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

**Ludek Klimes**
### 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.

### Whole paper

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In: Seismic Waves in Complex 3-D Structures, Report 18,
pp. 17-26, Dep. Geophys., Charles Univ., Prague, 2008.

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