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Source Parameters for the 1952 Kern County Earthquake, California: A JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. B1, PAGES 771-785, JANUARY 10, 2001 Sourceparameters for the 1952 Kern County earthquake, California: A joint inversionof leveling and triangulation observations Gerald W. Bawden u.s. GeologicalSurvey, Menlo Park,California Abstract.Coseismic leveling and triangulation observations are used to determinethe faulting geometryand slip distribution of theJuly 21, 1952,Mw 7.3 KernCounty earthquake on the White Wolf fault. A singularvalue decomposition inversion is usedto assessthe ability of thegeodetic networkto resolveslip alonga multisegmentfault andshows that the networkis sufficientto resolveslip along the surface rupture to a depthof 10km. Below10 km, thenetwork can only resolvedip slipnear the fault ends. The preferred source model is a two-segmentright-stepping faultwith a strikeof 51ø anda dipof 75ø SW. The epicentralpatch has deep (6-27 km) left- lateraloblique slip, while the northeastern patch has shallow (1-12.5 km) reverseslip. Thereis nearlyuniform reverse slip (epicentral,1.6 m; northeast,1.9 m), with 3.6 m of left-lateralstrike sliplimited to theepicentral patch. The seismic moment is Mo = 9.2 _+0.5 x1019N m (Mw=7.2). The signal-to-noiseratio of theleveling and triangulation data is reducedby 96% and49%, respectively.The slipdistribution from the preferred model matches regional geomorphic featuresand may provide a drivingmechanism for regionalshortening across the Comanche thrustand structural continuity with the Scodieseismic lineament to the northeast. 1. Introduction slip distributionalong the White Wolf fault. Finally, I compare the resultswith previousstudies and discussthe implicationsin a The Kern County earthquake was one of the largest regionalcontext. earthquakesin California during the twentiethcentury (M,• 7.7, Mw 7.3 [Richter, 1955;Ben-Menahern, 1978]), secondonly to the 2. Geodetic Data great 1906 San Franciscoearthquake. The 1952 eventruptured 2.1. Triangulation 60 km of the White Wolf fault, northof the junctionof the San Andreasand Garlock faults, and near a restrainingbend in the This studyuses coseismic angle changes for the triangulation San Andreasfault (Figure 1). Even thoughthis earthquakewas array that spansthe White Wolf fault (Figure 2 and Table l a). one of the most well-studied events in southern California at the The U.S. Coast and Geodetic Survey (USCGS) collectedover time [Oakeshott, 1955], nearly 30 years elapseduntil the first four decades(1926-1972) of triangulationdata throughoutthe rigorousgeodetic source models were published[Dunbar et al., Big Bend region of the San Andreas fault [Thatcher, 1979; 1980; Stein and Thatcher, 1981]. Unfortunately,differences in Dunbar et al., 1980;Stein and Thatcher,1981' King and Savage, the geometryand slip distributionbetween these models provide 1984;Eberhart-Phillips et al., 1990; Snayet al., 1996;Bawden et conflictinginterpretations on the relationshipbetween the White al., 1997], includingtwo surveysthat bracketthe July 21, 1952 Wolf fault and a number of other active faults and structures mainshock. Two months prior to the earthquakethe USCGS throughoutthe region. completeda comprehensive,6-month-long survey of the trian- I presenta simple sourcemodel for the Kern County earth- gulation array that spansthe southernhalf of the White Wolf quake based on a comprehensiveanalysis of the coseismic fault; this array was again reoccupiedbeginning 2 months triangulationand levelingobservations. This studydiffers from (September1952 to January1953) after the mainshock.Both the previous coseismic analysis by including a larger set of preseismicand postseismicsurveys were conductedto first-order triangulationobservations and by directlyinverting the geodetic tolerances,where the standarderror, o, assignedto each meas- observationsrather than using forward modelingtechniques to urementwas basedon the consistencyof the anglesturned during match shearstrain estimatesand uplift patterns. Furthermore,I each setup and the consistencyamong different setupsat the examinewhere the geodeticobservations can resolve slip and, same station. The standarderror values usedin this study are more importantly,where the resolutionis poor and slip cannotbe <0.8 arc sec. determined.I first constrainthe geometryof the fault modelby The 143 coseismic angle changes were calculated by combiningthe geodeticdata with aftershocklocations and then differencing654 preseismicand postseismic angles (Table lb and invert the observations,in a least squaressense, to estimatethe Figure 2). If repeatedmeasurements were made in either epoch (1951-1952 or 1952-1953), then the angle was determinedby averagingeach observation,weighted by its standarderror. To Thispaper is notsubject to U.S. copyfight.Published in 2001by the AmericanGeophysical Union. assessthe quality of the data, I evaluated the misclosuresfor monumentcombinations that formed a closedtriangle, a total of Papernumber 2000JB900315. 