Inversion of Complex Body Waves - - Iii

We have developed a method that inverts seismic body waves to determine the mechanism and rupture pattern of earthquakes. The rupture pattern is represented as a sequence of subevents distributed on the fault plane. This method is an extension of our earlier method in which the subevent mechanisms were fixed, in the new method, the subevent mechanisms are determined from the data and are allowed to vary during the sequence. When subevent mechanisms are allowed to vary, however, the inversion often becomes unstable because of the complex trade-offs between the mechanism, the timing, and the location of the subevents. Many different subevent sequences can explain the same data equally well, and it is important to determine the range of allowable solutions. Some constraints must be imposed on the solution to stabilize the inversion. We have developed a procedure to explore the range of allowable solutions and appropriate constraints. In this procedure, a network of grid points is constructed on the r I plane, where r and I are, respectively, the onset time and the distance from the epicenter of a subevent; the best-fit subevent is deter* mined at all grid points. Then the correlation is computed between the synthetic waveform for each subevent and the observed waveform. The correlation as a function of r and I and the best-fit mechanisms computed at each r I grid point depict the character of allowable solutions and facilitate a decision on the appropriate constraints to be imposed on the solution. The method is il lustrated using the data for the 1976 Guatemala earthquake. INTRODUCTION Seismic body waves are extensively used to determine the rupture pattern of earthquakes. The rupture patterns are generally very complex, and the results are interpreted in terms of a distribution of "asperities" and "barr iers" on the fault plane. The rupture pattern is important for an understanding of the mechanism of rupture initiation and termination and excitation of strong ground motions. Many methods have been used to determine the pattern of asperity distributions from seismic waveform data (e.g., Hartzell and Heaton, 1983; Ruff and Kanamori, 1983; Mori and Shimazaki, 1984; Kikuchi and Fukao, 1985). In the method we have previously presented (Kikuchi and Kanamori, 1982, 1986), the rupture sequence is represented by a sequence of subevents distributed on the fault plane. We assumed that all the subevents have the same mechanism, usually determined from the first-motion data. In some cases, a few subevents were allowed to have a different mechanism. This assumption was made to reduce the number of free parameters and stabilize the inversion. In this paper, we remove this l imitation and extend the method to a more general case where subevents are allowed to have different mechanisms. Several investigators have developed similar method. For example, in the inversion method of N~b~lek (1984), the mechanism of subevents is determined by an iterative least-squares method. Barker and Langston (1981, 1982) developed a generalized inverse technique utilizing the moment tensor formalism. Koyama (1987) 2335 2336 M. KIKUCHI AND H. KANAMORI inverted teleseismic long-period body waves to a time sequence of moment tensors. Hirata and Kawasaki (1988) analyzed body waves from a deep earthquake and investigated the change in the fault mechanism during the source process. Once subevents mechanisms are allowed to vary, the inversion often becomes unstable because of the complex trade-offs between the mechanism, the timing, and the location of the subevents. The solution is inevitably nonunique. Many different sequences can explain the same data equally well, and it is often difficult to determine the range of allowable solutions. In some cases, some constraints have to be imposed on the solution to stabilize the inversion; it is then important to know what constraints are reasonable. We developed a new method to invert body waves to obtain the mechanism and rupture patterns of complex events. In the earlier method, only P waves were used; in the new method, P, SH, SV, and PP phases can be used simultaneously, and a multi-layer structure is used to compute the response of the source, station, and PP bounce point structures. For this computation, we used the Haskell propagator matrix in the way described in Bouchon (1976) and Haskell (1960, 1962). In this paper, however, we will focus on the procedure to explore the range of allowable solutions and constraints. We will i l lustrate the method using the data set from the 1976 Guatemala earthquake. METHOD We describe a seismic source as a sequence of point sources with various focal mechanisms. As in our earlier papers, we determine the point sources iteratively by matching the observed records with the synthetic ones. We use a moment tensor to describe each point source. In general a moment tensor [Mij] has 6 independent elements. With a constraint of vanishing trace of [Mij], we obtain a pure-deviatoric moment tensor. With an additional constraint that the determinant of [ Mij] is zero, the moment tensor is reduced to a double-couple source. In the following, we first consider general moment tensors, and then double-couple sources. General Moment-Tensor Sources We choose the following 6 elementary moment tensors as the basis tensors to represent a seismic source: -0 MI: 1 0 0 M 4 : 0 1 10] [io0] [!oi] 0 0 ;M2: 1 0 ;M3: 0 ; 0 0 0 0 1 oil [ oo] [io!] 0 ;Ms: 0 0 0 ;M6 1 ; 0 0 0 1 0 where the coordinates (x, y, z) for Miy corresponds to (north, east, down). Any moment tensor can be represented by a linear combination of M n. Figure 1 shows the mechanism diagrams for these elementary tensors. The equal-area projection of the lower focal hemisphere is shown. I N V E R S I O N OF COMPLEX BODY W A V E S I I I 2337 @©@@@@