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101, 27,957-27,980, 1996
South of the basin, present day crustal deformation is dominated by NW-trending strike slip faults such as the SAF, the San Jacinto fault (SJF), the Elsinore fault, and the Newport-Inglewood fault. The SJF merges with the SAF east of the basin. The Whittier-Elsinore fault system, the Newport-Inglewood fault, and the Palos Verdes fault cut through the east and west flanks of the basin (Ziony and Yerkes, 1985) (Fig. 1). North of the basin, the San Gabriel Mountains have been pushed up by a frontal thrust fault system defined by the Sierra Madre-Cucamonga fault system along the SE and the Santa Susana fault along the SW. The E-W trending Malibu-Santa Monica-Raymond Hill fault system uplifted the Santa Monica Mountains (Davis et al., 1989). Horizontal detachment in the lower crust or at the Moho boundary has been suggested beneath most of the central and western Transverse Ranges (Bird and Rosenstock, 1984; Weldon and Humphreys, 1986; Namson and Davis, 1988; Huftile and Yeats, 1995). Furthermore, recent geomorphological and trenching studies have identified six major thrust or oblique fault systems in and around the Los Angeles basin area (Dolan et al., 1995): the Sierra Madre-Cucamonga system, the Los Angeles basin fault system, the Santa Monica Mountains fault system, the Oak Ridge fault system, the San Cayetano fault, and the Palos Verdes fault. Dolan et al. have described in detail the locations and scale of thrust and horizontal detachments taking place in the region.
Earthquakes also help illuminate the tectonics of the Los Angeles basin. Earthquake focal mechanisms show a mixture of NW dextral strike slip and N-S convergence (Hauksson, 1990). Earthquakes of right lateral strike slip faulting represented by the 1933 M 6.4 Long Beach earthquake dominate the seismicity south of the basin. (Throughout this paper, M represents moment magnitude). North of the basin, many of the earthquakes have thrust mechanisms, often coupled with left-lateral displacements. Examples include the 1971 San Fernando M 6.6, the 1987 Whittier Narrows M 5.9, the 1991 Sierra Madre M 5.8, and the 1994 Northridge M 6.7 earthquakes (Working Group on California Earthquake Probabilities [WGCEP], 1995).
Early geodetic studies in the Los Angeles basin (Cline et al., 1984) revealed about 10 mm/yr convergence across the basin from San Pedro to Mt. Wilson, but data available at that time were not good enough to make the estimate very accurate. North of the basin, Cheng et al. (1987) investigated more than ten years of trilateration measurements and estimated 6 mm/yr convergence normal to the SAF along a NW profile from the Malibu fault to the White Wolf fault. Lisowski et al. (1991) used updated trilateration data and found little convergence within the San Gabriel Mountains normal to the SAF. Along the southern frontal fault system, Shen (1991) revealed about 3 mm/yr convergence. Using a combination of Very Long Baseline Interferometry (VLBI) and GPS measurements, Feigl et al. (1993) reported 5.0 +- 1.2 mm/yr shortening from Palos Verdes to JPL, the latter being located in the SW foothills of the San Gabriel Mountains. West of the basin, Donnellan et al. (1993) used GPS methods to determine 7-10 mm/yr N-S convergence across the Ventura Basin. A recent study by Snay et al. (1995) found that the SAF is located near the center of a deformation band whose central line in the Big Bend region is oriented about 7 degree clockwise relative to the surface trace of the SAF.
This nineteenth century network was augmented by a group of stations west of the basin during the 1920s, which include Michelson 1923 (MICH), Antonio 1923 (ANTO), Pasadena West Base 1922 (PSWB), and Pasadena East Base 1922 (PSEB). These stations were connected to the earlier network at LAN0, LASE, SJUA, and WILP. The 1920s network was installed to support Dr. Michelson's speed-of-light experiment carried out between station MICH located at the peak of Mt. Wilson and station ANTO at the peak of Lookout Mountain south of Mt. San Antonio. A 36-km-long baseline between stations PSWB and PSEB was determined by adjusting a collection of angle and distance measurements. These measurements include invar-taped distances between PSEB and PSWB, passing through a cluster of intermediate stations, and directions observed among MICH, ANTO, PSWB, PSEB, Pasadena East Base 2 1922 (PSE2), Dimas 1922 (DIMA), and Joaquin 1922 (JOAQ) (Michelson, 1927). Uncertainty of this baseline is believed to be about 44 mm (Michelson, 1927). This means a relative accuracy of 10$^{-6}$, an order of magnitude better than the Los Angeles baseline measured during the 1890s. The ``Michelson baseline" provides high-accuracy scale control for the early triangulation network.
Additional stations were established in the basin during the 1930s; among them are stations Echo Rock 1933 (ECHO), Workman Hill 1932 (WORK), and San Tuze 1937 (SNT0). Observations were made at station WORK relative to the 1890s and 1920s stations in 1933. The three 1930s stations were occupied along with other stations in the network during the 1950s and 1960s. Station locations are shown in Fig. 2, and their occupation histories are listed in Table 1.
Raw triangulation measurements are directions with respect to a reference direction. For most of the triangulation data we use here, the reference directions were not oriented to stations included in our study. For the sake of convenience, we use azimuth differences as the data, with one reference station chosen from our network in each epoch. The typical uncertainty of a direction measurement is about 3.5 micro-rad (Gergen, 1975). We propagate uncertainties of the original directions to derive the uncertainties of the direction differences, assuming that the errors of the original directions are uncorrelated.
An astronomical azimuth is a direction pointing from a base station to another, measured from north in the horizontal plane of the base station. In the Los Angeles basin network, the astronomical azimuths were measured in two time epochs. Measurements of the first epoch were made between stations LAN0 and LASE in 1890. Measurements of the second epoch were made in the early 1920s; at that time almost all the existing stations in the network had their astronomical azimuths measured relative to their triangulation partners. Errors of these astronomical azimuths are about 1.5 seconds (7 micro-rad) (Carter et al., 1978).
Although these historical triangulation measurements cannot match the accuracy of electronic and space geodetic measurements made in the 1970s and the 1980s, their almost century-old observational history makes the data valuable for detecting long-term deformation signals. Assuming a constant deformation rate, the triangulation measurements help resolve the shear change, the taped distance measurements help control the network scale variation, and the astronomical azimuth measurements help pin down the network rotation, all up to $10^{-8}$ accuracy.
Trilateration
Since the early 1970s, the California Department of Mines and Geology (CDMG) and subsequently
the U.S. Geological Survey (USGS) have surveyed baseline lengths using electro-optical
distance measuring (EDM) instruments in southern California. These observations are one
order of magnitude better than the triangulation measurements (Savage and Prescott, 1973).
Data of about 20 years from two of the networks are used in this study: one is the
Tehachapi-San Gabriel network north of the Los Angeles basin covering the San Gabriel
Mountains area, and the other is the Anza network south of the Los Angeles basin spanning a
region from the Newport-Inglewood fault west to the Coachella valley section of the
SAF east. Errors of the data were found normally distributed with a standard deviation
$\sigma = (a^2 + b^2 L^2)^{1/2}$, where $L$ is the distance measured, $a$ = 3 mm, and
$b = 2 \times 10^{-7}$ (Savage and Prescott, 1973, King et al., 1987).
