Interseismic strain accumulation and anthropogenic motion in metropolitan Los Angeles

Authors


Abstract

[1] We use global positioning system (GPS) geodesy and synthetic aperture radar (SAR) interferometry to distinguish between interseismic strain accumulation and anthropogenic motion in metropolitan Los Angeles. We establish a relationship between horizontal and vertical seasonal oscillations of the Santa Ana aquifer, use this relationship to infer cumulative horizontal anthropogenic motions from cumulative vertical motions caused by water and oil resource management, and estimate horizontal interseismic velocities corrected for anthropogenic effects. Vertical anthropogenic rates from 1992 to 1999 are slower than 3 mm yr−1 in the Santa Ana and San Gabriel aquifers and faster than 5 mm yr−1 in the Chino aquifer and in many oil fields. Inferred horizontal anthropogenic velocities are faster than 1 mm yr−1 at 18 of 46 GPS sites. Northern metropolitan Los Angeles is contracting, with the 25 km south of the San Gabriel Mountains shortening at 4.5 ± 1 mm yr−1 (95% confidence limits). The thrust fault in an elastic edge dislocation model of the observed strain is creeping at 9 ± 2 mm yr−1 beneath and north of a position 6 ± 2 km deep and 8 ± 8 km north of downtown Los Angeles. The model fault is near the Los Angeles segment of the Puente Hills thrust but south of the Sante Fe Springs segment of the thrust. Disagreement between the 6 km locking depth in the model and the 15 km seismogenic depth inferred from earthquakes suggests that the elastic continuum model may be unsatisfactory; models with different stiffnesses of sedimentary basin and crystalline basement must be investigated.

1. Introduction

[2] The Mojave segment of the San Andreas fault passes 50 km north of metropolitan Los Angeles and trends west-northwest, 25° counterclockwise of the direction along which the Pacific plate is moving relative to the North American plate [DeMets et al., 1990, 1994; Argus and Gordon, 2001]. Motion between the two plates is taken up mainly in four ways: (1) by dextral slip along the northwest trending faults of the eastern California shear zone, (2) by dextral slip along the Mojave segment of the San Andreas fault, (3) by contraction from north to south across metropolitan Los Angeles, and (4) by dextral slip along northwest trending faults off the California coast (Figure 1, bottom). Dextral shear parallel to the Mojave segment of the San Andreas fault is accumulating quickly at 0.4 × 10−6 yr−1 within 20 km of the fault [Lisowski et al., 1991]. Most or all of this dextral shear is elastic strain that will be released in great earthquakes similar to the 1857 M 7.9 Fort Tejon earthquake, during which 3 to 9 m of slip occurred along 400 km of the San Andreas fault [Sieh, 1978].

Figure 1.

(top) Site velocities relative to the San Gabriel Mountains microplate after correcting for anthropogenic effects and removing elastic strain associated with locking of the San Andreas and San Jacinto faults. This residual velocity field consists of the velocities of permanent GPS and VLBI sites with 5 years or more of data (in black), permanent GPS sites with 3 to 5 years of data (in green), trilateration sites with 5 to 17 years of data (in blue), and campaign GPS sites with 3 to 5 years of data (in purple). Speeds are given in mm yr−1. The map also shows the limits of profiles A-A′ and B-B′ (maroon dashed lines) in Figures 9, 10, and 11; the position of the Puente Hills thrust (PHT) at 3 km depth [Plesch et al., 2003]; and the focal mechanisms of the 1971 San Fernando, 1987 Whittier, and 1994 Northridge earthquakes. SGM, San Gabriel Mountains microplate; WMD, west Mojave desert microplate. Faults are ChF, Chino fault; HF, Hollywood fault; ORF, Oak Ridge fault; RF, Raymond fault; SAF, San Andreas fault; SCF, San Cayetano fault; SFF, San Fernando fault; SGF, San Gabriel fault; SJF, San Jose fault; SMdF, Sierra Madre fault; SMnF, Santa Monica fault; SSF, Santa Susana fault; VF, Verdugo fault; WF, Whittier fault. Mountains and valleys are OR, Oak Ridge; SAM, Santa Ana Mountains; SCV, Santa Clarita valley; SGV, San Gabriel valley; SFV, San Fernando valley; SMM, Santa Monica Mountains; SSM, Santa Susana Mountains; VB, Ventura basin. Fault locations are from Jennings [1994]. (bottom) Plate velocities at the middle of the Mojave segment of the San Andreas fault (SAF) at 34.55°N 118.1°W. NA, North American plate; PA, Pacific plate; SGM, San Gabriel Mountains microplate; WMD, West Mojave Desert microplate. Speeds (in blue) are in mm yr−1 and azimuths (in red) are in degrees clockwise of north. The velocities of sites USC1, PVEP, and CAT1 (maroon circles) relative to the San Gabriel Mountains after removing elastic strain associated with locking of the San Andreas and San Jacinto faults are also shown.

[3] The continental crust between the San Andreas fault and the Palos Verdes peninsula is observed with geodesy to be shortening from north to south at 6 ± 1 mm yr−1 (Figure 1). (The 95% confidence limits follow the plus/minus symbol in this article. Elastic strain associated with locking of the San Andreas and San Jacinto faults has been subtracted from the velocities quoted in this introduction.) Shortening has over the past several million years built the Transverse ranges, which stretch for 400 km and reach elevations of 2 km [Blythe et al., 2002]. However, trilateration observations from 1973 to 1989 show that the San Gabriel Mountains, which comprise the 25 km south of the San Andreas fault, are no longer contracting [Lisowski et al., 1991]. Using GPS observations of the Southern California Integrated GPS Network (SCIGN) from 1991 to 1998, Argus et al. [1999] find the northern half of metropolitan Los Angeles to be to be contracting quickly. They find shortening at 5 mm yr−1 across a narrow (≤25 km wide) belt cutting east-southeast across the valleys and hills south of the San Gabriel Mountains. The belt is constrained to be north of the site (USC1) at the University of Southern California, which is estimated to move north at 6 mm yr−1 relative to the San Gabriel Mountains. However, the position of the belt is poorly constrained to the east near the site (WHC1) at Whittier College, which is estimated to move northeast at 2 mm yr−1 relative to the San Gabriel Mountains. That mountains are now growing in northern metropolitan Los Angeles is inferred from the young rugged topography there [Yeats et al., 1994] and in the 2 m of reverse slip that occurred during each the 1971 M 6.6 San Fernando [Heaton, 1982] and 1994 M 6.7 Northridge earthquakes [Wald et al., 1996]. Large M 6.5–7 earthquakes breaking thrust faults beneath metropolitan Los Angeles may be more harmful than great M 8 earthquakes rupturing the distant San Andreas fault [Dolan et al., 1995]. Indeed the 1994 Northridge shock was the most costly American earthquake since 1906, killing 33 people and causing $15 billion in financial loss [U.S. Geological Survey and the Southern California Earthquake Center (USGS and SCEC), 1994].

[4] Water going into and coming out of the permeable rock, gravel, and sand comprising the Santa Ana aquifer causes it to expand and contract. The Orange County Water District manages the water, recharging the aquifer with water from the Santa Ana river and to a lesser extent water imported from the Metropolitan Water District of California (Orange County Water District, fact sheet, available at http://www.ocwd.com/_assets/_pdfs/ocwd-fact_sheet.pdf, 2003). Water resource management thus increases the size of seasonal oscillations caused by nature's weather pattern. SAR interferometry shows the surface of the aquifer to each year rise ∼50 mm during the autumn and winter when it rains frequently and fall ∼50 mm during the spring and summer when it rains rarely [Bawden et al., 2001; Watson et al., 2002] (Figure 2). GPS shows the margins of the aquifer to each year move ∼8 mm away from the aquifer center when the aquifer rises and move ∼8 mm toward the aquifer center when the aquifer falls [Bawden et al., 2001].

Figure 2.

Seasonal vertical displacements inferred from SAR (color gradations), seasonal horizontal displacements observed with GPS (black vectors), and seasonal horizontal displacements predicted from SAR (blue vectors). (top) Uplift of the Santa Ana aquifer from July 1998 to January 1999. (bottom) Subsidence of the Santa Ana aquifer from February 1999 to August 1999. Vertical displacement is taken to be the SAR line of sight observation divided by the cosine of the angle at the surface between vertical and the ERS satellite. The observed horizontal displacement is computed from a sinusoid with a period of 1 year fit to GPS positions as a function of time. The predicted horizontal displacement is computed to be 1000 m times the vertical gradient (in mm m−1) inferred from SAR. Neglecting the horizontal displacement of CCCO results in an error in the vertical estimate at the site of −1.5 mm in the rising interferogram and +2.5 mm in the falling interferogram. (CCCO's displacement during the rising interferogram is 3.8 mm toward S80°W, which resolves into −1.4 mm in the line of sight of the satellite, yielding an error in vertical estimate of −1.5 mm. CCCO's displacement during the falling interferogram is 6.1 mm toward N84°E, which resolves into +2.3 mm in the line of sight of the satellite, yielding an error in vertical estimate of +2.4 mm.)

[5] Bawden et al. [2001] maintain that management of water resources caused the center of the Santa Ana aquifer to fall at 12 mm yr−1 from 1993 to 1998 and that related horizontal anthropogenic motions “contaminate” about half the SCIGN velocities. Calling the velocity of USC1 “contaminated”, Bawden et al. [2001] conclude that GPS observations do not constrain how shortening is distributed across metropolitan Los Angeles.

[6] In this study we distinguish between seasonal oscillations, cumulative anthropogenic motions, and tectonic velocities. Seasonal oscillations are that part of motion described by a sinusoid with a period of 1 year. Horizontal seasonal motions are observed with GPS to be in the direction of local subsidence and largest where vertical seasonal motions change most quickly with horizontal distance. We find horizontal seasonal oscillations (in mm) observed with GPS to roughly equal 1000 m times gradients (in mm m−1) in vertical seasonal oscillations inferred from SAR.

[7] Cumulative anthropogenic motions are that part of motion caused by management of water and oil resources over several years. Places that have accumulated uplift or subsidence are aquifers and oil fields. Steep vertical gradients are clearly anthropogenic and not tectonic. Using the relationship between horizontal and vertical seasonal oscillations, we estimate horizontal anthropogenic velocities (in mm yr−1) to be equal to 1000 m times gradients (in mm yr−1 m−1) in vertical rates over several years inferred from SAR. Inferred horizontal anthropogenic velocities are faster than 1 mm yr−1 at 18 of 46 GPS sites studied. USC1 is inferred to have moved northeast at 0.5 mm yr−1 in response to management of the Las Cienegas and Downtown Los Angeles oil fields, and WHC1 is inferred to have moved southwest at 2.7 mm yr−1 in response to management of the Whittier oil field.

[8] We present an interseismic velocity field corrected for anthropogenic effects. The field includes 69 SCIGN site velocities, all of which are based upon 3 or more years of observations. Northern metropolitan Los Angeles is contracting quickly, with shortening at 4.5 ± 1 mm yr−1 across a 12 to 25 km wide belt south of the San Gabriel Mountains. The shortening belt must lie north of USC1, which is moving north at 4.2 mm yr−1 relative to the San Gabriel Mountains. The shortening belt also must be north of WHC1, which is moving northeast at 4.5 mm yr−1 relative to the San Gabriel Mountains. Moreover, many new SCIGN velocities are consistent with the velocities of USC1 and WHC1, supporting the conclusion that northern metropolitan Los Angeles is quickly contracting.

2. Data and Methods

2.1. Global Positioning System (GPS) Geodesy

2.1.1. Estimating GPS Positions

[9] We determine two sets of GPS positions as a function of time, one “point positioned” set for the entire earth and one “spatially filtered” set for southern California.

[10] The global set consists of the positions of 526 GPS sites on the seven continents and on islands in the four oceans. We estimate positions using the GPS Inferred Positioning Software (GIPSY) and the “point positioning” data reduction procedure of Zumberge et al. [1997]. Positions are estimated on many days from January 1991 to December 1992 and on all days from January 1993 to October 2002.

