JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 89, NO. Bll, PAGES 9323-9332, OCTOBER 10, 1984 Near-Surface lo in Situ Stress Strain Relaxation MeasurementsAlong the San Andreas Fault in Southern California MARCL. SBAR, 1 RANDALL M. RICHARDSON, ANDCHRISTOPHER FLACCUS 2 Departmentof Geosciences, Universityof Arizona, Tucson TERRY ENGELDER Lamont-DohertyGeolo•licalObservatoryof ColumbiaUniversity,Palisades,New York Strainrelaxationstressmeasurements weremadein the Mojave Desertsoutheastof Palmdale,California, at two sitesduring the summersof 1979 and 1980, using the U.S. Bureau of Mines techniqueto depthsof about 30 m. The field data and finite elementmodelingstudiesdemonstratethat thermally inducedstressdominatesthe resultsobtained in the upper 6 m. At depthsgreater than 6 m the average orientationfor the horizontalmaximum compressivestressat thesesitesis N22øW ___ 9ø at 2 km south of the San Andreasfault and N13øW + 2ø at 20 km north of the fault. These azimuthscompare favorably with the averageof N21øW determinedwith nearby hydrofracturestressmeasurements (Zoback et al., 1980).Savageet al. (1981)also found a NNW orientationfor the maximumshorteningfrom a geodetic network with 'a 15-km aperaturein the Palmdalearea. The fact that essentiallythe sameorientationis recoveredby threedifferenttechniqueswhichsampleto differentdepthsand over differentareal extents arguesstronglyfor a contemporarytectonic origin for the stress.Finite element models of the San Andreasfault in southernCalifornia develop a stressfield similar to that observedregionally (-,•N15øE for the maximumcompressive stress)away from the fault when displacements correspondingto relative motion betweenlithosphericplatesare appliedon the boundariesof the models.Near the fault, however, the modelprincipalstresses are rotatedcounterclockwise similarto thosemeasured nearPalmdale, demonstrating the influenceof the faultson the principalstressorientations. are insufficient fault planesolutionsof earthquakes to define A knowledge of the stateof stressin the vicinityof active the principalstressorientations.In addition,the P and T axes INTRODUCTION faults is One necessaryingredient in the understanding of the from a singlefault plane solutionare poor approximationsfor constitutiveproperties of fault zones and the mechanismof the direction of the principal stresses[McKenzie, 1969; Raearthquake generation. Theoretical [Rodgers and Chinnery, leighet al., 1972]. Thus an effort was made during the summer 1973] and laboratory [Barber and Sowers,1974] researchon of 1977 to measurein situ stressusing strain relaxation techstrike-slip faultsindicates that changes in the orientation and niques at shallow depths [Sbar et al., 1979; Tullis, 1981]. At magnitudeof the stressfield shouldbe expectedin the vicinity that time it was questionable whether near-surface strain of thesefaultsWhentheyareloaded.Thesechanges in stress relaxation measurementscould indeed detect contemporary are most likely a result of somecombinationof lowered rigid- tectonic stress.Within the next year, deeper hydraulic fracity near the fault, the strain accumulation-release history of turing stressmeasurementswere initiated in a profile from the thefault,faultgeometry, andasperities alongthefault,which San Andreasfault northward into the Mojave block [Zoback serve as locking points. Our objectivesin initiating this researchwere to determineif contemporarytectonicstresscould be measuredin the near surfaceand also to test if the regional stress field near faults was indeed altered as in the model and Roller, 1979]. The strain relaxationmeasurements are characterizedby consistentorientations at adjacent sites but significantvariation between groups of sites, while the hydraulic fracturing techniqueproducedseveralreasonablycon- studies. sistent measurements The work of Castle et al. [1976-1in identifying the southern California uplift heightenedthe interest of the scientificcommunity in the section of the San Andreas fault that last ruptured in 1857. Simple estimatesof slip using global plate ve- also detecteda decreasein shear stressmagnitude as the fault is approachedfrom the north. Subsequentto the above research,further strain relaxation measurements of stress orientation. Zoback and Roller made in the winter and summer indicated that measurementslessthan 6 m from the surfacemay be seriously earthquake the size of the 1857 shock. Later more precise affectedby thermally inducedstress[Flaccusand Richardson, estimatesof recurrenceby Sieh [1978] are in general agree- 1981; Sbar and Richardson,1981]. The latest strain relaxation ment with thesenumbers.Sincethe area in the vicinity of this stressmeasurementswere made to depths of about 30 m at sectionof the SanAndreasfault is relativelyaseismic, there two sites south of Palmdale during the summer of 1980. A locity data suggestedrepeat times of 100-200 years for an third site was attemptedin the winter of 1980-1981but failed due to technicalproblems.These most recent data are reported in this paper and compared with nearby deep hydrofracture stress measurementsobtained by Zoback et al. [1980] and geodeticstrain data in southern California from Savageet al. [1981-1.Through this comparison,a caseis made • Now at Sohio Petroleum,Dallas, Texas. 