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A preliminary earthquake location method based on a hyperbolic approximation to travel times

CENTER FOR EARTHQUAKE RESEARCH AND INFORMATION MEMPHIS STATE UNIVERSITY, MEMPHIS, TENNESSEE 38152

Abstract

We present a fast, two-step method for preliminary earthquake location using the direct arrivals recorded by a local network by assuming that travel times follow a hyperbolic relationship. For a layered medium, hypocentral coordinates (x_e, y_e, h), arrival times (), origin time (T_o), travel times of either P or S waves (), and station coordinates (x, y) are approximately related by an equation describing a hyperbolic surface: , where v is the rms velocity between the surface and depth h. This equation is a good approximation when the angle between the vertical and the ray path is small. In the first step T_o and the coefficients of the hyperboloid that best fit the observed arrival times are determined by nonlinear inversion. The coordinates of the minimum of the hyperboloid give the event epicenter. In the second step all the unknown parameters are computed simultaneously by nonlinear inversion of equation (1). Testing with synthetic data shows that the method performs better than might have been expected given the approximations involved. The determination of epicentral locations is very robust even in the presence of noise. When the events are under or near the network and only P arrivals are used, the epicenters are mislocated by a few kilometers at most. When S arrivals are included, depths and origin times are also reliably estimated. This method can be applied when approximate, but expeditious, earthquake locations are required. It can be used, for example, as part of an automatic event location program, first to produce a set of P and S arrival times uncontaminated by gross errors, and then to generate initial estimates of hypocentral location and origin time to be used by standard, and more time-consuming, locating programs. Furthermore, in optimal cases, it is possible to obtain reliable and independent estimates of rms velocities.

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