Teleseismic Time Functions for Large, Shallow Subduction Zone Earthquakes

Broadband vertical P-wave records are analyzed from 63 of the largest shallow subduction zone earthquakes which have occurred in the circum-Pacific in the last 45 yr. Most of the records studied come from a common instrument, the Pasadena, California, Benioff 1-90 seismometer. Propagation and instrument effects are deconvolved from the P-wave records using a damped least-squares inversion to obtain the teleseismic source time function. The inversion has the additional constraint that the time function be positive everywhere. The period band over which the time functions are considered reliable is from 2.5 to 50 sec. Fourier displacement amplitude spectra computed for each of the 1-90 P-wave trains indicate spectral slopes measured between 2 and 50 sec of 00 -1° to o~ -=-=s with an average value of o~ -l's. These values assume an average attenuation of t* = 1.0. The seismic moments derived from the P-wave time functions compare well with other published values for earthquakes having moments smaller than 2.5 x 10 =8 dyne-cm (M,, = 8.2). Because the 1-90 seismometer has little response at very long periods, this technique underestimates the moments of the very largest events. The time functions are characterized using five parameters: (1) spectral slope between 2 and 50 sec; (2) roughness of the time function; (3) multiplicity of sources; (4) pulse widths of individual sources; and (5) overall signal duration. The 63 earthquakes studied come from 15 subduction zones with a wide range in the ages of subducted lithosphere, convergence rates, and maximum size of earthquakes. Comparing the time function parameters with age, rate, and M,, of the subduction zone does not yield obvious global trends. However, most of the subduction zones do behave characteristically and can be grouped accordingly. INTRODUCTION In terms of the details of fault rupture or source complexity, our knowledge of the very largest earthquakes is limited. Until very recently, most of what was known about major earthquakes consisted of estimates of their focal mechanism and moment. Although this information is of fundamental interest, it is desirable to know more about the spatial and temporal distribution of moment release. The very largest earthquakes have been shallow thrust events at convergent plate boundaries. In this paper, we present the results of a survey study of teleseismic source time functions for major shallow thrust earthquakes. Sixty-three of the largest shallow subduction zone earthquakes that have occurred in the circum-Pacific in the last 45 yr are studied. Earthquakes from 15 different subduction zones with very different ages of subducted lithosphere and plate convergence rates are included. The source complexity of the earthquakes is appraised by the physical features of the teleseismic source time functions. These features include the overall duration, multiple or single event character, individual source pulse widths, and roughness of the time function. The above measures of source size and complexity can then be compared with the age of subducted lithosphere, plate convergence rate, and other physical parameters of the subduction zone. Such comparisons are important for increasing our understanding of the worldwide distribution of the largest earth965 966 STEPHEN H. HARTZELL AND THOMAS H. HEATON quakes and their radiated energy. The teleseismic source time function gives information about source complexity which can be used in the estimation of strong ground motions. Studies of source complexity are also important to evaluate the validity of recent asperity models of faulting, where the fault is characterized by localized regions of higher strength. In subduction zone regimes, the maximum earthquake magnitude has been related to asperity size and to the mechanical coupling between the plates (Uyeda and Kanamori, 1979; Ruff and Kanamori, 1980, 1983; Lay et al., 1982). The earthquake time functions in this paper will, we hope, add insight to these interpretations. For the period range of interest, about 1 to 60 sec, P-wave radiation is the natural choice for study of source complexity. It is useful for later discussion to briefly review the most common techniques which have been used to estimate teleseismic body-wave, source time functions. The techniques can be grouped into two general types: (1) division of the record by the theoretical point impulse response in the frequency domain; and (2) parameterization of the time function. With the second approach, the optimum values of the parameters are obtained by various methods including cross-correlation, linear least-squares, and maximum likelihood. Boatwright (1980) utilizes a direct deconvolution approach. The source time function is obtained by a recursive deconvolution in the time domain of the seismogram by a bandpass-filtered theoretical impulse response of the earth. The effect of the filtering on the low-frequency baseline of the time function is approximately removed by subtracting the effect of the same processing performed on an idealized functional form of the seismogram. Source finiteness is neglected. Burdick and Mellman (1976) invert P waveforms from WWSSN stations for the 1968 Borrego Mountain earthquake. In their approach, the source time function is parameterized by a few variables whose optimum values are obtained by a numerical correlation between the synthetics and the observations. Care should be exercised in applying such a technique, since the time function can only reflect that amount of complexity that is allowed for by the particular parameterization used. Kanamori and Stewart (1978) and Stewart and Kanamori (1982) use a forward modeling procedure to examine the complexity of WWSSN P waveforms. In their technique, a single point source, having a trapezoidal far-field time function, is chosen