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

When applying a methodology for obtaining the 3-D shear-wave velocity struc ture of a medium from surface wave dispersion data, the problem must be con sidered 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 b e used to overcome these drawbacks. Actually, some spatial prediction techn iques are especially useful for analyzing short-range variability between s cattered points. We use here a pathwise reconstruction by means of an algor ithm that, from a mathematical viewpoint, can be understood through the app lication of the orthogonal projection theorem onto convex sets (POCS). In p articular, we are interested in exploring the possibilities of a POCS algor ithm operating on a very unfavorable case constrained by a lack of availabl e 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 (southeastem 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 R g-wave velocity structure of a small domain strongly constrained by the dat a. The method has allowed us to examine the sharply contrasting geology bet ween neighboring geological formations. Although the relationship between l ateral changes in Rg-wave dispersion and geologic structure may not be stra ightforward, 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 held observations prove the versatility of the method and the reliability of the imaging. (C) 2000 Elsevier Science B.V. A ll rights reserved.