All quality teleseismic recordings of the great 1906 San Francisco earthquake archived in the 1908 Carnegie Report by the State Earthquake Investigation Commission were scanned and digitized. First order results were obtained by comparing complexity and amplitudes of teleseismic waveforms from the 1906 earthquake with well calibrated, similarly located, more recent earthquakes (1979 Coyote Lake, 1984 Morgan Hill and 1989 Loma Prieta earthquakes) at nearly co-located modern stations. Peak amplitude ratios for calibration events indicated that a localized moment release of about 1-1.5 x 10^27> dyne-cm was responsible for producing the peak the teleseismic bodywave arrivals. At longer periods (50-80 sec), we found spectral amplitude ratios of the surface waves require a total moment release between 4-6 x 10^27 dyne-cm for the 1906 earthquake, comparable to previous geodetic and surface wave estimates (Thatcher, 1975). We then made a more detailed source analysis using Morgan Hill S bodywaves as empirical Green's Functions in a finite fault subevent summation. The Morgan Hill earthquake was deemed most appropriate for this purpose as its mechanism is that of the 1906 earthquake in the central portion of the rupture. From forward and inverse empirical summations of Morgan Hill Green's functions, we obtained a good fit to the best quality teleseismic waveforms with a relatively simple source model having two regions of localized strong radiation separated spatially by about 110 km. Assuming the 1906 epicenter determined by Bolt (1968), this corresponds with a large asperity (on the order of the Loma Prieta earthquake) in the Golden Gate/San Francisco region and one about three times larger located northwest along strike between Point Reyes and Fort Ross. This model implies that much of the 1906 rupture zone may have occurred with relatively little 10-20 sec radiation. Consideration of the amplitude and frequency content of the 1906 teleseismic data allowed us to estimate the scale length of the largest asperity to be less than about 40 km. With rough constraints on the largest asperity (size and magnitude) we produced a suite of estimated synthetic ground velocities assuming a slip distribution similar to that of the Loma Prieta earthquake but with three times as much slip. For purposes of comparison with the recent, abundant Loma Prieta strong motion data set, we ``moved'' the largest 1906 asperity into Loma Prieta region. Peak ground velocity amplitudes are substantially greater than those recorded during the Loma Prieta earthquake, and are comparable to those predicted by the attenuation relationship of Joyner and Boore (1988) for a magnitude Mw=7.7 earthquake.
The great 1906 San Francisco earthquake began an era in earthquake seismology. Following this earthquake, direct observations of surface displacement combined with the analysis of the surrounding crustal deformation led Reid (1910) to formulate the elastic rebound theory.
Although much has been learned from the numerous studies of the 1906 earthquake, a systematic analysis of the recorded teleseismic body and surface waveforms has not been made. Yet, the seismic recordings of the 1906 earthquake have been well preserved in the Atlas of the 1908 Carnegie Report by the State Earthquake Investigation Commission (Lawson, 1908), hereafter referred to as the Atlas or the Report. It is the authoritative reference and summary of the 1906 earthquake, including geological observations, the effects of ground shaking and all the data collected following the earthquake. In this study, we revisit the waveform data set contained in the Atlas and analyze the data in the context of modern source analysis.
The need to understand the ground motion hazard potential from earthquakes in the San Francisco area has been re-kindled by the occurrence of and damage from the 1989 Loma Prieta earthquake. The Loma Prieta event has provided a valuable strong motion data set for analysis of source complexity and ground motion damage from a magnitude 7 earthquake. Unfortunately, local strong ground motion data from the (much larger) 1906 earthquake was limited to one off-scale, partial recording on the Ewing three-component seismograph at Mt. Hamilton (Boore, 1977). Few strong motion recordings have been made from any large strike-slip earthquakes. However, it is possible to obtain source information relevant to understanding the local strong motions through analysis of the teleseismic data.
In a separate study of the Loma Prieta earthquake, Wald et al. (1991) inverted the broadband teleseismic and local strong motion to determine the temporal and spatial distribution of slip. Separate inversions of the teleseismic data (periods 3-30 sec) and strong motion data (periods 1-5 sec) resulted in similar rupture models. Hence the broadband teleseismic data has the capability of providing important constraints on the nature of the strong motions at long periods, independent of the strong motion recordings. In the study that follows, we apply this insight to the 1906 earthquake, though clearly the quality and bandwidth of the historic data are not as impressive as the modern digital, broadband data.
Our study focuses on several important unresolved issues relevant to the 1906 rupture. Was the 1906 rupture complex or were there large portions of the fault where rupture was fairly uniform? What was the nature and location of fault asperities? As we will show, the body waveforms are fairly simple considering the rupture duration expected for such a large rupture length (at least 300, and likely 430 km). Did the Loma Prieta section of the fault have a dip-slip component? The geodetic study of Segall and Lisowski (1990) requires a few meters of strike-slip motion for 1906 along the Loma Prieta segment of the fault, but their data does not rule out a thrust component comparable to the Loma Prieta earthquake at greater depths. Is there evidence for a dip-slip component in this or other portions of the fault? We address these issues in this study.
Processing and interpreting the turn-of-the-century seismic data recorded presented many challenges. However, we believe that the historic data are valuable in spite of their limitations, and thus, it is desirable to try and obtain as much information from them as possible considering the importance of the 1906 San Francisco earthquake. Hence, we have revisited the data available for the 1906 earthquake in an effort to place constraints on the nature of that rupture, relate the radiated seismic energy to fault breakage and geodetic offset measurements, and to determine its relationship to the Loma Prieta rupture.
