A Boltzmann machine for high-resolution prestack seismic inversion

Seismic inversion is one popular approach that aims at predicting some indicative properties to support the geologic interpretation process. Existing inversion techniques indicate weaknesses when dealing with complex geologic area, where the uncertainties arise from the guiding model, which are provided by the interpreters. We have developed a prestack seismic inversion algorithm using a machine-learning algorithm called the Boltzmann machine. Unlike common inversion approaches, this stochastic neural network does not require a starting model at the beginning of the process to guide the solution; however, low-frequency models are required to convert the inversion-derived reflectivity terms to the absolute elastic P- and S-impedance as well as density. Our algorithm incorporates a single-layer Hopfield neural network whose neurons can be treated as the desired reflectivity terms. The optimization process seeks the global minimum solution by combining the network with a stochastic model update from the mean-field annealing algorithm. Also, we use a Z-shaped sample sorting scheme and the first-order Tikhonov regularization to improve the lateral continuity of the results and to stabilize the inversion process. The algorithm is applied to a field 2D data set to invert for high-resolution indicative P- and S-impedance sections to better capture some features away from the reservoir zone. The resulting models are strongly supported by the well results and reveal some realistic features that are not clearly displayed in the model-based deterministic inversion result. In combination with well-log analyses, the new features appear to be a good prospect for hydrocarbon.