BOOTSTRAP STATISTICS FOR VELOCITY TOMOGRAPHY - APPLICATION OF A NEW INFORMATION CRITERION

A new information criterion, the extended information criterion (EIC) was applied in order to determine an optimum solution in simultaneous iterative reconstruction technique (SIRT) P-wave velocity tomography. The EIC is derived from information theory and statistics, and it meas ures the goodness-of-fit between the true (unknown) data distribution and the observed data distribution: the former gives the probability o f data realization from the true (unknown) model, whereas the latter g ives a probability of data realization calculated from a particular mo del of which parameters are estimated. The EIC is calculated using boo tstrap statistics, a numerical technique for calculating statistical e stimators. Bootstrap statistics enables us to obtain the bias between the log likelihood and the expected log likelihood, and then to obtain the expected log likelihood from the log likelihood. Since the EIC is obtained numerically, we can use it for most problems of model parame ter estimation without employing the maximum likelihood method. Taking weak anisotropy into account, we reconstructed the P-wave velocity st ructure of a rock sample during water infiltration under differential stress loading conditions. The results indicate that we can remove unr ealistic solutions sometimes encountered when too many iterations are made. In spite of much computation time, the EIC is a promising techni que for the near future, prompted by the rapid progress in current com puter technology.