The distribution of fault slip for the Northridge mainshock and two Mw 6.0 aftershocks is estimated using an approach which inverts the far-field moment rate functions derived by empirical Green's function deconvolution. The slip for these events has a strong negative correlation with the locations of small aftershocks. There is a notable clustering of aftershocks near the edges of slip suggesting that these events are triggered by a redistribution of stress following the mainshock rupture. The two large aftershocks ruptured the updip regions adjacent to the leading edge of the mainshock rupture. It is interesting to note that one aftershock, eleven hours after the main event, initiated 5 to 10 km west of the mainshock slip terminus and ruptured east to meet the mainshock slip. This event was found to have ruptured the same south dipping fault as the mainshock. The two events, however, are separated by a lateral offset in the depth of seismicity which serves as a geometrical barrier to through-going rupture. A Mw 6.0 aftershock approximately 1 minute after the main event is inferred to have ruptured an updip region of the mainshock fault which is relatively devoid of small aftershock seismicity. This event was located at the eastern edge of the sequence where it is also possible that it occurred on the north dipping fault involved in the 1971 San Fernando earthquake.
Introduction
The January 17, 1994 Northridge earthquake (Mw 6.7) received considerable attention due to its proximity to the dense population of Los Angeles and the level of damage that was inflicted. This earthquake sequence was one of the best ever recorded due to its location within the dense short-period Southern California Seismic Network (SCSN), the broadband high dynamic range TERRAscope network and Berkeley Digital Seismic Network (BDSN), the strong-motion instrumentation operated by the USGS and CDMG, and geodetic monuments.
It has become a more or less routine practice to estimate finite fault or distributed slip parameters of large damaging earthquakes. The detailed slip history of the Northridge mainshock was investigated using empirical Green's functions (Dreger, 1994), strong-motion, teleseismic and geodetic data sets (Wald and Heaton, 1994a; Wald et al., 1996), and using a genetic algorithm to invert local strong-motions (Zeng and Anderson, 1996). Song and Helmberger (1995) modeled regional broadband waveform data using theoretical Green’s functions to estimate the gross directivity properties of the mainshock, while Thio and Kanamori (1996) modeled teleseismic body waves using a time variable point-source approach. Hudnut et al. (1996) and Shen et al. (1996) modeled the fault slip from the static displacement field. Massonet et al. (1996) were able to model the mainshock and two moderate aftershocks using radar interferometry data. There is general agreement between the seismologically derived models. On the other hand, there is a notable lack of correlation between results derived from geodetic and seismologic data. This can be due to the inability of geodetic data to resolve temporal information about fault slip, the poorer resolution of geodetic modeling at greater depth, and perhaps more importantly the possibility that large aftershocks contributed to the observed static displacement field. The latter point is important in the context of how geodetic data is routinely incorporated into joint inversions for distributed slip parameters (e.g. Wald and Heaton, 1994b; Wald et al., 1996).
There has yet to be a detailed seismological study of the slip distribution of the Northridge sequence which includes the mainshock and the two largest Mw6.0 aftershocks. The purpose of this paper is to report on my continued study of the Northridge rupture process specifically the relationship of the two largest aftershocks to the mainshock rupture area. In this report the far-field moment rate functions derived for a 23:33 UTC aftershock are inverted to estimate the spatio-temporal distribution of fault slip. A 12:31 UTC aftershock will be considered in the context of the slip distribution map, the distribution of smaller aftershocks and in terms of fault complexity inferred from seismicity.
Overview
The Northridge earthquake occurred on a south dipping fault plane ( Figure 1) adjacent to the north dipping fault that ruptured during the Mw6.7 1971 San Fernando event. The Northridge and San Fernando events overlap at the eastern edge of the aftershock zone (Mori et al., 1995) and aftershock seismicity reveals the presence of lateral ramps or vertical deflections of the fault plane along the strike direction (Hauksson et al., 1995). It has been suggested by Hauksson et al. (1995) that these lateral ramp structures might be the slip limiting features of the mainshock rupture.
The Northridge earthquake sequence consists of over 10,000 aftershocks (Hauksson et al., 1994); two of which had Mw6.0 estimates (Dreger, 1994; Thio and Kanamori, 1996). These two events, one just over a minute after the mainshock (12:31 UTC) and the other 11 hours later (23:33 UTC), herein referred to as AS1 and AS2, are large enough that they would have slipped over considerable fault area which would be capable of producing damaging ground motions and contributing to the static displacement field. Figure 2 compares the north-south component of ground velocity recorded at PAS (distance=34 km) for the three events studied. Considering the fault structure complexity evident by the proximity of the Northridge and San Fernando events the goals of this study are to determine the fault plane and the spatial relationships of these large events relative to the Northridge mainshock.
