). A low‐pass filter was constructed to passtopography with wavelength > 600m. Three band‐pass filterswere created, one to pass all wavelengths in the 150–500 m


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range, and two to determine if the higher and lower parts ofthat wavelength range correspond to distinct portions of thelandscape. A high‐pass filter was designed to reconstruct<150 m wavelength features.[24] The resulting filtered topography is presented in

Figures 5a–5e. These filters use wavelength informationonly, discarding orientation information available in thetwo‐dimensional periodogram. This allows topographic fea-tures that may have similar wavelengths to features withstatistically significant spectral power to be passed throughthe filters despite the fact that spectral power at many ofthese orientations may not be significantly greater thanexpected in a randomly generated fractal landscape. Thisserves to over‐represent the fraction of the landscape thatcontributes to spectral peaks in the two‐dimensional period-ogram but highlights the strongly periodic nature of featuresat Mustang Ridge.

4.3. Two‐Dimensional Anisotropic Filtering

[25] To filter the topography using both wavelength andorientation information, we constructed anisotropic Fourierfilters. In Figure 5f, we present the topography that resultsfrom all frequencies and orientations that are distinct from arandomly generated fractal landscape with >99% confidence.

Before filtering, we removed the part of the filter corre-sponding to the longest wavelength features at MustangRidge (the significant spectral peaks nearest the center ofthe two‐dimensional periodogram in Figure 3). We did thisto avoid the visual domination of the filtered topographyby this wavelength and orientation. In Figure 5g, we presentthe filtered topography that results from selecting a portionof the two‐dimensional periodogram (Figure 3) that corre-sponds to the broadest spectral peak at 357 m wavelength.This filter design is shown as dashed ellipses on the two‐dimensional periodogram in Figure 3.

5. Discussion5.1. Shaded Relief and Aspect Maps

[26] Shaded relief maps of lidar‐derived topography alongMustang Ridge reveal several elongated ridges oriented20°–40° oblique to the SAF strike (Figure 2a). These ridgesand their intervening valleys dominate the topography in the1 km wide low‐relief zone on Mustang Ridge. The maintrace of the SAF is clearly visible on the shaded relief mapsas well, and is expressed primarily as a zone of local riverincision and by the presence of elongated fault‐parallelscarps and ridges. The trace of the SAF on Mustang Ridge is

Figure 3. Portion of the two‐dimensional normalized power spectrum for Mustang Ridge. Uncertaintiesare derived from assessing range of wavelengths and orientations that are greater that one half of the peakspectral power. This plot is linear in wave number but nonlinear in wavelength. Orientation of periodicstructures is indicated by the location of spectral peaks. Waveforms that plot along zero on the y axis rep-resent topographic features that are parallel to the regional strike of the SAF (azimuth of 313.5°). Featuresthat plot along zero on the x axis (of which there are none in this plot) represent waveforms (ridges and/orvalleys) that are perpendicular to the regional strike of the SAF. The large peak in spectral power centeredat 23° is the suite of landforms associated with subsidiary faults at Mustang Ridge. The dashed ellipsesindicate the approximate extent of the anisotropic filter designed to filter the topographic features associ-ated with that spectral peak.


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segmented, and several separate segments of the fault arenot colinear along its strike. The network of subsidiary faultsfrom Rymer’s [1981] mapping appears to have a strong first‐order correlation with the local topography (Figure 7a). Hemapped several faults based on lithologic contacts that do notcorrelate with topographic features, reinforcing the necessityof detailed field inspection in addition to topographic analysis.[27] Active faults are often expressed as linear alignments

of topography, and so they tend to be well defined on aslope aspect map. At Mustang Ridge, the slope aspect map

(Figure 2c) captures the strike of the main SAF and theoblique subsidiary fault scarps. Aspectmaps derived from lidardata also reveal minor anthropogenic features such as roads,ditches, and trails, so caution must be used when ascribinglinear discontinuities on aspect maps to tectonic origins.

