Adaptive minimum prediction‐error deconvolution and source wavelet estimation using Hopfield neural networks

Abstract

The massively parallel processing advantage of artificial neural networks makes them suitable for hardware implementations; therefore, using artificial neural networks for seismic signal processing problems has the potential of greatly speeding up seismic signal processing. A commonly used artificial neural network—Hopfield neural network—is used to implement a new adaptive minimum prediction‐error deconvolution (AMPED) procedure which decomposes deconvolution and wavelet estimation into three subprocesses: reflectivity location detection, reflectivity magnitude estimation, and source wavelet extraction. A random reflectivity model is not required. The basic idea of the approach is to relate the cost functions of the deconvolution and wavelet estimation problem with the energy functions of these Hopfield neural networks so that when these neural networks reach their stable states, for which the energy functions are locally minimized, the outputs of the networks give the solution to the deconvolution and wavelet estimation problem. Three Hopfield neural networks are constructed to implement the three subprocesses, respectively, and they are then connected in an iterative way to implement the entire deconvolution and wavelet estimation procedure. This approach is applied to synthetic and real seismic traces, and the results show that: (1) the Hopfield neural networks converge to their stable states in only one to four iterations; hence, this approach gives a solution to the deconvolution and wavelet estimation problem very quickly; (2) this approach works impressively well in the cases of low signal‐to‐noise ratio and nonminimum phase wavelets; and (3) this approach can treat backscatter either as noise or as useful signal.