Not all stations in the two networks are used in this study. The ones being used are shown in Fig. 2 and listed
in Table 2. Note that the trilateration sites occupied also by GPS are
listed in Table 1 rather than in Table 2.
GPS Measurements
GPS surveys in the Los Angeles basin and its vicinity started in 1986 and were carried out
by researchers from several universities and crews from government agencies such as
the National Geodetic Survey (NGS) and USGS. The early measurements were
made in a campaign mode, with each station occupied 1-3 days each time, and
several stations observed simultaneously. All the stations are shown in Fig. 2.
All the measurements used in this study are listed in Table 1, which can be classified
into three groups:
1. GPS-triangulation. The early GPS survey in the Los Angeles basin was designed partly to reoccupy the historical triangulation sites and their surrogates. The first GPS occupations of the sites are the following; 1986: Niguel A 1981 (NIGU, surrogate for NIG0); 1987: Solstice Cyn B2 Aux 1 (CATO, surrogate for CAT0), ECHO (surrogate for WILP), San Fernando Aux 2 Ecc 1 Rm 2 (SAFE, surrogate for SAF0), SJUA, Covina C7 Rm 1 1937 (SNTZ, surrogate for SNT0), and WORK; 1988: STIA; 1989: LASE, San Pedro Hill 1853 Rm 2 (SPED, surrogate for SPE0), and Whittier D11 1976 (WD11, surrogate for LAN0); 1990: ANTO, MICH, PSEB and PSWB. The local fiducial stations measured simultaneously during this time period were at Palos Verdes (PVER), JPL (JPLA and JPL1), and Pinyon Flat (PINY and PIN1). Because of constant urban development in the Los Angeles basin area, most of the historical sites are either destroyed or disturbed, requiring that some local stations with ties to the historical triangulation sites be used as surrogates. We give detailed description of those sites and the relationships between the original and the substitute sites in the Appendix.
2. GPS-GPS. In this study we include also a group of sites that were designed to measure deformation using repeated GPS measurements solely. These occupations started in the late 1980s and their first GPS epochs are: 1987: Mt. Lowe F2A 1978 (JSPH), Pearblossom NCMN 1983 (PEAR), and Pt. Dume 1947 (PTDU); 1988: Hawes 1958 Rm 2 (HAWE), Monday 1929 (MDAY), and UCL0. Those experiments to study tectonic deformation in southern California (Feigl et al., 1993) were part of an orchestrated effort by researchers from four universities: Massachusetts Institute of Technology, California Institute of Technology, U.C. Los Angeles, and U.C. San Diego. (In later analyses we will combine part of their results with those obtained from this study to show a velocity profile across the Los Angeles basin and the SAF.) More data were collected at those sites from 1990 to 1993 by UCLA crews. A number of the sites we use here including JSPH, LANW, NIGU, PEAR, PICO, SAFE, SJUA, and WORK were also occupied by crews from several counties in southern California in 1993.
3. GPS-trilateration. In late 1992 the NGS and the Southern California Earthquake Center jointly conducted a GPS survey in the central Transverse Ranges area. Among the stations surveyed were USGS trilateration sites whose trilateration data are also used here. Trilateration surveys are designed for horizontal control purposes and lack the capacity to measure vertical deformation. Unfortunately, large errors in elevation can introduce significant errors to the horizontal control adjustment. GPS surveys, on the other hand, produce 3-D measurements which not only add new measurements but also effectively determine the station elevations and improve the quality of the horizontal control adjustment of the trilateration network.
Dozens more GPS stations have been observed in the Los Angeles basin area since 1991, at the frequency of one occupation or so each year. However, perturbations from the 1992 Landers and the 1994 Northridge earthquakes make it difficult to determine accurately the interseismic station velocities, because the data include also coseismic displacement signals caused by the two quakes in addition to the interseismic displacement signals. These data are not included in this study. For the site being studied here, measurements made after 1993 are excluded and coseismic displacements caused by the 1992 Landers quake are modeled.
GPS Data Processing
Observational sessions of the GPS measurements used for this study range from
six to twenty-four hours long each day. Instruments used for data collection were
TI4100 receivers before 1990 and mainly Trimble 4000SSTs after. Data are processed
using GAMIT software (King and Bock, 1993) to produce daily solutions. Data
collected from the GPS global tracking sites (CIGNET stations before 1990 and IGS
after) are also used to solve for precise satellite orbits. In each solution,
dual-frequency beat-phase data are used to compute double-difference
ionosphere-free residuals, which are then inverted through a least-squares procedure
solving for the unknown parameters. These include station positions, satellite orbital
elements, phase ambiguity integer numbers, tropospheric delay residuals, etc.
Uncertainty of 10 mm is assumed for the carrier beat phase data. For a
detailed description of the data processing method, please refer to
Dong and Bock (1989), King and Bock (1993), and Feigl et al. (1993).
Data Corrections
Corrections are needed for the triangulation measurements to compare them
with predictions from a known earth model. One correction is for
deflection of the local vertical. We neglect this correction because preliminary
calculations show that the largest error caused by neglecting it in our network
would be about 0.35" (1.7 micro-rad) at stations PSEB and
ANTO. This is much smaller than our data errors. See the appendix of Sauber et al.
(1989) for an example of analysis with and without corrections for deflection of
the vertical; the corrections are negligible. Another correction to the
triangulation measurements is the skew normal correction, which should not exceed 0.1"
(0.48 micro-rad) because the maximum elevation difference between observational
stations is about 1 km (Bomford, 1980). We ignore this correction too.
A taped distance is measured from mark to mark. A correction has to be applied to convert the mark-to-mark distance into a geodesic on the surface of an ellipsoid, which is the WGS84 ellipsoid here to fit into our model. Such corrections are made following Vincenty (1975).
A Laplace correction is required for the astronomical azimuths in order to convert them into a geodetic coordinate system. This process corrects the bias caused by the coordinate difference between the Clarke 1866 coordinate used for historical triangulation and the WGS84 coordinate used for GPS. Such correction is made according to Bomford (1980).
Systematic comparisons have been made between GPS and EDM measurements. A recent study by Svarc et al. (1994) found a 0.300 +- 0.067 ppm systematic scale difference for EDM - GPS. We apply such a correction to the EDM line lengths used in this study.
We model the station displacements with constant interseismic velocities plus episodic coseismic displacements at times of significant earthquakes. Studies of 20 years EDM observations showed no significant temporal variations except at a few locations (Savage and Lisowski, 1995a, 1995b), suggesting that the constant interseismic velocity assumption is valid for combining 20 years trilateration with 6 years GPS. However, such studies would not automatically justify combination of century old triangulation with the GPS and EDM data. The most significant time dependent signals for interseismic deformation are usually from postseismic deformation following large earthquakes, which can cause significant acceleration of surface deformation in the epicentral region. The only quake which might have caused significant postseismic displacements to the triangulation sites in the Los Angeles basin area is the 1857 M 8.3 quake which ruptured the SAF from San Bernardino to the Carrizo plain (Thatcher, 1983). However, 40 years had passed since the quake when the first triangulation measurement was made in the basin. The postseismic deformation would have died out substantially and its remaining effects would probably be negligible comparing to the constant deformation rates at the sites. Therefore the constant deformation rate assumption may also hold for triangulation data used in this study.