5.2. Curvature and Fault Scarp Morphologic Analyses

[28] Slope curvature may indicate the length of timesince a soil mantled or unconsolidated tectonic or fluvialscarp has formed if the feature degrades in a manner that is

Figure 4. (a) One‐dimensional power spectra for Mustang Ridge. Wave number increases to right, andwavelength increases to left. Each point is from a single array location on the two‐dimensional DFT array.White circles are the mean values computed in logarithmically spaced bins. The black line is the backgroundspectra created from a statistically similar synthetic surface with spectral power evenly distributed across allwave numbers. At high wave numbers (low topographic wavelength) spectral power decreases rapidly withwave number. (b) Normalized one‐dimensional power spectra produced by dividing spectra in Figure 4aby the synthetic background spectra. This indicates spectral power is concentrated in intermediate andhigh wavelengths at Mustang Ridge. The 95% significance level is plotted as horizontal dashed line. Thefive colored and dashed lines are approximations of the form of the spectral filters described in the text.

Figure 5. Surfaces constructed from fast Fourier transform filtering of lidar derived DEM draped on original shaded reliefmaps. Filter edge effects were eliminated by buffering data with nonlidar elevation data outside the analysis domain beforefiltering and then cropping the filtered DEMs to the analysis domain. (a) Low‐pass filter, (b) band‐pass filter 1, (c) band‐pass filter 2, (d) band‐pass filter 3, and (e) high‐pass filter. (f) Filtered topography that results from an automatic anisotropicfiltering of all statistically significant periodic topography above a 99% confidence interval (with the longest wavelength,fault‐parallel features removed). (g) The resultant topography from anisotropic filtering of all topography correspondingwith the significant peaks in spectral power outlined in Figure 3.


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Figure 5


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well approximated by the linear diffusion equation. A two‐dimensional curvature map can act as a guide toward detailedslope‐profile studies derived from surveying in the field orfrom topographic profiles extracted from the lidar DEM.[29] At Mustang Ridge, zones of active geomorphic pro-

cess transitions, such as landslides and fluvial scarps tend tobe marked by high curvature (Figure 2d). Scarps and ridgecrests in active landslide terrain are characterized by strongconvex‐upward curvature, whereas strong concave‐upwardcurvature indicates zones of active gully and channel incision.While these zones of high curvature dominate the curvaturemap, the en echelon fault scarps within the lower relief faultzone on top of Mustang Ridge are visible as zones of inter-

mediate curvature. These scarps are characterized by convex‐upward curvature on their upper, eastern flanks and a slightlyweaker zone of concave‐upward curvature on their lowerwestern flanks. This suggests a down‐to‐the west faulting that,given the overall releasing geometry of the step over zone isconsistent the formation of these features by en echelonnormal or oblique‐normal faulting.[30] Low values of �t (Figure 2f) should be associated

with younger scarps than higher �t‐scarps if the materialproperties of the faulted rocks are similar. The faults onMustang Ridge generally offset Franciscan Formation, whichis a heterogeneous assemblage of oceanic material accretedduring subduction, so caution must be used when comparing

Figure 5. (continued)


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even closely spaced fault scarps because variability in litho-logic properties may cause variations in �, or may be such thatthe assumption of linear diffusion is not valid.[31] In general, scarp morphology at Mustang Ridge can be

classified into three groups. Several scarps in the southeasternpart of the array have apparent vertical offset between 14and 24 m and have �t values between 77 and 320 m2. Thescarp in the southeastern part of the step over zone with thelowest apparent offset of 14 m also has the lowest �t valueof 77 m2, and has considerably higher values (290 m2 and23 m) just a few hundred meters along the same scarp. Thismay indicate a sharp gradient in fault behavior along strike orfault slip superposed on preexisting topography. The secondpopulation of scarps includes the two prominent, large scarpsto the north of the middle of the fault array at MustangRidge (these are the two scarps with fluvial knickpoints inFigure 6a). These two scarps have apparent vertical offsetsbetween 28 and 34 m and �t values of 210–434 m2. On thenorthwestern end of Mustang Ridge, several short, sharp faultscarps have a range of apparent vertical offsets Dh between8 and 10.5 m and �t values between 67 and 70 m2.[32] This approach to scarp diffusion analysis is limited by

