A Method for Determination of the Three-Dimensional Seismic Velocity Structure from Local Earthquake Data.

Abstract

We have developed an inverse method to estimate a three-dimensional seismic wave velocity structure using seismic arrival time data obtained from local earthquakes. The method is characterized by a simultaneous determination of a two-dimensional depth distribution of a velocity boundary, a three-dimensional velocity distribution, station corrections and hypocenters. The depth distributions of velocity boundaries and the distributions of the slowness perturbations for P and S waves are modeled by power series of latitude, longitude, and depth, This representation of the three-dimensional seismic structure is advantageous not only in reducing the number of unknown parameters, but also in analytically evaluating the boundary depths, velocities, and partial derivatives of travel times with respect to the unknown parameters. Ray trajectories connected between hypocenters and stations are determined by the so-called shooting method for ray tracing scheme under a simplified velocity distribution with the exact boundary depth distribution. Numerical experiments have proved that our inverse method can successfully estimate the three-dimensional velocity structure.

Seismic Velocity Structure in the Crust and Upper Mantle beneath Northern Japan.

“…The estimated coefficients are listed in Appendix 2. According to the results obtained by Miyamachi (1994), even if the resolution is poor, the boundary depth distribution calculated by the estimated coefficients is reliable in the well-resolved region beneath the seismic network. The standard errors in depth for the 4.2 P and S wave velocity distributions Coefficients for P and S wave slowness perturbations in the crust, the mantle wedge and the plate obtained by the inversion have resolutions ranging from 0.1 to 0.9, and their standard errors are somewhat large.…”

“…In the figure, the standard deviation at the first iteration becomes larger than that at the 0th iteration (the initial model). The cause for this undesirable change, as discussed in Miyamachi (1994), may be a discontinuous change of the coefficients of the power series during the inversion. In the following sections, we describe the result of each parameter obtained by the inversion.…”

“…Our algorithm for searching ray paths could not determine about 1,100 ray paths. As discussed in Miyamachi (1994), the determination of the ray trajectory between earthquakes and stations is based on the shooting method by Julian and Gubbins (1977), and Snell's law is strictly applied when the ray paths cross the boundaries. Therefore, it sometimes happens that the ray paths can not be identified by our algorithm due to a discontinuous change of the ray trajectory.…”

“…Moreover, the previous velocity structure analyses are either to estimate the depth distributions of the velocity boundaries under the assigned velocity distribution Zhao et al, 1990 or to solve the velocity distribution under the fixed boundaries (Takanami, 1982;Miyamachi and Moriya, 1984;Hasemi et al, 1984;Obara et al, 1986;Sato et al, 1989;Zhao and Hasegawa, 1993). Recently, Miyamachi (1994) developed a method which simultaneously determines the velocity distribution and the boundary depth distribution using the local earthquake data. In this method, the P and S wave slowness distributions and the 2-D depth distributions of velocity boundaries are described using a power series of spatial coordinates.…”

“…The first aim of this study was to determine a 3-D P and S wave velocity structure beneath northern Japan by applying the inverse method of Miyamachi (1994) to P and S wave arrival time data obtained from local earthquakes. The second was to investigate the relation between the velocity structure and seismic activity.…”