An attempt at 3-D imaging of a small domain (Almeria, southern Spain)

Abstract

When applying a methodology for obtaining the 3-D shear-wave velocity structure of a medium from surface wave dispersion data, the problem must be considered with caution since one inverts path-averaged velocities and the use of any inversion method entails some drawbacks such as lack of uniqueness, unwarranted stability and constraints affecting the data. Several imaging techniques aimed at volumetric modeling and the visualization of data can be used to overcome these drawbacks. Actually, some spatial prediction techniques are especially useful for analyzing short-range variability between scattered points. We use here a pathwise reconstruction by means of an algorithm that, from a mathematical viewpoint, can be understood through the application of the orthogonal projection theorem onto convex sets (POCS). In particular, we are interested in exploring the possibilities of a POCS algorithm operating on a very unfavorable case constrained by a lack of available data. In this paper, we have tackled a small-sized problem and we present the results based on ray-path seismic velocities that we have obtained in the case of a sparsely sampled study area like Almeria (southeastern Spain) by way of tomographic images obtained by application of such an algorithm. The main goal of this procedure is the reconstruction of the very shallow Rg-wave velocity structure of a small domain strongly constrained by the data. The method has allowed us to examine the sharply contrasting geology between neighboring geological formations. Although the relationship between lateral changes in Rg-wave dispersion and geologic structure may not be straightforward, we have observed a correlation between the velocity structure of very shallow soils and the local geology at surface. The good agreement between our results and the field observations prove the versatility of the method and the reliability of the imaging.