Although the records of the 1906 earthquake alone may be insufficient to resolve the above questions, the use of records from the Loma Prieta, Morgan Hill and Coyote Lake earthquakes first as calibration events, and then as empirical Green's functions assists in extracting important information from this unique data set. The analysis of the teleseismic data prove useful in answering questions about fault rupture style on the San Andreas Fault and asperity positions in addition to allowing an estimation of strong ground motions likely experienced during the 1906 earthquake.
Alternatively, the strong shaking along the extension of the northwest terminus of a rupture propagating over 200 km in that direction would be expected from the effects of source directivity. Likewise, aftershocks commonly occur well off the end of the rupture zone (i.e., the 1992 Landers earthquake) and thus do not necessarily reflect the true source dimension. Concerning the geodetic evidence for large 1906 offsets offshore, the data of Thatcher and Lisowski (1987a) spanned a very long duration from about 1880-1940 and were of course limited to a one-sided, onshore network well east of the rupture. Therefore, their resolution in not good, and any displacement observed was not necessarily coseismic. There is no clear documented evidence for tectonic surface rupture associated with the 1906 earthquakes at the northernmost end of the assumed rupture, nor have any paleo-earthquakes been associated with the San Andreas north of Point Arena (D. Merrits, personal communication, 1991). Further, McLaughlin et al. (1979) discuss adularia veins (dated older than 10 million yrs BP) that cross the terraine boundary at Point Delgada. According to McLaughlin et al. (1979) these northeast striking veins, are crossed with a steeply dipping northwest-striking fault that many workers regard as the on-land extension of the San Andreas Fault. However, the mineralization and cross-cutting relation of the faults, which show little or no offset, indicate that no significant motion has occurred along the purported San Andreas Fault trace since late middle Miocene time. Lastly, the commonly assumed connection of the San Andreas Fault from Point Arena to Point Delgada, requires a bend in the San Andrea strike more significant (> 20 degrees) than anywhere else along the northern portion of the fault. It might be expected to behave as a source of high frequency radiation during a rupture that traversed such a geometric obstacle. There is little significant evidence for radiation from this section of the fault in the teleseismic recordings. The shorter (300 km) rupture length is more consistent with effective rupture length of 240 km determined by Ben-Menahem (1978) for this earthquake based on surface wave analysis. This is not to suggest that the rupture did not continue to offshore, but rather to point out that any conclusion on this issue is not without question.
In order to model this event, we divided the rupture length into three segments: the northwest, central and southeast portions of the full rupture. The arrows on Figure 1 depict the boundaries between these segments. Note that there is a significant change in strike between the segments going from N15 degrees W in the northeast to N35 degrees W in the central section to N50 degrees W in the southeast. In the central portion of the rupture, surface offset averaged nearly 4 meters from south of San Francisco to Point Arena where it heads offshore. In the southeastern section, the surface offset is difficult to quantify and is much smaller than to the northwest. The historical data provides no unequivocal estimates of surface slip, though offset in Wright's tunnel amounts to 1 to 1 1/2 meters and is considered one of the more reliable measurements (Prentice and Schwartz, 1991). The geodetic data require the slip at depth to be about 2 to 3 meters from San Juan Bautista through the Loma Prieta section and between about 5 and 7 meters along the central segment (Thatcher, 1975).
Note that within the narrow range of azimuths from which the 1906 Ms determination was made (20 degrees to 90 degrees), the other events have very large Ms values and would provide a biased estimate of the average Ms value. Using only magnitude values within this azimuthal range yields an Ms=7.4 for the 1989 Loma Prieta earthquake, while the computed value should be 7.0. As a side note, for the individual station Ms values published in the PDE's and shown in Figure 3, the average Loma Prieta Ms is 7.0, not 7.1 as commonly accepted. Similarly, the 1979 Imperial Valley Ms value of 6.9 was determined largely from European stations, yielding a biased value. For azimuths limited from 20 degrees to 90 degrees, Ms would be 7.1. Also note that for these two events, the moment magnitudes Mw computed from the seismic moments determined from waveform modeling are significantly smaller than Ms. For the Loma Prieta earthquake, Mw=6.9 (Wald et al. (1991) and Mw=6.4 for the Imperial Valley event (Hartzell and Heaton, 1983). Since for most events in this magnitude range Ms is approximately the same as Mw, the above disparity between Ms and Mw for these two events suggests that the Ms values for these two events are overestimated.
We found this azimuthal trend holds true for all other moderate to large California earthquakes (with the exception of the 1980 Ms=8.0 Eureka event) and is thus likely to be independent of focal mechanism. Loma Prieta has a good distribution of stations and only a slight azimuthal bias, and therefore, only a 0.1 unit difference between Ms and Mw. Imperial Valley has a considerable azimuthal bias and consequently shows a 0.5 unit difference between Ms and Mw.