2 Now at Gulf Oil Co., Casper,Wyoming. Copyright 1984by the AmericanGeophysicalUnion. Paper number 4B0180. 0148-0227/84/004B-0180505.00 that 9323 shallow strain relaxation measurements can detect con- $BAR ETAL.:NEAR-SURFACE 'INSITU STRESS 9324 IMS-13ø•3 ø-• ':---•-•[', ,'.'.-;'• •,'.:-•-,'•J-:,•l GENERALIZED GEOLOGIC /' .'-•---.,. ,'• !• • :..".,//.,;., ,-"1 MAP •;,,•;11•-,' ",-' a •- "Y •--•','_,?.'1 . ¾• DESERT ,-,"' / ' ,'' '" • Alluvium .':]•[ Punchbowl Fm(Mio) •,;?, 0 • WESTERN MOJAVE • ]• Sen Francisco Fm (Eo-Peleo) [• Qtz Monzonite t•Groinire (Mes) ]• Metomorphic Rocks (Mes to •i• Intrusives {MEG) o [ 5 I scole Km 118ol 45'W Fig. 1. Geologicmap of the studyarea. The heavyarrowsand solid circlesdenoteour strain relaxationsites.Light arrowsand solidsquares arehydrofracture sitesof ZobackandRollerr19791andZobacket al. r19801. -temporary tectonic stress. Theseresults aretheninterpreted in terms of the regional tectonicsof southernCalifornia and fault rheology and geometry with the aid of finite element models of southern California. SITE DESCRIPTION though in some outcropsthere are bedding plane fractures spacedat 1-3 m intervalsand someverticaljoints with locally varyingattitudes,spacedat 3-7 m intervals.In 28 m of core obtainedat LRS, however,only one fracturewasencountered. Site IMS (Figure 1) was drilled in the Mesozoic quartz monzonites which form the basement of much of the western The surfacegeologyof the westernMojave Desert consists of vast expansesof late Tertiary alluvium which fill wide shallow basinsbetweenscatteredbuttesof Mesozoicgranitesand quartz monzonites(Figure 1). These buttes are often highly Mojave Desert. Gravity data [Mabey, 1960] indicate that in the western Mojave there are two northeast trending basement highs separatingthree alluvium-filled basins.This site is along the southeasternmost of these highs on the southern fractured and weathered. To the southwest the foothills of the lobe of Piute Butte about 20 km northwest of the San Andreas San Gabriel Mountainscontainsandstoneconglomerates (late fault. Near the top of the core,severalsteeplydippingfrac- Miocene-early Pliocene Punchbowl Formation and the Paleocene-Eocene San FrancisquitoFormation), quartz monzonites,granites,and metamorphicrocks. Sites LRS and TKY (Figure 1) are on a flat outcrop surrounded by alluvium among the low-lying ridges of the tures striking N40øE were found. Between about 6 and 14 m depth a highly fracturedzone of altered rock was encountered in which no measurements couldbe made.No systematicfracture orientation was evidentat thesedepths.Near the bottom of the hole, steeply dipping fractures striking N85øE and gentlydipping fracturesstriking N30øW were found. Punchbowl formation between the San Andreas and Punchbowl faults. The two sites are within 10 m of each other on the north limb of a large synclinewhose axis trends N70øW and plungeswest. The bedding strikes N40ø-50øW and dips 50øSW.The PunchbowlFormation consistsof massive,light buff, cross-bedded,coarse terrestrial sandstonewith large lenses of pebble and cobble conglomerate [Noble, 1954; Dibblee,1967]. We madean effort to avoid the conglomerate TECHNIQUE The U.S. Bureau of Mines (USBM) borehole deformation techniquewas used at all sitesreportedin this manuscript (Figure 2). A detaileddescriptionof the USBM techniqueis foundin the work by Hookerand Bickel[1974]. The gauge consistsof 12 individual foil-resistancestrain gaugesmounted whenever possible in the selection of intervals for stress two apieceon six cantilevers, whichare housedwithin a cylinmeasurement.The formation is remarkably unfractured,al- drical steel borehole tool in a manner which will record hori- SBAR ET AL.' NEAR-SURFACE IN SITU STRESS 9325 tal componentsof diametrical borehole displacementare recorded from which a displacementellipseand the azimuth of its major axis are computed.The introductionof drilling fluid by a pump during overcoringsometimesresults in a slight compressionof the strain gaugesand/or deformation of the 3.8-cm borehole,resultingin a displacementoffset.To avoid this offset, interpretations of strain relaxation data are restricted to the "pump-on" period. A slight compressional bulgeis observedjust beforethe strain relaxation indicatedby the large expansion. Wong and Walsh ['1979] demonstrate ,o that this bulgeresultsfrom the Poissoneffectin elasticmateri- OVERCORING A BUREAU OF MINES GAUGE Fig. 2. Cross-sectional view of U.S. Bureau of Mines overcoring techniquebeforeand afterovercoring. zontal displacementsreflectingdeformation of a 3.8-cm (EX) borehole.The gaugeis azimuthally oriented and set at a specified depth inside the 3.8-cm borehole and overcored subsequently by a 15.9-cm outer diameter/14.3-cm inner diameter coring bit (Figure 2). The length of core cut in a single measurementwas usually about 30 cm. During the overcoringprocessthe 3.8-cmboreholedeforms in responseto relaxation of the core upon stressrelief. The USBM gauge records this deformation as a changein borehole diameter from which in situ stressmay be calculated usingthe elasticmoduli of the rock. The deformation observed is affected by the presenceof fractures and strong rock anisotropy within the core. The method used to determine