In the time span of our data coverage four earthquakes occurred in the network and measurably disturbed at least one station in the network. They are the 1971 M 6.6 San Fernando earthquake, about 22 km ENE of station SAFE; the 1989 M 5.9 Whittier Narrows earthquake, right beneath station WORK; the 1991 M 5.8 Sierra Madre earthquake, which caused possible centimeter level displacements at stations ECHO, JPLM, and PSWB; and the 1992 M 7.3 Landers earthquake, which affected all stations in southern California. We need to model the coseismic displacements at the sites but not the postseismic displacements, because the postseismic effects are indistinguishable from the coseismic effects in our data which were collected either long after the quake or only one epoch was measured since (i.e., the Landers quake).
The velocity adjustment algorithm is:
$$ O_j(t) - O_j(\vec X_i(t_0)) = \sum_{i}(\nabla_{i} O_j)^.\vec D_{i} + (t-t_0) \sum_{i}(\nabla_{i} O_j)^.\vec V_{i} - \sum_{k} H(T_{k}-t) \sum_{i} (\nabla_{i} O_j)^.\vec E_{ik} + \epsilon_j $$
where $O_j (t)$ is the $j^{th}$ observable, which can be an angle, a distance, an azimuth, or a component of a GPS baseline vector; $t_{0}$ is a reference time epoch; $\vec X_i(t_0)$ is the initial position of the $i^{th}$ station at time $t_0$; $O_j (\vec X_i(t_{0}))$ is the corresponding value predicted from initial station positions; $\vec D_{i}$ is unknown, the $i^{th}$ station initial position correction; $\vec V_{i}$ is unknown, the $i^{th}$ station velocity; $\vec E_{ik}$ is unknown, the coseismic displacement of $k^{th}$ earthquake at $i^{th}$ station, which is zero except for the earthquakes and their corresponding stations given above; $T_{k}$ is the $k^{th}$ earthquake epoch; $H(T_k - t)$ the Heaviside step function; and $\epsilon_j$ the random error for the $j^{th}$ measurement.
Triangulation and trilateration data lack good control for vertical components. GPS data can resolve vertical positions, but with uncertainties of a few centimeters (Larson and Agnew, 1991), too large to resolve the interseismic displacements. Such displacements were probably no more than a centimeter during the entire period the data were collected. Therefore, our velocity adjustment is performed in 2-D space. In the modeling algorithm described above, each datum is converted to the equivalent geodesic, angle, or azimuth observable on the surface of a WGS84 ellipsoid and is compared with that predicted by a model. To solve for the unknowns, the data residuals are then inverted using least-squares along with a priori conts such as the station velocity ties. The treatment of the a priori information follows Jackson (1979) and Jackson and Matsu'ura (1985).
We also use VLBI data to con station velocities at several fiducial sites located at JPL, Goldstone, Pearblossom, Pinyon Flat, and Palos Verdes. The VLBI velocities are taken from Table 4.2 of Ma et al. (1994), and are rotated from the NUVEL-NNR model frame to the North-American-plate-fixed coordinate frame. The rotation parameters are obtained from Argus and Gordon (1991). We then convert all velocities relative to station Goldstone, and use them and their uncertainties as the a priori data for our velocity adjustment. All inter-correlations between the VLBI velocity vectors are ignored. Errors caused by such negligence are minimal when station Goldstone is selected as the reference site because the velocity uncertainties for this site (2 mm/yr) are significantly smaller than those for all other VLBI sites (5-11 mm/yr) used here.
In the inversion the GPS baseline vector data are weighted by the inverse of their covariance matrix to properly account for the correlation between different baselines and between the baseline components. We also attempt to balance weights between different data types. We assign a scaling coefficient for each data group and examine the postfit residuals of each group to estimate their proper weight, i.e., whether the normalized postfit chi-square per degree of freedom of each group is close to one. If not, we reassign the scaling coefficients and redo the inversion. Our best-fit solution gives the coefficients for the angle, azimuth, taped distance, EDM line length, and GPS data as 1.0, 1.0, 1.0, 1.5, and 3.5, indicating that the uncertainties of only the GPS and EDM measurements need to be adjusted substantially.
Examples of input data and their fits to the model are shown in Fig. 2: (a) and (b) are the angle and line length measurements respectively, and (c) and (d) are the east and north components of the GPS baselines respectively. Each GPS site was usually observed many more times than the number of data points shown in the figure for two reasons. One is that the two stations in a pair were not always observed simultaneously. Another reason is that a single data point sometimes represents a multi-day solution of 2-3 consecutive days measurements, which is usually true for the early-year results from 1986 to 1988 (to better resolve the satellite orbits).
We notice from Fig. 3 (also from later residual studies) that the velocity field seems quite smooth across the network except in the Los Angles basin, where a few sites such as WORK, LANW, LASE, and SJUA show a bit more local scatter. This reflects the difficulty of obtaining good measurements in the basin; where most of the sites are in sediments and suffer from various problems. Station WORK has been reset three times including twice during our GPS survey time period, and we had to toss out early measurements. The original triangulation site at Los Angeles NW Base (LAN0) was destroyed, and there is no good tie to link the triangulation site to the GPS site LANW. Station LASE was reset during the time period between the last triangulation survey and the first GPS survey, and the sky at the site is partially obstructed for GPS observation. Nevertheless, these complications are limited to a local region and some useful conclusions can still be drawn.
A number of features can be seen from the velocity field:
1. South of 33.9 degree N latitude, crustal deformation is dominated by displacements parallel to the major strike slip faults: the SAF, the SJF, the Elsinore fault, and the Newport-Inglewood fault. This observation is consistent with the finding of Lisowski et al. (1991). The strike-slip rate difference across the SJF is about 10 +- 2 mm/yr, 4 +- 2 mm/yr across the Elsinore fault, and 3 +- 2 mm/yr across the southern portion of the Newport-Inglewood fault and the Palos Verdes fault.
2. Significant N-S convergence is found in the northern part of the Los Angeles basin, along the Malibu-Santa Monica-Raymond Hill fault zone, and along the Santa Susana-Sierra Madre-Cucamonga fault zone. The N-S convergence rate is about 4 +- 1 mm/yr between CATO and SAFE, 3 +- 1 mm/yr between PSWB and ECHO, and 4 +- 1 mm/yr between PSEB and ANTO. Convergence from PVER to ECHO is about 6 +- 1 mm/yr, consistent with the finding of Feigl et al. (1993).
3. Along the Mojave section of the SAF, the SAF seems to govern the deformation in the region. This finding is again consistent with the result of Lisowski et al. (1991).
4. In the Mojave desert, dominant features are screw-dislocation motion from the SAF and strike-slip motion across the Mojave Shear Zone, which is the southern part of the Eastern California Shear Zone. Such a strike-slip motion across the Mojave Shear Zone is about 5 +- 3 mm/yr from HAWE to MOJA in our solution. This is close to the finding of Savage et al.'s (1990) 8 mm/yr but less than Sauber et al.'s (1994) 12 mm/yr across the Mojave Shear Zone.
Velocity Profile Across Mojave Section of SAF
Fig. 4 shows the velocity components parallel and normal to the SAF for
a station group along a profile across the Mojave section of the SAF which
strikes N65 degree W. Velocities of three island sites are also displayed to
extend the profile further SW; where their values with respect to station
PVER are obtained from
Feigl et al. (1993). We compare these data with predicted station velocities
from a simple dislocation fault model with the SAF and the SJF included.
