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Yet another approach to the travel-time inversion problem

Hans, S.Jarosch

Physics of the Earth and Planetary Interiors 21(2-3): 0-108

1980

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 data provides difficulties with triplications and shadow zones, we have chosen to invert p data derived from the T 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 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 . 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 = a rb, where 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.

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