Conditioning of levy-stable fractal reservoir models to seismic data

摘要

We have developed methods of conditioning non-stationary Levy-stable geostatistical models to 3D seismic data. The technique involves adapting the sequential Levy simulation method such that the convolutional response of the realisations acceptably "matches" the seismic amplitude map. A rejection scheme is used, which requires fast repetitive simulation of gridblock columns and generation of convolutional responses. The non-stationarity of the model means that this cannot be achieved using the conventional large kriging system. We use a different, but comparably rapid method, based on storing the relevant parts of a sequential simulation calculation for the column. Working directly with the amplitude traces also has the advantage of avoiding the ambiguties and non-uniqueness involved in inverting the traces to acoustic impedance. The most difficult part of the problem is estimation of the seismic wavelet, and this is often done non-optimally. We describe a sophisticated method of estimating the wavelet, and show that this can yield better than expected results. Suitable rejection criteria are proposed, based on reasonable probabilistic models. The application of the technique is demonstrated with a field example.