In the model, the earth is assumed to be an elastic half-space, and the
faults are locked down to 20 km depth. At depth, the SAF moves at a rate
of 34 mm/yr through the Carrizo Plain section, 30 mm/yr along the Mojave section,
24 mm/yr along the San Bernardino Mtn section, and 25 mm/yr along the Coachella
valley section. At depth, the Imperial fault is assumed to slip
34 mm/yr. The SJF moves underneath at a rate of 12 mm/yr. This
model follows the fault slip estimates along the SAF and the SJF in a report
by the Working Group on California Earthquake Probabilities (WGCEP, 1995)
which will be described later.
Although simple, this model has included all single fault segments whose
slip rates are above 10 mm/yr, and is believed to represent
the major part of the crustal deformation field in southern California.
Although the fault-parallel motion of the stations demonstrates a sigmoidal pattern centered on the SAF, it is evident from Fig. 4a that the model does not describe the parallel motion of the stations adequately. The observed spreads over an area broader than the model prediction, and the observed rate is significantly lower than the prediction close to the fault. As drawn, with the observed and predicted velocities measured with respect to a point on the SAF, the observed velocity between the SAF and the farthest point to the SW agrees well with the predicted value. To NE of the SAF however, the observed and predicted values diverge. At Mojave, the farthest site to the NE, the observed velocity is approximately 6 mm/yr greater in the SE direction than the model prediction. It appears that the major discrepancy occurs at just one site MOJA. Because the relative velocity between Mojave to the NE and Palos Verdes to the SW of the SAF is well coned by VLBI measurements, the simplest explanation for this discrepancy is that one or more right lateral faults contribute at least 6 mm/yr in the eastern Mojave desert. However, the decision to refer displacements to a point on the SAF is completely arbitrary, and in principle, any constant may be added to the predicted curve. If this constant were chosen to minimize the sum of squared residuals, the discrepancy between the observed and predicted would be spread more evenly among the stations. Even so, the observed velocity gradient would still be much less than that observed near the SAF, and station MOJA would still stand out as anomalous.
The parallel motion discrepancy could be interpreted in different ways. One explanation is that the model does not include all faults which contribute to the region's crustal deformation. However, we know of no other major strike-slip faults that sufficiently active to explain the discrepancy. Another possibility is that the simple model does not describe the SAF and the SJF properly. For example the locking depths and slip rates given in the model may not be correct. Previous geodetic studies for this area tried tackling the problem (Cheng et al., 1987; Eberhart-Phillips et al. 1990; Lisowski et al. 1991); because of the limited areal coverage of the networks, these studies could not simultaneously resolve both the locking depth and the slip rate. Numerous geological studies have determined the average slip rate in the area (Sieh et al., 1989; Biasi and Weldon, 1994; Salyards et al., 1992), although the answers range from 20 to 36 mm/yr. A compromise estimate by the WGCEP (1988) and the WGCEP (1995) placed 30 mm/yr along this section of the SAF. Sieh and Jahns (1984) estimated 34 mm/yr relative motion along the SAF at Wallace Creek on the Carrizo plain. If we assume convergence is negligible on the Carrizo plain, the rate and the orientation of the SAF define the velocity of relative plate motion across the SAF in central California. If we also assume that the velocity in central California also represents the relative plate motion through the Mojave section of the SAF, the along-fault strike component would be about 31 mm/yr. If the convergence along the SAF in central California is not negligible and a 7 degree obliquity of relative plate motion with respect to the strike of the SAF is assumed there (Humphreys and Weldon, 1994), the along-fault strike component would be about 29 mm/yr. SW of the SAF, geological studies have shown that the San Gabriel fault is inactive (Crowell, 1973; Ehlig et al., 1975a; Ehlig, 1975b), and there are no other strike-slip faults to diversify the NW-trending shear motion from the Carrizo plain down to the San Gabriel Mountains. NW of the SAF, slip along the Garlock fault and White Wolf fault may diversify the NW-trending shear motion somewhat and further reduce the tangential slip on the SAF. However, such reduction is probably minor because of the low slip rates along the two faults. Therefore, we consider that the 30 mm/yr strike-slip motion is reasonable for the Mojave section of the SAF. Seismic studies revealed that the earthquake depths are relatively shallow, about 12 - 18 km along the Mojave segment of the SAF (Webb and Kanamori, 1985; Jones, 1988; Hill et al. 1990). If we use these estimates for the slip rate and the locking depth, the velocity discrepancy between the observed motion parallel to the SAF and the motion predicted by the model SW of the SAF would not be reduced. Other explanations must be found.
We propose that the broadening of the observed velocity profile shown in Fig. 4a is caused by different scenarios: detachment motion in the lower crust or upper mantle, visco-elastic behavior of the earth, a broad deformation across the SAF, or a combination of the three. Detachment motion has been proposed based on geological data (Davis et al. 1989; Shaw and Suppe, 1995) in the Los Angeles basin area. Seismic studies revealed that the San Gabriel Mountains lack of a ``root" sufficient to support the weight of the mountains, implying a possible horizontal detachment underneath (Hadley and Kanamori, 1977; Hearn and Clayton, 1986; Sung and Jackson, 1992). Such a detachment would reduce the basal traction at the detachment surface, thus weakening the lateral driving force transmitted from the lower to the upper plate, and changing the loading mechanism from ``vertical loading" toward ``horizontal loading" (Gilbert, et al., 1994). This would make the deformation pattern broader. Theoretical visco-elastic models and models based on realistic parameters of the SAF have been developed (Nur and Mavko, 1974; Rundle and Jackson, 1977a; Savage and Prescott, 1978; Thatcher, 1983; Li and Rice, 1987). Such models usually assume an elastic plate overlying a visco-elastic half-space. Model predictions vary depending on the parameters used. However, two distinct features are usually shared by these models. One is that given the same locking depth, the deformation predicted by the visco-elastic models is broader at the earth's surface than that predicted by elastic half-space models. As in the detachment case discussed above, this occurs because there is no strong basal traction transmitting lateral driving force from the visco-elastic lower plate to the elastic upper plate. Therefore the horizontal loading mechanism starts taking effect. The other feature is that late in an earthquake cycle, strain rates are more flattened across the fault zone compared to the profile obtained early in the cycle. Both features are consistent with our observations. Seismological studies suggested that decollement exists across the SAF (Hadley and Kanamori, 1977) and subduction might be taking place beneath the central Transverse Ranges (Humphreys and Clayton, 1990). If these models are valid, the SAF would be offset at depth by decollement and subduction, causing a much broader deformation zone than predicted for a simple model with only a vertical SAF.
The observed normal components of the velocities (Fig. 4b) close to the SAF are fairly consistent with that predicted by the WGCEP model, showing little compression in the San Gabriel Mountains within 40 km from the SAF. About 40 km SW of the SAF, convergence normal to the fault occurs mostly along the south and SW frontal faults and within the Los Angeles basin and the San Fernando Valley. The rate is about 7 +- 1 mm/yr from PTDU to PEAR, and about 5.5 +- 1 mm/yr from PVER to PEAR. Farther from the SAF offshore, the rate seems to increase gradually, up to 8-10 mm/yr at BLUF and TWIN. This trend may reflect a gradual change in the relative motion direction from the local plate motion to the one between the Pacific plate and the North America plate, the latter being about 7 degree clockwise with respect to the former (Humphreys and Weldon, 1994; Snay et al., 1995). However, the three island velocities are obtained from another study (Feigl et al. 1993) and integrated to this study with a common link at station PVER. Thus, any errors for these three stations would be highly correlated, possibly causing an apparent velocity contrast between the islands and mainland. Caution should be taken when interpreting solutions at the three island sites.
