Published in the Bulletin of the Seismological Society of America volume 86, No. 1B, pp. S19-S36, 1996. (Northridge earthquake special issue)

Figure Index & Captions

Text Index:

Abstract Introduction Data & Analysis Modeling Discussion Conclusions Acknowledgments References

Introduction

We have used Global Positioning System (GPS) geodetic data to quantify the static displacement field associated with the earthquake and its aftershocks. In this study, we sampled the displacement field at 66 stations (documented in Tables 1 & A1) with GPS-derived vectors measured with 1-sigma errors ranging 3 to 42 mm (east-west), 3 to 25 mm (north- south), and 3 to 90 mm (vertical). Our estimates are based on station positions measured within 15 months prior to and one month following the earthquake. In our analysis we corrected for secular velocities at all of the stations by spatially interpolating between velocities estimated previously for 15 stations, using measurements spanning 5 or more years.

From the set of co-seismic displacement vectors we determined, we modeled the earthquake source using previously established methods based on elastic dislocation theory. First, we estimated the dislocation source that could best explain the geodetic data with a single uniform- slip dislocation following the non-linear optimization approach of Murray et al. (submitted) and using a single rectangular dislocation in a homogeneous half-space. We then estimated the spatial distribution of slip on a larger (yet co-planar) fault surface following the Singular Value Decomposition inversion approach implemented by Larsen (1991). This modeling is secondary to the data portions of the paper, and should be viewed in the context of other studies of the earthquake's source (Wald and Heaton, 1994b; Dreger, 1994; Shen et al., this issue; and Wald et al., this issue). The models presented here interpret these GPS data independent of other information. Wald et al. (this issue) combine these GPS results with other data to estimate a more comprehensive source model.

Data and Analysis

Figure A1 - click to view

A total of 534 occupations of 66 survey stations were made during 92 field sessions. These data were combined with global and regional continuously-recorded GPS data covering 24 hours on the day of each field session.

We analyzed the data in two steps. In the first step we used the GPS phase and pseudorange measurements to estimate station coordinates, satellite orbital parameters, and atmospheric delay corrections for each day of observation. For this step we loosely constrained the coordinates and velocities of regional and global stations. In the second step we combined the estimates and their covariance matrices from all of the days, applying position and velocity constraints to 13 globally distributed stations (listed in Table 1 ) to obtain a consistent solution for displacements at the epoch of the earthquake. For all of the experiments we resolved integer-cycle ambiguities in the phase observations using the iterative technique described by Feigl et al. (1993). The two-step approach allowed us to distribute both the processing of the raw GPS observations and the combination of solutions among several groups, encouraging redundant and progressively improved analyses (see Table A2).

Fig.'s 1 and 2, and Table 1 , show our estimates of displacements for 66 GPS monuments within about 75 km of the Northridge epicenter.

Figure 1 Figure 2

The uncertainties given in Table 1 and plotted in Fig.'s 1 and 2 represent our best estimate of the 1-sigma error for each value or vector. These cannot be rigorously computed from the uncertainty in the GPS phase measurements because the error spectrum of these measurements is poorly understood. Rather, they are based on studies of short- and long-term repeatabilities for a subset of station position estimates from this analysis and the set for southern California between 1986 and 1992 (Feigl et al., 1993). These studies suggest that for short observation sessions (< 5 hrs.), the formal uncertainties are roughly consistent with long-term repeatability, for longer single-day sessions (5-8 hrs.) the formal uncertainties should be increased by a factor of 2-3, and for sessions of 24 hrs. or more the appropriate scale factor is 3-4. Since the present analysis includes data from observation sessions ranging from 2 to 24 hrs., a simple scaling of the formal uncertainties to achieve a chi-square of unity for the long-term scatter of estimates is inappropriate. The simplest approach, which we have adopted, is to add a constant value ( [3 mm]**2 ) to the variance estimated for each coordinate in the solution.