[11] The southern California set consists of the positions of 240 sites in California south of 36.5°N, 6 in east California, 21 in Nevada, 3 in Arizona, and 4 in Baja California. We estimate the positions in three steps. We first “point position” the sites using the procedure of Zumberge et al. [1997]. We next resolve ambiguities using the technique of Blewitt [1989], that is, we estimate the positions more accurately by determining the number of carrier waves between each satellite and each receiver. We next “spatially filter” the positions using a technique similar to that of Wdowinski et al. [1997], that is, we subtract from all position estimates on a given day the mean misfit of velocities fit to positions on that day. Positions are estimated on all days from January 1996 to October 2002.

[12] The global and southern California position sets are available in graphical and digital format at http://sideshow.jpl.nasa.gov/mbh/series.html.

2.1.2. Estimating GPS Velocities and Oscillations

[13] We fit the two sets of positions as a function of time with a position (3 parameters, 1 for each of the east, north, and up components), a velocity (3 parameters, 1 for each component), offsets when and where needed (3 parameters for each offset), and a sinusoid with a period of 1 year (4 parameters, 1 amplitude for each component and 1 phase assumed to be the same for the 3 components) (Figure 3). Constraining the phase of the sinusoid to be the same means that, neglecting the velocity, the site is moving back and forth each year along a line segment.

Figure 3.

East, north, and up components (small light blue dots) of positions of four GPS permanent sites as a function of time. The model (black curve) consists of a position, a velocity, offsets when and where needed, and a sinusoid with a period of 1 year. The phase of the sinusoid is the same for the three components. Given at the top left of each plot are the rate (in blue) in mm yr−1 and the amplitude of the sinusoid (in red) from peak to peak in mm. Offsets (vertical line segments) are given in mm. Coseismic offsets of the 1999 Hector Mine (“hm”) earthquake are set equal to the predictions of the dislocation model of Hurst et al. [2000]. An antenna offset at FVPK in July 1999 is estimated. The east component of the seasonal displacement of CCCO during the falling interferogram (purple line segments) and the north component of the seasonal displacement of FVPK during the rising interferogram (purple line segments) are given in mm. East and north rates are relative to the San Gabriel Mountains. Vertical rates are relative to the mean southern California reference defined by the 274 sites in the spatial filter. The southern California set of positions is plotted.

[14] The median root-mean-square (RMS) residuals for the global set of positions are 5 mm (east), 4 mm (north), and 10 mm (up). Ambiguity fixing and spatial filtering reduces dispersion by a factor of 2 to 5. The median RMS residuals of the southern California set of positions are 1.5 mm (east), 1.1 mm (north), and 4.5 mm (up).

[15] We use the velocities fit to the global position set to evaluate plate tectonics and interseismic strain accumulation. We do not use the velocities fit to the southern California position set because we believe that unmodeled transients not accounted for in the spatial filter may bias the velocities. Because the RMS difference between the two sets of velocities is just 1.0 mm yr−1, it matters little which velocity set we use.

[16] We use the sinusoids fit to the southern California position set to evaluate seasonal oscillations (Figure 4). The small dispersion of the southern California positions also allow small antenna offsets to be identified.

Figure 4.

Vector representations of seasonal vertical oscillations with a period of 1 year observed with GPS (vectors) are compared with the seasonal vertical displacements from February 1999 to August 1999 in Figure 2. The formula specifying the sinusoid fit to GPS positions as a function of time is A cos(360° t − B), where t is time (in years), A is amplitude (in mm), and B is phase (in degrees). The magnitude of the vector (= 2A) is the size of the oscillation from peak to peak. The azimuth of the vector (B) is the time of the year at which the oscillation is maximum, with north being 1 January, east being 1 April, south being July 1, and west being 1 October.

2.1.3. Removing Coseismic Motions and Postseismic Transients

[17] Because we aim to estimate interseismic velocities, we allow for coseismic motions and omit estimates of positions influenced by postseismic transients. A postseismic transient is the cumulative motion after an earthquake in excess of the mean interseismic velocity.

[18] We omit estimates of position before the 1992 Landers earthquake. We set the coseismic motion of JPLM during the 1994 Northridge earthquake to the prediction of the dislocation model of Hudnut et al. [1996]. For five sites predicted to have moved less than 1 mm during the 1994 Northridge earthquake, we set coseismic motion equal to zero. We assume postseismic transients of the 1992 Landers and 1994 Northridge earthquakes to be negligible.

[19] We decide how to treat coseismic motions and postseismic transients of the 1999 Hector Mine earthquake using predictions of coseismic motion from the dislocation model of Hurst et al. [2000]. For sites predicted to have moved less than 2 mm during the earthquake, we set coseismic motion equal to zero. For sites predicted to have moved between 2 and 10 mm during the earthquake, we set coseismic motion equal to the predicted value. For sites predicted to have moved between 10 and 50 mm during the earthquake, we discard the 6 months of data after the earthquake and estimate the sum of coseismic motion and postseismic transient over the 6 months. For sites predicted to have moved more than 50 mm during the earthquake, we discard the 2 years of data after the earthquake and estimate the sum of coseismic motion and postseismic transient over the 2 years. In all instances we assume the velocity after an earthquake to equal the velocity before the earthquake. Setting coseismic motions equal to predicted values for sites with small coseismic motions reduces the uncertainty in velocity estimates. If we were to instead estimate coseismic motions, the best fitting estimates would vary unreasonably across metropolitan Los Angeles and the velocity estimates would be less accurate.

[20] We find postseismic transients of the 1999 Hector Mine earthquake to be 15% or less of coseismic motions at the eight GPS sites (LDES, CTMS, BSRY, OAES, AVRY, DSSC, BBRY, and AZRY) that moved 15 mm or more during the earthquake, and we find the characteristic time describing the exponential decay of the postseismic transients to be about 1 year. Postseismic transients of the 1994 Northridge earthquake are not readily evident in the evolution of the positions of the eight GPS sites (ROCK, AOA1, DAM1, DAM2, SPK1, CMP9, CSN1, and OAT2) nearest the rupture, partly because observations at all but one site (AOA1) began no sooner than 1 year after the earthquake.

2.2. Synthetic Aperture Radar (SAR) Interferometry

[21] We use synthetic aperture radar interferometry to estimate vertical motions. SAR provides estimates of motion in the line of sight of the European Remote Sensing (ERS) satellite in the time between satellite passes. The ERS satellite sees metropolitan Los Angeles from an azimuth of S77°E and an angle from vertical ranging from 18° in the eastern part of the interferogram to 27° in the western part. Assuming horizontal motion in the line of sight of the satellite to be negligible, we take vertical motion to be the line-of-sight observation divided by the cosine of the angle at the surface between vertical and the ERS satellite.

[22] We evaluate seasonal oscillations of the Santa Ana aquifer using an interferogram recording uplift from July 1998 to January 1999 and an interferogram recording subsidence from February 1999 to August 1999 (Figure 2). We evaluate cumulative uplift and subsidence using a stack of 25 interferograms from June 1992 to November 1999 [Peltzer et al., 2001] (Figure 5) and an interferogram from May 1998 to May 2000 (Figure 6).

Figure 5.

Vertical rates from 1992 to 1999 inferred from SAR (color gradations), oil fields (colored dots in Figure 5, top), and inferred horizontal anthropogenic velocities (black and green vectors in Figure 5, bottom). Vertical rates are estimated from Peltzer et al.'s [2001] stack of 25 interferograms. Vertical rate is taken to be the SAR line-of-sight change rate divided by the cosine of the angle at the surface between vertical and the ERS satellite. Oil fields are from California Department of Conservation, Division of Oil, Gas, and Geothermal Resources (2004, available at http://www.consrv.ca.gov/DOG/index.htm) and are distinguished by the various colors of the dots: A, Alondra; B, Bandini; BH, Beverly Hills; BO, Brea-Olinda; CH, Cheviot Hills; cLA, city of Los Angeles; CS, Chino-Soquel; D, Dominguez; dLA, downtown Los Angeles; eC, east Coyote; E, Esperanza; eLA, east Los Angeles; ES, El Segundo; HB, Huntington Beach; HT, Howard Townsite; H, Hyperion; I, Inglewood; LB, Long Beach; LC, Las Cienegas; Lf, Leffingwell; Lw, Lawndale; Mh, Mahala; Mn, Montebello; N, Newport; oB, offshore Belmont; PdR, Playa del Rey; P, Potrero; Rc, Richfield; Rs, Rosecrans; SB, Seal Beach; SFS, Sante Fe Springs; SL, Salt Lake; Sn, Sansinena; sSL, south Salt Lake; Sw, Sawtelle; T, Torrance; US, Union Station; wC, west Coyote; Wh, Whittier; Wm, Wilmington; wN, west Newport; YL, Yorba Linda. The inferred horizontal anthropogenic velocity is computed to be 1000 m times the vertical rate gradient (in mm yr−1 m−1) inferred from SAR. We correct the velocities of the 12 GPS sites with 3 years or more data before November 1999 (black vectors) using inferred anthropogenic velocities estimated from this interferogram. The histogram at right shows the number of times the months of the year are sampled by the 25 interferograms. Neglecting the horizontal velocity between PVEP and JPLM results in an error in the vertical rate of PVEP relative to JPLM of −1.7 mm yr−1. (The velocities of PVEP and JPLM relative to the North American plate differ by 7.0 mm yr−1 toward N21°W, which resolves into −1.5 mm yr−1 in the line of sight of the satellite, yielding an error in the relative vertical motion of PVEP relative to JPLM of −1.7 mm yr−1.)

Figure 6.

Vertical rates from May 1998 to May 2000 inferred from SAR (color gradations) and inferred horizontal anthropogenic velocities (black and green vectors). Vertical rate is taken to be the SAR line-of-sight change rate divided by the cosine of the angle at the surface between vertical and the ERS satellite. The inferred horizontal anthropogenic velocity is computed to be 1000 m times the vertical rate gradient (in mm yr−1 m−1) inferred from SAR. We correct the velocities of the 34 GPS sites with no data before May 1998 (green vectors) using inferred anthropogenic velocities estimated from this interferogram.

[23] Assuming horizontal motion to be negligible results in small errors in vertical estimates. Horizontal motion of 1 mm yr−1 toward S77°E resolves into ∼0.4 mm yr−1 in the line of sight of the satellite. Horizontal motion of 1 mm yr−1 toward N13°E resolves into zero motion in the line of sight of the satellite. Using the largest seasonal horizontal displacements observed with GPS, we estimate that neglecting horizontal motions results in errors of vertical estimates of at most (at CCCO) 1.5 mm in the rising interferogram and 2.4 mm in the falling interferogram (see Figure 2 caption). Using the largest relative horizontal motion across the interferogram observed with GPS, we estimate that neglecting horizontal motions results in errors of vertical estimates of at most (between PVEP and JPLM) 1.7 mm yr−1 in the stacked interferogram and 3.3 mm in the 2 year interferogram (see Figure 5 caption).

2.2.1. Calibrating Interferograms

[24] Variations in unmodeled atmosphere delay across the interferograms result in errors in SAR line-of-sight observations equal to ∼15 mm over distances of 50 km [Emardson et al., 2003]. To estimate displacements more accurately, we calibrate the interferograms using GPS. We first compute GPS estimates of displacement in the line of sight of the ERS satellite from the velocity and the sinusoid fit to GPS position estimates. We next fit a surface to differences between GPS and SAR estimates of line-of-sight displacement using the program “surface” from Generic Mapping Tool (GMT) [Weissel and Smith, 1998]. We then add the surface to the interferogram. Calibrating the interferograms reduces confidence limits in vertical estimates from ±∼15 to ±∼5 mm.

[25] We use the southern California set of positions to calibrate the seasonal interferograms and the global set of positions to calibrate the 2 year interferogram. We do not calibrate the stacked interferogram but use the global set of positions to define its vertical reference.