Empirical Green's Function Method
The method that is used to determine the slip distribution of the aftershocks involves the inversion of far-field moment rate functions (MRF) that are derived from empirical Green's function (eGf) deconvolution of broadband waveforms. Data from both TERRAscope and BDSN are essential for this type of study for two primary reasons. First, the dynamic range (nominally 200 dB) of these networks enables the on-scale recording of the mainshock and aftershocks or eGfs. Second, the data has the bandwidth necessary to compute moment tensor solutions using long-period waves, and to capture the details of complicated fault slip. In contrast, high gain networks clip during the main events and strong motion recorders fail to record the smaller aftershocks or eGfs. Figure 3 shows the stations used in the eGf analysis.
Unfortunately as Figure 2 shows AS1 is affected by high levels of mainshock coda and consequently detailed waveform analysis is not possible. The extent of slip for AS1 is inferred from the mainshock and AS2 slip results and the distribution of smaller aftershocks. For the mainshock and AS2 a time domain moment tensor inverse method (Romanowicz et al., 1993; Dreger and Romanowicz, 1994; Pasyanos et al., 1996) was used to determine their focal mechanisms and to search for potential eGf events. Figure 1a shows the fault plane solutions for the mainshock, AS2 and their respective eGf. Table 1 lists the event parameters.
| Table 1 - Event Information | ||||||||||
| Event | mag | date,time (UTC) | lat.(oN) | lon.(oW) | z1 | z2 | str. | rake | dip | |
| mainshock | 6.7 | 1994.017,12:31 | 34.213 | 118.537 | 18.4 | 14 | 121 | 105 | 43 | |
| main-eGf | 4.4 | 1994.017,17:56 | 34.228 | 118.572 | 19.2 | 14 | 132 | 112 | 55 | |
| AS2 | 6.0 | 1994.017,23:33 | 34.326 | 118.698 | 9.8 | 5 | 116 | 89 | 46 | |
| after2-eGf | 4.3 | 1994.018,04:01 | 34.358 | 118.623 | 0.9 | 5 | 124 | 89 | 47 | |
1. Hypocentral depths (km) from the SCEC data center.
2. Centroid depths (km) from moment tensor analysis
Generally, a suitable eGf is an earthquake smaller than the mainshock by more than one order of magnitude (i.e. represents a point-source in a relative sense), is nearly collocated, and has a similar focal mechanism. As Table 1 shows the eGf used for each event has both a similar mechanism and location. It is worthwhile to note that the optimal eGf location is near the slip centroid (Dreger, 1995). Therefore, when dealing with large earthquakes, it is not always advantageous to have mainshock-eGf pairs with identical high frequency hypocentral locations. In the two cases examined in this paper the eGf events are within 8 km of the respective target event hypocenters. Moreover, the performance of a given eGf is more strongly correlated to the relative depths of the mainshock and eGf rather than the lateral location. As Table 1 shows the centroid depths obtained for the target events and their respective eGf events are the same. Although the eGf method for determining fault slip from local (e.g. Hartzell, 1978; Mori and Hartzell, 1990; Mori, 1993), regional (e.g. Dreger, 1994; Hough and Dreger, 1996; Li et al., 1995; Kanamori et al., 1992) and teleseismic (e.g. Antolik et al., 1996; Velasco et al., 1994) data is adequately presented elsewhere it is useful to define the model that will be used to invert the MRF data.
A rather simple finite fault model is fit to the MRF data. This model consists of a discretized fault plane with the orientation of one possible fault plane determined from the moment tensor analysis. In practice, both planes are inverted to find the plane that best fits the data and to provide an independent estimate of the actual fault plane. In this way it possible to determine the causative fault planes for small events or aftershocks that do not have their own aftershock distributions ( Mori and Hartzell, 1990). The overall model dimensions used for both the mainshock and AS2 were larger than the expected fault lengths and the slip in each inversion tapers to zero well away from the edge indicating that the finite edge constraints are not limiting the slip map results. Synthetic MRF are constructed by summing subfault MRF (in this case a simple box car function with fixed duration) which take into account the propagation delay of a radially expanding rupture front (i.e. causality) and the relative subfault-station distances.
