Spatial prediction procedures for regionalization and 3D imaging of Earth structures
Abstract
The imaging of threedimensional (3D) Earth structures from tomographic results is an especially delicate subject due to various problems. When the data provided by the seismic surveys are averaged values that do not describe locally the medium, surface wave tomography is a relevant example of this, the regularization constraints to be imposed in the inverse process are fairly subjective. In fact, the methods for regionalization of the seismic information (dispersion data, attenuation parameters, etc.) involve an inverse problem that usually must be solved by following a mathematical approach. Opposite to this, we propose various noninverse procedures with a common target: to reconstruct 3D Earth structures from irregularly sampled seismic data consisting of pathaveraged values depending on the wavelength or varying with depth. For this purpose we review different imaging techniques aimed at volumetric modeling and visualization of data. We refer to special rendering methods and the key operations concerning the methodology to follow: gridding and interpolation. In order to get a faster and simpler volume visualization way, we use a regular voxel grid that we achieve by means of a selected gridding algorithm under specific controls. Exacttype methods (inverse distance weighting, kriging, splines, finite differences, gridding triangulation, wavelets and gradientwavelets) and approximate methods (leastsquare fitting with splines) are very briefly described. In particular, both a modified 2D slicing Laplacian method, based on interpolation by finite differences, and the 3D direct wavelets and gradientwavelets methods are original. To compare the accuracy and computational efficiency of all these methods, we have them applied to synthetic data trying the reconstruction of specific volumes whose (geometrical and physical) characteristics are known. We also have used real data and hereby show some tomographic solutions related to the research of domains at different scales and depths.
 Publication:

Physics of the Earth and Planetary Interiors
 Pub Date:
 April 2001
 DOI:
 10.1016/S00319201(00)002077
 Bibcode:
 2001PEPI..123..149S