Time Functions Appropriate for Some Aftershocks of the Point Mugu, California Earthquake of February

Broad-band recordings of aftershocks of the Pt. Mugu earthquake at small epicentral distances provided an excellent opportunity to test source models for small earthquakes. Simple events recorded at nearly vertical incidence produced a single P-wave pulse of a duration of about 0.07 sec and a somewhat more complicated S wave with a slightly longer duration. Such events are consistent with a point dislocation source for which Q~ = 100 or for which there is directivity with the fault breaking downward. We attribute the more usual complexities of small earthquake records to multiple events, some of which we observed, layering effects combined with greater epicentral distances, and scattering. INTRODUCTION Aftershocks of the Point Mugu earthquake provided an opportunity to measure the local displacements at relatively small epicentral distances. Within a few hours of the main event, we positioned four broad-band three-component trailer units in the epicentral area. Of the dozen or so shocks recorded in the following 2 weeks, a few events were well recorded on all three components at each station. In this study, we will examine these seismograms in terms of recent source models. Small earthquakes recorded locally are generally quite complicated. That is, the P waves are rather emergent followed by larger and longer period S waves. The San Fernando aftershocks are typical examples as determined from a recent report of observations of the aftershocks by Molnar et al. (1974). Following the corner-frequency approach as applied by Molnar et al. (1974), one assumes that the first few seconds of motion represents the primary (P) radiations and the next few seconds represents the shear (S) contribution. On the average, a plot of the spectra generated from sections of time series of this type yields a lower corner frequency for the S-wave pulse than for the P-wave pulse. The above authors suggest a relatively simple circular dislocation model to explain this relative shift in corner frequencies. However, since the corresponding fault dimension is very small (usually less than 1 kin) and the source is assumed to radiate essentially simultaneously, one would expect to see two sharp pulses with the S being slightly longer period. Their model explains the spectra but fails to explain the sequential information and does not predict realistic looking synthetic seismograms. How does one explain such complicated looking seismograms ? Possible explanations are: (1) horizontal layers are producing wave-guide effects, (2) multiple events, (3) random scattering produced by irregularities in the medium, or perhaps all three. For the case of shallow events, it is easy to show synthetically that shear-dominated surface waves trapped in the soft material near the Earth's surface can be "quite important. For instance, Love waves can be larger than the direct arrival at ratios of source depth to epicentral distances greater than four, Helmberger (1974). For the case of deep events, at ratios less than one, it becomes much more difficult to explain complicated records in terms of propagational effects and one must resort to multiple events or perhaps scattering at the higher frequencies. 127 128 DAVID KING AND DONALD V. HELMBERGER SELECTED OBSERVATIONS AND DISCUSSION Since we are primarily interested in getting an accurate determination of time functions appropriate for small earthquakes, we chose to analyze in detail two simple events that were recorded at very small epicentral distances (see SYC in Figure 1). Some observations of these events are displayed in Figures 2 and 3. The locations and fault-plane solutions are taken from Cambell et al. (1973). These two events are quite deep as indicated by their ( S P ) times. However, their epicenters are not well known because of lack of control to the west, but they are probably good to within several kilometers. The relatively small P 3 4 ° I0' I &CAM 0 i 2 km 5 4 0 0 0 ' 119"05' ~":~:v';::h'i!~'~:;~:?:!':~::::':":)~':'::'c": ;!' %?~:: ~..~C..:....: : ~::..:. ,o Feb. 22, 1975 04h l6 rn~ %