Finally, the 1906 Ms determination has both a severe azimuthal bias and in addition is further biased by the use of undamped instruments as suggested by the work of Abe and Noguchi (1983). They recognized that Ms determinations during the period from 1904-1906 were 0.5 magnitude units too large. They attributed this bias to the combined use of damped and undamped seismographs (undamped were slowly phased out). Abe and Noguchi (1983) used (undamped) Milne instrument recordings with a correction for damping and obtained Ms = 7.8 for the San Francisco earthquake. At the time, Milne instruments had a better worldwide (hence azimuthal) coverage than damped instruments for 1906. Most Ms magnitudes based on damped instruments relied heavily on European stations which clearly show a path bias for events from California (Gutenberg, 1955).
An Ms value of 7 3/4 is consistent with the Mw=7.7 estimate of Thatcher (1975) based on amplitudes of 50-100 sec period surface waves at (stations ZIE, UPP and GOT). It is also in agreement with the geodetic data which gave an Mw=7.7 (Thatcher and Lisowski, 1987a) from their estimated moment of 5x10^27 dyne-cm. Ben-Menahem (1978) found the seismic potency to be 25,000 m-km^2, based on from modeling 50-100 sec surface waves. Using the same average rigidity, mu = 3.0 x 10^11 dyne/cm^2, as Thatcher (1975) this implies a seismic moment of 7.5x10^27 dyne-cm (Mw=7.9).
The implication of the lower Ms=7 3/4 is very important, in that the moment magnitude equivalent of Ms=7 3/4 requires an average slip based on the estimated rupture area on the order of several meters, compatible with surface and geodetic observations. A moment magnitude of 8 1/4 requires an average of about 15 m over the entire rupture length, even assuming rupture along the maximum estimated length (450 km) and a conservatively large average width of 15 km. This is much larger than the geodetic and surface offset observations allow.
The waveforms were scanned and digitized, and care was taken to remove the instrument pen arc and to preserve absolute timing. In addition to the 1906 San Francisco data, analogue recordings of more recent events were digitized from long-period World-Wide Standardized Seismic Network (WWSSN) stations to be used for calibration and empirical Green's functions. Those data will be discussed in a later section.
epsilon = exp {pi h} / sqrt{1-h^2}
All values were contained in the Report, with the exception of the several damping constants given in Table 2 as .20. These values estimated to be near .20 and reasonable deviations from this value modify the waveforms only slightly; the conclusions obtained in this study do not rely on the few stations with unknown damping constants. For the purpose of this study, we removed the mechanical instrument response and convolved in the WWSSN long period response (with a gain of 1500) to facilitate comparisons with the recent calibration events. Therefore the waveforms shown, unless otherwise stated, are as if recorded on a WWSSN long period instrument and amplitudes are given in millimeters. A comparison of the mechanical instrument responses used here with that of the WWSSN long-period instrument is shown in Helmberger et al., 1992.
Remarkably, the same instrument that recorded the 1906 earthquake at G\"ottingen, Germany recorded the 1989 Loma Prieta earthquake (Mw=6.9). Although the instrument constants were given for 1906 in the Report and were available for 1989, they were nearly the same as in 1906, with a slight change in the To, the natural period of the pendulum. Comparison of the two earthquake recordings is shown in Figure 6 The travel times are shown for bodywave phases using Jeffreys-Bullen (1958) travel times and assuming the epicentral parameters for the 1906 earthquake of Bolt (1968). Note the changes in the vertical scale and the difference in the noise levels between the two events; only the larger arrivals are successfully retrieved by digitizing the analogue records for the Loma Prieta event. The S waves are distinctly different. The Loma Prieta S waveform is short in duration and is indicative of an oblique mechanism while the San Francisco S wave has a much longer duration and an amplitude on average nearly 5 times larger. Observing the Loma Prieta S wave on this instrument well above the noise level indicates that we should expect to see many subevents for 1906 on such an instrument if the San Francisco earthquake was comprised of many Loma Prieta style subevents.
Figure 7 shows the north and east components for station GOT after instrument normalization and convolution with the WWSSN long-period response. Again, expected body wave phase arrival times are given. The start time labels refer to seconds after the origin time. There is a close correspondence of observed and predicted arrival times. Figure 8 shows the data from station UPP with a similar format. Both stations show a complicated S wavetrain indicative of complex faulting.
Figure 9 displays the radial component of motion recorded at San Jose, Puerto Rico for both the 1906 San Francisco (top) and 1984 Morgan Hill (bottom) earthquakes. Note that the dominant S wave arrival is very similar in character, even in the overall frequency content. However, the main 1906 S phase is delayed relative to the the Morgan Hill S wave even though the P wave is nearly aligned. This is explained in a later section and is due to source finiteness and complexity for the 1906 earthquake. The amplitude ratio of the 1906 S wave compared to that of the Morgan Hill earthquake is nearly a factor of 35.
The complete set of S teleseismic body waves deemed usable for this study are shown in Figure 10. The vertical arrows indicate the predicted S arrival times. The locations of these stations on SH and SV focal spheres for a vertical strike-slip fault striking with the azimuth along the central portion of the 1906 rupture zone (145 degrees) are shown in Figure 11. It is quite apparent that there are limitations with the 1906 data set. The body wave information is predominantly direct S waves and multiples ( SS and SSS). There is only a single vertical component Wiechert instrument (at G\"ottingen). It has a good P wave which can be compared with those from other large strike-slip events, but that is the only teleseismic vertical recording. Hence, we are basically limited to shear bodywaves. To compound this, the European stations, for which we have highest quality Wiechert recordings, are nearly SH nodal (Fig. 11). Unfortunately the SV waves are noticeably contaminated by shear-coupled PL waves ( SPL) which can often obscure the direct S waveforms on teleseismic seismograms (Baag and Langston, 1985). In order to model these waveforms for the purpose of source determination, it is necessary to address the effects of SPL contamination.
