T H E Use of Body-wave Spectra in the Determination of Seismic-source Parameters by Thomas C. Hanks and Max Wyss

Teleseismic determinations of body-wave (P, S) spectra, interpreted in terms of the Brune (1970) seismic-source model, are used to estimate the parameters seismic moment (Mo) and source dimension (r) for three large, shallow, strike-slip earthquakes occurring on nearly vertical fault planes and for which the same parameters can be determined from field (F) data. These earthquakes are (I) the Borrego Mountain, California, earthquake (April 9, 1968) for which [~¢o(P) = 10, M o ( S ) = 6.6, and Mo(F ) = 3.6]×102s dyne-cm and [r (P)= 14, ~(S) = 23, and L/2(F) = 17] km; (2) the Mudurnu Valley, Turkey, earthquake (July 22, 1967) for which [~ro(P ) = 9.1, Mo(S) = 8.5, and Mo(F ) = 7.4]×1026 dyne-era, and [~(P) = 39, ~(S) = 48, and L/2(F) = 40] km; and (3) the Dasht-e-Bay~z, Iran, earthquake (August 31, 1968) for which D~o(P) = 4.8, ~,1o(S) = 8.6, and Mo(F) = 18]×1026 dyne-era, and [i(P) = S1, r(S) = 48, and L/2(F) = 40] kin. The Brune (1970) model is well-calibrated with respect to the determination of these parameters for the earthquakes considered. A minimum estimate for the radiated energy can be expressed in terms of M o and r; this estimate is low by a factor of 10 with respect to the estimate obtained from energy-magnitude relations for these three earthquakes. The stress drops of these events are of the order of 10 bars. INTRODUCTION In this paper, we will use body-wave spectra to determine both the source dimension and seismic moment for three earthquakes for which these same parameters can be determined from field observations. These events are the Borrego Mountain, California, earthquake (M r = 6.4), the Mudurnu Valley, Turkey, earthquake (M = 7.1) and the Dasht-e-Bay~z, Iran, earthquake (M = 7.2). These three earthquakes generated predominantly strike-slip motion on a nearly vertical fault plane; all produced well-defined surface ruptures and measurable offsets across the fault surface. A general feature of theoretical, far-field displacement spectra D(~o) generated by a spatially stationary seismic or explosive source is the corner (or peak) frequency fo (~o is circular frequency and f = c0/2~z is frequency in Hz), which can be related to the source dimension through the equation fo = (cv/r). (1) Here v is the elastic wave velocity of the body phase in the vicinity of the source, and r is the source dimension; c is a constant of order 1 and depends on the particular source model. An equation of the form of (1) holds whether the model be an explosion (Sharpe, 1942; Kasahara, 1957), a shear dislocation (Jeffreys, 1931; Haskell, 1964~ Aki, 1967; Brune, 1970), or a stress relaxation source (Archambeau, 1964, 1968). Kasahara (1957) utilized this result and spectral data obtained from P waves to determine source dimensions for deep and shallow Japanese earthquakes. Berckhemer and Jacob (1968), with a variation of (1) involving the rupture velocity of a propagating source, estimated source dimensions and stress drops for some deep South American 561 562 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA earthquakes. Wyss et al. (1971) used spectral information in the frequency band 0.03 < f < 2 Hz to demonstrate that three nuclear explosions had source dimensions almost an order of magnitude less than four earthquakes of comparable magnitude m~. For frequencies higher than fo, f~(m) reflects the short time behavior of the source displacement function; f o r f >> fo, the spectral amplitudes must decay at least as fast as f ~ , ? > 1.5, so that the energy integral is bounded. An important aspect of the Brune (1970) model of shear-wave spectra is that ~(m) falls off only as f 1 in the rangefo < f < role where ~ is the fractional stress drop e = (Ao'/a~ff). (2) Here Act is the stress drop and ~f~ is the effective stress (prestress minus frictional stress opposing motion on the fault surface). An equally important result follows from the dislocation model of a seismic source: for f ~ fo, f~(~o) assumes a constant value that can be related to the seismic moment M o (either of the moments associated with the double-couple representation of the seismic source (Keilis-Borok, 1960)). Aki (1966) demonstrated that the seismic moment can also be obtained directly from field (F) observations Mo(F) = t~AF~ (3) where F! is the shear modulus, A is the area of the fault surface, and ff is the average displacement across the fault surface. The seismic moment determination obtained from the spectra of radiated waves has not been systematically compared to field observations because reliable long-period azimuth coverage has only been available since the installation of the WWSSN system in 1963 and because large earthquakes often occur in regions inaccessible to field measurements. Seismic moments are generally obtained from spectra derived from well-dispersed surface waves, following a procedure similar to that of Ben-Menahem and Harkrider (1964). The preference for surface-wave spectra is that, for large shallow earthquakes, spectral information at periods in the range of several hundred seconds can readily be obtained; for body phases, the long-period spectral data will be contaminated by multiple arrivals that follow within 60 to 100 sec, except at very restricted ranges of depths and epicentral distances. On the other hand, the smaller and deeper earthquakes, generate significantly smaller surface waves, and the use of body-wave spectra in the moment determinations for these events is preferable. Again with the exception of the larger shallow earthquakes, body-wave spectra are also preferable for the determination of the source dimension, sincefo is generally in a period range at which surface-wave amplitudes are a sensitive function of the propagation path. The intent of this paper is to demonstrate that both the source dimension and seismic moment can be reliably, and relatively easily, obtained from the interpretation of the body-wave spectra in terms of Brune's (1970) seismic-source model. This "calibration check" provides justification for its use in current studies of source parameter determinations for which there is no field evidence available. DETERMINATION AND INTERPRETATION OF BODY-WAVE SPECTRA Summary of theoretical results. Before presenting our method to determine the source spectrum from a teleseismically-observed body phase, we will summarize the theoretical relations with which the spectrum will be interpreted. In a later section, we will return to both the theoretical and observational limitations associated with their use. Figure 1 gives the far-field displacement spectra following Brune (1970). The S-wave spectrum USE OF BODY-WAVE SPECTRA IN DETERMINING SEISMIC-SOURCE PARAMETERS 563 is for the case of complete effective stress drop. The seismic moment Mo(S) is determined from the S-wave spectrum through the relation Mo(S ) f2°(S) 47rpR# 3 (Keilis-Borok, 1960) (4) ,~'o,~ ( S )