Computer representation of the model covariance function resulting from travel-time tomography

Summary

This paper represents a supplement to the paper by Klimes (2002b) on the stochastic travel-time tomography. It contains brief generalization of the equations from interpolation of slowness to interpolation of general power of velocity, along with some notes on numerical implementation of the algorithm. The results of the inversion are represented by the velocity model and the model covariance function which describes the accuracy of the velocity model. Whereas the velocity model is composed of smooth functions of 3 coordinates, the model covariance function is a function of 6 coordinates with pronounced singularities. The computer representation of the model covariance function in terms of two matrices and the rays used for inversion is designed.

Keywords

Travel-time tomographic inversion, resolution, velocity model, medium covariance function, model covariance function, covariance matrices, heterogeneous media.

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