WGCEP Model Comparison
The Southern California Earthquake Center recently released a report to assess
the earthquake probabilities
in southern California (WGCEP, 1995). The report listed estimated fault slip
rates and reoccurrence time intervals for so called ``Type A" fault
segments: those whose slip rates are believed greater than or equal
to 3 mm/yr and whose earthquake histories for the last several events
are known. The report listed also some fault segments labeled
``Type B," whose fault slip rates are equal or exceed
3 mm/yr but whose earthquake histories are not well known.
We adopt both Type A and Type B fault segments to make
a forward model of the crustal deformation, with the Type A
segment information from Table 1 and the Type B segment
information from Table 5 and Fig. 3 of their report.
All the fault parameters are given in our Table 4, except the fault widths
below locking-depths which will be discussed later in this section.
For to dislocation modeling we specify additional model parameters
undefined in the WGCEP report. For example, we assume that the SAF extends
from NW and SE end points in the report to infinity, following its strike
directions and slip
rates there. The same is true for the Eastern California Shear Zone
north extension. We give uniform 20-km locking depths for all the
faults. All the vertical strike-slip faults are assumed
to have infinite fault width. The Palos Verdes fault is treated as dipping 45 degree SW
(WGCEP, 1995) and extending to infinity below the locking depth.
The Eastern California Shear Zone is modeled as a single fault. This
representation differs from previous findings (e.g. Sauber et al., 1994)
that apportioned the Eastern California Shear Zone at the
Mojave desert across several strands of faults. However, the difference
should not significantly affect our modeling because our data coverage is
sparse in the region and all the major faults north of the Mojave Shear Zone
are located between stations HAWE and MOJA; our model reveals only the gross effect
and not the details
of the slip distribution along the faults. It is still an open question
how thrust faults behave beneath seismogenic depths; we will model them
under two possible scenarios to be discussed next.
We adopt the elastic half-space model and use dislocation theory to propagate fault slip into displacements at the earth's surface (Okada, 1985). We consider such a model adequate for all regions except the central Transverse Ranges area, where visco-elasticity may play an important role in controlling crustal deformation. However, as Rundle and Jackson (1977b) and Savage and Prescott (1978) showed, by varying the slip rates and locking depths, an elastic half-space model could produce almost the same surface deformation as does a visco-elastic model. We use the elastic half-space model for convenience, but caution the reader that our interpretation is not unique. The predicted station displacements are compared with the data, and the postfit residual chi-square is evaluated. Two fault models are tested in our forward modeling. Model HD (for ``horizontal detachment"), assumes that thrust faults such as the Cucamonga fault, Santa Susana fault, San Cayetano fault, and Oak Ridge fault slip horizontally below the 20-km locking depth. This model tests the existence of a horizontal decollement suggested by cross-section balancing studies of the region (Davis et al., 1989; Huftile and Yeats, 1995; Shaw and Suppe, 1995). We con these thrust faults to slip in the same direction, so that they do not pinch each other or leave gaps at depth. We allow the fault widths to vary in the same way simultaneously and find that the postfit chi-square reaches a minimum when the horizontal extent of the decollement reaches about 38 km.
In Model CD (for ``constant dip"), we keep the dip angles of the thrust faults unchanged and assume the faults slip aseismically below the seismogenic zone. This model tests the arguments that subduction is taking place locally underneath the thrust fault zones, as suggested by seismic tomography (Humphreys et al., 1984; Humphreys and Clayton, 1990). However, the model itself lacks the sophistication that subduction models usually require. We use a 45 degree dip angle and allow the fault widths to vary. We find that the postfit residual chi-square reaches a minimum when the fault width below locking depth reaches 49 km. Its horizontal projection is 35 km, close to 38 km extent that we estimated for model HD. Thus, the thrust faults cut through the SAF at depth in both models. Although 49 km is the best estimate of the fault width, a broad range of fault widths between 49 and 70 km would fit the data almost equally well. We choose 49 km as the fault width in our model, knowing that the actual faults could extend much beyond.
Fig. 5 shows the dislocation fault model of Model CD and the postfit residual velocities of the stations. The residual velocities are listed in Table 3. Net translation of the network has been subtracted from the residual velocities in Fig. 5. Agreement between the data and the predictions from the WGCEP fault model is very good, considering that the WGCEP fault model is mainly geological with little input from geodesy. This observation suggests that present-day deformation is dominated by slip along faults whose present-day slip rates do not differ significantly from their averages over thousands or even hundreds of thousands of years. Nevertheless, there are still systematic differences at a few regions, which will be our focus below.
The residual velocity vectors show three prominent features. First is an apparent NW-SE extension, observable from the fact that the stations in the upper left part of the diagram have residual velocities to the NW, and stations in the lower right have SE residual velocities. The magnitude of these residual velocities generally increases with distance from the geographical center of the stations. The second feature is an apparent left-lateral shear across the Mojave section of the San Andreas fault, and an apparent right-lateral shear across the southern San Jacinto fault. The third feature is an apparent left-lateral shear across the Sierra Madre-Cucamonga fault system.
The residual extension may be a natural reaction to the NNE-SSW contraction across the Los Angeles Basin and San Gabriel Mountains. The contraction built into the WGCEP model is produced by thrust faulting which balances the horizontal shortening by thicking in the vertical direction. However, the model features no corresponding extension that would prevent horizontal areal contraction. In other words, the crust may be responding to the NNE-SSW contraction in a way not incorporated into the WGCEP model.
The residual shear on the SJF could result from underestimating the right-lateral slip or using an inadequate locking depth along the SJF in the WGCEP model. Seismicity along the southern section of the fault (Webb and Kanamori, 1985; Jones, 1988; Hill et al. 1990) shows a shallower profile (< 15 km) than that of the northern section, suggesting that adjusting the locking depth of the WGCEP model may improve the fit and also help reduce the apparent NW-SE extension.
In the SW part of the network, station PVER moves about 3 mm/yr more northerly than the WGCEP model predicts with respect to the sites between the Whittier-Elsinore fault and the Palos Verdes fault. Part of this discrepancy could be blamed on limited mapping of the Palos Verdes fault in the WGCEP model. Had the fault been mapped farther along its NW and SE ends, the discrepancy could be reduced by half or so. Stations CATO and PTDU also show 3-4 mm/yr residual northward motion, which can be partly explained by a lack of NW continuation of the Palos Verdes fault, and partly by the absence of convergent faulting along the Malibu-Santa Monica fault system in the WGCEP model. There is about 4 mm/yr NNW residual velocity at station LANW. Further continuation of the Whittier fault from its current NW end may help reduce the discrepancy. In the NE part of the network, residual velocities between MOJA and HAWE show a right-lateral slip pattern, which could be reduced by more dextral slip along the Mojave Shear Zone than the 4 mm/yr placed by the WGCEP model.