the model assumptions of vertical motion and single eventinitial form. The larger scarps in the middle of our study areamay have experienced coseismic slip and/or creep over alonger time than the smaller scarps, and may not be producedby higher slip rates. This is supported by their relatively oldmorphologic ages, and complicates our ability to assign rel-ative rates of activity to scarps of different sizes. The shorter

scarps with lower �t values in the northwest part of the studyarea are likely younger active scarps, as indicated by their lessdegraded morphology and lower apparent offset. While wecannot entirely separate relative landform ages from relativeslip rates, we can infer that the largest scarps have accom-modated significant slip, and slip has recently been trans-ferred to the smaller scarps to the northwest. We also inferthat the shorter scarps in the southeastern part of the fieldarea with relatively old morphologic ages must be slippingrelatively slowly or have stopped accommodating slip.


[33] The two‐dimensional spectral analyses indicate thatthere are significant periodic features at ∼800 m wavelength.Filtering revealed that this feature is composed of the twoslightly elevated flanks of Mustang Ridge on each side ofthe low‐relief step over that are bounded by steep slopes atthe margin of the analysis area. There is also a strong periodicsignal that subsumes a range of fault scarp spacing (∼300–500 m) and orientation (∼13°–32°) into a broad spectral peak.This second peak is the manifestation of the subsidiary faultscarps mapped by Rymer et al. [1984]. There are many lesssignificant outliers as well as the two main peaks. These arelikely topographic features such as landslide scarps, fluvialscarps, and bedrock outcrops that may have orientationssimilar to that of the main fault scarps due to their strongcontrol of the shape of the landscape at Mustang Ridge atmany scales.

Figure 6. (a) Shaded relief map showing channel trace (white line) crossing fault scarps (black lines) inthe central portion of Mustang Ridge, whose profile is plotted in the top right. Points B and C correlatewith prominent knick zones on channel profile. (b) Channel trace and profile on a shaded relief in thesoutheastern portion of Mustang Ridge. Point A may be a knickpoint; the remainder of the channel profileis convex up and is not obviously disrupted by additional knickpoints.


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[34] The three band‐pass‐filtered DEMs (Figures 5b–5d)show that landscape features that have significant spectralpower between 300 and 500 m are fault scarps orientedoblique to the SAF fault. The largest scarp in the middle ofMustang Ridge appears to dominate the spectral signal,though several faults scarps are resolved in the three band‐pass‐filtered DEMs as periodic features.[35] The anisotropic filters that passed all nonfractal

topography successfully isolated landforms associated withthe central subsidiary faults (Figure 5f). This filter alsoresolved the landslide headwalls on the flanks of MustangRidge. Filtering the topography based on selection of aportion of the two‐dimensional periodogram centered at357 m shown in Figure 3 recovers the large scarp in themiddle of the step over region, the two scarps flanking thisfeature and, to a lesser degree, the edges of the low‐reliefsurface at Mustang Ridge (Figure 5g). This DEM is fairlysimilar to Figure 5f, which reflects the fact that the spectralpower peak centered at 357 m wavelength dominates theother, generally shorter‐wavelength features.

5.4. Fluvial Channel Profiles and Topographic Sinks

[36] Two prominent channels cross the subsidiary faultnetwork at Mustang Ridge at fairly high angles (Figure 6).One of these channels is in the central portion of MustangRidge, and crosses at least two subsidiary faults and theSAF. The profile has two prominent knick‐zones in an other-wise strongly concave longitudinal profile. These two knick‐zones are coincident with two of the largest subsidiary faultscarps, suggesting that fluvial erosion is unable to keep pacewith relief generated by vertical fault offset. The otherchannel crosses two distinct fault scarps in the southeasternportion of Mustang Ridge. The channel has a distinctknickpoint where is crosses a fault scarp near its headwaters;however no knickpoints exist where it crosses a second scarp∼400 m downstream. The entire profile however has a pro-nounced convex upward form, perhaps indicating that thechannel is unable to keep pace with ongoing uplift in itsmiddle reaches.[37] Sag ponds are also evidence for active fault slip,