rock propertiesfor the calculationof stresspartially compensates for these effects. Field procedure. Figure 3 showsa typical borehole deformation curverecordedwith the USBM gauge.Three horizonAZIMUTH LRS -# 19.38 U1=-86 ø als. The same effect is observedby Hooker et al. ['1974] in a two-dimensionalnumerical simulation of the overcoring process.The displacementfor each componentwas then found by fitting horizontal lines to the data beforethe bulge and ffter the strain relaxation and noting their difference. Once a displacementellipseis determinedfrom the borehole deformationmeasuredduring overcoring,an estimateof the elasticmoduli of the rock is necessaryto computethe corresponding stress. To obtain static determinations of these moduli, the USBM gauge is reoriented inside the 14.3-cm coresat the samepositionit occupiedduring the initial overcoring.A biaxial compressionchamberappliesa known radial load to a 20-cm length of core containingthe gauge.Secant moduli are obtained usingthe recordeddisplacementsin each of the three gauge componentdirectionsas functionsof applied pressure(Figure 4). Becausecrack closingand rock anisotropy causethe moduli to be stressdependent,the moduli usedfor stresscalculationsare determinedat the approximate displacementmagnitudes observed during the initial overcoring of eachcore. The unloadingrather than loading part of the curve is used,sincestrain relief is an unloadingprocess.A small nonrecoverablestrain is observedonly during the first loading and unloading cycle. When the maximum applied pressureis constant,the secondand later cyclesreturn to the samevalue of displacementat zero applied pressure. Data reduction. Since we do not measure D2 2dPo Ei='•-• D2--d Ui UI U3 • -50 0 100 200 300 400 OVERCORE DEPTH (MM) 500 a sufficient number of elasticmoduli to correct exactly for the anisotropy of the rock, we use an approximate technique developed by Tullis [1981] to account for elastic anistropy in calculating the stress.Equation (1) is determined from the stress/strain analysisof a thick-walled cylinder, which yields Young's modulus for isotropic rock. This equation is then applied separately along each of the three axesof the strain cell' (1) where E• is Young's modulus, D is the outer diameter of the core, d is the inner diameter of the core, P0 is the applied radial pressure,and U• is the increasein diameter of the inner hole upon releaseof the pressure.The three valuesof E• obtained are averagedto form E. Equation (2) is then applied to calculatea modified U• along eachaxis' Ui m: UiEi/E (2) Following this procedure,the equationscited by Merrill and Peterson [1961] for the deformation of a borehole in an infiFig. 3. Example of a strain relaxation history during overcoring nite plate with stressapplied at infinity are applied to calcuof the USBM gauge. Values along the abscissaindicate distance of overcoring.The location of the strain gauge(GD) is 120 mm below late the stressusing the average Young's modulus E and the the depth where overcoring begins. Values along the ordinate are modifieddisplacementsUi m.Calculationswere made for both displacementrecorded by the gauge,which is transformedto stress. Symbolsand nominal azimuth: triangles,north; squares,southeast; the plane strain and plane stresscases.With the exceptionof the near-surfacepoints, which are plane stress,neither ascircles,southwest.The true azimuth of U1 (north) is noted at the top of the figure. sumption is exact. We chose the plane strain equations for 9326 SBAR ET AL.' NEAR-SURFACE IN SITU STRESS QUARTZ MONZON ITE SANDSTONE LRS 19.38m I M S 4.50m U2 UI U3 I I0 20 I 20 DIAMETRALCONTRACTION (/.LM) Fig. 4. Applied pressureversusdiametral contractionfor samplesfrom sitesIMS and LRS. Secantmoduli are determined fromthesecurvesat approximately thedisplacement observed in theoriginalovercore. Notationasin Figure 3. these data as a better approximation. The procedure and equationsare explained by Tullis [1981] and will not be repeated here. D^z^ Thus the averagemoduli determinedfrom the LRS data were usedfor computingstressat TKY. An obviousfeature of the stressprofile versusdepth for LRS (Figure 5) is substantiallyhigher stresses in the near surface above about 6 m which decayexponentiallyto a background level of the order of 1.5 MPa. Such an exponential decay is most easilyexplainedin terms of seasonaltemperature variationsat the surface,wherethe surfacetemperature Tsis givenby The data reportedin this paper were taken at sitesIMS and LRS in the summerof 1980.TKY was sampledin the summer of 1979 and is included for comparisonwith LRS. The measurementsat LRS and IMS were made to depthsof about 30 m specifically to avoid the effects of thermally induced T•: To + A cos (cot) (3) stress.The previousyear TKY was drilled to a depth of 10 m. Observationsby Hooker and Duvall [1971] and our previous where Tois the meanannual temperature,the amplitudeA of measurementsin the Mojave Desert [Flaccus and Richardson, the surfacetemperaturevariation from NOAA climatological 1981; Sbar and Richardson,1981] convincedus that thermally LRS inducedstressis a significantsourceof noisein the upper 6 m. The Punchbowl Formation in which LRS and TKY were sited is essentiallyunfractured. This permitted