We are able to check the validity of our weighting by examining the estimated displacements of stations sufficiently far from the epicenter that we expect small errors in their modeled displacements. If we adopt the arbitrary criteria that these stations should have model- predicted displacements less than 10 mm in all components, and estimated uncertainties less than 10 mm in the horizontal and 40 mm in the vertical components, then 12 stations are available for analysis. One of these stations, HOPP, has a 4-sigma residual in its east component (-13 +/- 3 mm), a result that may be related to unmodeled motion on a second fault plane (discussed below). A second station, PEAR, has a 5-sigma residual in east (16 +/- 3 mm) that is not yet understood. For the remaining 10 stations (whose names are italicized in Table 1 ), the values of the square root of the reduced chi-square (nrms) for the east, north, and vertical residuals are 1.5, 1.0, and 1.2, respectively. From this, we conclude that the uncertainties given in Table 1 are reasonable estimates of the 1-sigma errors for most stations.

Another concern arises from the small number of independent measurements for many stations ( Fig. A1 ). For monuments with only one or two measurements in either the period before or after the earthquake, there is significant chance of undetected error. Such an error could arise in either the observations (e.g., by receiver malfunction, or by improperly positioning the antenna over the survey monument, or by mis-measuring the antenna height) or the analysis (e.g., improperly repairing cycle slips).

All pre-earthquake data we used were collected within 15 months of the earthquake. Since the relative interseismic motions of most of the stations are small or well known, there is little error introduced by mismodeling these motions. The assumed velocities for the stations involved in this study ( Table A1 ) were interpolated using 15 well- determined secular velocities and a simple model for slip on the San Andreas fault system (Feigl et al., 1993). We believe that the velocity errors for the stations we used are less than 3 mm/yr.

Modeling

Figure 3

Both approaches are based on elastic dislocation theory, which can be used to compute the displacements at a given point on the ground surface from a slip distribution model (e.g., Steketee, 1958; Chinnery, 1961; Savage and Hastie, 1966; Mansinha and Smylie, 1971; Okada, 1985). Both our forward and inverse modeling approaches incorporated a combination of algorithms from these references. The model geometry is displayed in Fig.'s 1 and 3 , where we indicate the map view and cross-section geometry of the model fault surfaces. Modeled displacements are shown in Fig.'s 1 and 2 , and the residuals between the observations and each of the two models are given in Table 1 and Fig.'s 6 and 7.

Non-linear Optimization Method

We used the following procedures and assumptions, based on Murray et al. (submitted). Slip was assumed to be uniform on a single rectangular fault, with its top edge parallel to the Earth's surface and embedded in a homogeneous isotropic elastic halfspace with rigidity = 30 GPa. A polyconic projection was used, and east-north correlations were neglected. While the modeling procedure could be improved mathematically by including the correlations, which are available from the GPS data analysis (Table 1), such a change would be unlikely to cause substantive changes in our results.

For the optimal model, chi^2=2082 (with 198 data, and estimating 9 parameters), yielding an nrms residual of 3.32. To assess uncertainties in the model, trial models were compared to the optimal model using an F-ratio test (Draper and Smith, 1981). Table 2 gives the parameters for the optimal model (and its 95% confidence limits), and Table 1 and Fig. 6 show the distribution of normalized residual values. We believe that the large nrms residual results primarily from using too simple a model, and not necessarily from an underestimate of uncertainties in the displacements, as discussed below. Nevertheless, this model explains 95% of the variance in the GPS data (for the null model, i.e., no deformation, chi^2=41,600).

The plane estimated by this approach dips towards the SSW, and indicates that the main slip concentration occurred up-dip and towards the northwest of the mainshock hypocenter. This plane is evidently not coplanar with the aftershocks. Fig. 3 shows the model plane plotted in cross- section with respect to relocated aftershocks from Mori et al. (1995).

The model plane is nearly parallel to the seismicity plane, lying 1 to 2 km above it. At the hypocenter, the vertical distance from the hypocenter to the (projected) model plane is about 2 km, considerably greater than the stated error in hypocentral depth of 0.4 km. One possible explanation that has not yet been evaluated is that the hypocenter determination and GPS-based modeling approaches have different datums, causing a shift in apparent depth that is due mainly to differences in methods. However, it seems highly unlikely that so large a shift could occur from that alone. More importantly, our assumption of a uniform Poisson solid for the physical model may introduce inaccuracy. A similar discrepancy has been observed and discussed elsewhere (e.g., Ekstrom et al., 1992; Stein and Ekstrom, 1992), in which case it was attributed to assuming a half space in the presence of variable crustal rigidity surrounding the modeled fault. This issue is also noted by Shen et al. (this issue), and treated in more detail there.