2.2.2. Stacking Interferograms

[26] We use Peltzer et al.'s [2001] stack of 25 interferograms to evaluate mean vertical rates from 1992 to 1999. Peltzer et al. [2001] first removed coseismic motions of the 1992 Landers, 1994 Northridge, and 1999 Hector Mine earthquakes. They next estimated line-of-sight change rates for each interferogram, then estimated mean line-of-sight change rates by stacking the 25 rate interferograms. This stacked interferogram is unbiased by seasonal oscillations because the 25 interferograms evenly sample the months of the year (histogram on right of Figure 5). Stacking the interferograms eliminates errors due to variations in unmodeled atmosphere delay, reducing confidence limits from ±∼15 to ±∼2 mm.

[27] Vertical rates inferred from the 2 year interferogram are unbiased by seasonal oscillations because the interferogram begins (16 May 1998) and ends (20 May 2000) on nearly the same day of the year. Coseismic motions of the Hector Mine earthquake, which are as large as 1 mm in the vertical and 5 mm in the horizontal, were not removed from the interferogram.

2.2.3. Defining Vertical Reference

[28] The global set of positions is relative to the center of mass of the solid earth, the oceans, and the atmosphere, which defines vertical in International Terrestrial Reference Frame 2000 [Altamimi et al., 2002; Heflin et al., 2002], as are the stacked interferogram and the 2 year interferogram. The southern California set of positions is relative to a mean southern California reference defined by the 274 GPS sites used in the spatial filter, as are the two seasonal interferograms.

[29] Relative to ITRF2000 we find southern California to be moving up ∼5 mm from March to September and down ∼5 mm from September to March [see also Blewitt et al., 2001; Dong et al., 2002; Wu et al., 2003]. This oscillation is opposite that of the surface of the Santa Ana aquifer.

2.2.4. Relating Horizontal to Vertical Seasonal Oscillations

[30] Horizontal seasonal displacements appear to be proportional to gradients in vertical seasonal displacements:

display math

where h is the horizontal displacement vector (in mm), A is a constant (in m), ∇ is the gradient vector, and v is the vertical displacement (in mm) as a function of position. The minus sign means that horizontal displacement is in the direction of decreasing uplift.

[31] We use horizontal and vertical displacements over the two seasonal interferograms to estimate A. The horizontal displacement is determined from the sinusoid fit to the southern California set of GPS positions. The horizontal displacement is computed to be the value of the sinusoid at the end of the interferogram minus the value of the sinusoid at the start of the interferogram (Figure 3). The constant velocity is not taken to be part of the seasonal displacement. About half the GPS sites have observations during the interferograms. For the half that do not, sinsuoids fit to GPS observations after the interferograms are used to predict horizontal seasonal displacements during the interferograms. The vertical seasonal displacement is taken to be the SAR line-of-sight observation divided by the cosine of the angle at the surface between vertical and the ERS satellite. The vertical gradient at a GPS site is computed from the seasonal interferogram over a circle with a diameter of 5000 m. A gradient computed over a smaller circle is too uncertain to be reliable.

2.2.5. Estimating Horizontal Anthropogenic Velocities

[32] Using the relationship between horizontal and vertical seasonal oscillations, we estimate horizontal cumulative anthropogenic velocities. Assuming gradients in tectonic vertical motions to be negligible, we compute the horizontal anthropogenic velocity at a GPS site to be the value of A (1000 m) estimated from seasonal oscillations times the gradient (in mm yr−1 m−1) at the site in cumulative vertical rate inferred from SAR (Figures 5 and 6 and Table 1). The gradient in vertical rate is computed from either the stacked interferogram or the 2 year interferogram, whichever more closely matches the time period of observations at the GPS site. The stacked interferogram is used to estimate the anthropogenic horizontal velocities of 12 GPS sites with 3 or more years data before November 1999, and the 2 year interferogram is used to the anthropogenic horizontal velocities of 34 GPS sites with no data before May 1998. Vertical rate gradients are computed from the stacked interferogram over circles with a diameter of 1000 m and from the 2 year interferogram over circles with a diameter of 5000 m. The better accuracy of the stacked interferogram allows reliable gradients to be estimated over smaller circles.

Table 1. Inferred Anthropogenic Horizontal Velocities
SiteSpeed, mm yr−1Azimuth, °CW of North
From 1992 to 1999 Estimated Using the Stacked Interferogram
AZU10.2−90
BRAN0.2−45
CIT10.490
CLAR1.429
JPLM2.074
LONG0.1180
MATH0.921
PVEP0.3135
TORP0.318
UCLP0.1180
USC10.563
WHC12.7−122
 
From 1998 to 2000 Estimated Using the 2 Year Interferogram
BKMS1.7−41
CCCO1.752
CCCS0.8−113
CRHS0.2−104
CSDH0.7−61
CVHS1.4−86
DSHS1.519
DYHS1.9−116
ECCO0.584
ELSC0.7−175
EWPP0.845
FXHS1.2−131
FVPK2.6−17
LASC0.6165
LBC11.426
LBC21.1−104
LFRS0.6−153
LORS1.5−17
LPHS1.3−55
MLFP0.4−23
NOPK1.3−165
PMHS0.3−171
PVHS0.6121
PVRS0.7−138
RHCL1.1−79
RTHS0.673
SACY0.7135
SCMS0.4−166
SNHS0.727
SPMS0.8−172
VTIS0.3−72
VYAS2.872
WCHS1.5−66
WRHS0.7−129

[33] Our assumption that gradients in vertical motions are anthropogenic and not tectonic is justified. Vertical rate gradients along the margins of aquifers and oil fields are in places observed to be ≥2 mm yr−1 km−1, yielding inferred horizontal anthropogenic velocities of ≥2 mm yr−1. Mountains in most places are believed to rise at ≤1 mm yr−1 [cf. Argus and Gordon, 2001], which is slower than the speeds at which aquifers and oil fields are rising and falling. An elastic edge dislocation model in which the Puente Hills thrust is slipping at 9 mm yr−1 beneath a locking depth of 6 km predicts vertical rate gradients to be as high as 0.2 mm yr−1 km−1, which, if mistaken as anthropogenic, would result in an error of just 0.2 mm yr−1.

3. Results

3.1. Seasonal Oscillations

[34] GPS and SAR record big vertical oscillations of the Santa Ana aquifer. SAR constrains how the size of the vertical oscillation varies across the aquifer (Figure 2). Maximum subsidence from February 1999 to August 1999 is −62 ± 5 mm 4 km south of SACY and −54 ± 5 mm 5 km east of LBC1. Maximum uplift from July 1998 to January 1999 is +46 ± 5 mm south of SACY and +37 ± 5 mm east of LBC1. Using the time periods of the two interferograms and maximum and minimum times of March 8 and September 8, we calculate that the falling interferogram records 95% and the rising interferogram records 67% of the total oscillation. Extrapolating, we calculate the total subsidence in the spring and summer of 1999 to be −67 mm in the southeast part of the aquifer and −58 mm in the northwest part, nearly equal to the total uplift in the fall of 1998 and winter of 1999 of +69 mm in the southeast part of the aquifer and +55 mm in the northwest part. The two SAR interferograms show the aquifer to be 40 km long and 18 km wide and bounded on the southwest by the Newport-Inglewood fault, on the east by the Santa Ana mountains, on the northeast by the Puente Hills, and on the west partly by the Dominguez Hills.

[35] GPS tightly constrains the size of vertical oscillations in places (Figure 4). The vertical oscillation is 44 ± 4 mm at SACY and 38 ± 4 mm at LBC1. PMHS (15 ± 2 mm), DYHS (12 ± 2 mm), HOLP (12 ± 4 mm), CCCO (11 ± 3 mm), CCCS (9 ± 3 mm), FVPK (9 ± 3 mm), BGIS (9 ± 4 mm), and BKMS (7 ± 3 mm) all rise in the autumn and winter and fall in the spring and summer.

[36] GPS also tightly constrains the size of horizontal oscillations (Figure 2). The horizontal oscillation is biggest at FVPK (8 ± 2 mm, maximum north position in September) and CCCO (7 ± 2 mm, maximum east position in September). PMHS (4 ± 2 mm, south), LBC2 (4 ± 2 mm, northeast), SACY (4 ± 2 mm, southeast), HOLP (3 ± 2 mm, south), DYHS (3 ± 2 mm, southwest), and LBC1 (3 ± 2 mm, northeast) all move away from the aquifer center in the autumn and winter and toward the aquifer center in the spring and summer. The 8 ± 2 mm FVPK horizontal oscillation we estimate is smaller than the 14 mm that Bawden et al. [2001] estimate.

[37] Horizontal seasonal motions are observed with GPS to be in the direction of local subsidence and largest where vertical seasonal motions change most quickly with horizontal distance. Using seasonal displacements of 10 GPS sites in and near the Santa Ana aquifer over the time period of the falling interferogram, we estimate the value of A in Equation (1) to be 1000 ± 300 m. The model reduces the RMS of the 10 horizontal displacements by two thirds, from 4.4 to 1.6 mm. The model predicts horizontal displacement at six sites well (FVPK, CCCO, SACY, LBC2, LBC1, and DYHS), those at three sites moderately well (PMHS, HOLP, and BGIS), and that at one site poorly (CCCS) (Figure 2, bottom). The model reduces the RMS of horizontal displacements over the time period of the rising interferogram by one third, from 2.9 to 1.9 mm. The model predicts horizontal displacements at four sites well (FVPK, SACY, LBC2, and DYHS), those at five sites moderately well (CCCS, HOLP, PMHS, BGIS, and CCCO), and at that one site poorly (LBC1) (Figure 2, top).

3.2. Cumulative Anthropogenic Motions

3.2.1. Anthropogenic Vertical Rates

[38] SAR shows uplift and subsidence in metropolitan Los Angeles to accumulate in response to management of water and oil resources.

3.2.1.1. Aquifers

[39] The Santa Ana aquifer accumulated neither significant uplift nor significant subsidence from 1992 to 1999. The stacked interferogram shows vertical rates in the aquifer ranging from +1 to −3 mm yr−1. This observation disagrees with that of Bawden et al. [2001], who estimate maximum subsidence from 20 October 1993 to 3 October 1998 to be 60 mm in the southeast part of the aquifer. (Using an interferogram we constructed from the same observations as Bawden et al. [2001], we find maximum subsidence from 20 October 1993 to 3 October 1998 to be −50 mm in the southeast part of the aquifer. GPS observations show that SACY has risen about +10 mm between 3 October and 20 October in each of the past 5 years, suggesting that the southeast part of the aquifer rose +10 mm between 3 October 1993 and 20 October 1993, thus reducing the estimate of cumulative subsidence from −50 to −40 mm. The stacked interferogram predicts maximum subsidence over 5 years to be −15 mm (= −3 mm yr−1 × 5 years). The 25 mm difference between the cumulative subsidence estimated from the individual interferogram and that inferred from the stacked interferogram is bigger than the ±∼15 mm uncertainty in a vertical displacement across 50 km estimated from a single interferogram [Emardson et al., 2003], but perhaps might be explained by the different time periods over which the two interferograms are averaged.) The Santa Ana aquifer accumulated subsidence from 1998 to 2000. The 2 year interferogram shows the northwest part of the aquifer to have subsided at a maximum rate of −11 mm yr−1 and the southeast part to have subsided at a maximum rate of −12 mm yr−1 (Figure 6). This maximum subsidence rate equals the −12 mm yr−1 that Bawden et al. [2001] find from October 1997 to October 1999. The subsidence is furthermore consistent with the Orange County Water District's press release (dated 23 September 2002, Orange County groundwater basin overdrafted due to increased production and recent dry years, 2002, available at http://www.ocwd.com/_html/_pr/_pr02/pr02_0923_overdraft.htm) that water was overdrawn from the aquifer over the three years ending in the summer of 2002. SACY is observed with GPS to have subsided at −7 ± 5 mm yr−1 from 1999 to 2002. LBC1 is observed with GPS to have had no vertical motion (0 ± 5 mm yr−1) from 1999 to 2002. These vertical rates are estimated from the global set of positions and are more reliable than the vertical rates (in Figure 3) estimated from the southern California set of positions.