us to make a relatively large number of measurementsin each of these holes. Both sets of data are plotted in Figure 5 to show the consistencyin data from year to year (Tables 1 and 2); however, only the LRS data are usedin the following analysisfor reasonsthat will be explainedbelow. Twenty-one setsof elastic moduli were measuredout of 40 possibleat LRS becauseof breakage of the core on removal from the hole or core barrel. These moduli would be equivalent to the Young's moduli for isotropic rocks. The 21 measuredmoduli were averaged,and this value was applied to all of the displacementdata for which no moduli were determined. The average values are essentiallyisotropic, since the anisotropyat this site has no preferredorientation (Figures 6 and 7 and Table 2). Note that the degree of anisotropy is relatively low for most individual measurements.Poisson's ratio, also needed in the calculation of stress, could not be measured with the biaxial chamber used to determine determined on the cores from TKY STRESS I 2 3 (MPo) 4 5 o •01 ß 0i ß 5 D I0 E P T H 15 2O (M) )10 0ß0 o 2e-- 25 o • o ß the Young'smodulus.A value of 0.4 was selectedfor the LRS and TKY stresscalculation becauseof the relatively soft nature of theserocks (J. Daemon, personalcommunication,1982). The moduli HORIZONTAL 0 were measured under a loading rather than unloading situation and were thereforeunusablefor calculatingstressfrom strain relief data. 3O Fig. 5. Stressvaluesfor LRS and TKY. The solid symbolsare the maximum horizontal stress.The open symbolsare minimum horizontal stress.Circles are LRS data. Squares are TKY data. Azimuth is indicatedby the bar on the solid symbols.The azimuth is indicatedin plan view with north up and east to the right. Azimuthsare only plotted for data with a stressratio _• 1.4. SBAR ET AL.: NEAR-SURFACE IN SITU STRESS TABLE Horizontal MPa Depth, Maximum Minimum Azimuth of Maximum Stress Shear Stress, E of N Ratio MPa 1.4 1.0 1.3 1.3 0.74 0.12 0.72 0.55 0.84 1.40 1.98 2.59 4.95 5.69 6.12 6.48 7.19 7.52 7.87 9.57 9.93 10.26 5.05 5.54 5.74 5.03 1.81 1.30 1.87 2.69 2.02 1.82 2.05 0.80 1.65 1.61 3.56 5.30 4.30 3.93 1.31 0.71 1.64 2.39 1.10 1.08 1.14 0.77 0.80 0.91 7 1 88 - 25 - 18 43 -83 -47 - 17 - 27 -45 - 59 - 52 - 78 10.52 2.19 0.87 -49 MPa Depth, 5.17 3.63 2.87 3.93 3.14 2.63 2.43 2.42 1.40 1.45 1.36 1.56 1.29 1.21 2.69 1.58 1.26 1.42 1.87 1.34 1.98 1.01 1.84 1.21 1.89 1.77 1.63 1.65 1.32 19.38 21.03 21.51 22.40 22.91 23.37 24.16 24.56 25.88 26.34 27.58 2.08 1.41 0.73 1.30 1.97 1.96 1.53 1.62 2.45 1.83 4.19 E of N 90.2 88.1 97.7 86.2 42.2 78.1 55.9 51.3 6 2 88 -23 Azimuth Modulus, GPa Maximum 4.25 4.25 4.25 4.25 Minimum 4.10 4.10 4.10 4.10 of Maximum Modulus Modulus Anisotropy, E of N % -84 -84 -84 -84 3 3 3 3 1.4 0.25 32.0 16.0 - 16 4.25 4.10 -84 3 0.29 0.11 0.15 0.46 0.37 0.45 0.02 0.43 0.35 0.66 24.3 29.9 43.4 38.5 33.7 38.2 12.3 31.6 29.6 43.3 6.5 23.8 34.5 9.6 10.9 10.7 11.6 5.9 8.9 3.5 42 -83 -43 - 17 -26 -44 -46 -51 -78 -49 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.10 4.10 4.10 4.10 4.10 4.10 4.10 4.10 4.10 4.10 -84 -84 -84 -84 -84 -84 -84 -84 -84 -84 3 3 3 3 3 3 3 3 3 3 2. Stress Data for Site LRS Horizontal Stress, 0.89 1.93 2.51 2.95 3.30 4.04 4.45 4.85 6.55 6.96 7.37 8.10 8.53 9.09 9.53 10.06 10.54 11.43 12.12 12.37 13.26 14.91 15.32 15.72 16.81 17.25 17.78 18.57 18.97 Minimum Azimuth of Maximum Displacement 1.8 1.1 1.1 1.8 1.7 1.8 1.0 2.1 1.8 2.5 Horizontal Maximum Displacement, #m Maximum TABLE m Stress Data for Site TKY Horizontal Stress, m 1. 9327 Minimum 4.90 2.79 2.25 3.60 2.68 2.32 1.78 1.56 0.73 1.17 0.48 0.99 0.92 0.69 0.72 1.36 0.92 1.27 1.27 0.84 1.86 0.85 1.42 0.81 1.23 1.57 1.41 1.44 1.04 1.20 0.63 0.20 1.02 1.48 1.63 0.36 0.32 1.83 1.15 3.10 Azimuth of Maximum Stress Shear Stress, Displacement, #m E of N Ratio MPa Maximum -86 -57 -62 27 86 60 -46 - 51 - 39 -48 - 34 -23 - 28 - 27 - 23 - 73 -60 46 -2 -85 -2 -78 38 -28 - 1 -50 77 -52 -65 56 -77 85 -40 - 27 -28 - 38 - 13 - 10 -29 29 1.1 1.3 1.3 1.1 1.2 1.1 1.4 1.6 1.9 1.2 2.9 1.6 1.4 0.14 0.42 0.31 0.16 0.23 0.15 0.32 0.43 0.34 0.14 0.44 0.29 0.19 1.7 0.26 i8.7 5.7 3.7 1.2 1.4 1.1 1.5 1.6 1.1 1.2 1.3 1.5 1.5 1.1 1.2 1.1 1.3 1.7 2.2 3.7 1.3 1.3 1.2 4.3 5.1 1.3 1.6 1.4 0.98 0.11 0.17 0.08 0.30 0.25 0.06 0.08 0.21 0.20 0.33 0.10 0.11 0.10 0.14 0.44 0.39 0.27 0.14 0.24 0.17 0.59 0.65 0.31 0.34 0.55 31.1 17.6 20.9 22.5 31.0 24.0 31.8 21.4 29.2 30.1 34.7 28.4 26.5 26.7 28.4 46.3 27.3 15.1 32.6 34.1 36.7 32.4 35.4 42.9 31.9 73.4 -3.7 11.8 13.3 13.7 17.5 9.3 27.2 15.3 18.3 12.8 13.3 22.8 20.1 20.7 20.9 35.7 3.8 - 1.1 17.7 18.8 19.9 - 3.4 -5.4 22.9 11.0 38.6 100.7 42.1 83.1 63.4 88.4 42.5 42.0 43.4 26.6 24.2 31.3 32.3 19.6 Minimum 90.5 28.1 45.7 52.1 65.8 33.5 22.5 17.5 6.1 15.8 -0.0 12.4 9.0 Azimuth of Maximum Displacement E of N -81 -71 -71 23 64 57 -44 -50 - 38 -46 -37 -21 -27 -29 - 15 -69 -63 51 - 12 -85 0 -74 47 - 27 - 1 -46 75 -48 88 29 - 77 85 -38 -26 - 15 - 37 -12 -9 -36 28 Azimuth Modulus, GPa Maximum Minimum of Maximum Modulus Modulus Anisotropy, E of N % 3.40 6.55 2.85 4.25 2.70 4.25 4.25 4.25 4.25 4.25 5.26 3.80 5.20 5.11 10.29 6.71 4.41 5.42 4.67 4.25 4.25 3.33 4.75 3.04 4.25 4.25 4.25 3.35 5.13 2.29 4.10 2.14 4.10 4.10 4.10 4.10 4.10 3.26 3.50 4.80 4.83 6.42 6.13 3.72 4.23 3.55 4.10 4.10 3.12 