In quest of the grid

Abstract

The possible nonuniqueness and inaccuracy of tomographic inversion solutions may be the result of an inadequate discretization of the model space with respect to the acquisition geometry and the velocity field sought. Void pixels and linearly dependent equations are introduced if the grid shape does not match the spatial distribution of rays, originating the well‐known null space. This is a common drawback when using regular pixels. By definition, the null space does not depend on the picked traveltimes, and so we cannot eliminate it by minimising the traveltime residuals. We show that the inversion quality can be improved by following a trial and error approach, that is, by adapting the pixels’ shape and distribution to the layer interfaces and velocity field. The resolution can be increased or decreased locally to search for an optimal grid, although this introduces a personal bias. On the other hand, we can so decide where, why, and which a priori information is introduced in the sought velocity field, which is hardly feasible by managing other stabilising tools such as damping factors and smoothing filters.