[40] The San Gabriel aquifer also accumulated neither uplift nor subsidence from 1992 to 1999, with vertical rates ranging from 0 to +2 mm yr−1. The center of the San Gabriel aquifer subsided at −8 mm yr−1 from 1998 to 2000.

[41] The center of the Chino aquifer subsided from 1992 to 1999 at an average rate of −25 mm yr−1, while an area of uplift north of the aquifer rose at an average rate of +11 mm yr−1.

[42] Our examination of tables of water and oil production and water injection (California Department of Conservation, Division of Oil, Gas, and Geothermal Resources, 2004, available at http://www.consrv.ca.gov/DOG/index.htm) suggests that the rise and subsidence of oil fields are not strongly correlated with the reported increase and decrease of water and oil. We compute the increase in the volume of liquid in each oil field to be water injection minus the sum of water production and oil production. On one hand the volume of the Beverly Hills and Montebello oil fields is decreasing, consistent with the observed subsidence of the two oil fields. On the other hand the volume of Sante Fe Springs and West Coyote oil fields is neither increasing nor decreasing, inconsistent with the observed uplift of the two oil fields. The volume of the Yorba Linda oil field is decreasing quickly, but the oil field is not observed to be subsiding. The apparent inconsistencies might be explained by a more thorough analysis of the records, inaccuracy in the reported volumes of water and oil production and water injection, or by gas going into oil fields (repressurization).

3.2.1.2. Oil Fields

[43] Except for the Chino aquifer, oil fields are the places with the largest cumulative uplift and subsidence from 1992 to 1999 (Figure 5). A subsidence belt cutting east across Los Angeles consists of the Beverly Hills oil field (−10 mm yr−1), the Las Cienegas and Downtown Los Angeles oil fields (−5 mm yr−1), the East Los Angeles and Montebello oil fields (−3 mm yr−1), and the Whittier oil field (−5 mm yr−1). The Sante Fe Springs oil field (+9 mm yr−1) and the West Coyote oil field (+5 mm yr−1) rose quickly from 1992 to 1999. Oil fields lying along the Newport-Inglewood fault include the Inglewood oil field (+3 mm yr−1), the Long Beach oil field (+5 mm yr−1), and the Huntington Beach oil field (−8 mm yr−1). Oil fields lying along the Palos Verdes fault include the Torrance oil field (+4 mm yr−1 in the northwest, −8 mm yr−1 in the middle), and the Wilmington oil field (−6 mm yr−1 in the northwest, +9 mm yr−1 in the southeast).

3.2.2. Inferred Anthropogenic Horizontal Velocities

[44] Inferred horizontal anthropogenic velocities from 1992 to 1999 are faster than 1 mm yr−1 at 3 of the 12 GPS sites for which we use the stacked interferogram to correct for anthropogenic effects (Figure 5, bottom). WHC1 is estimated to have moved southwest at 2.7 mm yr−1 toward the subsidence belt southwest of Whittier oil field. JPLM is inferred to have moved east at 2.0 mm yr−1 toward the canyon (the Arroyo Seco) cutting through Pasadena. CLAR is estimated to have moved northeast at 1.4 mm yr−1 away from the area of uplift north of Chino aquifer. USC1 is inferred to have moved northeast at just 0.5 mm yr−1 in response to management of the Las Cienegas and Downtown Los Angeles oil fields. Correcting WHC1's velocity for anthropogenic effects makes it more consistent with the velocities of USC1, BKMS, RHC1, VYAS, and SNHS (Figure 7).

Figure 7.

Comparison of velocities corrected for anthropogenic effects (black, green, and blue vectors) with uncorrected velocities (magenta vectors). Uncorrected velocities are not shown at sites with inferred horizontal anthropogenic speeds ≤0.5 mm yr−1.

[45] Inferred horizontal anthropogenic velocities from 1998 to 2000 are faster than 1 mm yr−1 at 15 of the 34 GPS sites for which we use the 2 year interferogram to correct for anthropogenic effects (Figure 6). Four sites along the margin of the southeast part of the subsiding San Gabriel aquifer are inferred to have moved toward the aquifer: VYAS east at 2.8 mm yr−1, LPHS northwest at 1.3 mm yr−1, WCHS northwest at 1.5 mm yr−1, and CVHS west at 1.4 mm yr−1. Correcting the four velocities for anthropogenic effects makes them more consistent with each other (Figure 7). Four sites along the margin of the subsiding Santa Ana aquifer are estimated to have moved toward the aquifer: FVPK north at 2.6 mm yr−1, DYHS southwest at 1.9 mm yr−1, CCCO northeast at 1.7 mm yr−1, and LBC1 northeast at 1.4 mm yr−1. BKMS is estimated to have moved northwest at 1.7 mm yr−1 away from the rising Sante Fe Springs oil field. NOPK is estimated to have moved south at 1.3 mm yr−1 away from the rising Inglewood oil field. FXHS is estimated to have moved southwest at 1.2 mm yr−1 toward the falling Beverly Hills oil field.

[46] The Ventura basin and San Fernando valley are beyond the western limit of SAR observations, but most sites there are in the mountains and unlikely to be influenced by management of water and oil resources.

[47] Water and oil going into and coming out of aquifers and oil fields may behave differently at different places, and the relationship between horizontal and vertical displacements may depend upon the depth of sediments. The inferred anthropogenic horizontal velocity of JPLM is likely too fast because the site is nearly on bedrock and not subject to sediment volume changes. Comparison of the uncorrected and corrected velocities with the velocity field suggests that the inferred anthropogenic horizontal velocity is too slow by a factor of ∼2 at FXHS, DYHS, BKMS, RHCL, VYAS, and LPHS. For example, if we were to correct the velocity of DYHS by twice as much, we would find its corrected velocity to be 4.5 mm yr−1 toward N05°E, which would be more consistent with the velocities of PMHS and BKMS (Figure 7). Thus anthropogenic motion is more uncertain at the sites at which we infer it to be faster. We estimate the uncertainty in the corrected velocity by summing two covariances matrices, one describing uncertainty in the observed velocity and the second describing the uncertainty in the inferred anthropogenic velocity. We take the anthropogenic uncertainty to be described by a 95% confidence ellipse with a semimajor axis and semiminor axis equal to, respectively, the speed and half the speed of the inferred anthropogenic velocity.

4. Interseismic Velocity Field

4.1. Integrating Geodetic Techniques

[48] We estimate interseismic velocities using five geodetic techniques, three of which are global (VLBI, SLR, GPS) and two of which are for California (campaign GPS, trilateration). The velocities of the 526 permanent GPS sites that we estimate from observations from 1991 to 2002 are the primary basis for this study. The velocities of 77 VLBI sites estimated from observations from 1979 to 1999 (model GLB1122) (C. Ma, Goddard Space Flight Center, electronic communication, 2000) constrain 11 site velocities in southern California and plate velocities. The velocities of 47 SLR sites estimated from observations from 1976 to 2000 (model CSR00L01, R. J. Eanes, Center for Space Research, electronic communication, 2000) constrain plate velocities and the velocity of the site (MNPEAK) at Monument Peak. A total of 383 line length rates among 155 trilateration sites estimated from observations from 1971 to 1992 (K. Wendt, U.S. Geological Survey, electronic communication, 1998) constrain strain rates near the San Andreas fault. The velocities of 43 campaign GPS sites estimated from observations from 1984 to 1992 (D. Dong, Southern California Earthquake Center, electronic communication, 1998) constrain velocities across the Ventura basin and help tie the trilateration results to the plates. We impose velocity ties at 20 places. The ties involve 12 permanent GPS, 9 VLBI, 1 SLR, 13 trilateration, and 14 campaign GPS sites. The ties allow the velocities of trilateration and campaign GPS sites to be estimated relative to the plates.

4.2. Steadiness of Interseismic Strain Accumulation

[49] The degree to which interseismic strain rates vary is subject to debate. On one hand triangulation results indicate that strain rates in northern California over the 24 years following the 1906 San Francisco earthquake were nearly three times the mean interseismic strain rate [Thatcher, 1983; Kenner and Segall, 2000]. On the other hand rates of change of 32 trilateration lines along the San Andreas fault in southern California were, excepting coseismic motion, nearly constant from 1971 to 1992 [Savage and Lisowski, 1995]. Studies of postseismic transients of the 1992 Landers [Savage and Svarc, 1997; Shen et al., 1994; Peltzer et al., 1998], the 1994 Northridge [Donnellan and Lyzenga, 1998; Donnellan et al., 2002], and the 1999 Hector Mine [Pollitz et al., 2001; Savage et al., 2003; Jacobs et al., 2002] earthquakes suggest that postseismic transients are no more than 1/4 of coseismic motions and have characteristic times describing exponential decay of no longer than 2 years. However, Savage and Svarc [1997] maintain that velocities changed at the time of the 1992 Landers earthquake and Hudnut et al. [2002] suggest that velocities changed at the time of the 1999 Hector Mine earthquake.

[50] The time over which the five geodetic techniques have observations provide a practical test of whether velocities after the 1992 Landers earthquake equal velocities before the earthquake. We estimated two sets of velocities, one set for the time period 1971 to June 1992 from the VLBI, SLR, campaign GPS, and trilateration results, and a second set for the time period June 1992 to 1999 from the permanent GPS results. The velocities of all but one VLBI site (DSS15) and one SLR site (MNPEAK) are estimated from data taken before the 1992 Landers earthquake. The velocity of all permanent GPS sites are estimated from data taken after the earthquake. Velocities after the earthquake differ insignificantly from those before the earthquake at 11 of 12 sites (Figure 8). The velocity of the site (JPLM) at the Jet Propulsion Laboratory after the 1992 Landers earthquake differs from the velocity before it by 3.6 mm yr−1 toward N13°W. (This 3.5 mm yr−1 increase in the north component of JPLM's velocity, which is inferred from VLBI data before 1992 and GPS data after 1992, differs from the 5 mm yr−1 increase in the east component of the velocity at the time of the 1994 Northridge earthquake that Heflin et al. [1998] deduce from only GPS data.) That the pre- and post-Landers velocities are nearly equal suggests that our assumption that velocities are constant from 1971 to 2002 is reasonable.

Figure 8.

Comparison of site velocities and their 95% confidence limits estimated from permanent GPS observations from June 1992 to 2002 (in green) with 95% confidence limits in site velocities estimated from VLBI, SLR, campaign GPS, and trilateration observations from 1971 to June 1992 (in red). The rupture zones of the 1992 Landers and 1857 Fort Tejon earthquakes are shown.

4.3. Removing San Andreas Fault System Elastic Strain

[51] Because we want to evaluate strain that is being or will be released in metropolitan Los Angeles, we remove from the interseismic velocity field elastic strain that will be released along the San Andreas and San Jacinto faults. We approximate this elastic strain using a screw dislocation model consisting of six San Andreas fault segments and seven San Jacinto fault segments (Table 2). We assume the fault to be locked from the surface to the maximum depth of seismicity and to be slipping beneath this depth at a constant rate. We estimate maximum seismicity depths from the profiles of Hill et al. [1990] and Magistrale and Zhou [1996]. We estimate deep slip rates using the geodetic results in this study.