such that it simulates the very beginning of the P wave train. The synthetic for this point source is then subtracted from the observations. This process is repeated using the remaining waveform until all significant arrivals are accounted for. Depending on the complexity of the waveforms, this procedure can be quite tedious. Kikuchi and Kanamori (1982) extend the method of Kanamori and Stewart (1978) so that complex body waves can be formally inverted for the source time function. The synthetic seismogram for an initial source with a ramp dislocation function, rise time r, and rupture duration T is subtracted from the observations. The strength and arrival time of this source are determined by cross-correlation of the synthetic and data records. The process is continued for N iterations until an acceptable fit, measured in a least-squares sense, is obtained to the data. The best value of r is obtained by trial and error. A linear baseline trend, which is a result of the band-limited nature of the data, is removed from the source time function. For multiple-station data, the relative timing of sources between stations can be used to locate each source with respect to a given hypocenter. Ruff and Kanamori (1983) estimate the source time function for several great earthquakes by solving the leastsquares problem [ A / ~ I ] X ~[b/0]. Here, A is a matrix of phase shifted Green's functions for the earth with narrow source time histories, I is the identity matrix, TELESEISMIC TIME FUNCTIONS FOR LARGE EARTHQUAKES 967 ~, is a damping or moment minimization parameter, X is the discretized source time function, and b is the observation vector. A long-period, half-sine function is added to the time function to shift the baseline. This adjustment is done to approximately compensate for the band-limited nature of the data and to obtain a mostly positive time function. Nabelek (1984a, b) parameterizes the teleseismic source time function either as a series of overlapping isosceles triangles for a point source, or overlapping trapezoids for a line source. The number of elementary sources, N, the rise time of each source, 7, and the duration of each source as seen at different azimuths (for the line source problem) are all set a priori. An iterative maximum likelihood inverse is used to find the best-fitting weight to be applied to each of the N sources. All of the above techniques share the common limitations of the bandwidth of the data and the accuracy of the computed impulse response of the earth for the earthquake mechanism. DATA SET Rather than study a few earthquakes in detail, we considered a survey study of a larger number of events in order to characterize the overall nature of shallow subduction zone earthquakes. The objective is to compare as many earthquakes of this type as possible by using body-wave records that have all been recorded on the same instrument. Although the full effect of the receiver structure may not be known, by using a common site and instrument, comparison studies between earthquakes are possible. The determination of the spatial and temporal rupture history of a three-dimensional source requires good azimuthal coverage of the radiated energy. In this study, only one station is used. Therefore, we obtain an estimate of the teleseismic source time function as viewed from one particular azimuth. The desirable characteristics of the recording instrument for this study are: (1) a long time period of continuous operation; (2) a well-calibrated, broadband frequency response; and (3) a location such that most of the circum-Pacific lies at a distance between 30 ° and 90 °, the distance range where direct P waves bottom in the lower mantle. The first two requirements rule out WWSSN stations. The instruments which do the best job of meeting the above requirements are the southern California array of Benioff 1-90 seismometers operated by the California Institute of Technology. These instruments have a 1-sec natural period seismometer, a 90-sec natural period galvanometer, and a peak gain of 3000 at 1 sec. Benioff 1-90 seismometers have operated at four sites in southern California: Pasadena; Riverside; Barrett; and Tinemaha. The Pasadena instrument was chosen because of its longer period of operation and because the records are free from obvious site reverberations. In a few cases, when Pasadena records could not be found, the Barrett record is used. The Barrett station writes seismograms very similar to those of the Pasadena station. On-scale records are available for almost every large, shallow subduction zone earthquake that has occurred since 1938. One notable exception is the 1964 Alaska earthquake. For completeness, we have substituted the Pasadena WoodAnderson torsion seismometer record for the 1964 Alaska earthquake. Besides the 1964 Alaska event, the only other gap in the data set is for e~thquakes in Mexico. These events are less than 30 ° from Pasadena and have been omitted to avoid upper mantle triplications. The locations of the earthquakes studied are given in Figure 1 and Table 1. In total, 63 events are analyzed. In Figure 1 and Table 1 a numbering scheme is adopted for identification of the events and is used throughout this paper. The data 968 STEPHEN H. HARTZELL AND THOMAS H. HEATON have been processed as follows. The vertical component of the Benioff 1-90 instrument is first digitized and bandpass-filtered from 1 to 60 sec using a doublepass zero phase Butterworth filter (Oppenheim and Schafer, 1975). The filtering is done to remove longand short-period noise, primarily from digitizing. The records are then interpolated to a uniform time step of 0.2 sec. This time spacing gives a Nyquist frequency of 2.5 Hz, which is more than sufficient for the following analysis. The effects of the earth's structure, attenuation, and the instrument response are removed in the inversion process described below.