An examination of the Morgan Hill and Coyote Lake shear arrivals demonstrates the importance of receiver complications and SPL waves. The source mechanisms are very similar, although the Coyote Lake geometry shows a slight non-vertical dip (Fig. 1). Hence, we expect the waveforms to be quite compatible. Figure 12 shows the recorded and synthetic SH and SV waveforms at Uppsala, Sweden for both events displaying similarity of the waveforms. Observe that the amplitudes for these recordings are very small (less than 1 mm on the original paper records), yet the scanning/digitizing system we employ can recover the details remarkably well. The waveform similarity suggests that these magnitude 6 events can be effectively used as Green's functions for a much larger event. They differ only in amplitude, the ratio reflecting the moment ratio of Morgan Hill with respect to Coyote Lake (between 3.5 to 4.5).
Synthetic waveforms were produced for the Morgan Hill earthquake using the finite fault slip distribution of Hartzell and Heaton (1986); for the Coyote Lake simulations the source model of Liu and Helmberger (1983) was employed. As can be seen in the synthetic waveforms in Figure 12, the source contribution to the waveform complexity is negligible when viewed through the long-period WWSSN response (peaked at 15 sec period) since the entire duration of either event is less than 7 sec. The synthetic waveforms predict only the simple first S wave arrival, though the observations indicate the arrival of ScS, approximately 26 sec after the direct S wave arrival, as indicated with arrows. Theoretically, ScS should be less than half the size of S. It should have the same sign as direct SH and opposite to that of direct SV assuming a strike-slip orientation. These features are not obvious in these observed waveforms nor at other European stations. Thus, this complexity in the S waves in not easily modelled. The large, later arrivals on the SV component is composed of SPL energy. In order to investigate the later part of the shear wave train for the 1906 records, it is critical that we include these later contributions. Otherwise, we may not be able to attribute later arrivals in the S wavetrain to complexities of the source rupture process. Fortunately, these arrivals can be effectively included with the use of these recordings as empirical Green's functions.
In a forward modeling sense, we determine the best locations and amplitudes for subevents along the trend of the San Andreas fault in order to fit the recorded 1906 teleseismic waveforms and amplitudes. We use approximately 200 sec of the Morgan Hill S wave records as empirical Green's functions. By assuming a constant rupture velocity Vr of 2.7 km/sec, we compute the delay at each station, Delta ti, for a number of subevent positions along strike within the onshore rupture zone. For a distance D along strike from the epicenter,
Delta ti = D / Vr - D cos phio - phi) P
where Vr is the assumed rupture velocity, phio is the station azimuth, phi is the fault strike and P is the ray parameter. We then determined the best multiplicative amplitude scaling factor, N, to weight each subfault Green's function by in order to obtain the observed 1906 amplitudes.
Using the relationship equating seismic moment to fault slip, Mo = uAU , where u is the rigidity, A is the area and U is the average dislocation, we can estimate the average slip and the area over which it occurred for the Morgan Hill earthquake. Based on the strong motion inversion models of Hartzell and Heaton (1986) and Beroza and Spudich (1988), we assume a rupture approximately 12 km in length and 10 km deep having a seismic moment of 2.5 x 10^25 dyne-cm. Using u = 3.2 x 10^11 dyne/cm^2, based on their crustal models, we find the average slip to be about 65 cm. This allows us to relate the scale factor, N, for the number of Morgan Hill Green's functions to the approximate slip on the fault we allow it to represent.
Initially, we computed the teleseismic body wave signal based on the geodetic slip model of Thatcher (1975). Using the above conversion from a single Morgan Hill Green's function to slip, we summed the appropriate number of Green's functions to approximate the geodetic slip model. The geodetic model of Thatcher (1975) is shown as a function of position along strike with filled triangles in the bottom portion of Figure 13. The observed surface offset, also from Thatcher (1975), is also shown with filled squares. Note that the distance corresponds to km from the epicenter south of San Francisco and increases along strike to the northwest. Atop Figure 13 is a schematic diagram of the fault slip model used to approximate the geodetic slip. The subfault weights correspond to the multiplicative weighting factor N. There are 28 subfaults, numbered from northwest to southeast beginning at Point Arena. The hypocenter, indicated with a star, is located in subfault 22. The area of each subfault corresponds to the effective rupture area of the Morgan Hill subevent. Note that we did not include a model for the offshore region (205-340 km) in our simulations. As described above, there is little evidence in the later part of the teleseismic records of substantial 5-20 energy release from this portion of the fault.
Figure 14 shows the observed 1906 S waves modeled with the corresponding S waves computed with the Morgan Hill empirical Green's function scaled to the geodetic slip. For each component, the top trace is the observation, the middle trace is the synthetic, and the third trace shows an overlay of the two for comparison, the synthetic being distinguished with a dashed line. The overall amplitudes of the synthetics for the geodetic model are about 50% of the observed amplitudes, suggesting the need for more intense slip variations. In general there is marginal agreement with the data for some features of the waveforms, though the timing of the largest arrival is poor and does not fit the data. Further, the synthetic traces often are longer period than the data.
