Seismic data inversion by cross-hole tomography using geometrically uniform spatial coverage

One of the inversion schemes most employed in seismic tomography processing is least squares and derived algorithms, using as input data the vector of frst arrivals. A division of the whole space between sources and receivers is performed, constructing a pixel model with its elements of the same size. Spatial coverage is defned, then, as the sum of traveled length by all rays through every pixel that conform the medium considered. It is related, therefore, with the source-receiver's distribution and the form of the domain among them. In cross-hole array, rays do not evenly sample the properties of the medium, leading to non-uniform spatial coverage. It is known that this affects the inversion process. The purpose of this paper, then, was to study the problem of spatial coverage uniformity to obtain travel path matrices leading to inversion algorithms with better convergence. The medium was divided in elements of different size but with an even spatial coverage (named as 'ipixels'), and then it was explored how this improved the inversion process. A theoretical model was implemented with added noise to emulate real data; and then the vector of measured times was generated with known velocity distribution. Afterwards an inversion method using minimum length solution was performed to test the two domain divisions. The results showed that the fact of using ipixels not only improved the inversion scheme used in all cases; but in addition allowed to get convergence where it was impossible to do using pixels; particularly through the method considered. This is a direct result of the improvement of condition number of the associated matrices.