Table 2. Screw Dislocation Model of Elastic Strain Associated With Locking of the San Andreas and San Jacinto Faults
Latitude, °NLongitude, °WSlip Rate, mm yr−1Locking Depth, kmFault Segment
San Andreas Fault
35.98120.531215Cholame
35.82120.382315Cholame
35.66120.223418North Carrizo Plain
35.35119.903420North Carrizo Plain
35.11119.653422North Carrizo Plain
34.91119.353023South Carrizo Plain
34.85119.093018South Carrizo Plain
34.79118.812018Mojave Desert
34.68118.452013Mojave Desert
34.55118.102014Mojave Desert
34.42117.792015Mojave Desert
34.28117.481518San Bernardino Mountains
34.10117.101523San Bernardino Mountains
33.95116.652015Coachella Valley
33.80116.282014Coachella Valley
33.58116.002010Coachella Valley
33.36115.72   
 
San Jacinto Fault
34.28117.481218San Bernardino Valley
34.02117.241220San Jacinto Valley
33.74116.921220Anza
33.46116.511417Anza
33.26116.12   
33.46116.51417Coyote Creek
33.20116.19416Borrego Mountain
33.01115.98   
32.99115.92415Superstition Mountains
32.89115.70   
33.01115.84415Superstition Hills
32.89115.64   

[52] We use geodesy to simultaneously estimate the deep slip rate and locking depth of the Mojave segment of the San Andreas fault. After finding the best fitting locking depth to be consistent with the maximum seismicity depth, we take the maximum seismicity depth to be the locking depth. We assume that the lithosphere on either side of the San Andreas fault comprises two elastic microplates, the west Mojave desert microplate northeast of the fault and the San Gabriel Mountains microplate southwest of the fault. We assume that the two microplates deform only elastically as predicted by the dislocation model of strain accumulating on the San Andreas and San Jacinto faults. The west Mojave desert microplate is bounded on the southwest by the San Andreas fault, on the north by the Garlock fault, and on the east by the east California shear zone. The San Gabriel Mountains microplate is bounded on the northeast by the San Andreas fault, on the south by the San Fernando-Sierra Madre-Cucamonga fault, and on the west by the San Gabriel fault. The west Mojave desert microplate has 15 trilateration, 11 permanent GPS, 2 campaign GPS, and 1 VLBI site. The San Gabriel Mountains microplate has 17 trilateration, 4 permanent GPS, and 1 campaign GPS site.

[53] We find the best fitting parameters for the Mojave segment of the San Andreas fault to be a deep slip rate of 20 ± 4 mm yr−1 and a locking depth of 15 ± 5 km (two-dimensional 95% confidence limits). The two parameters are highly correlated, with faster deep slip rates going with deeper locking depths. The 95% confidence region has values of 17 mm yr−1 and 12 km at one end and 24 mm yr−1 and 20 km at the other end.

[54] The 20 ± 4 mm yr−1 deep slip rate that we estimate is slower than the 30 ± 8 mm yr−1 mean Holocene slip rate that the Working Group on California Earthquake Probabilities [1995] estimate from paleoseismology. The 15 ± 5 km locking depth that we estimate is consistent with the maximum seismicity depth of 13–18 km along the Mojave segment of the San Andreas fault.

[55] Our best fitting parameters are slower and shallower than the 34 mm yr−1 deep slip rate and 25 km locking depth that Savage and Lisowski [1998] and Eberhart-Phillips et al. [1990] estimate. Our parameters fit the trilateration line length rates better than Savage and Lisowski's, with our normalized sample standard deviation (which is the square root of reduced chi-square) being 1.06, 1/5 lower than their 1.29. Our parameters fit to ≤1 mm yr−1 the four line length rates (PICONCER-WHITAKER, PICONCER-WARMSPR, TEJON41- WARMSPR, TEJON41-WHITAKER) their best fitting parameters misfit by ≥2 mm yr−1 [Savage and Lisowski, 1998, Figure 4]. Savage and Lisowski [1998] maintain that the Mojave segment of the San Andreas fault must be locked to at least 25 km depth, but our parameters fit to ≤1.5 mm yr−1 the eight line length rates (PICONCER-WHITAKER, PICONCER-WARMSPR, TEJON41-WARMSPR, TEJON41-WHITAKER, BADPOW-TOM, HAUECC1-TOM, BADPOW-PACIFICO, DIORITE-TEJON41) they show to be misfit by ≥2 mm yr−1 by a deep slip rate of 34 mm yr−1 and a locking depth of 15 km [Savage and Lisowski, 1998, Figure 5]. Their 34 mm yr−1 and 25 km predicts shear strain rates to be faster at distances of 5 to 50 km from the fault than does our 20 mm yr−1 and 15 km. Their parameters predict five lines (DENIS-TOM, HAUECC1-PACIFICO, HAUECC1- MTGLEASN, ANTAUX-BADPOW, and BADPOW-TOM) to shorten or lengthen more quickly than observed.

[56] Our best fitting model fits the observations well. The weighted root-mean-square (WRMS) residual of 71 trilateration line length rates is just 0.5 mm yr−1. Residual speeds of 26 sites on the west Mojave desert microplate have a WRMS of 0.7 mm yr−1. Residual speeds of 21 sites on the San Gabriel Mountains microplate have a WRMS of 0.5 mm yr−1. The excellent fit indicates that, aside from elastic strain that will be released along the San Andreas and San Jacinto faults, the west Mojave desert and the San Gabriel mountains are not deforming. The lack of major faults and large earthquakes between the eastern California shear zone and the San Andreas fault support the inference that the west Mojave desert behaves as an elastic microplate. The high elevation of the San Gabriel mountains suggest that they may be shortening from north to south, but the trilateration results show shortening perpendicular to the Mojave segment of the San Andreas fault to be ≤2 mm yr−1.

[57] We estimate deep slip rates along other segments of the San Andreas and San Jacinto faults assuming the locking depth equals the maximum seismicity depth. We find the best fitting deep slip rate by comparing our geodetic observations of fault-parallel motion with predictions from two-dimensional screw dislocation models generated at slip rate increments of 1 mm yr−1. We estimate deep slip rates along the North Carrizo plain, South Carrizo plain, San Bernardino mountains, and Coachella Valleys segments of the San Andreas fault to be, respectively, equal to, 4 mm yr−1 slower than, 9 mm yr−1 slower than, and 5 mm yr−1 slower than those the Working Group on California Earthquake Probability [1995] estimate from paleoseismology.

[58] Our formulation of the dislocation model is identical to that of Argus et al. [1999] and Murray and Segall [2001] but different from that of Feigl et al. [1993]. We take the model prediction to be the microplate velocity plus the result of a screw dislocation along the locked part of the fault in the direction opposite of plate motion. Feigl et al. [1993] take the model prediction to be the result of a screw dislocation along the slipping part of the fault in the direction of plate motion. Our residual velocity field includes plate motion but not the effect of locking of the San Andreas and Jacinto faults. Thus in our residual velocity field the San Andreas fault appears to be creeping at the surface at the deep slip rate (Figure 1). Their residual velocity field does not include plate motion. Thus in their residual velocity field the San Andreas fault appears to have no dextral slip across it. Feigl et al.'s [1993] model poorly fits the velocities of sites far from faults, resulting in poor estimates of the component of shortening perpendicular to the San Andreas fault in central California [Argus and Gordon, 2001].

4.4. Tectonics of Metropolitan Los Angeles

[59] We assess interseismic strain accumulation across metropolitan Los Angeles placing emphasis on tightly constrained velocities (Figures 1 and 7 and Table 3). One-dimensional 95% confidence limits in velocities relative to the San Gabriel mountains are approximately ± 1 mm yr−1 for a trilateration site with 15 years of data (in blue in Figures 1 and 7), ± 1.5 mm yr−1 for a GPS or VLBI site with 5 years of data (in black), ± 2.5 mm yr−1 for a GPS site with 3 years of data (green), and ± 3 mm yr−1 for a campaign GPS site with 5 years of data (purple). Correcting for inferred anthropogenic motions makes nearby velocities more similar to each other. Because the elastic strain that will be released along the San Andreas and San Jacinto faults has been removed from the velocity field, the San Gabriel mountains appear to be hardly deforming and the west Mojave desert appears to be moving southeast relative to the San Gabriel mountains at 20 mm yr−1.

Table 3. Horizontal Site Velocities Relative to the San Gabriel Mountains Microplate After Removing Anthropogenic Motions and Elastic Strain Due to Locking of the San Andreas and San Jacinto Faultsa
SiteLatitude, °NLongitude, °WSpeed, mm/yrAzimuth, °CWMajor AxisMinor AxisAngleTime, years
  • a

    Values following the ± are the 95% confidence limits. The 95% error ellipses in horizontal velocities are described by lengths of semimajor (major) and semiminor (minor) axes in mm/yr and by azimuths (angle) of major axes in degrees clockwise of north. The trilateration network was tied to one or more of the other techniques at sites ASBESTOS, CAMP 9, JPL1 RM1, LOCKED, MADRE 80, MONU RES, NIGUEL, PICONCER, REYES, SANDHILL, SAN JOAQ, SAN JUAN, and TANK. The SCEC campaign GPS network was tied to one or more of the global techniques at sites ECHO, MADC, MOJA, MOJM, MUNS, NIGU, PEAR, PIN1, PVER, SAFE, SIO1, SJUA, and VNDN. The velocities of seven permanent GPS sites on the west Mojave desert microplate and one permanent GPS site on the San Gabriel Mountains microplate estimated from 2 to 3 years of data are excluded.

Sites Not on a Microplate: Permanent GPS
AOA134.157118.8306.0 ± 2.0−6 ± 142.51.8−218.1
AZU134.126117.8961.0 ± 1.9−16 ± 832.42.3786.2
BKMS33.962118.0956.5 ± 3.7−4 ± 314.74.3−543.3
BRAN34.185118.2772.0 ± 1.631 ± 462.12.0−457.4
CAT133.446118.4838.7 ± 1.73 ± 163.22.0−667.3
CBHS34.139118.6305.5 ± 3.2−3 ± 324.13.8−293.6
CCCO33.876118.2115.4 ± 3.411 ± 324.23.9793.7
CCCS33.863117.8655.6 ± 3.318 ± 304.13.8783.7
CIT134.137118.1271.7 ± 1.564 ± 502.01.8−718.1
CLAR34.110117.7091.0 ± 2.244 ± 872.82.4386.2
CMP934.353118.4110.6 ± 1.276 ± 961.61.5−107.3
CRHS33.824118.2736.3 ± 3.418 ± 304.34.1−683.4
CSDH33.862118.2574.7 ± 2.91 ± 323.63.3−674.2
CSN134.254118.5242.6 ± 2.0−1 ± 392.52.2−216.5
CVHS34.082117.9022.6 ± 2.9−7 ± 543.73.4894.2
DAM134.334118.3970.8 ± 2.5−157 ± 1103.13.0−174.6
DAM234.335118.3970.9 ± 2.0−4 ± 912.52.4−166.0
DSHS34.024118.3494.1 ± 3.432 ± 454.34.2−93.5
DYHS33.938118.1264.1 ± 3.0−24 ± 393.93.4774.2
ECCO33.887118.3296.0 ± 3.34 ± 304.24.0−643.5
ELSC34.030118.2081.1 ± 3.44 ± 1124.24.1−593.4
EWPP34.104117.5263.6 ± 3.314 ± 494.24.0423.5
FVPK33.662117.9367.6 ± 3.225 ± 264.44.0−344.0
FXHS34.081118.3593.3 ± 3.4−44 ± 534.24.2−893.4
FZHS34.800118.8935.8 ± 2.8−99 ± 283.93.3254.2
JPLM34.205118.1731.0 ± 1.8−126 ± 802.51.9756.0
LAPC34.182118.5754.9 ± 3.6−3 ± 394.54.3−283.2
LASC33.928118.3074.7 ± 3.0−3 ± 343.83.6−573.9
LBC133.832118.1374.7 ± 3.42 ± 394.34.1823.5
LBC233.792118.1734.1 ± 3.5−2 ± 424.34.0−823.5
LEEP34.135118.3222.7 ± 1.73 ± 352.22.0−467.2
LFRS34.095118.4133.7 ± 3.211 ± 494.24.0−393.5
LONG34.112118.0031.6 ± 1.7−10 ± 522.12.0−847.4
LORS34.133117.7540.9 ± 3.897 ± 1274.74.6−103.0
LPHS34.027117.9575.2 ± 2.9−8 ± 293.63.4−694.2
MATH33.857117.4374.5 ± 2.763 ± 303.42.9464.9
MLFP33.918117.3187.0 ± 3.223 ± 244.13.7433.7
MUSD34.262119.0967.4 ± 3.2−38 ± 224.13.4−104.0
NOPK33.980118.3485.8 ± 3.49 ± 334.34.2−333.4
OAT234.330118.6012.2 ± 1.1−3 ± 371.81.3−885.9
OVLS34.327119.1425.5 ± 3.8−12 ± 344.74.1−63.3
PMHS33.903118.1544.5 ± 2.811 ± 333.63.3−734.2
PVEP33.743118.4045.8 ± 2.06 ± 172.72.0−626.2
PVHS33.779118.3726.4 ± 3.6−7 ± 304.64.2−633.3
PVRS33.774118.3217.1 ± 3.30 ± 244.13.8−693.7
RHCL34.019118.0263.7 ± 3.238 ± 464.13.9−813.6
ROCK34.236118.6765.0 ± 2.0−3 ± 192.52.0−187.2
RTHS34.089117.3535.5 ± 2.76 ± 283.53.2374.3
SACY33.743117.8965.1 ± 3.544 ± 384.54.2873.3
SCMS33.444117.6359.5 ± 3.46 ± 174.23.5734.0
SNHS33.927117.9293.9 ± 3.320 ± 454.14.0763.5
SNI133.248119.5248.7 ± 3.20 ± 204.92.6−425.4
SPK134.059118.6465.3 ± 1.9−1 ± 182.52.0−347.3
SPMS33.993117.8493.3 ± 3.417 ± 534.34.2683.3
TORP33.798118.3316.0 ± 2.33 ± 203.02.5−645.6
TRAK33.618117.8035.7 ± 1.511 ± 202.61.8797.2
UCLP34.069118.4423.8 ± 1.615 ± 262.31.9−427.8
USC134.024118.2854.2 ± 1.79 ± 222.21.9−617.9
VTIS33.713118.2947.1 ± 3.38 ± 254.33.8−703.6
VYAS34.031117.9924.3 ± 3.531 ± 384.43.6744.2
WCHS34.062117.9113.5 ± 3.212 ± 484.13.8−763.7
WHC133.980118.0314.5 ± 2.737 ± 253.42.4637.6
WRHS33.958118.4285.5 ± 3.88 ± 384.84.6−553.0
 