4.02 2.98 4.10 4.10 4.10 53 -31 - 5 -84 -64 -84 -84 -84 -84 -84 52 - 55 69 7 -69 34 -52 - 36 18 -84 - 84 71 9 -80 -84 -84 -84 2 22 20 3 21 3 3 3 3 3 38 8 8 5 38 9 16 22 24 3 3 6 15 2 3 3 3 4.25 3.60 3.69 4.25 4.25 3.20 4.25 4.71 4.25 4.25 4.25 4.92 4.25 4.10 2.52 1.36 4.10 4.10 2.78 4.10 3.57 4.10 4.10 4.10 4.07 4.10 -84 -45 60 -84 -84 60 -84 88 -84 -84 -84 23 -84 3 30 63 3 3 13 3 24 3 3 3 17 3 9328 SBAR ET AL.' NEAR-SURFACE IN SITU STRESS LRS plained by a contemporarytectonicstressthat accountsfor YOUNG'SMODULUS (G Po) 2 2O 4 6 8 stressdifferencesbelow 6 m. Removal of the contemporary I0 tectonic stress inferred below 6 m from measurements above 6 m producedlittle changein either azimuth or shearstress.The origin of the stressdifferencesin the upper 6 m may be anisotropy of either thermal or elastic constantsor variation in the lateral constraint against expansion.The thermal stress problem is discussedin greater detail by R. M. Richardson (unpublished manuscript, 1983), which includes twodimensionaltime dependentfinite element modeling of the outcrop/alluvium environment. The parameters we are most interested in are the mean azimuth and magnitude of the principal horizontal stresses and any possiblevariation of thesewith depth. We also seek to demonstratethat the observedstressis tectonic in origin. For the following analysis the upper 6 m of the data are o o '• (M) removed to eliminate 25 the influence of thermal and standard deviation this method 3O Fig. 6. stress. Fisher statistics[Mardia, 1972] are used to find the mean is treated as a unit data. In vector. The assumptionis made that the azimuthal variation of the maximum horizontal compressivestress has a Gaussian distri- Moduli for LRS. Symbolsas in Figure 5. bution data is 9.85øC [NOAA, 1977, 1978], ro= 2 x 10-7 for a period of 1 year, and t -0 correspondsto the time of maximum annual surfacetemperature.The temperatureat depth as a function of time for a thermally isotopic half spaceis then givenby T(z, t)= To+ Ae-•'z cos(rot- kz) of the mean for the azimuthal each azimuth (4) wherek = (ro/2k)•/2 and k is the thermaldiffusivity.The hori- about some mean value. The azimuthal data are fur- ther edited by eliminating those sampleswhich have poor resolution in azimuth. A measure of this is the ratio of the maximum to the minimum horizontal stresses(e.g.,see Table 2). If the two stressesare approximately equal, the stressellipse is essentiallya circle and the azimuthal resolution is poor. Table 3 shows the effect of eliminating successively higher ratio data. For LRS the mean convergesto N22øW with a standard error of the mean of + 9 ø for ratios > 1.4. The zontally induced thermal stressfor an isotropic elastic half TKY data with a population of six indicatea mean of N44øW spacein a state of plane strain which is constrainedagainst with a standard error of _+9ø. Although this is inconsistent with the total LRS sample,it is in agreementwith the LRS lateral expansionand freeto expandverticallyis givenby data between 6 and 10.6 m which have a mean of N33øW at(z, t)= -- o•E[T(z, t)- To] 1-v (5) or aT(Z, t)= - •EAe -•'z cos(rot- kz) 1-v (6) a standard between19 and 21 m that trend east-westerly.The reasonsfor thesesystematicvariations in azimuth are not obvious from the data. It is clearly valuable at this site to have a large number of samplesto average these variations. Although the TKY data appear to be consistentwith the LRS data both in where • is the coefficientof thermal expansion,E is Young's modulus, and v is Poisson'sratio. An averagevalue of 4 GPa for E was obtainedfrom Table 2 LRS averagestressof 1.6 MPa with k = 1.4 x 10-6 m2 s-', v = 0.4, and • = 8 x 10-5øK-•. The fit to the observeddata is good, although the adopted value for • is a factor of 2-3 larger than observedfor this rock type. One possibleexplanationfor the large value for • is the expansionof water in isolated pore spaces.Also, while the predictedthermal stressesare isotropic,there are significant differencesin the upper 6 m betweenthe observedmaximum and minimum horizontal stresses.In fact, the stressdifferences above 6 m are approximately equal in magnitude to the averagestressdifferencesbelow 6 m. It doesnot appear, however, that the stressdifferencesin the upper 6 m can be ex- DISPLACEMENT ;•.M)i00 2o 40 60 i i i i o; 0 for the upper6 m, and a time of 2.96x 107s was adopted, correspondingto about three quartersof a month beforepeak annual temperature.No directmeasurements of •, k, or v were made at the sites, and values were tested from the range of reportedvaluesfor standstones from the LINDAS data series [Touloukian et al., 1981]. The predicted curve shown in Figure 5 correspondsto thermal stresssuperimposedon an with error of + 5 ø. Also there are several measurements 0 o •oo •o 5t I 0,0I F P] T 15 oOo )0 0 O0 ß ß o ß oo oøO ß H / oo%' ß • 8%0 (m) 20•oøß ß / 2 54Oo 30 . % %. o ee ß 1'0 ß0 ß Fig. 7. Displacementdata for LRS. Symbolsas in Figure 5. SBAR ET AL.' NEAR-SURFACE IN SITU STRESS TABLE 3. Mean Azimuth Mean E of N Site IMS LRS LRS LRS LRS TKY of Maximum Standard Error of Mean Horizontal 9329 Stress Number of Observations Remarks* -13 ø -25 ø +2 ø +8 ø 9 28 D > 14 m D>6m, R> -22 ø -22 ø +8 ø +9 ø 23 18 D>6m, R> 1.3 D > 6 m, R > 1.4 -33 ø +5 