Singular Value Decomposition Inversion Method

This modeling approach assumes a fault geometry. We assumed the model fault to be co-planar with that estimated by our non-linear optimization approach ( Fig. 3 ). We roughly doubled the length and width dimensions, and extended the model plane up-dip; we used the strike, dip, and location of the optimal plane ( Table 2 ). We assumed the fault plane to be 20 km by 26 km, and specified it to be composed of 130 subfaults, each 2 km by 2 km. The model fault plane extends to within 1 km of the ground surface, and the center point of this plane is located at 9.86 km depth. We inverted the GPS estimates of displacement vector components and their associated errors (from Table 1 ) to estimate the thrust and strike-slip components of slip on each subfault, as described by Larsen (1991) and Hudnut and Larsen (submitted). The number of parameters estimated was 260, and the number of data was 198 (each displacement vector contains 3 components).

We did not employ positivity or slip constraints in the inversions. No smoothing was performed separately from that which occurs because of the SVD method of inversion. In SVD, when the eigenvalue matrix is truncated, a form of smoothing is implemented. In this case, the number of singular values chosen was 23, because this solution was within the range of most reasonable solutions, obtaining a total moment of 1.63 x 10^19 N-m and fitting the GPS data relatively well (chi^2 = 1681). Other solutions at higher and lower singular values yielded qualitatively similar slip distributions in the range 18 < k < 25, where k is the number of singular values. Within this 'stable' range, the total moment increased from 1.55 to 1.71 x 10^19 N-m, and the nrms decreased slightly. Although a more rigorous selection of the optimal result from this approach is possible using an F-test (Jacobsen and Shaw, 1977), we made our selection by inspection. It is valid, yet somewhat subjective, to select the number of singular values retained in this manner (e.g., Parker, 1977). Fig. 4 shows the changes in key parameters with increasing number of singular values, allowing our selection to be evaluated. The additional parameter shown (subfault nrms) indicates dispersion in the amount of slip on each subfault.

As expected, the variable slip model does fit the data better than the uniform slip model, with a 40% reduction in variance. For this variable slip model, we effectively estimated 23 parameters, whereas the uniform slip model has only 9. Taking this into account, we still find that the variable slip model (nrms = 3.10) fits the data better than does the uniform slip model (nrms = 3.32).

Figure 4 Figure 5

Both models explain 95% or more of the variance in the data, but neither provides a statistically satisfactory fit to the data. Using a less stringent norm, say by doubling all of the stated errors, one could claim that either model fits the data adequately, but we do not feel this would do justice to the problem. In one test, we doubled the stated vertical errors (but kept the horizontal errors the same) and re-ran the variable slip model. The result of this test, however, was a barely reduced total nrms within the 'stable' range of singular values, at the expense of a considerably higher total moment and subfault nrms. That is, loosening the error constraints made the model less physically reasonable. For these reasons, we feel this issue requires discussion, as there are many possible sources of the misfit, and simply doubling the stated errors would not explain the recognized and suspected problems.

Figure 6 Figure 7

Discussion

Aftershocks. The displacement field contributions of aftershocks that occurred soon after the mainshock are, by necessity, included in our GPS data. Relatively shallow aftershocks, especially with M>5, may have contributed to the displacement field we measured. For example, about one minute after the mainshock, a shallow M=5.9 aftershock occurred, and within ten minutes another shallow M=5.2 occurred (according to the Caltech/USGS catalog based on Southern California Seismic Network data). Because these two events occurred so early after the mainshock, their locations and especially their depths are not well known. Hence, it is not possible to confidently forward-model their contributions to the displacement field based solely on seismological information. In the preceding modeling section, we made no attempt to remove the effects of these two aftershocks, so what we call 'co-seismic' actually includes these two early aftershocks. In that sense, our data differ from the seismological data used by Wald and Heaton (1994b) or Dreger (1994) to arrive at slip distribution models. Wald et al. (this issue) evaluate and discuss this issue.