Sites Not on a Microplate: VLBI
SANPAULA34.388118.9992.0 ± 2.3−51 ± 593.22.4−66.4
 
Sites Not on a Microplate: Trilateration
SANPAULA34.388118.9992.0 ± 2.3−51 ± 593.22.4−66.4
ARLING33.871117.4713.4 ± 2.658 ± 483.93.2−128.0
BACHELOR33.605117.0613.7 ± 3.548 ± 434.92.91214.1
BEE33.729117.6994.6 ± 2.144 ± 323.52.4−7210.3
BLACK33.806117.6623.6 ± 2.344 ± 393.42.7−7912.0
DOUBLE33.717117.1254.0 ± 3.750 ± 515.53.724.5
DUGO34.215118.2751.5 ± 2.629 ± 763.82.2−109.6
ELSINORE33.602117.3424.0 ± 3.339 ± 374.33.11414.1
FLINT34.164118.1540.7 ± 2.0140 ± 1294.12.4609.6
IDA33.798117.3223.5 ± 2.660 ± 484.32.8114.2
LOMAS33.765117.7464.2 ± 2.543 ± 394.02.7−7810.3
MENIFEE33.718117.2283.7 ± 3.150 ± 434.52.977.8
MICRO33.874117.1903.3 ± 3.235 ± 474.53.1−214.2
NELSON33.823117.0703.5 ± 3.238 ± 454.62.9014.2
SANTIAGO33.711117.5335.4 ± 2.541 ± 253.32.8114.1
SIER33.850117.6533.2 ± 2.648 ± 423.33.06414.1
WHITAKER34.568118.7422.2 ± 1.5−157 ± 331.91.63014.4
 
Sites Not on a Microplate: Campaign GPS
BLUF32.927118.5199.0 ± 3.814 ± 306.14.8−764.6
BRSH33.407118.4057.1 ± 3.810 ± 355.54.8−774.1
CATO34.086118.7864.7 ± 3.6−25 ± 394.54.1−324.6
HAPY34.358118.8504.8 ± 3.619 ± 414.64.4−264.6
HOPP34.478118.8663.0 ± 3.4114 ± 604.54.2−44.6
LOVE34.496118.6691.6 ± 3.5153 ± 934.44.3−114.6
NIGU33.515117.7306.2 ± 2.119 ± 233.52.0745.8
SJUA33.914117.7385.2 ± 2.859 ± 243.52.7744.5
SNP234.440119.0102.7 ± 3.8141 ± 684.74.4−224.6
SNTZ34.043117.8841.8 ± 4.1−94 ± 895.14.6−844.4
WORK33.992118.0031.9 ± 5.0−127 ± 986.35.6714.5
 
Sites on the San Gabriel Mountains Microplate: Permanent GPS
CHIL34.334118.0260.7 ± 1.6138 ± 952.02.0−737.4
VNPS34.502118.1210.6 ± 3.7−109 ± 1444.64.5593.0
WLSN34.226118.0561.7 ± 1.761 ± 532.22.1−756.0
 
Sites on the San Gabriel Mountains Microplate: Trilateration
ANT AUX34.249117.6741.1 ± 3.052 ± 563.71.44814.4
BAD POW34.358117.7640.4 ± 0.9142 ± 1292.21.14614.4
BEND34.642118.3760.9 ± 0.715 ± 350.90.6−1417.2
BURN34.621118.3630.5 ± 0.4−19 ± 390.50.4−1417.2
DISPOINT34.249118.1030.7 ± 1.3−170 ± 851.91.3−3714.4
GRANITE34.598118.3130.1 ± 0.4−113 ± 1180.50.45117.2
HAU ECC134.548118.2150.3 ± 0.450 ± 660.60.55814.4
MINT34.567118.2780.4 ± 0.4−172 ± 510.50.42717.2
MTGLEASN34.387118.1840.5 ± 0.7137 ± 761.00.96214.4
PACIFICO34.382118.0340.8 ± 0.8117 ± 461.10.8−3414.4
PARKER34.460118.2180.8 ± 1.5100 ± 561.81.1−8214.4
PELONA34.561118.3550.4 ± 0.6123 ± 540.70.5−5317.2
PORT RM134.386118.3290.6 ± 0.7−117 ± 691.10.9−3214.4
SAW ECC34.693118.5600.9 ± 1.0−55 ± 461.31.0−6716.1
SISELSIE34.269118.2380.7 ± 1.0−108 ± 671.21.1−7914.4
TENHI34.531118.1470.5 ± 0.625 ± 490.90.45717.2
WARM SPR34.596118.5791.3 ± 1.3−128 ± 451.71.35814.4
 
Sites on the West Mojave Desert Microplate: Permanent GPS
HOLC34.458117.84519.8 ± 1.6119 ± 52.02.0−227.4
LINJ34.662118.13919.0 ± 3.4116 ± 104.34.3643.2
TABL34.382117.67818.4 ± 1.7120 ± 52.22.1127.0
 
Sites on West Mojave Desert: VLBI
PBLOSSOM34.512117.92220.3 ± 1.2115 ± 42.11.445.0
 
Sites on the West Mojave Desert Microplate: Trilateration
ANDREAS34.642118.34319.9 ± 0.5114 ± 20.70.5−817.2
AVENUE34.777118.21920.6 ± 1.2112 ± 11.50.6−7317.2
BULL34.818118.55220.5 ± 1.3111 ± 83.51.6219.7
DENIS34.631118.14320.5 ± 0.8116 ± 21.10.7−3217.3
DESU RM134.636118.29519.9 ± 0.5114 ± 20.80.6−916.2
FAIRMONT34.749118.40619.4 ± 1.2109 ± 41.61.577.7
LEONA34.644118.32320.0 ± 0.3114 ± 10.50.4317.2
LOCKED34.616118.24519.9 ± 0.4113 ± 10.60.41717.2
PORTAL34.666118.36819.6 ± 0.6116 ± 20.90.56917.2
RIT RID34.607118.21420.3 ± 0.3113 ± 10.50.42417.2
SOLEDAD34.983118.18821.0 ± 1.5115 ± 21.90.9−6217.2
THUMB34.863118.41823.3 ± 1.2115 ± 21.60.9−4116.1
TOM34.631117.89819.7 ± 1.0116 ± 31.41.1−2517.3
VERDE34.575118.15220.0 ± 0.6118 ± 20.80.75217.2
 
Sites on the West Mojave Desert Microplate: Campaign GPS
MDAY34.743117.70622.5 ± 4.7119 ± 115.95.2−723.9

[60] The Palos Verdes peninsula is moving relative to the San Gabriel mountains north at about 6 mm yr−1. PVEP is moving at 5.8 ± 2.0 mm yr−1 toward N06°E. That the velocities of the fives sites on the peninsula (PVEP, PVRS, TORP, PVRS, and VTIS) are similar shows that their mean velocity, 6.0 ± 1.0 mm yr−1 toward N05°E, is reliable. Site velocities decrease going from the Palos Verdes peninsula to USC1, with the mean velocity of eight sites in southern Los Angeles (WRHS, NOPK, ECCO, LASC, CSDH, CCCO, PMHS, and LBC1) being 5.1 ± 1.2 mm yr−1 toward N06°E.

[61] USC1, which is 3 km southwest of downtown Los Angeles, is moving relative to the San Gabriel mountains at 4.2 mm yr−1 toward N09°E. Nearby site velocities are consistent with USC1's velocity. The site (UCLP) at the University of California Los Angeles is moving at 3.8 mm yr−1 toward N15°E. Site velocities decrease going north from UCLP to the southern front of the San Gabriel mountains (UCLP, LFRS, LEEP, BRAN, DUGO, CIT1, FLINT, JPLM). The velocity of WHC1, 4.5 mm yr−1 toward N37°E, is uncertain because the site lies along the margin of the subsidence belt near Whittier oil field. Site velocities decrease going north from WHC1 to the southern front of the San Gabriel mountains (WHC1, RHCL, VYAS, LPHS, WCHS, CVHS, LONG, AZU1). The velocities of FXHS and ELSC are inconsistent with USC1's velocity. If FXHS's anthropogenic velocity toward the subsiding Beverly Hills oil field were faster than inferred, then the site's tectonic velocity would be nearer USC1's.

[62] Contractional strain in metropolitan Los Angeles north of USC1 is 3 times that south of the site. The 23 km between USC1 and the southern front of the San Gabriel mountains are contracting at 0.18 × 10−6 yr−1. The 33 km between PVEP and USC1 are contracting at 0.05 × 10−6 yr−1. The high contractional strain rate across northern metropolitan Los Angeles is evident in the steep gradient in the component of velocity perpendicular to the San Andreas fault between USC1 and JPLM along profile A-A′ and between WHC1 and AZU1 along profile B-B′ (Figure 9a).

Figure 9.

Comparison of observations of interseismic strain accumulation along profile A-A′ and profile B-B′ with predictions of elastic edge dislocations models of reverse slip along a hypothetical fault. How model predictions depend upon four parameters is shown for (a) the horizontal component of the deep slip rate, (b) the vertical locking position, (c) the horizontal locking position, and (d) the dip of the fault. We vary one parameter at a time beginning with a model with a horizontal component of slip of 8 mm yr−1, a vertical locking position 6 km deep, a horizontal locking position 12 km north-northeast of USC1 along profile A-A′ and 15 km north-northeast of WHC1 along profile B-B′, and a fault dip of 27°. (top) Cross sections of the fault segments that are creeping (dashed lines of various colors) in the models. Fault segments are creeping to an infinite depth. (bottom) Components of site velocity along the profile as a function of distance along the profile are compared with model predictions (dashed lines of various colors). The velocity components consist of permanent GPS and VLBI sites with 5 years or more of data (black circles), permanent GPS sites with 3 to 5 years of data (gray circles), and trilateration sites with 5 to 17 years of data (black triangles). Velocity components are corrected for anthropogenic motions. Sites with horizontal anthropogenic velocities faster than 0.5 mm yr−1 (open symbols) are distinguished from sites with horizontal anthropogenic velocities slower than 0.5 mm yr−1 (solid symbols). Anthropogenic horizontal corrections estimated from the stacked interferogram are shown (magenta vectors) at the sites (JPLM, WHC1, CLAR) where they are faster than 0.5 mm yr−1. JPLM's uncorrected velocity component is plotted because the site is nearly on bedrock and not subject to sediment volume changes. Faults are PHT, Puente Hills thrust; EPT, upper Elysian Park thrust; SMF, Sierra Madre fault; SAF, San Andreas fault; WF, Whittier fault.

