Determination of Rupture Duration and Stress Drop for Earthquakes in Southern California by Arthur Frankel and Hiroo Kanamori

A simple technique is developed for determining the rupture duration and stress drop of earthquakes between magnitudes 3.5 and 4.0 using the time between the P-wave onset and the first zero crossing (71/=) on seismograms from local seismic networks. This method is applied to 10 main shocks in southern California to investigate regional variations in stress drop. The initial pulse widths of 65 foreshocks or aftershocks of these events were measured. Values of ~t/2 for small earthquakes below about magnitude 2.2 are generally observed to remain constant with decreasing magnitude in four sequences studied. The relative pulse width of a particular main shock (M ~ 3.5) at a given station is found to be correlated with the relative pulse width of its aftershocks recorded at that station. These observations are interpreted to signify that the waveforms of these small events (M ~ 2.2) are essentially the impulse response of the path between the source and receiver. Values of rv2 determined from small foreshocks and aftershocks are, therefore, subtracted (in effect deconvolved) from those of each main shock to obtain an estimate of the rupture duration of the main shock which is corrected for path effects. Significant variations in rupture duration and stress drop are observed for the main shocks studied. Aftershock locations and azimuthal variations in T1/2 both indicate that the rupture zone of one earthquake expanded unilaterally. A factor of 10 variation in stress drop is calculated for two adjacent events of similar seismic moments occurring 1 hr apart on the San Jacinto fault system. The first event in this pair had the highest stress drop of the events studied (860 bars) and was followed within 8 months by a magnitude 5.5 earthquake 2 km away. INTRODUCTION The measurement of seismic stress drop constitutes one of the few methods for constraining estimates of the tectonic stress at depth. Although earthquake stress drops cannot specify the absolute level of tectonic stress, they represent a lower bound. Areas containing earthquakes with relatively high stress drops are presumably regions of comparatively large tectonic stress. The determination of spatial and temporal variations in stress drop would improve our understanding of the accumulation of tectonic stress and may have application to earthquake prediction. The seismic stress drop is one of the parameters which determines the level of accelerations produced by an earthquake, and regional variations in stress drop could have importance to seismic risk analysis. This paper presents a simple technique for estimating the rupture duration and hence stress drop of earthquakes between about magnitudes 3.5 and 4.0 using seismograms from local seismic networks. Routine determination of stress drop for the large numbers of earthquakes recorded by short-period networks (]co ~ 1 Hz) could provide substantial information on the temporal and spatial variations of the tectonic stress field. We measure the time between the P-wave onset and the first zero crossing directly from the seismogram (denoted as rl/2) to estimate the rupture duration of earthquakes greater than magnitude 3.4 in southern California. The seismograms were collected by the array of short-period seismometers operated in southern California 1527 1528 ARTHUR FRANKEL AND HIRO0 KANAMORI jointly by the U.S. Geological Survey (USGS) and the California Institute of Technology (CIT). The initial pulse width on the seismogram is a function of the rupture duration, the instrumental response, and the broadening caused by the apparent attentuation of the path. The term "apparent attenuation" refers to the loss of high-frequency energy relative to low-frequency energy by either intrinsic dissipation in the crustal rocks or by scattering from heterogeneities. The essential problem in stress drop determination that we address in this paper is the effect of the source-receiver path on the initial pulse width of the seismogram. We seek to compare stress drop estimates from earthquakes in a variety of tectonic regimes, and we require a simple method that corrects for the propagation effects between each source-station pair. This task is also complicated by the fact that the network stations are usually separated from the earthquakes by a distance of several source depths. For such stations, the first arrival may not represent the direct wave but may consist of the interference of diving waves refracted by positive velocity gradients in the crust (see Cerven~, 1966). The influence of apparent attenuation on high-frequency seismic energy (f > 5 Hz) is poorly understood, and its severity is debated. Recent evidence implies that large amounts of apparent attenuation may occur at shallow depths (0 to 3 km) beneath the receiving sites, a process referred to as the site response. This site response can produce corner frequencies in displacement spectra and pulse durations in the waveforms of microearthquakes which are unrelated to source duration. Frankel (1982) reported corner frequencies for microearthquakes in the northeastern Caribbean that were characteristic of the receiving sites. Hanks (1982) observed that the acceleration spectra derived from strong motion records rapidly fall off above a certain frequency, which he denoted as fmax. He noted that fmax was related to site characteristics for recordings of aftershocks in Oroville, California. Andrews (1982) reported