particularly in strike slip zones. As fault slip steps in a sensesimilar to the offset motion (i.e., right‐step in a right‐lateralfault or left‐step in a left‐lateral fault), local zones of exten-sion create small basins, which are gradually reintegratedinto the fluvial system once slip has been transferred else-where in the fault zone. At Mustang Ridge, the main traceof the SAF is dotted with topographic sinks that are oftensag ponds made deeper by ranchers; in addition, numerousnatural topographic sinks are aligned with the subsidiaryfault scarps (Figure 2e) and are likely tectonic sag ponds.The distribution of topographic sinks generated by the auto-mated extraction procedure indicates that some subsidiaryfaults may have less activity due to the lack of sag pondsobserved along these features.[38] There is good correlation between both the largest

fault scarps and large topographic sinks. Additionally, theshort but sharp scarps in the northwestern part of MustangRidge also have associated topographic sinks. The presenceof sag ponds on these faults in particular (and the near

absence of sag ponds in the southeastern part of the step overzone) may indicate that considerable creep is accommodatedby the largest scarps, and that distributed deformation hasmore recently begun to transfer to the smaller fault scarps tothe northwest.

5.5. Fault Mapping

[39] The correlation between Rymer’s [1981] mappedfaults and landscape features visible on the lidar‐derivedshaded relief maps indicate that refinements can be madefrom the lidar data analysis (Figure 7a). Mapped faultsgenerally correlate with the approximately north‐strikingridges that are oriented oblique to the main SAF. One of themost striking features of Mustang Ridge is the large numberof sag ponds that are observed off of the trace of the SAF.These sag ponds were a primary mapping criterion inRymer’s [1981] efforts to locate subsidiary structures. Theautomatically extracted sag ponds visible in Figure 2e areclearly aligned with Rymer’s [1981] subsidiary fault array,and even very small sag features can be identified usingstandard hydrological analysis tools.[40] Using the mapping criteria established by Rymer

[1981] in combination with the suite of lidar‐derivedhigh‐resolution grids, we propose several refinements to thelocations of active faults at Mustang Ridge (Figure 7b). Theoriginal mapping was done largely on the basis of landscapefeatures that are easier to visualize using the high‐resolutiontopographic data than in the field, so the proposed refine-ments follow similar criteria as the original mapping. Fur-thermore, they do not violate any constraints evident in thefull geologic map detail of Rymer [1981]. For this study,faults on the Pacific plate mapped by Rymer [1981] werenot evaluated, nor were the reverse‐sense boundary faultsexposed farther from the fault trace than the subsidiary faultson which we focus (Figure 7). These appear to be the surfaceexpression of a “palm tree” structure [Ramsay et al., 2000]with no evidence of Holocene activity.[41] We additionally speculate that the queried fault trace

in the northern portion of Figure 7b may be a zone of futureslip transfer from the main SAF, based on evidence dis-cussed in this work, as well as the presence of a subtle linearfeature visible in the shaded relied maps. This possiblerealignment is the logical extension of slip accommodationon the subsidiary faults that appear to be rotating the mainSAF, and if slip accommodation on this subsidiary faultincreases, it should propagate along strike to the north, andeventually be a continuous fault that connects to the mainSAF further north.

5.6. Fault Zone Kinematics

[42] While detailed understanding of planform structuralgeometry is useful, gaining a better understanding of faultzone kinematics is necessary to evaluate slip partitioningacross Mustang Ridge. A comparison of creep rates derivedfrom (1) the Monarch Peak creepmeter (∼15 mm/yr acrossan aperture <5 m) [Schulz et al., 1982]; (2) the MonarchPeak alignment array: ∼17.3 mm/yr across an aperture of∼100 m measured with a theodolite over 9 years [Burfordand Harsh, 1980], and 17.9 mm/yr over ∼41 years (this


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Figure

7.Propo

sedrefinementto

arrang

ementof

active

faults

atMustang

Ridge.(a)location

ofallsurfacefaults

asmappedby

Rym

er[1981].(b)Refined

faultlocatio

nswith

inferred

senseof

slip.Queried

faulttracein

northern

partof

map

follo

wsasubtle

linearfeature,

which

may

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themainSAF.