Figure 9.

(continued)

[63] The Santa Monica mountains are moving north at about 5 mm yr−1 relative to the San Gabriel mountains. Taking six sites (AOA1, ROCK, SPK1, CBHS, UCLP, and LFRS) to be on the Santa Monica Mountains microplate [Donnellan et al., 1993b], we estimate the Santa Monica Mountains to be rotating counterclockwise relative to the San Gabriel mountains at 2.4° Myr−1 about a pole of rotation (34.1°N 117.4°W) 100 km east of UCLP. The western part of the Santa Monica mountains (at AOA1) is moving at 5.6 ± 1.8 mm yr−1 toward N01°E and the eastern part (at UCLP) is moving at 4.1 ± 1.4 mm yr−1 toward N04°W. The 25 km between CBHS and the southern front of the San Gabriel mountains are contracting at 0.20 × 10−6 yr−1.

[64] The Ventura basin is contracting from north to south at about 6 mm yr−1 [Donnellan et al., 1993a, 1993b; Hager et al., 1999]. The 12 km between campaign GPS sites HAPY and HOPP are shortening at 6.0 ± 2.5 mm yr−1, yielding a strain rate of 0.50 × 10−6 yr−1. The velocities of the five campaign GPS sites are uncertain because there are just 3 or 4 observations at each site from 1987 to June 1992.

[65] We conclude that a belt of high contractional strain cutting across northern metropolitan Los Angeles 12 to 25 km south of the San Gabriel mountains is shortening from north to south at 4 to 5.5 mm yr−1. We find places in metropolitan Los Angeles to be moving approximately toward north relative to the San Gabriel mountains, not “escaping” toward the northwest as postulated by Walls et al. [1998], nor moving toward N36°E as found by Bawden et al. [2001].

4.5. Edge Dislocation Models of Interseismic Strain Accumulation

[66] The place contracting quickly is between the Puente Hills thrust and the Sierra Madre fault. Reverse slip along the Puente Hills thrust [Shaw and Shearer, 1999; Shaw et al., 2002], the upper Elysian Park thrust [Oskin et al., 2000; Shaw et al., 2002], and the Sierra Madre fault can accommodate shortening from north to south across northern metropolitan Los Angeles. The three faults are believed to merge at a depth of 10 to 18 km along a decollement [U.S. Geological Survey, 1999], a nearly horizontal fault along which all slip occurs (Figure 10). In places the decollement is at the seismogenic depth and is believed to be the boundary along which brittle lithosphere is detached from ductile asthenosphere. The major reflector mapped by the Los Angeles Region Seismic Experiment (LARSE) [U.S. Geological Survey, 1999; Fuis et al., 2001], which begins 15 km below the southern front of the San Gabriel mountains and dips to the north at 12°, is likely the decollement into which the Puente Hills thrust, the upper Elysian Park thrust, and the Sierra Madre fault go.

Figure 10.

Observations of interseismic strain accumulation along the two profiles are compared with predictions of elastic edge dislocation models of reverse slip along thrust faults. In all models the horizontal component of slip is 8 mm yr−1. Profile A-A′ is (light blue) a model in which the Puente Hills thrust and upper Elysian Park thrust are creeping beneath a locking position 6 km deep with slip split evenly between the two faults, (orange) a model in which the Puente Hills thrust is creeping beneath a locking position 8 km deep, (red) a model in which the LARSE decollement is creeping beneath a locking position 15 km deep, and (dark blue) the model best fitting the geodetic observations. Profile B-B′ is (light blue) a model in which the Whittier fault is creeping beneath a locking position 6 km deep, (orange) a model in which a hypothetical fault is creeping beneath a locking position 8 km deep, (red) a model in which the LARSE decollement is creeping beneath a locking position 15 km deep, and (dark blue) the model best fitting the geodetic observations. The focal mechanism of the 1987 Whittier Narrows earthquake is plotted. Faults are PHT, Puente Hills thrust; EPT, upper Elysian Park thrust; SMF, Sierra Madre fault; SAF, San Andreas fault; WF, Whittier fault. Fault locations are from Plesch et al. [2003]. Seismicity from 1975 to 1998 is from Richards-Dinger and Shearer [2000].

[67] We construct two-dimensional elastic edge dislocation models of interseismic strain accumulation above a reverse fault. In the standard model [Savage, 1983] a reverse fault is locked from the surface to a depth beneath which the fault creeps (slips continuously). Strain accumulates at a constant rate in the time between earthquakes. All strain is recovered during an earthquake, when the locked segment of the fault slips. We modify Savage's [1983] model, taking there to be a transition zone 8 km wide over which the creep rate increases from zero to a constant value. In the discussion below we take the locking point to be at the middle of the transition zone.

4.5.1. Model Parameters and Uncertainties

[68] To estimate model parameters and uncertainties, we first construct models with a single hypothetical reverse fault. We assume the strike of the reverse fault to be N65°W, the trend of the Mojave segment of the San Andreas fault. The model has four parameters: (1) the horizontal component of the rate at which the deep part of the fault creeps, (2) the vertical position of the locking point, (3) the horizontal position of the locking point, and (4) the dip of the fault. Three of the four parameters are constrained well by the geodetic observations. We take the fault dip, which is constrained poorly, to be 27°, the dip of the Puente Hills thrust [Shaw and Shearer, 1999]. Because estimates of the other four parameters are not strongly correlated, we can estimate the best fitting parameters and their uncertainties by varying one parameter at a time (Figure 9a). The model predictions depend upon fault segments that are creeping but not upon fault segments that are locked.

[69] We find the best fitting horizontal component of deep slip rate to be 8 mm yr−1 and the best fitting vertical locking position to be 6 km along both profile A-A′ and profile B-B′ (blue dashed lines in Figure 9a). The best fitting horizontal locking position along profile B-B′ is 8 km nearer the San Andreas fault than along profile A-A′. The model fits the observations well, predicting high contractional strain in northern metropolitan Los Angeles, low contractional strain in the San Gabriel mountains and in southern Los Angeles, and the proper convergence rate between the Palos Verdes peninsula and the San Gabriel mountains. (We aim to fit the JPLM's uncorrected velocity component because the site is nearly on bedrock and not subject to sediment volume changes induced by man. The velocity components of trilateration sites FLINT, SISELSIE, and DISPOINT are not well fit by the model.)

[70] The horizontal component of the deep slip rate is constrained well (Figure 9a). In a model in which the vertical locking position is 6 km deep, 75% of the convergence between the two blocks is taken up in the 60 km with center at the horizontal locking position. Thus the horizontal component of the deep slip rate must approximately equal the 6 mm yr−1 convergence rate between the Palos Verdes peninsula and the San Gabriel mountains divided by 0.75. Horizontal components of slip faster than 10 mm yr−1 predict convergence between the peninsula and the mountains to be too fast, and horizontal components of slip slower than 6 mm yr−1 predict convergence between the two places to be too slow. The horizontal component of the slip rate is 8 ± 2 mm yr−1.

[71] The vertical locking position is constrained well (Figure 9b). The vertical locking position must fit the gradient in the velocity component along the profile where it is steepest. Locking positions deeper than 8 km predict the gradient to be too gentle. Locking positions shallower than 4 km predict the gradient to be too steep. The vertical locking position is 6 ± 2 km. Along profile A-A′ the 95% confidence limits nearly include the hypothesis that the Puente Hills thrust is taking up all slip beneath a locking position 8 km deep. Along profile B-B′ the 95% confidence limits very much exclude the hypothesis that the Puente Hills thrust is taking up all slip beneath a locking position 15 km deep.

[72] The horizontal locking position is constrained tightly (Figure 9c). The horizontal locking position must be at the place at which the velocity component along the profile changes quickly from that of southern Los Angeles to that of the San Gabriel mountains. Along profile A-A′ the horizontal locking position is 12 ± 8 km north-northeast of USC1. Along profile B-B′ the horizontal locking position is 15 ± 8 km north-northeast of WHC1. The best fitting horizontal locking position along profile B-B′ is 8 km nearer the San Andreas fault than along profile A-A′. This 8 km offset suggests that the real reverse fault strikes N80°W (not N65°W as in the model), which is more consistent with the strike of the Puente Hills thrust. Along profile A-A′ the 95% confidence limits just include the hypothesis that the Puente Hills thrust is taking up all slip beneath a locking position 6 km deep. Along profile B-B′ the 95% confidence limits very much exclude the hypothesis that the Puente Hills thrust is taking up all slip beneath a locking position 6 km deep.

[73] The dip of the fault is constrained poorly (Figure 9d). Fault dips from 1° to 45° fit the data well. Fault dips greater than 45° not only poorly fit the horizontal GPS observations, they also predict the overriding block to be rising at ≥8 mm yr−1 relative to the downgoing block, a prediction excluded by the GPS vertical observations and by the SAR line-of-sight observations.

4.5.2. Assessing Slip Along Known Faults

[74] To assess slip rates along known faults, we next construct edge dislocation models in which creep occurs along faults mapped with geology and seismology (Figure 10). The two-dimensional dislocation models we construct provide minimum estimates of the deep slip rate because going from two to three dimensions means placing slip along faults not in a plane, which broadens the zone across which contraction is predicted to be occurring. We take the horizontal component of slip rate to be 8 mm yr−1 in all models but vary the fault or faults that are creeping.

4.5.2.1. LARSE Decollement

[75] The edge dislocation model suggests that the LARSE decollement cannot be the only fault that is creeping. A model (red dashed lines in Figure 10) in which the horizontal component of slip along the decollement is 8 mm yr−1 and the locking position is 15 km deep predicts the gradient in the velocity component along the profile in northern metropolitan Los Angeles to be much gentler than it is observed to be. The horizontal component of slip would have to be increased to 16 mm yr−1 to fit the high strain rate there, but then convergence between the Palos Verdes peninsula and the San Gabriel mountains would be predicted to be much too high.

4.5.2.2. Puente Hills-Upper Elysian Park Thrust Along Profile A-A′

[76] The edge dislocation model suggests that along profile A-A′ the Puente Hills-Upper Elysian Park thrust system is creeping at about 9 mm yr−1 beneath a locking position about 6 km deep. A model (light blue dashed lines at top of Figure 10) with a locking position 6 km deep and in which the horizontal component of slip is 8 mm yr−1 and is split evenly between the Puente Hills thrust and the upper Elysian Park thrust fits the geodetic observations well. In the model slip along the upper Elysian Park thrust goes into the Puente Hills thrust at 14 km depth. Between depths of 6 and 14 km the upper Elysian Park thrust is creeping at 5.2 mm yr−1 (= 4 mm yr−1/cos 40°) and the Puente Hills thrust is creeping at 4.5 mm yr−1(= 4 mm yr−1/cos 27°). Beneath a depth of 14 km the Puente Hills thrust is creeping at 9.0 mm yr−1(= 8 mm yr−1/cos 27°).

[77] Creep may be occurring along only the upper Elysian Park thrust, along only the Puente Hills thrust, or along both thrusts. The locking position can be no shallower than 8 km deep. A model (orange dashed line at top of Figure 10) in which the Puente Hills thrust is creeping beneath a locking position 8 km deep with a horizontal component of slip of 8 mm yr−1 fits the observations fairly well. Models with locking positions greater than 8 km deep predict the gradient in the velocity component along the profile between USC1 and the southern front of the San Gabriel mountains to be gentler than it is observed to be.

