CALCULATION OF THE INVERSE OF THE COVARIANCE

In reservoir characterization, the covariance is often used to describ e the spatial correlation and variation in rock properties or the unce rtainty in rock properties. The inverse of the covariance, on the othe r hand, is seldom discussed in geostatistics. In this paper, I show th at the inverse is required for simulation and estimation of Gaussian r andom fields, and that it can be identified with the differential oper ator in regularized inverse theory. Unfortunately, because the covaria nce matrix for parameters in reservoir models can be extremely large, calculation of the inverse can be a problem. In this paper, I discuss Jolts methods of calculating the inverse of the covariance, two of whi ch are analytical, and two of which are purely numerical. By taking ad vantage of the assumed stationarity of the covariance, none of the met hods require inversion of the full covariance matrix.