Subsequent to these two early aftershocks, all other M>5 aftershocks occurred between depths of 9 and 20 km, except for the shallow M=5.1 event on January 29. Displacement estimates given for the three GPS stations on Oat Mountain, PICO, SAFE, and SAFR are from data collected prior to the January 29 aftershock, and other GPS stations were unlikely to have been perturbed by that event. Over 40 aftershocks with M>4 occurred within the first two weeks, many of which were shallow.

Monument Instability. Some errors may arise from infidelity of our survey monuments in representing tectonic signals. Although long-term monument stability is a serious issue for studies of interseismic motion, over the 16 month period of our observations, its effects are likely at the level of only a few millimeters (Langbein et al., 1993 a & b; Wyatt, 1982; Johnson & Wyatt, 1994). More serious is the possibility that the strong shaking some of these monuments experienced during the Northridge earthquake may have created local non-tectonic displacements (that are not representative of the upper crust).

Practices of surveying monument construction vary, as does the type of material in which monuments are emplaced. The simplest type of monument, several of which are used in this study, consists of a metal disk set with concrete into a drill hole in bedrock. Another common type consists of a concrete mass poured into a shallow hole that has been excavated in the soft rock or soil, with a metal disk at the top. Each of the older monuments used is one of these two types. More recently, for example when Caltrans and NGS established the High Precision Geodetic Network (HPGN) and HPGN-Densification (HPGN-D) networks in the early 1990's, monuments called 3-D rod marks were set in soft rock or soil. These marks are now preferred over the concrete mass type since they are not coupled to the uppermost soil and provide a deeper point of attachment to the ground. Still other monuments, of which there are few, are installed by attaching a metal disk to existing masonry such as retaining walls.

Because we typically have measured only one geodetic station at each location in our network, the contribution of monument instability to our errors is difficult to quantify. We have only one site (Oat Mountain) where coincidentally we had 3 separate monuments for which we obtained both pre- and post-seismic GPS data of good quality. Also coincidentally, this site is the location of the largest displacements measured with GPS and presumably where ground shaking was very strong. The three Oat Mountain monuments (PICO, SAFE, and SAFR) are all set in soft, highly fractured rock capped with a thin (<0.5 meter) veneer of soil. During the earthquake, these monuments likely experienced 0.5 to 1.0 g accelerations and 0.5 to 1.0 meter/second velocities. Monuments SAFE and SAFR are concrete masses with metal disks. From visual inspection before and after the earthquake, we concluded that SAFE was the better of the two because soil around the base of the concrete mass for SAFR had eroded away. PICO is a metal disk attached to a metal rod that was driven into the ground 'to refusal' with a sledge hammer, and hence it is probably less susceptible to surficial movements than either SAFE or SAFR. In Table 1 , the results for motion of PICO, SAFE and SAFR are given. The displacements estimated for these three sites disagree by up to 25 mm in the east component, up to 2 mm in the north component, and up to 28 mm in the vertical component. The differences in east and vertical displacements are outside our estimated 1-sigma measurement errors. These discrepancies occur between PICO and SAFE, the stations with better data. PICO was observed twice before and 9 times after the earthquake, while SAFE was observed 10 times before and three times after ( Fig. A1 ). SAFR has just one measurement each before and after the earthquake, and is therefore suspect on geodetic grounds. We do not understand the discrepancy between our measurements at Oat Mountain, but we tentatively attribute them to localized monument instability induced by ground shaking in the earthquake. For this paper, we have included the displacement estimates for PICO, SAFE, and SAFR in our modeling.