4.5.2.3. Puente Hills Thrust-Whittier Fault Along Profile B-B′

[78] The edge dislocation model suggests that along profile B-B′ a hypothetical fault halfway between the Puente Hills thrust and the upper Elysian Park thrust is creeping at about 9 mm yr−1 beneath a locking position about 6 km deep. A model (dark blue dashed line at bottom of Figure 10) in which a hypothetical fault 14 km north-northeast of the Puente Hills thrust is creeping beneath a locking position 6 km deep with a horizontal component of slip of 8 mm yr−1 fits the observations well. In the model the hypothetical fault is creeping at 9.0 mm yr−1(= 8 mm yr−1/cos 27°). The hypothetical fault lies near the western part of the reverse-slipping San Jose fault [Yeats, 2004], but the San Jose fault trends at a 45° angle to the model fault.

[79] The locking position can be no shallower than 8 km deep. A model (orange dashed line at bottom of Figure 10) in which the hypothetical thrust is creeping beneath a locking position 8 km deep with a horizontal component of slip of 8 mm yr−1 fits the observations fairly well. However, models with locking positions greater than 8 km deep predict the gradient in the velocity component along the profile between WHC1 and the southern front of the San Gabriel mountains to be gentler than it is observed to be.

[80] The Whittier fault-Puente Hills thrust system cannot be taking up most of the slip. A model (light blue dashed line at bottom of Figure 10) in which the Whittier fault is creeping beneath a locking position 6 km deep with a horizontal component of slip of 8 mm yr−1 fits the observations poorly, predicting the place at which the velocity component along the profile changes quickly from that of southern Los Angeles to that of the San Gabriel mountains to be 12 km south of where it is observed to be. In the model slip along the Whittier fault goes into the Puente Hills thrust at 9 km depth. Between depths of 6 and 9 km the Whittier fault is creeping at 16 mm yr−1(= 8 mm yr−1/cos 60°). Beneath a depth of 9 km the Puente Hills thrust is creeping at 9.0 mm yr−1(= 8 mm yr−1/cos 27°).

[81] A model with horizontal component of slip of 8 mm yr−1 split evenly between the Puente Hills thrust and the Sierra Madre thrust fits the observations poorly, predicting shortening to be distributed more widely than observed no matter how shallow the locking position is.

5. Discussion

5.1. Disagreement Between the Locking Depth and the Seismogenic Depth

[82] Faults creeping to within 6 km of the surface seems inconsistent with large earthquakes breaking a brittle lithosphere down to 15 km depth. In metropolitan Los Angeles the seismogenic depth is 15–20 km, the approximate maximum depth of seismicity [Richards-Dinger and Shearer, 2000] and the depth to which three large earthquakes since 1964 ruptured. The 1971 M 6.6 San Fernando earthquake ruptured the Sierra Madre fault from 3 to 15 km deep and the San Fernando fault from 0 to 8 km deep [Heaton, 1982], the 1987 M 5.9 Whittier Narrows earthquake ruptured the Puente Hills thrust from 12 to 17 km deep [Hartzell and Iida, 1990], and the 1994 M 6.7 Northridge earthquake ruptured the Santa Susana fault from 5 to 20 km deep [Wald et al., 1996]. Thus the 6 ± 2 km locking depth in the elastic dislocation model disagrees with the 15–20 km seismogenic depth. This disagreement suggests that the model, in which an edge dislocation occurs along a planar reverse fault in an elastic continuum, may be unsatisfactory.

[83] Fast shortening is also observed to be occurring over the narrow distance across the Ventura basin [Donnellan et al., 1993b]. The high strain rate there can be fit with an elastic dislocation model only if creep occurs along reverse faults to within 5 km of the surface [Donnellan et al., 1993b]. Reverse slip along the San Cayetano and Oak Ridge faults has placed crystalline basement above the sedimentary basin between the two faults. Hager et al. [1999] find that the high observed strain rate can be fit with a locking depth of 15 km if the sedimentary basin is assumed to be less stiff than the surrounding crystalline basement.

[84] Whether a model like Hager et al.'s [1999] can explain the high contractional rate across northern metropolitan Los Angeles is an outstanding research question. To be successful a study with such a model must address the following: (1) Using the viscoelastic code (GeoFEST) of Hager et al. [1999] to model a reverse fault dividing sedimentary basin from crystalline rock, Glasscoe [2003] find that fast contractional strain across metropolitan Los Angeles occurs only in the 30 years after an earthquake with 5 m slip across the length of the reverse fault. Because no such historical earthquake has occurred, Glasscoe [2003] cannot explain the high contractional rate between USC1 and the southern front of the San Gabriel mountains. (2) The shear moduli that Hager et al. [1999] use for the Ventura basin differ from the values that we compute from Southern California Earthquake Center (SCEC) Seismic Velocity Model 2 [Magistrale et al. 2000; H. Magistrale, electronic communication, 2001] taking the shear modulus to be density times shear wave speed squared (Figure 11). For example, sedimentary basin at 3 km depth has a shear modulus of 10 GPa in Hager et al.'s [1999] model, twice the value of 5 GPa that we compute from the SCEC seismic velocity model. (3) In SCEC Seismic Velocity Model 2 [Magistrale et al., 2000; H. Magistrale, Los Angeles basin depth map, 2004, available at http://www.scec.org/phase3/basinmap.html] the Los Angeles sedimentary basin is no more than 6 km deep, shallower than the 15 km Ventura basin depth of Hager et al. [1999] and the 18 km Los Angeles basin depth of Glasscoe [2003].

Figure 11.

(top) Comparison of seismic shear wave speeds (color gradations) along profiles through the Los Angeles basin and the Ventura basin. (bottom) Comparison of elastic shear moduli that we compute (solid red and blue lines) taking the shear modulus to be the density times the shear wave speed squared with the shear moduli used by Hager et al. [1999] (dashed red and dashed blue lines). The red and blue vertical lines through the top profiles show the positions for which we calculate the shear moduli at bottom. Shear wave speeds and densities are from the SCEC Seismic Velocity Model 2 [Magistrale et al., 2000; H. Magistrale, electronic communication, 2001]. In the cross section across the Los Angeles basin the dashed gray line shows the sedimentary basin as determined by Davis et al. [1989, Plate 1]. Faults are ORF, Oak Ridge fault; SCF, San Cayetano fault; PHT, Puente Hills thrust; EPT, upper Elysian Park thrust; SMF, Sierra Madre fault; SAF, San Andreas fault.

[85] The depth of the sedimentary basin may be taken to be either the depth of young sedimentary rocks or the depth at which the seismic speeds exceed threshold values. We next describe the basins using the depth of young sedimentary rocks. The geologic cross section of Davis et al. [1989] shows the sedimentary basin in the footwall of the Los Angeles segment of the Puente Hills thrust to be 9 km deep and that in the hanging wall to be 2–5 km deep (Figure 11). The seismic cross section of Shaw and Shearer [1999] shows the sedimentary basin in the footwall of the Sante Fe Springs segment of the Puente Hills thrust to be 5–7 km deep and that in the hanging wall to be 3–5 km deep, with the vertical offset at the fault being just 1 km. The sedimentary basin in the footwall of the San Cayetano and Oak Ridge faults is believed to be more than 12 km thick, but the sedimentary basin in the hanging wall of the two faults is less than 1 km thick [Namson and Davis, 1988].

[86] Defining sedimentary basin depth on the basis of the depth of young sedimentary rocks has the weakness that the age taken to be “young” must be specified. As sedimentary rocks get older and buried deeper, they begin to behave more like crystalline basement. When assessing rock rheology and constructing models of interseismic strain accumulation, it is more instructive to define the sedimentary basin on the basis of seismic structure. SCEC Seismic Velocity Model 2 [Magistrale et al., 2000; H. Magistrale, electronic communication, 2001] specifies the seismic body wave speed, seismic shear wave speed, and density as a function of position and depth in southern California. H. Magistrale (Los Angeles basin depth map, 2004, available at http://www.scec.org/phase3/basinmap.html) defines the depth of the sedimentary basin to be the depth at which the shear wave speed reaches 2.5 km s−1. Using this definition, we find the SCEC seismic velocity model to give the depth of the Los Angeles sedimentary basin to be 4–6 km in the footwall of the Puente Hills thrust and 3–4 km in the hanging wall, and the depth of the Ventura basin to be 7 km in the footwall of the San Cayetano and Oak Ridge faults and less than 1 km in the hanging walls. Shear moduli as a function of depth computed from the SCEC seismic velocity model are similar for the Los Angeles basin and the Ventura basin, except that there is a zone of low stiffness rock between depths of 9 and 12 km in the Ventura basin not in the Los Angeles basin.

[87] We look forward to scientists constructing and assessing models with different stiffnesses of sedimentary basin and crystalline basement using elastic moduli calculated from SCEC's seismic velocity model. Constructing three-dimensional models using the SCEC community fault model [Plesch et al., 2003] will bring a more realistic representation of slip along faults and elastic strain accumulation.

5.2. Estimates of Reverse Slip From Paleoseismology

[88] Shaw et al. [2002] estimate the mean Quaternary slip rate along the Puente Hills thrust to be 0.6–1.3 mm yr−1 and the magnitude of an earthquake rupturing the thrust to be M 6.6 if one of three segments rupture and M 7.1 if the three segments rupture simultaneously. Dolan et al. [2003] maintain that four M 7.2–7.5 earthquakes ruptured the Coyote Springs segment of the Puente Hills thrust since 9.5–10.7 ka, each with a minimum of 2–5 m of reverse slip, yielding a minimum mean Holocene slip rate of 1.1–1.6 mm yr−1. Oskin et al. [2000] estimate the mean Holocene slip rate along the upper Elysian Park thrust to be 0.8–2.2 mm yr−1 and the magnitude of an earthquake rupturing the thrust to be M 6.2–6.7. The horizontal component of Dolan et al.'s [2003] estimate of the Puente Hills slip rate is 1.0–1.4 mm yr−1 (taking the fault dip to be 27°), and the horizontal component of Oskin et al.'s [2000] estimate of the upper Elysian Park slip rate is 0.6–1.7 mm yr−1 (taking the fault dip to be 40°). The total horizontal rate across the two faults is 1.6–3.1 mm yr−1, which is less than half the 8 ± 2 mm yr−1 horizontal component of fault slip inferred from the fit of the elastic dislocation model to the observations. The difference between the two estimates of total convergence could be accounted for by slip along faults outside the zones studied by Dolan et al. [2003] and Oskin et al. [2000], or the convergence rate over the past several years could have been faster than the mean Holocene convergence rate.

6. Conclusion

[89] Bawden et al. [2001] maintain that cumulative horizontal motions in response to management of water resources are so big that the velocities of about half the SCIGN sites are of little use. In this study we quantify cumulative anthropogenic motions, finding horizontal anthropogenic motions at most sites to average away to less than 1 mm yr−1. We find that correcting for anthropogenic effects improves the consistency among the velocities of nearby sites. The corrected interseismic velocity field well constrains the tectonics of metropolitan Los Angeles. Whereas Bawden et al. [2001] conclude that the SCIGN observations poorly constrain how shortening is taken up across metropolitan Los Angeles, we find contraction to be fastest in northern metropolitan Los Angeles. The elastic dislocation model we present suggests that reverse faults beneath northern metropolitan Los Angeles are creeping to within 6 km of the surface, but models with different stiffnesses of sedimentary basin and crystalline rock need to be explored to support this conclusion.

Acknowledgments

[90] The Southern California Integrated GPS Network (SCIGN) and its sponsors, the W.M. Keck Foundation, the National Aeronautics and Space Administration (NASA), the National Science Foundation, the United States Geological Survey, and the Southern California Earthquake Center, provided the observations on which this study is based. This research was supported by NASA's Solid Earth and Natural Hazards Research and Applications program. We are grateful to Michelle Cooke, James Dolan, and Joan Golmberg for their careful and constructive reviews. Research by Argus, Heflin, and Webb was performed at the Jet Propulsion Laboratory (JPL), California Institute of Technology, under contract with NASA. Research by Peltzer and Crampé was performed at the University of California at Los Angeles and at JPL, Caltech, under contract with NASA.

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