ø XTLR, MOJ1, and MOJ2 -44 ø -21 ø +9 ø q- 7 ø 7 6 5 6m>D>_ 10.5m D>6m, R_> 1.7 80 m > 787 m Palmdale trilateration -15 ø 1.2 ~80x25km *D is the depth. magnitude and azimuth, we have chosen not to use them, Only 16 measurementswere made at IMS (Figure 8) com- sincetheywouldbiasthe statistics of a reasonably uniformly pared with the 40 at LRS becauseof higherfracturedensityat sampleddata set.The LRS meanazimuthis plottedin Figure IMS. Unlike LRS, there is no evidencefor an exponential 1 and referred to in later discussion. decayin stressin the upper6-10 m. Nevertheless, thereis The averagemagnitudefor the maximum horizontal stress ßreason to believe thatthermaleffects maystillbeimportant in for depthsbelow 6 m is 1.6 MPa. The averagefor the mini- this region. The near-surfaceazimuthal data show considermum horizontal stressis 1.1 MPa, while that for the shear able scatter.The scattermay be due to thermal expansionof stressis 0.28 MPa. A statisticallysignificantincreasewith the rock in a fractured medium. There are numerous fractures depth can be seenfor each of theseparameters.A linear re- at IMS, and expansion of the rock, closing fractures,could gressionof stressversusdepth was computedfor a varietyof relievethe thermal stress.Unlike LRS, the near-surfaceregion cases,someof which are listedin Table 4. All data were in- is not constrainedvery well in horizontal directionsagainst cluded below cutoff levelsof 6, 7, and 9 m for LRS. Data were expansionbecauseof the fractures.Thus no large near-surface not excludedby ratio, sincethis characteristiconly appliesto thermalstressbuildsup. The scatterof azimuthaldirections azimuthalreliability.The differencein either the slopeor in- could result from an uneven distribution of fracture orientaterceptamongthe differentcutofflevelsis not significantcon- tions. Thedisplacements at IMS arelowerthanthose at LRS,but sideringthe standarderrorsof the data. The valuesfor depth (Table > 6 m are usedin the remainderof this paper. The errorsin the stiffnessis 4-5 timesgreateryieldinghigherstresses slopeare relativelylargebecauseof the smalldepthrangeover 5 and Figures 9 and 10). A Poisson'sratio of 0.2 was selected which the data were taken and the scatter of the individual for the stresscalculationat this sitebasedon typical valuesfor points.A regressionon the data of Zoback and Roller [1979] granitic type rocks [Haas, 1981]. Although only sevensetsof and Zoback et al. [1980] yieldssimilar valuesfor the vertical moduli were determined,it can be seenthat the anisotropyin stressgradient, although their resultsare better constrained. this rock, a quartz-monzonite,is quite uniform in azimuth. The error in slopefor the LRS data is too largefor a meaning- The magnitude of the moduli is lower for the shallower ful comparisonwith the deeperhydrofracturedata. It should measurements (Figure 9). This may be becausethe shallower be notedthat both the maximumand minimumhorizontal rock is more weathered.The magnitudeof the anisotropyis stress valuesforLRSaregreaterthantheverticalstress dueto modestat this site and does not significantlychangethe azilithostatiCloading in this depth range (Table 5). This implies muth in the calculation of stress(Table 4). The differencesin that the stresses measuredare not solelya resultof lithostatic stressmagnitude using the plane stressequations instead of loading. If they were, the horizontal stresseswould be less planestrainis lessthan 5% for this site,whichis not significant. than or at mostequal to the verticalstress. TABLE 4. RegressionAnalysisof StressMagnitude Site Number of Observations Dependent Variable* Zero Depth Intercept Slope, MPa/m Correlation Coefficient LRS 32 O'iH 1.09q-0.57 0.0379 q-.0158 0.402 LRS 30 O'iH 1.05q- 0.58 0.0396q- .0177 0.389 LRS XTLR, MOJI, andMOJ2 27 15 ax• O'iH 1.03q-0.62 0.778q-2.15 0.0408q-.0215 0.0422q-.0021 0.355 XTLR and MOJ2 XTLR LRS LRS LRS XTLR, MOJI, and MOJ2 XTLR and MOJ2 XTLR IMS LRS 10 7 32 30 27 15 10 7 ax• a• a2• a2• a2• 0'2H a2H a2H av av 2.50 q- 2.42 0.251 q- 2.72 0.702 q- 0.540 0.678 q- 0.556 0.762 q- 0.582 1.51q- 1.14 2.08 q- 1.26 1.33 q- 1.40 0.0 0.0 0.0397 q- .0029 0.0428 q- .0049 0.0267q- .0151 0.0279 q- .0168 0.0238q- .0202 0.0215q- .0019 0.0205q- .0015 0.0216 q- .0025 0.0262 0.0235 *O'iH, maximumhorizontalstress;O'2H , minimumhorizontalstress;av,verticalstress. I'D, depth. 0.985 0.979 0.969 0.308 0.299 0.229 0.984 0.979 0.966 Remarkst D_>6m D>_7m D>_9m 80m_>D_>49m 149 m >_ D >_ 849 m 266 m _> D _> 849 m D_>6m D_>7m D_>9m 80 m > D >_ 849 m 149 m_> D _> 849 in 266 m >_ D _> 849 m 9330 SBAR ET AL.' NEAR-SURFACE IN SITU STRESS IMS IMS HORIZONTAL 0 I i 0 STRESS 2 3 YOUNG'SMODULUS (MPa) 4 IO 5 (G Pa) 20 30 I0 15 15 o 2O 2O (M) (M) 25 25 3O 3O • oø/• Fig.8. Stress values forIMS.Symbols asin Figure 5. Fig. 9. Moduli for IMS. Symbolsas in Figure 5. The mean azimuth of the data >_6 m is N13øW + 2 ø. Since at IMS comparedwith LRS undera constantstrainrate situ- the rock is highly fractured between 5.26 and 14.63 m, only ation, which may be a reasonableapproximation for a plate boundary. data > 14 m are considered.The azimuths have little scatter, thus the mean is tightly constrained.Also note that the stress ratio is uniformlyhigherfor the IMS data than the LRS data, indicating