The residual shear on the Mojave section of the SAF could result from overestimating right-lateral slip on the SAF in the WGCEP model, or using an inadequate elastic dislocation model as discussed earlier. A number of models are tested to explore the two possibilities. First we test whether the residuals are caused by inadequate modeling of the Mojave section of the SAF. By altering the locking depth and the slip rate along that section of the fault, we find a maximum reduction of about 6% to the postfit residual chi-square, achieved by a model with 30-km locking depth and 30-mm/yr slip rate (Table 5). If the locking depth is fixed at 20 km, the best-fit fault slip rate is about 25 mm/yr, but the postfit chi-square reduction is less significant than in the case of depth variation. We think the 30 mm/yr slip rate is probably closer to the truth. The 30-km fault locking depth may not mean that the fault is locked that deep but may imply a broader distribution of the wrench-style deformation than a reasonable elastic half-space fault model would predict. Such broad deformation distribution may be caused by visco-elastic motion in the lower crust and upper mantle around the Mojave section of the SAF.
We test also a case of greater slip rate along the Eastern California Shear Zone than the WGCEP model predicted. A minimum post fit residual is obtained at a rate of 9 mm/yr for Model HD and 7 mm/yr for Model CD. The improvements to the two thrust-fault models are significant at 98% and 90% confidence levels, respectively. The confidence levels are determined based on the F-test, which tests the significance of introducing new model parameter(s) to improved of model fitting. In the tests given above and a number of other tests listed in Table 5, the input data have 134 degrees of freedom, the base model has zero degree of freedom in the parameter space, and the model being tested usually has one degree of freedom.
Using a modified WGCEP model with 30-km locking depths for the Mojave section of the SAF and 7-9 mm/yr right-lateral shear along the Eastern California Shear Zone, we find about 1-4 mm/yr WNW residual motion left for the sites in the San Gabriel Mountains and the western Mojave desert. Although modest, this motion appears to be systematic. We showed earlier that thrust motion or decollement under the San Gabriel Mountains may explain the N-S contraction in the region. The same mechanism, coupled with oblique slip across the detachment, can explain the WNW motion of the block. Allowing a uniform left-lateral slip component along the Cucamonga fault, Sierra Madre fault Santa Susana fault, and Oak Ridge fault, we find maximum postfit chi-square reductions when the left-lateral slip equals 4 mm/yr for the Model HD and 13 mm/yr for the Model CD, respectively. The model improvement is at 87% confidence for Model HD and 99% for Model CD. These results suggest that adding a left-lateral slip component along the thrust faults improves the fit of both models. However, Model CD fits the data significantly better than Model HD. The left-lateral slip along the thrust faults could be lower than 13 mm/yr depending on how the motion direction is defined. We define N-S motion as normal and E-W motion as lateral. The definition is precise for the Cucamonga fault, San Cayetano fault, and the east portion of Sierra Madre fault, but not so for the Santa Susana fault and the west portion of Sierra Madre fault which strikes about 28 degree clockwise from the strike of Cucamonga fault. If we evaluate the lateral motion parallel to the strike of the Santa Susana fault, the left-lateral slip for Model CD at the thrust fault surface is about 9 mm/yr. The residual velocities of the modified Model CD are shown in Fig. 6. Significant along-strike motion of the thrust faults can be interpreted as the result of shear motion across the SAF. We will discuss in more detail the mechanisms of this along-strike motion along the thrust faults.
This method, like most previous methods (e.g. Frank, 1966; Prescott, 1976), interpolates of the strain rates using discretized geodetic measurements. However, unlike other previous methods, this one models strain rates as continuous functions within the entire network. At each location, a uniform rate field is assumed, a least-squares inversion is performed over the station velocity solutions and their covariances to solve for six parameters: the velocity components $U_x$ and $U_y$, rotation rate w, and rate components $\tau_{xx}$, $\tau_{yy}$, and $\tau_{xy}$. Other commonly used rate terms, such as the maximum shear rate $\tau_{max}$ and the dilatation rate $\tau_{dil}$ can be derived afterwards from the three rate components. The modeling algorithm can be written in the following form:
$$ \pmatrix{ V_x^I \cr V_y^I \cr} = \pmatrix{ 1 & 0 & \Delta x_I & \Delta y_I & 0 & \Delta y_I \cr 0 & 1 & 0 & \Delta x_I & \Delta y_I & -\Delta x_I \cr} \pmatrix{ U_x \cr U_y \cr \tau_{xx} \cr \tau_{xy} \cr \tau_{yy} \cr w \cr} + \pmatrix{ \epsilon_x^I \cr \epsilon_y^I \cr} $$
where $V_x^I$ and $V_y^I$ are the observed $I^{th}$ station velocity components at a location $\vec r_I$. All variables on the right hand side of the equation are to be evaluated at a location $\vec R$, $\Delta x_I$ and $\Delta y_I$ are the vector components of $ \Delta \vec R_I = \vec r_I - \vec R$. The $2 \times 6$ matrix is the partial derivative matrix and $\epsilon_x^I$ and $\epsilon_y^I$ are the errors of the corresponding velocity components. The covariance matrix for $\epsilon_x^I$ and $\epsilon_y^I$ is $E_{ij}$ which is a weighted version of $C_{ij}$ used for constructing the local averages. $C_{ij}$ is the covariance matrix of the velocity estimation errors obtained from our geodetic data adjustment. The weighting is given as,
$$ E_{ij} = C_{ij} exp {{\Delta R_I^2 + \Delta R_J^2} \over {\sigma_D^2}} $$
where $i$ and $j$ are the velocity components corresponding to the $I^{th}$ and the $J^{th}$ stations, $\Delta R_I$ and $\Delta R_J$ the distances from the $I^{th}$ and the $J^{th}$ stations to the spot to be estimated, and $\sigma_D$ is a distance-decaying constant, taken as 25 km. This weighting means that a station 20.8 km away from the spot to be evaluated will contribute only one-half its unweighted value to the velocity solution. The contribution is reduced to 14% if the station is 35 km away. To save computation time, we exclude stations from the least-squares inversion if the distance exceeds 50 km and the calculated contribution would be less than 2%. This algorithm has certain advantages. The major one is that the model represents the rate field in a realistic way; i.e., for a local region of about 20 km in diameter the rate field is quasi-uniform; but for a region of 100 km in diameter the rate field varies continuously. Our rate estimates are less biased because of proper weighting, and they are stable because they are evaluated as weighted averages over the region. Strain uncertainties can also be derived.
Strain Rate Results
Fig. 7 and Fig. 8 illustrate the strain rates in the region. Fig. 7 shows
the maximum shear strain rates and directions, and Fig. 8 the principal strain
rates and axes. The strain rates are
plotted only when the solutions reach a reasonable level of confidence
(uncertainties less than 0.15 micro-rad/yr).
A number of features are found from the distributions:
1. The maximum shear strain rates distribute along three faults: the SAF, SJF, and Sierra Madre-Cucamon-ga fault system. It is no surprise to see significant shear rates along the first two faults, known to have the greatest slip rates of all faults in southern California. For the Sierra Madre-Cucamonga fault system, however, a dextral shear rate of 0.20 +- 0.03 micro-rad/yr oriented N45 degree W newly reveals that it is probably the thirdmost geodetically active fault system in the region whose shear strain rates are resolved here, with N-S compression and E-W extension about equally active. The maximum shear strain rates in the San Gabriel Mountains are quite close to 0.13 micro-rad/yr striking N63 degree W determined by Savage and Lisowski [1994].
