Yet another approach to the travel-time inversion problem

Abstract

A new technique for the inversion of travel-times is being developed in which it is hoped to combine all the good features of the other known techniques. Since the inversion of T − Δ data provides difficulties with triplications and shadow zones, we have chosen to invert p − τ data derived from the T − Δ data using the Bessonova method. Many computer subroutines capable of minimising very general non-linear functions, including linear and/or nonlinear constraints, are now available. Using this “black box” technique we can decide on the type of model we wish to allow, construct the model with or without low-velocity zones, incorporate smoothness considerations, and specify which velocities are already known sufficiently accurately and thus do not need to be varied. All we need to provide is a function subroutine to calculate the delay τ for a set of ray parameters p, and a suitable function to be minimised such as the weighted sum of the squares of the difference between the calculated and observed delay times τ. We can use spherical layers or use a transformation to flat layers and transform back at the end of the calculation. We can choose a model having layers of constant velocities, having linear velocity distribution through a layer, or having exponential-type spherical layers whose velocities are represented by such relationships as ν = a r b , where ν is the velocity and r is the radius, both of which vary through the layer, and a and b are constants determined from the velocity at the inner and outer radii of the layer. At present the method uses a great deal of computing time, but it is hoped that this can be improved.