that each azimuth is itself better constrained.The TECTONIC INTERPRETATION It is difficult to demonstrateunequivocallythat the stresses mean azimtlth at IMS is not statisticallydifferent from those measuredin the Palmdale region are indeed tectonicin origin. at LRS or XTLR, MOJ1, and MOJ2. However, several argumentscan be postulated that support The Stressmagnitudesdo not vary in any systematicway this assumption.The stressorientation measuredat sitesIMS with depthat IMS, soa regression analysiswasnot performed and LRS, which are 22 km apart, is the same.This orientation on the data. The average values are, however, higher than is the sameas that obtained by Zoback et al. [1980] at several thoseat LRs. The maximumhorizontalstressis 2.1 MPa, the sites near LRS using the hydrofracture technique (Figure 1). minimum horizontal stressis 0.76 MPa, and the shear stressis An average azimuth was determined for the sites XTLR, 0.66 MPa. This is consistent with the observations of Zoback MOJI, and MOJ2 for the five azimuths reported as fair or et al. [1980] in whichtheynotedhighershearstresses at sites better quality by Zoback et al. [1980]. These three siteswere farther away from the San Andreas fault than MOJ1 and combinedto include as many data as possiblein the average. MOJ2. Their principal stresseswere also higher. The higher The average for all three sites is N21øW _+7ø (Table 3). A magnitudescould result from the greater stiffnessfor the rock separateaverage is plotted in Figure 1 for the two measureTABLE Horizontal Stress, Depth, Maximum Stress Data for Site IMS Horizontal Azimuth of Maximum Stress MPa m 5. Minimum 0.19 0.62 0.40 0.33 -0.16 -0.56 0.30 E of N 0.79 1.07 1.68 1.93 2.69 4.50 5.26 0.47 0.82 1.01 1.57 0.71 0.23 0.84 14.63 3.30 20.47 21.56 21.97 26.44 26.90 27.15 2.68 1.62 2.46 0.90 0.81 1.31 0.82 0.46 0.66 -0.14 0.19 0.56 - 17 - 16 - 3 -27 -20 - 11 28.12 3.00 0.91 - 16 28.60 2.66 1.68 -6 1.67 -57 20 21 32 37 81 59 -5 Shear Stress, Ratio MPa Displacement, #m Maximum Minimun• Azimuth of Maximum Displacement E of N Azimuth Modulus, GPa Maximum Minimum 2.4 0.14 4.42 0.59 - 58 10.2 8.7 1.3 0.10 3.37 2.45 25 20.2 15.5 2.5 4.8 -4.4 -0.4 2.9 2.0 3.3 3.5 3.7 0.31 0.62 0.44 0.39 0.27 0.81 0.93 0.58 0.90 4.98 8.66 4.69 4.22 0.53 -1.42 -2.80 - 5.86 0.49 3.75 -0.22 -0.10 -0.02 24 34 37 79 20.2 20.2 20.2 12.4 15.5 15.5 15.5 7.7 63 - 11 - 19 -22 -6 10.2 24.6 24.5 28.6 32.4 6.5 18.4 22.3 20.6 23.0 -6.2 0.52 -2.69 -30 20.2 15.5 -0.37 1.08 -0.03 5.70 -25 -17 -21 - 14 20.2 20.2 20.2 20.2 15.5 15.5 15.5 15.5 4.2 2.3 3.3 1.6 0.31 0.37 1.05 0.49 9.35 12.83 11.14 6.15 7.81 5.80 4.43 6.43 15.79 11.90 of Maximum Modulus Modulus Anisotropy, E of N % -44 16 16 16 16 14 21 19 22 15 16 16 16 16 16 16 15 24 24 24 24 38 37 25 9 28 29 24 24 24 24 24 SBAR ET AL.: NEAR-SURFACE IN SITU STRESS topographicstressproduce no significantinfluenceon our results. Thermal effectsare clearly of concern for shallow stress IMS DISPLAGEMENT o 5 I 0 15 IO 20 I measurements.This implies that the Sbar et al. [1979] I measurementsshould not be taken as indicators of contemporary tectonicstress.Our measurementsin this study, however, extendto depthsbelow the zone of thermal influence.Residual stressremaining from previoustectoniceventsor due to some characteristicof the rock is another problem which must be 0 • •0 9331 ß 5• • considered. I0 A double overcore was made at site LRS which produced very little strain relief compared with the original overcore [Sbar et al., 1979]. This suggeststhat very little residual stress was stored in that rock. Double 15 overcores were not made at site IMS, but the similar orientation for the principal stressesat both sitesin very different kinds of rock of 2O differentagesmakesthe possibilityof residualstresslesslikely. (M) We argue that the stressobtained at sitesIMS and LRS is of contemporarytectonic origin and can be interpreted with 25 other data from southernCalifornia in terms of the regional framework.The maximum compressionalstressinferred from o ß fault plane solutionsof earthquakesfor the entire San Andreas 3O region including areas as far east as the California-Nevada Fig. 10. Displacementdata for IMS. Symbolsas in Figure 5. border is N14øE + 9ø [Sbar, 1982]. Stress and strain data from Palmdale and surroundingareas near the fault, however, indicatea maximumcompressive stressof about N20øW. This mentsat MOJ1, and the three at MOJ2 and XTLR, sincethey counterclockwiserotation of about 35ø can be interpreted are at different locations.The overall averageis essentiallythe usingfinite elementmodelsdevelopedby Richardsonand Bergsame as that for LRS. man [1979] and Sbar and Richardson[1981]. In those models In addition, the azimuth of maximum shorteningaveraged over9.6yearsbySavage et al. •1981]fortheirPalmdale net- a counterclockwiserotation of the principal stressesis observedin the vicinity of the San Andreasfault (Figure 12).This work with an aperture of 15 krn is of nearly identical orientais a result of the changein the orientationof the San Andreas tion (Figure 11). The axis of maximum shorteningand the fault system in the Big Bend region. Different fault orientamaximum compressionalstressare equivalentin an isotropic tions with respectto the regional stressfield will produce