At another station, NORT, we had different concerns. The station is located about 3 km NNW of the mainshock epicenter: hence, its observed southeastward displacement is counter-intuitive. However, the displacement was primarily upwards; the uplift here was 213 +/- 8 mm, and horizontal motion was only 68 +/- 3 mm. This monument, an HPGN-D station, is a metal disk set in a poured concrete wall along a train track and flood control channel. The earthquake caused a train to derail adjacent to this station, and during the first occupations of this station after the event we observed heavy equipment moving past the monument, within one meter of the base of the wall. The equipment, which was being used to clear the train wreck from the tracks, compacted the asphalt road bed on the south side of the wall. When we arrived at the station, we observed a new crack in the wall (<10 mm movement), about 5 meters southeast of the monument. The situation of the monument in such a wall, the crack that indicated damage to the structure, and the compaction of soil on the south side of the wall, gave rise to concerns about monument instability. This monument was geodetically leveled before and after the earthquake relative to other benchmarks in the NGS/Caltrans vertical control network, and from this leveling it appears that NORT went up by an amount similar to nearby benchmarks. We have no way to independently ascertain the horizontal integrity of the monument, except to say that by visual inspection the wall appears to still be in line with the extension of the wall to the NW, and appears not to be tilted. In one test of the uniform slip model, the displacement of station NORT was left out, and this did not substantively change the model results.

The station we have most difficulty fitting within errors is LOVE (Fig.'s 6 and 7 ). This station's displacement is very well determined, but the monument is a mass of concrete set in soft rock and soil. One possibility is that the motion of this monument included non-tectonic motion induced by shaking since it also is located where strong ground motions occurred. There was a landslide and considerable ground cracking downhill from the site, but no cracks were observed north (uphill) of the site. A minor crack was observed to run in the soil through the monument. Although the assessment of those who visited the site was that the monument was probably not disturbed by more than 10 to 20 mm, the potential for significant non-tectonic motion should not be overlooked.

The horizontal residual for NEWH is similar to that of LOVE, yet NEWH's residual is up (150-180 mm) whereas LOVE's is down (60 mm). Of course, since NEWH's displacement is less accurately determined, the modeling approaches we used would tend to allow its residual to be large. That is why we focus more on LOVE as the outlier station, even though the absolute residuals at NEWH are larger. The monument at NEWH is a concrete mass set in soil. Both NEWH and 0704 are both located very close to the up-dip displacement node, and we suspect that the misfits at these two stations may indicate some unmodeled slip on shallow structures (perhaps in combination with other potential problems we've mentioned). Aftershock seismicity indicates a steeper- dipping up-dip extension of the main rupture plane that would project to a line between these two stations, for example. Alternatively, the misfits could be explained by some sympathetic slip on hanging wall structures.

Other stations in the vicinity of LOVE and NEWH (0704, CHAT, HAPY, HOPP, U145, and WHIT) are misfit less drastically, yet with a somewhat consistent westward component in the residual vectors ( Fig. 7 ). Furthermore, preliminary results from leveling along highway 126 show unmodeled uplift of 10 to 20 mm in the vicinity of LOVE. We have considered the possibility that the misfits to data here may be due to seismic deformation associated with aftershocks, but we find it is not possible to account for the anomalies with the small displacement contributions of the aftershocks. An M=5.1 aftershock that occurred on Jan. 19, 1994 and located at 11 km depth was located close to these geodetic anomalies. This event had a pure reverse mechanism and is associated with seismicity on a north- dipping plane. The M=4.9 aftershock on June 26, 1995 also occurred in this vicinity. If one postulates some aseismic slip may have occurred on this north-dipping plane, it may be possible to improve fits to the geodetic data in the vicinity of stations LOVE and NEWH, and along the highway 126 level line.

This apparently anomalous crustal deformation surrounds the intersection of the eastern Ventura Basin with the San Gabriel fault. It occurs in the area where the aftershocks most notably do not fall within the area of our model fault planes ( Fig. 2 ). Furthermore, this area produced 4 preshocks from M 1.3 to M 1.9 at about 15 km depth within the 16 hours before the mainshock, called the Holser cluster (Hauksson et al., 1995). It is not yet clear whether the proximity of these preshocks and some larger aftershocks to the anomalous geodetic measurements is purely coincidental or may have a physical connection.

Fault Geometry and Material Properties

Preliminary Comparisons with Other Data

General Observations and Implications

The southward dip of the rupture plane in this event indicates the fault is a backthrust, dipping contrary to the Sierra Madre fault system's orientation, for example. The Oak Ridge fault system to the west also dips southward, implying that the Northridge earthquake occurred on an eastern extension of that fault system (e.g, Yeats, in press). The Northridge fault plane, in turn, seems (from the aftershock seismicity) to be truncated at the upper edge by the fault that ruptured in the 1971 San Fernando (a.k.a. Sylmar) earthquake (USGS & SCEC, 1994; Mori et al., 1995). We appear to have imaged the up-dip truncation of slip at a depth of 4-6 km with our variable slip model (Fig.'s 3 & and 5 ). This is slightly shallower than the intersection depth indicated by the seismicity. In places, the aftershocks extend spatially beyond the edges of the slip distribution model that we find best explains the geodetic data, especially near the northwest up-dip corner of the model fault (Fig.'s 2 & 3 ).