Next, in a forward modeling sense, we determined the best simple, rupture model in order to satisfy the observation of the relatively small, initial phase at the S wave arrival time and the larger arrival 35-45 sec later seen in Figure 10. The best model found by trial-and-error came from a relatively simple summation consisting of two regions of strong radiation separated in time by an average of about 38 sec. The relative weighting factor N was determined to be about 14 for the hypocentral subfault and 30 for subfault 10. This corresponds to about 110 km of separation between the two major regions of strong radiation at these periods (about 5-20 sec), placing the largest between Point Reyes and Fort Ross.
In short, we see that the teleseismics can be explained by about 14 Morgan Hill events summed near the epicenter, a region where the amount of slip changes quite abruptly according to surface offset, and about 30 Morgan Hill events concentrated at about 110 km from the epicenter, where the geodetic and surface slip is near its greatest (Fig. 15) The synthetics from the empirical summation are shown in Figure 16 A good portion of the shear wave train is fit at most stations.
The result of the inversion, shown in Figure 17, is nearly that of the forward estimation also showing two main regions of radiation, though several more subfaults contribute to the solution. On the bottom of Figure 17 we show the corresponding slip values determined from the inversion (open circles), along with an estimate of the uncertainty in these values (error bars). The uncertainty in the subfault slip was estimated from the covariance of the model parameters due to a variance in the data (for details, see Hartzell and Iida, 1990 and Olson and Apsel, 1982); it does not address errors due to assumptions in the fault rupture model parameterization. The waveform fits are given in Figure 18. In a formal sense, the solution from the inversion has a slightly lower misfit to the data, but there are features in waveforms produced by the forward modeling which are more favorable.
As shown in the forward and inverse models, the arrival in the data corresponding to the largest subsource can be fit well with a very limited dimension along strike. In order to place constraints on the dimensions of the region of large source radiation near subfault 10, we performed a summation of empirical Green's functions lagged in space over various linear dimensions. We found that as the along strike length increase above about 40 km, the match of the details of the waveforms at the best modeled stations is degraded (Fig. 19). With an extended source dimension of 55 km, the higher frequency content of the data at station GOT, the most reliable station, is difficult to simulate.
In the previous section, we found that the amplitudes and frequency content of the teleseismic data for 1906 allowed us to roughly constrain the scale length of the largest asperity to be less than 40 km. Slightly larger dimensions are not ruled out, but for the purpose of this estimate of strong motions for the 1906 earthquake, we use a compact asperity size to produce relatively conservative strong motions predictions. Having a rough constraint on the largest asperity (size and magnitude) we produced synthetic ground velocities as follows. For purposes of comparison with the recent, abundant Loma Prieta strong motion data set, we ``moved'' the largest 1906 asperity into Loma Prieta region. In this way, we could compare our simulations to observations from a Mw=6.9 at the same distances and station geometries. We then took the Loma Prieta slip model of Wald et al. (1991) and by rotating the model fault to a vertical plane and constraining the dislocation to be pure right-lateral strike-slip, we approximated rupture along the San Andreas fault. The Loma Prieta rupture was bilateral, but we use a northwest propagating unilateral rupture to simulate the 1906 model determined from the teleseismic data.
To be consistent with the average depth of significant slip from other strong motion waveform inversions of California vertical strike-slip earthquakes (Hartzell and Heaton, 1983; Hartzell and Heaton, 1986; Beroza and Spudich, 1988; Wald et al., 1990) we needed to decrease the asperity depth relative to the Loma Prieta model. This was done by bringing the top of the fault to within 0.5 km of the surface and translating the slip (shown in Fig. 20, top) 5 km closer to the top of the fault than the Loma Prieta slip model.
To simulate the 1906 asperity, we spatially shifted and summed three Loma Prieta slip distributions (Fig. 20, bottom) to preserve the amplitude of slip determined from the forward empirical summation model keeping the dimension in line with the 35 km length used to best model the 1906 body waves. Ground motion velocity estimates were made with the finite fault ground motion techniques used in Wald et al. (1991), with synthetic Green's functions appropriate for the Loma Prieta region. The frequency bandwidth of the simulations is from 0.0 to 1.0 Hz.
Although many well studied earthquakes require very short slip durations (see Heaton, 1990), there have been no studies of strike-slip earthquakes of this magnitude with the strong motion recordings necessary to constrain the local slip duration. Heaton (1990) points out that the duration of slip for the 1985 Michoacan earthquake (Ms=8.5) was on the order of 5 sec as indicated from near-field displacements obtained from twice integrated accelerograms. However, the tectonic environment was that of subduction thrusting, and the fault aspect ratio was quite different from that of the 1906 earthquake. Consider that for a rupture length of 430 km and a fault width of 10-15 km, the aspect ratio for the 1906 rupture was between about 30-45 to 1, nearly a line source. For earthquakes in the tectonic regime more similar to the northern San Andreas Fault, the slip durations are observed to be very short. For example, recent eyewitness observations of ground rupture during the 1990 Philippines earthquake (Ms=7.8) suggest that the slip duration was less than about 1 sec (T. Nakata, personal communication, 1991), yet the displacement was 3-4 m. Further, Wald et al. (1991) found that the majority of slip during the Loma Prieta earthquake occurred in less than 1 sec over most of the fault plane and less than 2 sec everywhere. From these observations, we assumed a 4-sec rise time for the 1906 slip. However, the derivative of the actual slip function is not a simple triangle, rather a time expanded version of the Loma Prieta slip model determined by Wald et al. (1991). The Loma Prieta slip function has 3 time windows, each 0.7-sec triangles overlapping by 0.1 sec. On average, the first window contributes half the slip, and the second and third each contain 25% of the slip, but these values change slightly as a function of position on the fault. For the 1906 ground motion simulations, we carry through the spatial rise time variations determined for the Loma Prieta earthquake from the strong motion data, but use 3 time windows each 1.4 sec long for a total duration of 4.2 sec. We also tested the dependence on rise time by computing synthetic ground motions for longer and shorter total rise times.