16 closedtriangle (48 angles)for bothpreseismic and postseismi- 771 772 BAWDEN: KERN COUNTY EARTHQUAKE SOURCE MODEL Bakersfield ........ Ca/iente ', ! __L.........i--.: :!:--:½• ......... ",,.i. % • 7':"L'•: ! ;. .. ! ! ß--* I i .,.,,,,•,•..•.•....... •, .......... •..................... ß ..•.• ..-•.:•,-: . ....•..•.•..•l% I IJ I II IIII ............:•-:•,.. 110l• .... .....:..:•:"•:.•:: ?'•"'::".•-•,•;;•!•.:(:::•';•...;.--•-•:'"::.'•...•:• -, -•;.:.-..--::':;::' .. Figure1. Topography,monument, and fault map of theWhite Wolf fault area. The 1952 surface ruptures areshown in boldblack lines, dashed where buried. Star, 1952 epicenter; triangles, triangulation stations; circles,leveling benchmarks.. The figure generated with GMT [Wesseland Smith, 1991]. c epochs. If the misclosurewas largerthan the sum of the errors whereN is the numberof observations,Oi is the ith observation, in the three angle measurements,then the misclosure was and o'• is the ith standarderror. The S/N for the triangulation distributed equally among the three measurements[Bomford, data is 3.33. About 27% of the angle changesare equal to or 1980; Hodgkinsonet al., 1996]. Such misclosureadjustments smallerthan the observationuncertainties. The low S/N is likely were made to 12 of the 654 observations. a functionof the geometryof the network:the majority of the The signal available for modeling is best describedby the triangulationobservations are within the upthrownblock and do signal-to-noiseratio (S/N). The signal representedhere is the not spanthe 1952 surfacerupture. Furthermore,the orientations coseismicangle change, and the standarddeviation of eachangle of many of the observedtriangles are not optimal for resolving changeis set to 1.18 arc sec. The standarddeviation is basedon deformationalong the fault. the weightedaverage of the triangleclosures [King and Thatcher, 1998]and is consistentwith first-order uncertainties (0.8 x/•) 2.2. Leveling . typically assignedto triangulationobservations [Gergen, 1975]. The leveling data used in this study were collected by the The signal-to-noiseratio can be expressedas USCGS [Whitten, 1955] and evaluatedby Stein and Thatcher [1981] for slope-dependentand misclosureerrors (Table 2a). S/N= 1 The majority of the monumentswere initially surveyedin 1926 N-1 and then resurveyedin 1953 following the mainshock. A small segmentof the southernleveling line was surveyedin 1947 and BAWDEN: KERN COUNTY EARTHQUAKE SOURCE MODEL 773 ,,,, Caliente 35' 15' C-07 35 39 G-14 * • 35 ø 00' LevelingEpochs 1952-53 Seismicity -•-1926-1953 • M> 7.0 + 1942-1953 • M6.0 • 1948-1953 e M 5.0 • M 4.0 0 10km • M 3.0 I -119' 00' -118' 45' -118' 30' Figure 2. Geodeticnetwork and seismicity, 1952-1953. The numberedtriangulation stations (triangles) and levelingbenchmarks (circles) correspond to observationsin Tables1 and2. The 1952 surfaceruptures are shownin bold black lines. Star, 1952 epicenter. 1953 (Figure2). In the analysis,I usetwo primaryleveling lines 3. SingularValue Decomposition thatspan both the northernand southern end of the 1952surface rupture,as well as the spur line (1948-1953) to the top of I use single-valuedecomposition [Menke, 1989] to estimate WheelerRidge near the 1952 epicenter(Figure 2). Most of the slip alongthe White Wolf fault andto evaluatewhere fault slip is levelingmonuments used in the inversionsfor all threelines are well constrained(resolution) and to what limits the slip can be locatedon thehanging wall blockof theWhite Wolf fault (Figure determined(uncertainty). I solved = Am, where A is a partial 1) and are lesssusceptible to possiblenontectonic contamination derivative matrix that relates the observeddata, d (i = 1, m) to the from groundwaterand hydrocarbon-relatedsubsidence observed modelparameters that I seek,m (j = 1, m). The modelparameter northof theWhite Wolf fault [Lofgren,1975; Stein and Thatcher, mk is eitherthe dip-slipor strike-slipcomponent of displacement 1981]. I use the elevationchanges between successive bench- on a rectangularfault segment.The A matrixcan be decomposed markpairs as the levelingobservable, so that the observations are to A = UAVx, whereU is an M x J set of eigenvectorswhich independentof elevation changes at the endp_?ints (Table 2b). spanthe dataspace, V is a J x M matrixof eigenvectorsthat span The standarderror for each segmentis axil in millimeters, the modelparameter space, and A is a diagonalmatrix of singular where •x is a constantbased on the precisionof the leveling valuesordered by size [Menke, 1989]. The solutionvector m = surveyset to 2.0 mm andL is thedistance between monuments in V•,At,Up
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