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study) and ∼17.4 mm/yr measured with GPS [Titus et al.,2006]; and (3) an intermediate trilateration network (28 ±3 mm/yr across an aperture of ∼1.1 km) [Lisowski andPrescott, 1981] suggests that the subsidiary fault networkis carrying ∼11 ± 3 mm/yr of creep. It should be noted that afault identified byRymer [1981] and visible in the lidar‐shadedrelief maps west of the alignment array on Figure 8 may alsocarry an unknown amount of creep; its extent to the north-west in unknown though no surface trace is obvious adjacentto the alignment array. The trilateration network does notspan the entire subsidiary fault zone, so it is possible that theremaining imbalance between the trilateration network sliprate, and the slip rates several km northwest and southeast ofMustang Ridge (30.0 mm/yr at Slack Canyon, ∼22.5 km SE,and 31.4 mm/yr at DeAlvarez Ranch, ∼14.5 km NW [Burfordand Harsh, 1980]) is accommodated on the NE edge of theMustang Ridge step over zone.

[43] The dominantly west facing aspect of the steep slopeson the subsidiary fault scarps suggest either down to thewest normal or reverse faulting. The overall right step withinthe dextral San Andreas fault system at Mustang ridgeindicates a releasing geometry and would favor dextraloblique faulting with a strong normal component.

5.7. Constraints on Subsidiary Fault Creep Ratesand Scarp Relief

[44] Along subsidiary faults in an extensional step over, wecan estimate maximum slip‐rates for a range of geometries ofthese features (Figure 9). We assume that the missing slipacross the main SAF is transferred across 2–3 oblique normalsubsidiary faults that dip at an angle g between 30° and 60°(locations of these structures are shown in Figure 8). Definingthe angle between the subsidiary faults and the SAF as a,and the slip transferred on to the subsidiary faults as Vss, themaximum subsidiary‐fault‐parallel strike‐slip rate (Vsss)must not exceed

Vsss ¼ Vss � cos�: ð2Þ

Similarly, the maximum subsidiary‐fault‐perpendicular hor-izontal separation rate Vshs on any one subsidiary fault is

Vshs ¼ Vss � sin�: ð3Þ

This leads to a maximum subsidiary fault dip‐slip rate for asubsidiary fault dip g of

Vsds ¼ 1

cos�� Vss � sin�; ð4Þ

and a subsidiary fault vertical separation rate of

Vsv ¼ tan� � Vss � sin�: ð5Þ

Vsv is the vertical component of the slip rate of the subsidiaryfaults, which is strongly dependent on g. For a reasonablerange of g between 30° and 60°, the maximum summed

Figure 8. Location of Monarch Peak alignment array,creepmeter, and intermediate array within fault network atMustang Ridge.

Figure 9. Schematic illustration of faults in map view and subsidiary faults in cross section.


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vertical separation rate across the subsidiary oblique normalfaults is between 28% and 86% of Vss. From Figure 8, it isapparent that slip distributed to the NE of the SAF acrossthe Monarch Peak intermediate array is accommodated onbetween 2 and 5 subsidiary faults. In our simple model(Figure 9), the creep rate deficit across the step over (Vss)is distributed between the three major subsidiary faults. Fora local slip rate deficit (Vss) of ∼10–14 mm/yr, the averagesubsidiary fault vertical separation rate is 4 mm/yr if g =60° \ or 1.33 mm/yr if g = 30°. Experimental work suggeststhat vertical relief generated in a releasing step over zone ison the order of ∼35% of horizontal strain [Hempton andNeher, 1986]. This is consistent with our estimates ofrelief production on subsidiary faults.[45] Near the center of the study area, a straight segment

of the SAF bends anticlockwise ∼11° forming two distinctright steps in the SAF (Figure 6a). These right steps arelocated at the intersection of the two largest subsidiary faultsand the main SAF. Slip on the subsidiary faults likelycaused this deflection in the SAF as the block bounded bythe SAF and the two subsidiary faults rotates. Thus, the slipalong subsidiary faults may alter the surface trace of theSAF as finite deformation accrues in this zone.[46] The evidence for the relatively high rates of activity

