INTRODUCTION

Risk assessment is a key component to any business decision. Geostatistics has recognized this need and has introduced methods such as simulation to attempt to assess uncertainty in their estimates of earth properties Isaaks and Srivastava (1989). The problem is that the geostatistical methods are generally concerned with local, rather than global, solutions to problems and therefore can not be easily applied to the global inversion problems that are common in geophysics.

In previous works Clapp (2000, 2001b,c), I showed how we can modify standard geophysical inverse techniques by adding random noise into the model styling goal to obtain multiple realizations. In Clapp (2002a) and Chen and Clapp (2002), these multiple realizations were used to produce a series of equi-probable velocity models. The velocity models were used in a series of migrations, and the effect on Amplitude vs. Angle (AVA) was analyzed. In Clapp (2003a), I showed how the data fitting goal can be modified to account for data uncertainty. I demonstrated its applicability to a simple Super Dix Clapp et al. (1998) problem.

In this paper I extend the data uncertainty concept to a ray based tomography problem Clapp (2001b); Stork and Clayton (1991). I show how we can produce multiple, realistic velocity models. On a complex synthetic I produce a range of equi-probable velocity models, for migration to produce kinetically different images.