Where i is the station index, j is the subfault index, m is the rigidity, U is the subfault slip that is solved for, A is the subfault area, M0 is the scalar seismic moment, B is the subfault MRF, and t is the delay due to rupture propagation and the relative station-subfault distance. A linear non-negative least squares inversion is performed to find the slip amplitudes. A variety of smoothing constraints can also be applied and in this study a spatial first derivative minimization constraint is employed. While this approach adequately takes multi-dimensional directivity into account it fails to consider complexities such as geometrical bends, multiple rupture planes, variable rupture velocity and dislocation rise time. Nevertheless, the comparison of Northridge mainshock results using this approach (Dreger, 1994) with the strong motion results of Wald and Heaton (1994a), Wald et al. (1996) and Zeng and Anderson (1996) indicates that this simple methodology is capable of recovering the gross slip distribution quite well.
Figure 4a shows the MRF obtained for the mainshock which clearly shows evidence of northward directivity and two subevents (Dreger, 1994). Figure 5 shows the MRF obtained for AS2. AS2’s MRF are simpler than those obtained for the mainshock however it is interesting to note that the duration is of the same order. The AS2 MRF show that pulse widths narrow at stations GSC and VTV (east-northeast) indicating rupture directivity to the east. This differs from what was observed for the mainshock in which the rupture was observed to propagate to the north. While the mainshock ruptured primarily updip, AS2 ruptured east with a small component of updip rupture. The fit of synthetic MRF to the data for both events is very good (Figure 4b, 5b) and result in the combined slip map shown in Figure 6. Note that the slip of both events is located in regions where there are relatively fewer small aftershocks. This has been observed for other events (Mendoza and Hartzell, 1988), and may indicate that much of the stress in the high slip regions was relieved. Alternatively, the clustering of aftershocks near the edges of slip may simply reflect the loading of adjacent areas of the fault.
The seismicity which bounds the bottom edge of AS2 (Figure 6b) lies beneath AS2 and there is a suggestion of a northward fault dip, however the extent of these aftershocks is insufficient to unambiguously define the fault plane. In addition, the slip map that is obtained with a north-dipping plane tends to plot over these aftershocks. The mainshock in contrast is bounded by aftershocks which are located predominately in the hanging block (Hauksson et al., 1995).
The radially expanding rupture model with constant rupture velocity is certainly an over-simplification of the actual rupture history. Recent studies using local strong-motion data (e.g. Wald and Heaton, 1994b; Cohee and Beroza, 1994a) indicate that there may be substantial acceleration and deceleration of fault rupture near regions that experience substantial slip or have geometrical complexities. Wald et al. (1996) examined the possibility of variable rupture velocity in the Northridge earthquake by allowing slip to occur in multiple time windows. Their results indicate that most slip occurs in the first window which lends support to the constant rupture velocity assumed in this paper. Although the model used in this paper does not take into account these additional complexities the favorable comparison of the mainshock results (Dreger, 1994) with the strong-motion results of Wald and Heaton (1994a) and Zeng and Anderson (1996) demonstrates that the approach is capable of resolving the gross distribution of fault slip.
Mori and Hartzell (1990) demonstrated that it is possible to use this method to test both possible nodal planes of the moment tensor solution to independently determine the actual fault plane. This is done by performing a number of inversions for different rupture velocities and finding the inversion which gives the best fit to the data determined by a minimum variance. Figure 7a shows that for the mainshock the south dipping plane provides a significantly better fit to the data. Of course for the mainshock the aftershock distribution can be used to directly map the fault plane. Both data sets for the Northridge mainshock yield the south dipping plane. Figure 7b compares the same plot for AS2. In this case the difference between the two planes is not large, however, the south dipping plane gives consistently better fits to the data for all of the rupture velocities that were tried.
The difference in the variance/rupture-velocity plots for the two events is probably due to different levels of source complexity. Since the smaller event (AS2) is not as complex there is less information which can be used to determine the fault plane. In other words the subevents provide the information which is necessary for determining the timing and position of fault slip. Interestingly, the rupture velocity for the mainshock was 3.0 km/s while AS2 yields a minimum variance for a rupture velocity of 1.6 km/s. This substantial difference in rupture velocity can only be partially explained by the shallow depth of the event within the sediments of the San Fernando basin which are approximately 10-15 km thick in this region (Huftile and Yeats, 1996; Haase et al., 1996). It is possible that the slower rupture velocity represents a difference in the materials involved in the faulting process or in the frictional properties of the fault. The shallow depth suggested by the slip inversion results for AS2 is corroborated by the shallow depths obtained from the moment tensor analyses. For example, Thio and Kanamori (1996) find a depth of 3 km and a depth of 5 km was obtained in this study (Table 1). Furthermore, the greater relative excitation of surface waves of AS2 (Figure 2b) compared to either the mainshock or AS1 (Figure 2a) is suggestive of a relatively shallower source.