Slip in the Northridge earthquake was concentrated between depths of 5 and 20 km. Geologists have found no compelling evidence for a primary surface rupture (USGS & SCEC, 1994). Modeling indicates that in parts of the Santa Susana Range where we had no geodetic stations, uplift of as much as 520 mm may have occurred. In contrast, the 1971 earthquake, which was similar in magnitude, had large amounts of shallow slip and produced clear surface faulting (e.g., Heaton, 1982). As a result, the 1971 earthquake also produced much larger maximum displacements, and commensurately larger strains and tilts at the ground surface (e.g., Savage et al., 1975; Cline et al., 1984). In that case, up to 2.5 meters of vertical motion occurred over distances of 5 to 10 km, whereas the wavelength of vertical displacement associated with the Northridge event was several times longer as a result of the deeper concentration of large slip.

Conclusions

As a result of performing extensive analyses of the GPS data set, we feel that we understand the errors in the GPS data well enough to expect our models to fit these data appropriately within the stated errors, except for undetected problems at the less frequently measured stations. The exact reasons why our relatively simple models do not satisfactorily explain these GPS data remain unresolved, though we discuss the relevant issues and speculate that, perhaps most importantly, the source was too complex to be represented adequately with any single-plane model. The fact that we are not able to match the observations in a fairly well localized region to the north of the near-surface part of the fault plane suggests that the primary cause of the mismatch is using too simple a model, rather than monument instability.

From our GPS measurements, we produced a single dislocation model independent of seismological and other information. Furthermore, the data were sufficient to allow an inversion in order to estimate the distribution of slip on the main fault plane. The observed displacement field was evidently produced mainly by slip on a SSW-dipping reverse fault in the mid-crust, under the northern edge of the San Fernando Valley. The Santa Susana Range was uplifted by the earthquake by as much as 400 mm (measured) to 520 mm (modeled), and the northern part of the San Fernando Valley was uplifted by more than 200 mm. The pattern of uplift caused by the Northridge earthquake appears discordant with the topography. Both of our modeling approaches indicate that in order to explain most of the variance in the GPS data, the largest amount of slip must have occurred up-dip and northwest of the event's hypocenter. We find that less than one meter of slip occurred above a depth of about 5 km. We appear to have confirmed the suggestion by Mori et al. (1995) that the subsurface intersection with the 1971 earthquake fault plane formed the up-dip terminus of slip in the Northridge earthquake.

Our modeling indicates a simpler slip distribution than has been inferred on the basis of seismological data alone (Wald and Heaton, 1994b; Dreger, 1994). Clearly, the geodetic data and seismological data do not invoke identical images of the slip distribution. We present our variable slip model here partly to emphasize this point. Seismological data indicate slip concentrations near the down-dip edge of the rupture plane, whereas the geodetic data do not (see also; Wald et al., this issue). This may be because there are too few GPS stations in the southern San Fernando Valley to resolve such features, or because contributions of these slip patches to the surface displacement field are too small to resolve with the available GPS data.

Geodetic data are well suited to mapping the final slip distribution of an earthquake, and can therefore enhance imaging of rupture propagation beyond the capabilities of imaging based on seismological data alone, as was the case for the Landers earthquake (Hudnut et al., 1994; Wald and Heaton, 1994a). By combining seismological and geodetic data, Wald et al. (this issue) attempt to resolve the differences noted above by using the combined seismological and geodetic data sets. It is also possible that the discrepancies seen result from aseismic slip; the geodetic measurements would include such phenomena, whereas the seismological data might not. Seismological and geodetic data are complementary, and combining the seismological data with geodetic data can provide the best available methods for imaging details of the earthquake source.

Acknowledgments

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