Fast geostatistical seismic inversion coupling machine learning and Fourier decomposition

Geostatistical seismic inversion uses stochastic sequential simulation and co-simulation as techniques to generate and perturb subsurface elastic models. These steps are computational demanding and, depending on the size of the inversion grid, time consuming. This paper introduces a technique to achieve considerable reductions in the consumption of computational resources of geostatistical seismic inversion without compromising the quality of the inverse elastic models. We achieve these improvements by reducing one of the dimensions of the data domain to a periodic function approximated by a Fourier series of n terms. Then, instead of simulating over the entire original data volume, in the original data domain, we simulate independently each term of the series over the area of interest. If the number of terms in the series is considerably smaller than the size of the collapsed data domain, then the computational overhead of the inversion procedure decreases. Symbolic regression is used to obtain automatically the approximation to the periodic function that captures the behavior of the property in the reduced dimension. The advantages related to the use of symbolic regression over alternative machine learning algorithms are discussed. We use the method to simulate acoustic impedance in a geostatistical seismic inversion of a synthetic dataset representing a hydrocarbon reservoir, where the true acoustic impedance model is available. Results demonstrate a considerable speedup over traditional methods while achieving similar performance in terms of the misfit between real and synthetic seismic and a good representation of the true impedance model. The frequency content of the resulting inverted data is discussed and compared with the one inferred from traditional methods, demonstrating an expected reduction of the high-frequency component.