Initially, we computed ground motions for the top model on Figure 20 to compare with the simulated ground motions (Wald et al., 1992) of the Loma Prieta earthquake. This simply allows us to compare the ground motions for a deep, oblique-slip event with that of vertical strike-slip. The comparison of peak ground velocities plotted as a function of distance is shown in Figure 21 The distance, r_o, is defined as in Joyner and Boore (1988) as the shortest distance (km) from the recording site to the vertical projection of the fault rupture on the surface of the earth. Solid circles denote the Loma Prieta simulations and the shaded circles represent the vertical strike-slip modified model results. The overall amplitudes are slightly higher for the vertical strike-slip case. Considering the source rupture model is identical in all other aspects, differences in the resulting ground motions can be attributed to the combined effects of change in rake and source depth.
In general, vertical strike-slip model predicts slightly larger velocities, especially on tangential components at near fault stations. The vertical components are slightly smaller due to the radiation pattern. Also plotted as a dashed line is the attenuation relationship of Joyner and Boore (1988) for peak ground velocity:
log y = a + b(M-6) + c(M-6)^2 + d log r + kr + s
for 5.0 < M < 7.7
where constants a=2.17, b=0.49, c=0.0, d=-1.0, k=-0.0026, s=0.17 and r = sqrt ( (ro)^2 + (h)^2 )
Results of the simulation of the 1906 main asperity compared with the simulation of the vertical strike-slip version of Loma Prieta are shown in Figure 22. The synthetic velocity and displacement waveforms are displayed in Figure 23 for a station adjacent to the fault trace. The peak ground velocity amplitudes are substantially greater than those recorded during the Loma Prieta earthquake, and are comparable to those predicted by Joyner and Boore (1988) for a Mw=7.7 earthquake. Again, the tangential components are dominant due to the along strike SH pulse from a vertical strike-slip rupture. Since the station distribution is fairly random, several stations are off the southeast end of the rupture and show fairly small ground motions. This is attributed to the lack of directivity at southeastern stations, and the fact that we do not add in the contributions from adjacent portions of the fault. Recall, we model only a small (40 km) portion of the entire 1906 rupture and not the entire rupture length, so our durations are much shorter than would be expected. Here we are more interested in the largest possible motions due to a magnitude 7 3/4 earthquake, rather than the average ground motions. Considering the large amount of slip known have occurred on adjacent segments, these contributions may be important, but would not significantly alter the estimation of the greatest contribution to the ground motions.
It appears that the Joyner and Boore (1988) curve is a fairly conservative estimate considering our data points represent the largest peak velocities expected from the greatest asperity. An overall average of stations along the length of the rupture would be considerably lower.
The locations of the two sources of strong 10-20 sec radiation is consistent with Boore's (1977) observation that the source of the main strong motions observed at Mt. Hamilton was at least 75 km away. This corresponds with the location of the first main asperity in our 1906 source model. The second, larger asperity certainly contributed later in the record, but was radiated from a much greater distance, nearly 200 km away.
By comparing the slip model derived from the inversion (Fig. 17, top) with the surface offset and the modeled slip from the geodetic data Fig. 17, bottom), we found a general correspondence between the hypocentral asperity and a gradient in slip in the amount of slip in the region. The larger asperity between Point Reyes and Fort Ross corresponds roughly with the region of largest surface offset and geodetic slip. Note that there may really be more variation in the static slip than suggested by the geodetic models. Thatcher (1975) assumed a constant slip with depth and a fixed depth of rupture along the fault. If the actual depth of rupture varied, or the functional form of the slip with depth is similar to other strike-slip earthquakes in California, that is a peak in slip at 8-9 km and tapering off both shallower and deeper, the solution to the geodetic displacements would be different.
Another factor which is difficult to evaluate is the effect of rupture dynamics on the teleseismic arrivals. Abrupt accelerations of the rupture front can result in starting and stopping phases on the teleseismic records. In effect, a model with uniform slip, tapered to zero at each end can produce complex records if the rupture front is inhibited and then allowed to re-accelerate a number of times. If rupture along the central portion of the 1906 rupture zone had a complex rupture progression, the total slip estimated in our model could be reduced. Likewise, a model with a relatively homogeneous slip and a constant rupture velocity might be difficult to recognize teleseismically due to uniformity of the radiation. It is likely that the offshore segment of the fault, ruptured in this fashion.
