Estimation of the rocks statistical parameters from traveltime measurements

Abstract

In this paper the method for estimating the statistical parameters of the medium from traveltime measurements of refracted waves is applied to study the statistical characteristics of crystalline rocks at the Multifunctional Station Faido (Gotthard Base Tunnel, Switzerland). The method is based on the geometrical optics (GO) approximation. A covariance function for traveltime fluctuations has been obtained by considering quasihomogeneous fluctuations of sound velocity in a plain-stratified medium. Strongly anisometric (having unequal dimensions in different directions) random inhomogeneities were embedded in this medium. To estimate the statistical parameters around the tunnel, the traveltime fluctuations are calculated. It is assumed that each observation of traveltime-distance relation for a given shot-receiver group corresponds to a particular realization of a medium statistical ensemble. By calculating the variance and the zero cross intervals of the first derivative of traveltime fluctuations, the standard deviation of the velocity fluctuations and the characteristic horizontal scale of the inhomogeneities are estimated. Although the method allows to obtain the characteristic lengths of the inhomogeneities in vertical as well as in horizontal direction, the limited offset of the field data made it only possible to measure the latter. The estimated horizontal characteristic scale is about 13 m, which is reasonably close to the direct geological measurements in the studied region, where quartz lenses are dominant among the inhomogeneities. The standard deviation of the velocity is estimated as 4.5%, which might be caused by the fractured structure around the tunnel and also by the fault zone near the study area.