2. The maximum compressions (Fig. 8) seem to reach peaks at the western-most Mojave desert near the GF and along the SJF close to its triple junction with the Banning fault. Such high compression could be interpreted as local SSE convergence near the White Wolf fault and as N-S convergence near the Banning fault. However, the reliability of the estimated compressions there may be questioned, as the two maxima are located at the boundaries of our network. A well-resolved compressional belt runs from the Malibu-Santa Monica-Raymond Hill fault system to the Sierra Madre-Cucamonga fault system, where the N-S compressional rate ranges from 0.12 to 0.22 micro-rad/yr. This compressional belt has produced several moderate-to-large thrust and oblique-thrust earthquakes during the last few decades: 1973 M 5.9 Point Mugu, 1987 M 5.9 Whittier Narrows, and 1991 M 5.8 Sierra Madre earthquakes. The 1971 M 6.6 Sylmar and the 1994 M 6.7 Northridge quakes are located close to but not within this high compressional belt. The western section of the compression belt has been previously identified as the northern flank of the Elysian Park fold and thrust system (Hauksson, 1990). Hauksson (1990) reported that the compressional axes of the earthquakes had a systematic trend from a N-S direction east of the Los Angeles basin to NNE west of the basin. This pattern is consistent with our study.
3. South of the Los Angeles basin, our velocity solutions show that strike-slip motions dominate. From the Newport-Inglewood fault to the SJF, the region undergoes a deformation of about equal amounts N-S compression and E-W extension, from about 0.1 micro-rad/yr along the Newport-Inglewood fault and Elsinore fault to about 0.2 micro-rad/yr along the SJF. This result is consistent with the finding by Johnson et al. [1994], who studied strain rates in the Anza trilateration network using the same set of EDM data that we use here. The maximum shear strain rates are relatively low in the Los Angeles basin and the San Fernando valley; the maximum convergence rates are low at the center of the San Gabriel Mountains, San Fernando valley, and south of the Los Angeles basin.
4. Virtually no extension is found from the SW foothills of the San Gabriel Mountains to the coast, a region that includes the Santa Susana fault and the Malibu-Santa Monica fault system. The region therefore shows significant areal contraction. The amount of horizontal areal contraction rate might indicated active thrusting and orogeny taking place in such environments.
5. There is about 0.14 micro-rad/yr E-W extension at the northern tip of the Whittier fault. Such extension is possibly caused by the bifurcation of the Whittier fault and the Elsinore fault and by the local ending of the Whittier fault there. This notion makes sense because the station postfit residuals of the WGCEP model are small in the region except for LANW. However, we do not want to overinterpret the results there since the velocity solutions for the sites in the region are probably weaker than for other sites.
Rotation rates for the network are shown in Fig. 9. Large rotation rates are found along the SAF and the SJF, as expected from active wrenching dislocations along the two faults. Of interest is the rotation pattern's elliptical high around the center of the Mojave section of the SAF, with the maximum located about ten kilometers north of the fault. An initial interpretation for this rotation pattern could be that the San Gabriel Mountains has a distinct rotation compared to its south and west neighbors: the San Gabriel Mountains moves like a solid block. However, a close examination of the postfit residuals in Fig. 6 shows no systematic rotation pattern left in this region, indicating that the concentrated rotation in the region has been explained by the model, in which the SAF, the oblique-thrust faults, and the Garlock fault all play important parts. We choose not to show the translation rates, because they resemble roughly the original velocity field as shown in Fig. 4.
Our study fills an observational gap along the Cucamonga-Sierra Madre-Santa Monica fault system, so that we can better understand interactions between the San Gabriel Mountains and the Los Angeles basin. Convergence is significant only at the northern part of the basin. N-S convergence is accommodated mainly along the Cucamonga-Sierra Madre-Santa Susana and Malibu-Santa Monica-Raymond Hill fault systems.
Two important observations suggest the abnormal behaviors of the San Gabriel Mountains. The first one shows that the deformation across the block along a profile normal to the SAF is broader than would be predicted by an elastic dislocation model with reasonable locking depth and slip rate parameters of the SAF. This finding implies that the displacements beneath the upper crust cannot be described as slip between two elastic blocks, but rather as shear motion across a broad deformation zone. The second observation is that the San Gabriel Mountains and the SW Mojave desert move about 3 mm/yr WNW with respect to the southern region. Such motion might be part of a NW-SE extension across the SJF and the Mojave section of the SAF caused by NE compression in the central Transverse Ranges area. Alternatively, it might be the result of left-lateral oblique thrust underneath the San Gabriel Mountains and possibly the SW Mojave desert, with the topmost crust being peeled off the upper mantle base. Although previous geological studies revealed that such blind thrust motions could happen [Davis et al., 1989; Dolan et al., 1995] they could not determine exactly the direction and extent of the motions (e.g., whether penetrating the SAF). A trenching study at the Cucamonga fault [Morton and Matti, 1987] showed no oblique component for the thrust fault. However, this may not directly contradict to our model, since the oblique motion might not be significant until the material thrusts to certain depth.
Seismological studies have revealed that the San Gabriel Mountains do not have a significant root [Hadley and Kanamori, 1977; Sung and Jackson, 1992]. The observation could be explained by having a horizontal decollement underneath the mountains which would shift the plate boundary to the east north of the Big Bend. Although such a scenario is possible, however, no one has offered a quantitative deformation model. If our thrust or oblique-thrust model is valid, the thrusts of the Cucamonga-Sierra Madre system may eventually cross the SAF as shown in Figures 5 and 6. If the oblique-thrust model holds, a left-lateral motion along the faults might be as large as 10 mm/yr. This might occur if the San Gabriel Mountains were glued by friction to the Mojave desert block, at least in the upper crust and between earthquakes, but separated from the lower crust by a detachment surface. Relative motion across this thrust ramp might be caused by horizontal compressive stress along the Cucamonga system, preventing the San Gabriel Mountains and the SW Mojave block from keeping up with the southeastward motion of the Mojave block, resulting in a delay of the lateral motion of the upper block with respect to the lower block. For the surface mass transport in the San Gabriel Mountains region, our oblique-thrust model supports the kinematic model of Weldon and Humphreys [1986] but differs from it in describing the deformation at depth.
Fig. 10 is a cartoon of our kinematic model. In the model the Mojave section of the SAF is intersected at depth by the north dipping thrust faults, making the San Gabriel Mountains a sliver block deformed both by thrust motion underneath and lateral shear on the NE. It is still problematic if the SAF is cut off completely or partially by the thrust faults beneath its surface trace, and how far (if any) the SAF is shifted NE at depth. An altered and/or shifted boundary zone beneath the surface expression of the SAF would support Snay et al.'s (1995) finding that the major deformation band at the Big Bend region is wider than that at the Carrizo plain section of the SAF, and orients about 7 degree clockwise relative to the surface trace of the SAF.
1. The fault model provided by the Southern California Earthquake Center earthquake probability report (WGCEP, 1995) describes the crustal deformation in general; i.e. crustal deformation is apparently dominated by a few major faults in southern California, such as the SAF, SJF, Garlock fault, and Eastern California Shear Zone.
2. Significant convergence and shear motion occur along the southern frontal fault system of the San Gabriel Mountains. The shear motion rate along the Sierra Madre-Cucamonga fault system is the third largest behind the SAF and the SJF within the central Transverse Ranges and Peninsular Ranges.