spectral differences dependent on receiver site for earthquakes in Mammoth Lakes. These studies suggest that it is necessary to correct for the site response before using spectra or pulse widths to estimate the source dimensions of small earthquakes. In the first part of this paper, we summarize our observations on the dependence of initial pulse width on magnitude in three main shock-aftershock sequences and one swarm in southern California. We find that T1/2 usually decreases to a minimum value that remains constant as the magnitude of the earthquake decreases below about 2.2. These minimum pulse widths differ between stations at comparable distances from each of these sequences. We interpret these minimum pulse widths as being produced solely by propagation effects. One of the key points we wish to demonstrate is that the source duration can only be determined for earthquakes whose rupture times are sufficiently long to be separated from the pulse broadening caused by the path. Therefore, we limit our investigation to the source parameters of earthquakes of magnitude 3.5 and greater. Unfortunately, the high gain and limited dynamic range of the seismic network cause the seismograms of such events to be severely clipped. This clipping occurs during the modulation of the signal at the seismometer site before it is transmitted by radio or telephone line to the central recording site. Although the seismometer accurately tracks the ground motion of these larger events, the voltage controlled oscillator (VCO) has a limited range of frequency modulation. Ellis and Lindh (1976) demonstrated that the zero crossings of clipped seismograms from the USGS network instrumentation accurately reflect the zero crossings of the unclipped seismometer output. O'Neill and Healy (1973) have used z~/2 from clipped records DETERMINATION OF RUPTURE DURATION AND STRESS DROP 1529 of local network stations to estimate the source parameters of earthquakes in central California and Colorado. In this paper, we use the waveforms of small aftershocks and foreshocks (M < 2.4) as empirical Green's functions to correct for the effects of the path and the instrument on the initial pulse width of the larger events (3.5 < M < 4.0) studied. We then estimate the rupture duration and stress drop of 10 main shocks in southern California. We felt that the zero crossings of events greater than magnitude 4.0 may represent subevents and that such earthquakes would not be appropriate for this study. The technique presented in this paper reveals that significant differences in stress drop occur in southern California for events in the magnitude range studied. DATA We measured the rl/2's for II main shocks (M _-> 3.5) and 65 smaller events that accompanied them. The pertinent data are listed in Tables 1 and 2. The locations of the main shocks and stations used in this study are shown in Figure I. We limited our study to stations within 70 km of the earthquakes, z,/2 was measured only if the foreshock/aftershock waveform had the same first motion as the main shock. Only waveforms with relatively impulsive P waves were analyzed. Each station of the southern California network (SCARLET) consists of a vertical seismometer with a l-Hz natural period. At the frequencies of interest to this study (>5 Hz), the output of the seismometer is flat to velocity. Figure 2 shows the response of the system (standard USGS configuration) to an impulse of ground displacement determined from the response characteristics given by Archambeau (1979). The value of rl/2 measured from the seismogram is, to within 0.012 sec, equivalent to the zi/2 of the ground velocity. At the central recording site, the signals are recorded on analog magnetic tape and on digital tape when an event detector is triggered (see Johnson, 1979). The digital system samples the waveforms at 50 samples/sec. The determination of the relative magnitude of these events was complicated by the limited dynamic range of the network. For the events less than magnitude 3, we measured the peak-to-peak amplitude of the first cycle of the P wave from one to three unc]ipped stations for each event. The relative magnitude of each event was calculated directly from the log of the ratio of the P-wave amplitudes averaged over these stations. For the events accompanying main shock number 11, the magnitudes were estimated from values of the maximum S-wave amplitudes. Magnitudes listed for the main shocks represent the local magnitudes determined from the maximum ~mplitude of the S wave recorded on Wood-Anderson seismometers. A change in the instrumentation at the central recording site during late 1978 necessitated the use of seismograms played back from both the digital and analog tapes. The pulse widths of events prior to late 1978 (events 1 through 5 and their accompanying earthquakes) were read directly from playbacks of the digital recordings. In late 1978, antialiasing filters were installed at the recording site. This produces the impulse response shown in Figure 2 as the modified USGS configuration. These filters altered the signals that entered the digital recording system but were not applied to the signals recorded on analog tape. We found that the addition of the antialiasing filter severely distorts the zero crossings of the clipped seismograms. Therefore, we utilized playbacks from the analog tapes to measure the pulse widths of the main shocks after 1978. The measurement of rl/2 for the smaller events after 1978 presented another 1 5 3 0 ARTHUR FRANKEL AND HIROO KANAMORI