Simulated ground velocities were produced from our estimate of the largest asperity. In so doing, we have placed a few ``data'' points on the attenuation curve of Joyner and Boore (1988) which has few observational constraints for these close in distances and this large magnitude. Unfortunately, it appears that the distribution of Modified Mercalli intensities shown in Figure 2 provides little information about variations in the nature of the rupture as a function of position along strike, making it difficult to relate our model to the ground motions and damage experienced in 1906. Rather, the Modified Mercalli map shows a fairly uniform along strike distribution. This observation is also apparent in the full-sized isoseismal map (Rossi-Forel scale) given in the Atlas. As carefully noted by Lawson (1908), the most striking feature in the apparent intensity map is the correlation between the regions of strong shaking and the underlying geological conditions, particularly with river and sedimentary basins and reclaimed and tidal marsh lands. With the exception of the gradual decrease in intensity with increasing distance to the fault trace, this correlation dominates the variations in the intensities. We found no obvious independent constraints (i.e., density of topped trees or eyewitness accounts) on the variations in shaking intensity along strike.
It should be noted that there is no significant change in the nature of the surface expression of the San Andreas Fault in the region of maximum slip and radiation (between Point Reyes and Fort Ross) and, in fact, the fault tends to be simpler than along other portions of the San Andreas Fault. Hence, there is no correspondence between the largest asperity (or greatest slip) and surface fault trace complexity for the 1906 earthquake. There is, however, a substantial right-stepping (releasing) bend just north of the epicentral asperity west of the Golden Gate. This step-over is recognizable but not impressive on the scale of Figure 1.
We have not addressed the issue of dip-slip components in the vicinity of the Loma Prieta earthquake. From our modeling, we do not consider that the bodywave data requires a significant component of dip-slip, though it is not clear that the historic seismic data can fully resolve this issue. Recent comparison of the horizontal displacements accompanying the 1906 San Francisco and the 1989 Loma Prieta earthquakes indicate that although the Loma Prieta event exhibited nearly equal strike- and dip-slip components of faulting, the 1906 data is consistent with strike-slip on a vertical plane (Segall and Lisowski, 1990). Likewise, although rupture along the northernmost 140 km of the San Andreas (offshore) is not observed in the teleseismic bodywave arrivals, based on the historical data alone, we do have the resolving power to rule it out. Most likely, though, any slip along that portion of the fault was also relatively uniform and of low stress-drop.
Considering the enormous rupture length of 1906 compared with other large ruptures, more complexity in the waveforms might be expected. The above observations suggest relatively uniform slip on lengthy portions of the northern San Andreas fault occurred during the 1906 rupture, and not 10 end-to-end ``Loma Prieta'' style ruptures. Since we can recognize the Loma Prieta rupture clearly on the Wiechert instruments at UPP and GOT, such a complex rupture would likely be recognizable on the historical records.
In contrast to the 1906 San Francisco earthquake, other large, continental strike-slip earthquakes have had considerably more rupture complexity. For example, comparison of WWSSN shear-wave amplitudes and waveforms for the 1976 Guatemala earthquake (Ms=7.5) shows that the 1906 amplitudes are nearly three times larger, yet the waveforms are clearly less complicated. Based on the long period WWSSN bodywaves, Kikuchi and Kanamori (1991) and Young et al. (1989) associated many large subevents during the Guatemalan earthquake with later arrivals in the teleseismic data. As with our model of the 1906 rupture, for the Guatemalan event, the region of greatest surface slip coincides roughly with the largest subevent of the Kikuchi and Kanamori (1991) rupture model. Though fairly continuous with few splays, the 1976 rupture trace follows an arcuate route with a nearly 35 degree chttp://www.scecdc.scec.orgpture length (about 240 km), perhaps contributing to the relative complexity and numerous identifiable subevents.
We have suggested that portions of the 1906 rupture occurred such that they did not produce large signals in the teleseismic recordings in a bandwidth of 5-20 sec. This does not necessarily imply that those portions of the rupture produced only relatively moderate high-frequency ground motions. In fact, this remains a pressing issue. Can a smooth rupture, as observed at 15 sec periods, be produced by a uniform, but short duration slip which is capable of radiating very damaging near-field motions? Alternatively, does the complexity of the 1976 Guatemala teleseismic recordings (Kikuchi and Kanamori, 1991) require that the local ground motions were comparably complex and damaging? Current data collections are not sufficient for fully addressing these questions; it will be interesting to independently analyze data sets from future large strike-slip earthquakes that are recorded at both teleseismic and local distances.
Baag, C., and C. A. Langston (1985). Shear-coupled PL, Geophys. J. R. astr. Soc., 80, 363-385.
Ben-Menahem, A. (1978). Source mechanism of the 1906 San Francisco earthquake, Phys. Earth and Planet. Int. 17, 163-181.
Bent, A. L., D. V. Helmberger, R. J. Stead, and P. Ho-Liu (1989). Waveform modeling of the 1987 Superstition Hills earthquake, Bull. Seism. Soc. Am. 79, 500-514.
Beroza, G. C. and P. Spudich (1988). Linearized inversion for fault rupture behavior: application to the 1984 Morgan Hill, California, earthquake, Bull. Seism. Soc Am., 93, 6275-6296.
Bolt, B. A. (1968). The focus of the 1906 California earthquake, Bull. Seism. Soc. Am. 58, 457-471.
Boore, D. M. (1977). Strong motion recordings of the California earthquake of April 16, 1906, Bull. Seism. Soc. Am. 67, 561-576.