3. After removing the velocity field predicted by the WGCEP model, residual velocities show systematic patterns in the San Gabriel Mountains area and along the southern SJF. Some residuals can be explained by adjusting the WGCEP model along the SAF and SJF. Other residuals can be explained by either a NW-SE extension caused possibly by NE-SW compression in the region, or a left-lateral oblique thrust along an extension of the Cucamonga-Sierra Madre thrust system.
4. Low strain rates are found along the Elsinore fault, Newport-Inglewood fault, and Palos Verdes fault. N-S Compression is stronger along the Malibu-Santa Monica-Raymond Hill fault system than in its southern neighbors, with the maximum compression direction being rotated gradually from N-S to NNE across the fault system from east to west. The San Fernando valley is being compressed N-S with little E-W extension.
CATO: Main station Castro 1898 (CAT0) is difficult to observe using GPS because of strong radio interference. A GPS occupation has been made at another site, Solstice Cyn B2 Aux 1 (CATO), about 14 m south of CAT0. A GPS tie was made between the two sites in 1990. Another site, Castro 1898 Rm 3 (CAT3), has been measured in triangulation surveys along with CAT0 and is tied to CAT0 locally. CAT3 is also included in this study.
ECHO: Main station Echo Rock 1933 (ECHO) has been repeatedly observed using GPS since 1987. A reference mark, Echo Rock Rm 2 (ECH2), was measured with GPS in 1990 and tied to ECHO later. Their velocities are assumed equal.
JPL1: Three GPS stations are used in this study. JPL Aries 1 1975 (JPLA), JPL Aries 1 1975 Rm 1 (JPLR), and JPL MESA (JPL1). JPL1 has been observed since 1990 and is used as a fiducial station in southern California. This site has been tied to the other two sites with GPS. JPLA and JPLR have also been measured in USGS trilateration surveys.
LANW: The original triangulation site Los Angeles NW Base 1889 (LAN0) was destroyed in the late 1950s or early 1960s. A distance between this station and station Los Angeles NW BS 2 1956 (LAN2) was measured, and angles involving the two stations plus a remote site, SPE0, were observed in the 1950s. After the destruction of LAN0, LAN2 was subsequently observed in triangulation surveys in the 1960s, sometimes involving another local station, LA NW BS Aux 3 1964 (LAN3), which now has been occupied using GPS. All the local measurements are used to tie LAN0 to the GPS station at the site, although the local ties are not that accurate. The postfit uncertainty for LAN0 is about 50 mm for the two horizontal components. Another station, Whittier D11 (WD11), was located about 1 km west, measured using GPS, and intended as a substitute for LAN0. However, this station was lost after two epochs of measurements in 1989 and in 1991. The station velocity of WD11 is assumed equal to the station velocity of LANW in this study.
LASE: Main station Los Angeles SE Base 1889 1957 (LASE) is seated in a courtyard of a private residence. This station was reset in 1957. Comments in the LA County Survey Control Station Description referred to the new marker's ``geographic position remaining unchanged." Our assumption is that the marker was reset faithfully to its original horizontal position within a few millimeters.
MICH: Main station Michelson 1923 (MICH) still exists but is covered by heavy foliage which makes GPS occupation difficult. A GPS tie was made between one of its reference markers, Rm 1 (MIC1), and ECHO. This tie has been used along with local tie measurements between MICH and MIC1 to link MICH to ECHO.
MOJA: Several GPS stations have been used as fiducial stations at Goldstone, Mojave. The early ones were MOJA, using a TI4100 antenna; MOJF, a FRPA-2 antenna; and MOJ1, a MiniMac antenna. A TurboRogue station DS10 has been in operation since 1990 but is located about 10 km north of the other three. Unfortunately no reliable ties exist between the early three that we know of (problems may exist for the vertical components of the local ties; see Appendix of Feigl et al., 1993). There are GPS ties between MOJ1 and DS10. In this study we tie the velocities of the four stations together but make no local ties between them except for the GPS ties between MOJ1 and DS10.
NIGU: Main station Niguel 1884 (NIG0) was destroyed in the early 1980s. There is no reliable tie between this station and our GPS station Niguel A 1981 (NIGU), hundreds of meters away. In this study we tie only the two station velocities together.
PINY: An early GPS occupation at the site was made at station Pinyon Flat NCMN 1981 (PINY). Since 1990, a permanent station, PIN1, was established as a local fiducial station, although different antenna types have been used at the site. We use data from both stations and tie their velocities together.
PSEB: A local station, Pasadena East Base 2 1922 (PSE2), is about 80 m from the main station Pasadena East Base 1922 (PSEB). PSE2 has also been surveyed during some of the triangulation experiments. This site and the corresponding data are included in this study; its velocity is tied to PSEB.
SAFE: Main station San Fernando 1898 (SAF0) was destroyed in the late 1950s. An existing mark, San Fernando 1898 Aux 3 (SAF3), was also observed in some of the triangulation surveys and SAF3 is about 22 m from SAFE and tied to it locally. GPS occupations have been made at two sites: San Fernando Aux 2 Ecc 1 Rm 2 1967 (SAFE) and PICO NCER 1977 (PICO). Station PICO is also a USGS trilateration site. SAFE has been tied to SAF3 and PICO separately using GPS, and the uncertainty of the tie between SAFE and SAF0 is estimated to be about a couple of centimeters.
SNTZ: Main station Covina C7 San Tuze 1957 (SNT0) was reset in 1957 in a mass of concrete, but the mark was lost in 1987. The first GPS survey of the site was made at one of its reference marks, Rm 1 (SNTZ). The main mark was reset in a large concrete mass in 1991 and stamped Johnson Frank Assoc., GPS Station, Covina C7, San Tuze 1957, Reset 1990. A local tie between the reset mark and SNTZ was made using GPS. The reset we believe should be within a few millimeters of its original horizontal position.
SPE0: The original triangulation station San Pedro 1853 1880 (SPE0) still exists, but strong radio interference from a swamp of microwave antennae nearby makes GPS occupation difficult. A local tie recovered from a LA City Engineering survey control map to the GPS observed reference station, Rm 2 (SPED), is used here. The tie is believed precise at the millimeter level.
UCLA: Two GPS stations (UCLA and UCL0) are used in this study. They are located atop two buildings and are about 42 meters apart. A local tie between the two sites was made using GPS.
WILP: Main station Wilson Peak 1890 (WILP) was demolished in the late 1950s. There is no local tie for this station to any other locally existing station. However, stations Echo Rock 1933 (ECHO) and Michelson 1923 (MICH) are also located atop Mt. Wilson, and a number of triangulation measurements were made to the three sites from other remote sites in the past. These measurements provide somewhat weak ties between the three. ECHO and MICH are about 600 m and 700 m away from WILP, respectively. Because all three are bedrock sites, we assume safely that there has been no relative motion between them. Velocity ties are made between the three in this study.
WORK: Main station Workman Hill 1932 (WORK) was reset in 1978 and again in 1989. The 1987 Whittier Narrows earthquake may have also perturbed the site by a centimeter or so. Our first GPS observations were made right after the 1987 quake. Our 1989 measurements were made after the 1989 reset. Although the reset by a crew from LA City was claimed accurate, modeling of displacement at the site raises some doubt. In this study we ignore the 1987 GPS measurements at the site, and treat the two resets and the 1987 coseismic effect as one unknown jump.