Geostatistical Seismic Inversion Using Well Log Constraints

Information about reservoir properties usually comes from two sources: seismic data and well logs. The former provide an indirect, low resolution image of rock velocity and density. The latter provide direct, high resolution (but laterally sparse) sampling of these and other rock parameters. An important problem in reservoir characterization is how best to combine these data sets, allowing the well information to constrain the seismic inversion and, conversely, using the seismic data to spatially interpolate and extrapolate the well logs. We have developed a seismic/well log inversion method that combines geostatistical methods for well log interpolation (i.e., kriging) with a Monte Carlo search technique for seismic inversion. Our method follows the approach used by Haas and Dubrule (1994) in their sequential inversion algorithm. Kriging is applied to the well data to obtain velocity estimates and their variances for use as a priori constraints in the seismic inversion. Further, inversion of a complete 2-D seismic section is performed one trace at a time. The velocity profiles derived from previous seismic traces are incorporated as "pseudo well logs" in subsequent applications of kriging. Our version of this algorithm employs a more efficient Monte Carlo search algorithm in the seismic inversion step, and moves progressively away from the wells so as to minimize the kriging variance at each step. Numerical experiments with synthetic data demonstrate the viability of our seismic/well data inversion scheme.