medium. The comparisonbetweengeodeticstrain resultsand different amounts and directions of rotation. In this model all in situ stressdata is justified, sincein most situationsthe two of the elements have the same thickness.Only the elements agree quite well. This would be especiallytrue in high strain rate regions.Both the hydrofracturedata and the geodetic resultsmeasure deformation to much greater depth than the SAN ANDREAS FAULT IN SOUTHERN CALIFORNIA 30 m we have obtained. Either the agreementin orientation is PRINClPAL STRESSES fortuitous or we are all measuringa regional scalephenomenon, which impliesthat it is tectonicin origin. ß ß o ß Other influences on our stress measurments should also be considered. Excessive reliefin topography canproduce significant stresses[Harrison, 1976; Jaegerand Cook, 1969]. At both sites IMS and LRS the relief is minimal and calculations of _•_ Tehachapi • %,.. .......... ..................... Garlock / Palmdale :?:.?:?.. ........ ......... . ..:..::...... ....................... i 50 Km os Padres ' / Fig. 1. Principal stresses are shown atrepresentati location + Anza •'"'>----• ........... Calon f for afinite element model of southern Californi The San Andr fault is modeledby elementswith Young'smodulussmallerby a #strain/year %'Salton I O. 0 0 I 100 I I 200 • km I Fig. 11. Map of southernCalifornia showingthe locationsof the seven trilateration networks and the average principal strain rates measuredat each. The heavy sinuouslines representthe major faults [after Savageet al., 1981]. factor of 2.5 than the bulk of the model.The Gariock fault has the sameelementtype as the majority of the model. The maximum com- pressive stress isindicated byinward pointing arrows and the least compressivestressby outward pointing arrows. Shear stressis ap- pliedat thesidesof themodel,asindicated by thelargearrows.Note that thesesidesare parallel to the relativemotion betweenthe Pacific and North American plates. North is inclined in the diagram. The stresses on the NW strikingpart of the fault are rotated counterclock- wisewith respectto the far-fieldstresses and the NNW strikingparts of the fault. 9332 SBAR ET AL.' NEAR-SURFACE IN SITU STRESS of model. three-componentboreholedeformationgaugeand overcoringtechniques,Rep.Invest.U.S. Bur. Mines, 7894,29 pp., 1974. Jaeger,J. C., and N. G. W. Cook, Fundamentals of Rock Mechanics, 515 pp., Chapman and Hill, London, 1969. Mabey, D. R., Gravity surveyof the westernMojave Desert,California, U.S. Geol.Surv.Prof Pap., 316-D, 73 pp., 1960. Mardia, K. V., Statisticsof DirectionalData, 357 pp., Academic,New The strain data of Savageet al. [1981] stronglysupportthis model. All of their networks that span the locked portion of McKenzie, D, P., The relationshipbetweenfault plane solutionsfor earthquakesand the directionsof the principalstresses, Bull. Seis- composingthe San Andreas fault, however, are more compliant than the remaining elements.This effect causesthe stressesto be lower along the fault and producesa counter- clockwiserotation of principal axes along the NW striking branchcomparedwith the NNW strikingbranchand the bulk the San Andreas fault show a counterclockwise rotation of the maximumshorteningto NNW, while thosenetworksin other parts of southern California show the regional trend for the maximum shortening. SUMMARY One of the most significantaspectsof this researchprogram is the demonstrationthat reliable measurementsof contemporary tectonicstresscan be made near the surface.Analysisof our field data and finite element modeling of thermal stresses reported elsewhereindicate that samples should be taken below about 6 m to obtain reliable observationsof contemporary tectonicstress.The resultsat two sitespresentedin this paper are consistentin stressorientation and in averagemagnitude variation with those obtained in the same area by Zoback et al. [1980] at depths to 849 m with the hydrofracturetechniqueand in orientationwith thoseof Savage et al. [1981] from geodeticobservations.We measuredazimuths of N22øW + 9ø and N13øW + 2ø compared with N21øW + 7ø for Zoback et al. and NNW for Savage et al. These data plus other data along the locked sectionof the fault from Savageet al. (Figure 11) all show a counterclockwise rotation away from the azimuth of the regionalhorizontal maximum compressivestress(N14øE). This rotation is also observed in the numerical models of the San Andreas fault in southernCalifornia [Richardsonand Bergman,1979]. Acknowledgments.We owe specialthanksto David Yale (Stanford University),Joyce Kruger (University of Arizona), and Christian Paquin (University of Paris-South)for their patience and untiring assistancein the field. Financial support for this researchcame from U.S. Geological Survey contracts 14-08-0001-17703 to LamontDoherty Geological Observatoryand 14-08-0001-17705to the University of Arizona. Lamont-Doherty Geological Observatorycontribution 3694. REFERENCES York, 1972. mol. Soc. Am., 59, 591-602, 1969. Merrill, R. H., and J. R. Peterson,Deformation of a boreholein rock, Rep.Invest. U.S. Bur. Mines,5881, 32 pp., 1961. NOAA, Climatological data for California, vol. 81, Environ. Data Serv.Natl. Clim. Cent.,AsheVille,N. 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