of the subsidiary faults that rotate the main SAF suggest thatthe near‐fault creep rate on the SAF in the northwestern partof Mustang Ridge may be even lower than the ∼17 mm/yrmeasured at the alignment array to the southeast. The faultsadjacent to the alignment array lack sag ponds, have rela-tively old morphologic ages and less distinct fluvial knick-points; nonetheless, they must carry the difference in slipmeasured across the two apertures of the alignment andintermediate arrays. These observations point to a possiblelocation for current and ongoing reorganization of the maintrace of the SAF through the middle portion of MustangRidge as fault slip decreases on the main SAF and istransferred to the most active subsidiary faults.

6. Conclusions[47] Of the analyses we have utilized, shaded relief, slope,

and aspect mapping are clearly valuable for visualizationand mapping. High‐resolution topographic data make itpossible to extract topographic profiles with a resolutionsimilar to field surveys. This allows for detailed scarp mor-phologic analysis. Sag ponds show a close association withactive fault traces. Channel profile analysis successfullyidentified knickpoints that may be associated with activefaulting or the juxtaposition of rocks of differing erodibility.In this study, spectral analysis provided an objective mea-sure of the periodicity and significance of subsidiary scarps.The spectral analysis suggests that at least the identified

portion of the subsidiary fault array at Mustang Ridge isquasiperiodic. If this model of a periodic structure to the enechelon step over zone at Mustang Ridge can be extrapolatedto other areas, it provides another criterion for fault mappingin releasing strike‐slip step over zones. As such, isolation ofsuch quasiperiodic features provides a promising guide forlocating surface expressions of the subsidiary faults.[48] At Mustang Ridge, subsidiary faults are well expressed

in the landscape. The local geologic structure is that of areleasing right step in the SAF, and is expressed as a set ofen echelon oblique‐normal (right lateral and down to thewest) subsidiary faults. These subsidiary structures per-missibly accommodate the ∼10–14 mm/yr creep deficit onthe main trace of the San Andreas Fault at the location ofexisting creep measurements, and perhaps more to the north-west. Subsidiary faults at Mustang Ridge are oriented 13–32°obliquely to the main trace of the SAF, and fault spacingranges from ∼300 to 500 m. Evidence for higher relativeslip rates on some of the subsidiary faults include high apparentvertical fault scarp offsets, young fault scarp morphologicages, presence of associated sag ponds, zones of local highfluvial channel steepness, and by involvement in block rota-tion that bends a segment of the main trace of the SAF. Thesubsidiary faults in the middle and northwestern part of thestudy area appear to be most active. In contrast, several faultsin the southeastern part of the step over have older morpho-logic ages, fewer associated sag ponds and less distinct fluvialknickpoints. The two large faults in the center of the step overzone appear to be the most active, and perhaps the largerof the two scarps will be the location of a realigned mainSAF as finite deformation accrues and rotates the surfacetrace of the currently creeping trace of the SAF. The contin-uation of this possible realignment to the north is indicated onFigure 7b, where it is manifest as a subtle linear feature onthe shaded relief and slope maps. This study confirms thatlidar data, used in conjunction with detailed geologic andgeomorphic observations, can illuminate the geometry andkinematics of complex active fault zones such as that presentat Mustang Ridge. This study location may also provide anear‐surface site to test the hypothesis that talc‐bearing ser-pentinite is a prerequisite for fault creep [Moore and Rymer,2007].

[49] Acknowledgments. This work was funded by a USGSMendenhall Fellowship to S.B.D. Thanks to J. T. Perron for his publiclyavailable DFT codes. Thanks to J. Lienkeamper for helpful discussions. Thiswork was possible thanks to several decades of access granted to USGS andother workers to private lands at Peach Tree Ranch. Thanks to J. Stock for ahelpful review of an early version, and J. R. Arrowsmith, M. Taylor, and ananonymous reviewer for their helpful reviews. We acknowledge NCALM andthe GeoEarthScope program for collecting these lidar data and C. Crosby andthe rest of the opentopography.org team for making the data easily accessible.

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