3D adaptive tomography using Delaunay triangles and Voronoi polygons

The solutions of traveltime inversion problems are often not unique because of the poor match between the raypath distribution and the tomographic gri d. However, by adapting the local resolution iteratively, by means of a sin gular value analysis of the tomographic matrix, we can reduce or eliminate the null space influence on our earth image: in this way, we get a much mor e reliable estimate of the velocity field of seismic waves. We describe an algorithm for an automatic regridding, able to fit the local resolution to the available raypaths, which is based on Delaunay triangulation and Vorono i tessellation. It increases the local pixel density where the null space e nergy is low or the velocity gradient is large, and reduces it elsewhere. C onsequently, the tomographic image can reveal the boundaries of complex obj ects, but is not affected by the ambiguities that occur when the grid resol ution is not adequately supported by the available raypaths.