Geodetic Slip Maps
The results of this study have important implications for the modeling of geodetic displacements for fault slip. Hudnut et al. (1996) report that large aftershocks could indeed affect static displacement calculations and Shen et al., (1996) demonstrate that the geodetic data are better fit by a model with two planes, one of which is constrained to lie within the south dipping aftershock distribution and the second within the hanging block. Massonet et al. (1996) conclude that radar interferometry data show static displacements of aftershocks and that a single fault model fails to explain the geodetic data, particularly along the western edge of the sequence. Both the geodetic (Shen et al., 1996) and radar interferometry (Massonet et al., 1996) data require shallow slip with seismic moments of and dyne-cm respectively. The seismic moment for AS2 ( ) and the location of slip in map view near the western edge of the sequence is in general agreement with the Shen et al. (1996) and Massonet et al. (1996). Although Shen et al. (1996) and Massonet et al. (1996) favor north dipping planes they both state that the dip of the secondary fault plane is poorly constrained and what is required of the geodetic data is shallow slip at the western margin of the sequence. The preferred interpretation of the eGf data is that AS2 ruptured an adjacent segment of the south dipping mainshock fault plane.
AS1 and other M>5.0 aftershocks could account for some of the remaining seismic moment discrepancy (approximately a factor of two) with the geodetic (Shen et al., 1996) results. It is interesting to note that there is no evidence of AS1 in the radar interferometry images of Massonet et al. (1996). The images are either too noisy to see an anomaly or perhaps the lack of an anomaly is suggestive of slip on the south dipping mainshock plane.
Discussion and Conclusions
This paper serves to document the distribution of fault slip of the 1994 Northridge earthquake sequence. Two Mw6.0 aftershocks are located along the updip terminus of the mainshock rupture. AS1 is somewhat of an enigma. It was not possible to analyze the waveforms for this event because of high noise levels due to mainshock coda. It is possible, however, to consider this event in the context of the slip distribution for both the mainshock and AS2 and the relationship to small aftershocks. If the hypocenter of AS1 is well constrained then this event occurred in the hanging block. If, on the other hand, the epicenter is mislocated to the south by approximately 6 km then this event could have ruptured an updip portion of the mainshock plane in a region which is relatively devoid of small aftershocks (Figure 6b). It is equally possible that this event ruptured the adjacent Sierra Madre fault which caused the 1971 San Fernando earthquake. Generally, there appears to be a negative correlation between the location of fault slip and the occurrence of small aftershocks (Figure 6). It should be noted, however, that although the aftershocks tend to cluster near the edges of slip they do not cluster along all edges.
Both the mainshock and AS2 appear to have been limited in extent by the Gilibrand Canyon lateral ramp. AS2 initiated at the western edge of the Gilibrand Canyon lateral ramp (e.g. Hauksson et al., 1995) approximately 10 km west of the mainshock rupture terminus, and ruptured east stopping at the mainshock rupture terminus.
The clustering of small aftershocks and the locations of the two large aftershocks at the terminus of mainshock slip suggest that these events were triggered by changes in stress due to the mainshock rupture. Stein, et al. (1994) illustrate that the Coulomb stress changes on optimally oriented thrust faults of the order of 0.5 to 1.0 bar would be expected in the vicinity of AS2. In fact their Figure 3c shows that these positive Coulomb stress changes extend in the updip direction toward the north which is in agreement with the determination of the south dipping fault plane determined by this study. These stress changes are quite small, approximately 1% of the static stress drop of AS2, and suggest that these adjacent regions were already close to failure at the time of the earthquake.
The seismological results of this study and the geodetic results of Shen et al. (1996) and Massonet et al. (1996) have important implications regarding the use of geodetic data jointly with seismic data in distributed slip inversions. Geodetic data can clearly be affected by the static displacements of moderate sized aftershocks particularly if they are shallow. The static displacement field is the cumulative displacement of all of the events in the sequence while strong-motion data sets are only sensitive to the mainshock dislocations. This poses a problem because, as Cohee and Beroza (1994) discuss, the temporal details of rupture propagation cannot be recovered unless the distribution of slip amplitude is constrained by other independent data. In practice this data has been geodetic from either GPS or leveling. Therefore when incorporating diverse data sets such as seismic waveforms and geodetic displacements to recover the distribution of fault slip care is required to ensure that each data set is representative of the same physical process.
The results of this study demonstrate that it is possible to recover the details of fault slip from aftershocks as well as the main events. The methodology used in this study can be used to effectively to provide additional constraints that could be helpful in analyses utilizing geodetic data sets.
Acknowledgments
The event locations and TERRAscope data used in this study were obtained from the SCEC Data Center. This research was supported in part by NSF grant no. EAR-9416219 and USDI 1434-HQ-96-GR-02742. This is contribution number 96-7 of the UC Berkeley Seismographic
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