The Tau Method for Inversion of Travel Times--I. Deep Seismic Sounding Data

A new method for solving the inverse problem of seismology is described in this paper. The problem is formulated as follows: the travel times of body waves are given at a discrete set of points, and we are required to find in the (V, Y) plane (V being the velocity and Y the depth) the closed area which contains all velocity-depth curves corresponding to the given data. The method is based on the use of the function τ(p) =T(p)–pX(p), p being the ray parameter, T the travel time, and X the epicentral distance. This method has the following advantages: it does not necessarily involve the estimation of p by numerical differentiation of the travel times; and it does not involve any interpolation of the travel-time curve between actual observations. Only two assumptions are made: spherical symmetry of the structure (the absence of horizontal inhomogeneities), and the postulation of a lower limit for the velocity in low velocity zones. The function τ(p) is estimated directly from the observed (Ti, Xi) as a singular solution of the Clairaut equation with free term (T(X)). Application of the method is illustrated using data from deep seismic sounding in Turkmenistan.