Geostatistical and Fourier analysis applied to cross-hole tomography seismic data

Geophysical methods, for instance seismic cross-hole tomography, are fundamental investigation tools in geotechnical site characterization. Tomographic inversion procedures allow associating an average P and/or S seismic wave velocity to a set of cells and, by "contraction", to their central points. It is then possible to deduce soil elastic modulii necessary to geotechnical design. Geostatistical tools may be a useful methodology in modeling the spatial variability of such regionalized geophysical and geotechnical variables as well as in their final mapping. However there are various aspects that shall be taken in consideration. In this study geostatistical and Fourier analysis procedures are applied to data resulting from a seismic cross-hole tomography survey using three boreholes defining two sections, in a site of heterogeneous granite weathered profile of Porto area, in the framework of the city metro construction. Mapping of both shear modulus and Poisson ratio, obtained with different interpolation methods and strategies, are presented and discussed, including their related estimation and "contraction" variances. It is also discussed the application of Fourier analysis aiming namely at quantifying increases or decreases of variability due to changes of data frequency content in estimation, as well as an inference of the necessary sampling rate capable of detecting high frequency events, i.e. a measure of the possibility of recovering the "original" regionalized continuous function through bandlimited interpolation, within a certain error, based on Shannon sampling theorem.