Time-domain Observation and Synthesis of Split Spheroidal and Torsional Free Oscillations of the 1960 Chilean Earthquake: Preliminary Results by Seth Stein and Robert

The rotationally and elliptically split normal modes of the earth are observed for the 1960 Chilean earthquake by analysis in the time domain. One hundred and fifty hours of the Isabella, California, strain record are narrow band filtered about the central frequency of each split multiplet to isolate the complex wave form resulting from the interference of the different singlets. We compute synthetic seismograms using our previous theoretical results, which show the dependence of the amplitude and phase of the singlets on source location, depth, mechanism, and the position of the receiver. By comparing these synthetics to the filtered record, we conclusively demonstrate the splitting of modes whose splitting had not been definitely resolved: torsional modes (0T3, oT4) and spheroidal modes (0S4, 0S5). The splitting of 0S2 and 0S3 is reconfirmed. We obtain good agreement between the synthetics and the filtered data for a source mechanism (previously determined from long-period surface waves) of thrust motion on a shallow dipping fault. INTRODUCTION Split peaks in the earth's normal mode spectrum were first observed for the 1960 Chilean earthquake. The splitting of 0S2 and 0S3 was reported by Benioff, Press, and Smith (1961) and Ness, Harrison, and Slichter (1961). Slichter (1967) observed the splitting of oS3 for the 1964 Alaskan earthquake. Splitting has never been conclusively demonstrated for other spheroidal modes or for any torsional modes. Extensive theoretical efforts (summarized in our earlier papers) have been devoted to the computation of the eigenfrequencies of the 2l ÷ 1 individual singlets into which the multiplet of angular order l (e.g., nSz) is split. This frequency splitting of the very long-period modes is primarily due to the earth's rotation (Pekeris et al., 1961 and Backus and Gilbert, 1961) and ellipticity (Dahlen, 1968). In an earlier paper (Stein and Geller, 1977) we derived theoretical results that allow us to calculate the amplitudes and phases of the split normal modes (or equivalently, their time history) excited by a double couple of arbitrary orientation resulting from slip on a fault plane. These results were applied successfully (Geller and Stein, 1977) to split spectra of the Chilean and Alaskan earthquakes. In this paper we use source models derived from long-period surface wave studies to generate synthetic seismograms for each of six multiplets (oS2 0S5, 0T3, 0T4), and compare them to a time-domain record of the Chilean earthquake which has been narrow band filtered to isolate that multiplet. This procedure yields several results which were not obtained by earlier studies in the frequency domain. We show that splitting is present for modes for which it has not been previously resolved, including torsional modes. Our results are derived entirely from wave-form shapes, and make no use of absolute amplitude information, due to calibration complexities. The absolute amplitudes are used in a forthcoming study (Stein and Geller, 1978) to determine the moment at very long periods. We also determine accurate Q's for the low-order modes. * Also Department of Geophysics, Stanford University, Stanford, California 94305. 325 326 SETH STEIN AND ROBERT J. GELLER D A T A AND ANALYSIS Figure 1 shows 150 hr of the strain record (filtered electronically to reduce the tidal amplitudes) from Isabella, California (Benioff et al., 1961) for the great 1960 Chilean earthquake. The record (top) was processed to remove tides by twice subtracting 3-h running averages. The resulting record (bottom) was tapered at both ends and then filtered to isolate and resolve individual low angular order modes. The resulting narrow band filtered data are shown in the upper traces of Figures 2 through 7, for four spheroidal and two torsional modes. All these wave forms show the general (e -wt/2q) attenuation of the entire mode superimposed on a complicated pattern which results from the interference of the split singlets. The middle trace of each figure shows a synthetic seismogram for each mode which includes the effects of splitting. The results of Stein and Geller {1977) for CHILEAN EARTHQUAKE Mey 22, 1960 STRAINMETER AT ISABELLA, CALIFORNIA E l t/': 'i/ ' ~ t I ' :~l,t b J '" ' t/ ~, i . , j:, '~' 4