Ekstr\"om, G. (1984). Centroid-moment tensor solution for the April 24, 1984 Morgan Hill earthquake, in The 1984 Morgan Hill, California Earthquake, CDMG Special Publication 68.
Gutenberg, B. (1955). Magnitude determination for larger Kern County shocks, 1952; effects of station azimuth and calculation methods, in Earthquakes in Kern County, California during 1952, Cal. Div. Mines. Geol. Bull., 171, 171-176.
Hartzell, S. H. and T. H. Heaton (1983). Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California earthquake, Bull. Seismol. Soc Am., 73, 1553-1583.
Hartzell, S. H. and T. H. Heaton (1986). Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records, Bull. Seism. Soc Am., 76, 649-674.
Hartzell, S. H. and M. Iida (1990). Source complexity of the 1987 Whittier Narrows, California, Earthquake from the inversion of strong motion records, J. Geophys. Res. 95, 12,475-12,485.
Heaton, T. H. (1990). Evidence for and implications of self-healing pulses of slip in earthquake rupture, Phys. Earth Planet. Inter., 64, 1-20.
Helmberger, D. V., P. G. Somerville, and E. Garnero (1992). The location and mechanism of the Lompoc, California earthquake of 4 November, 1927, Bull. Seism. Soc Am., 82, 1678-1709.
Jeffreys, H., and K. E. Bullen (1958). Seismological Tables, Office of the British Association, Burlington House, London.
Jennings, P. C. and H. Kanamori (1979). Determination of local magnitude, Ml, from seismoscope records, Bull. Seism. Soc. Am., 69, 1267-1288.
Joyner, W. B. and D. M. Boore (1988). Measuremnt, chararacterization, and Prediction of strong ground motion, In: Proceedings of the Earthquake Engineering and Soil Dynamics II Conference, American Society of Civil Engineers, Geotechnical Special Publication No. 20, 43-102. Kanamori, H. (1988). in Lee, W. H. K., Meyers, Importance of historical seismograms for geophysical research, H. and K. Shimazaki, eds., Historical seismograms and earthquakes of the world, San Diego, Calif., Academic Press, p.16-36.
Kikuchi, M. and H. Kanamori (1991). Inversion of Complex Body Waves - III, Bull. Seism. Soc. Am., 81, 2335-235.
Lawson, A. C., chairman (1908). The California earthquake of April 18, 1906: Rep. State Earthquake Invest. Comm. Vols. I and II; Atlas, Carnegie Inst. Washington, D. C.
Liu, H. and D. V. Helmberger (1983). The near-source ground motion of the August, 1979 Coyote Lake, California, earthquake, Bull. Seism. Soc Am., 73, 201-218.
McLaughlin, R. J, D. H. Sorg, J. L. Morton, J. N. Batchelder, R. A Leveque, C. Heropoulus, H. N. Ohlin, and M. B. Norman (1979). EOS, 60, p. 883.
Olson, A. and R. Apsel, Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake, Bull. Seism. Soc. Am. 72, 1969-2001.
Prentice, C. S. and D. P. Schwartz (1991). Re-evalation of 1906 surface faulting, geomorphic expression, and seismic hazard along the San Andreas fault in the southern Santa Cruz Mountains, Bull. Seism. Soc Am., 81, 1424-1479.
Reid, H. F. (1910). The Mechanics of the Earthquake, Vol. II of The California Earthquake of April 18, 1906, Carnegie Institution of Washington (reprinted 1969), 192 pp.
Richter, C. F. (1958). Elementary Seismology, W. H. Freeman and Company, San Francisco and London, 768 pp.
Segall, P. and M. Lisowski (1990). Comparison of surface displacements in the 1906 San Francisco and 1989 Loma Prieta earthquakes, Science 250, 1241-1244.
Thatcher, W. and M. Lisowski (1987a). 1906 earthquake slip on the San Andreas fault in offshore northwestern California, EOS, 68, p. 1507
Thatcher, W. and M. Lisowski (1987b). Long-term seismic potential of the San Andreas fault southeast of San Francisco, California, J. Geophys. Res. 92, 4771-4784.
Thatcher, W. (1975). Strain accumulation and release mechanism of the 1906 San Francisco earthquake, J. Geophys. Res. 80, 4862-4872.
Thatcher, W. (1975). Strain accumulation on the northern San Andreas fault zone since 1906, J. Geophys. Res. 80, 4873-4880.
Toppozada, T. R. and D. L. Parke (1982). Areas damaged by California earthquakes, 1900-1949, California Division of Mines and Geology, Open-File Rept. 82-17.
Wald, D. J., S. H. Hartzell and D. V. Helmberger (1990). Rupture process of the 1987 Superstition Hills earthquake from the inversion of strong motion data, Bull. Seism. Soc. Am., 80, 1079-1098.
Wald, D. J., T. H. Heaton and D. V. Helmberger (1991). Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong motion and broadband teleseismic data, Bull. Seism. Soc. Am.,, 81 1540-1572.
Wald, D. J., T. H. Heaton and D. V. Helmberger, (1992). Strong Motion and Broadband Teleseismic Analysis of the 1989 Loma Prieta Earthquake for Rupture Process and Hazards Assessment, submitted to U.S.G.S. Professional Paper, January, 1992.
Young, C. J., T. Lay and C. S. Lynnes (1989). Rupture of the 4 February 1976 Guatemalan earthquake, Bull. Seism. Soc. Am., 79, 670-689.