#### Technical Report USC-SIPI-168

“Adaptive Minimum Prediction-Error Deconvolution and Source Wavelet Estimation Using Hopfield Neural Networks”

by Li-Xin Wang and Jerry M. Mendel

January 1991

In this report, three Hopfield neural networks are developed to realize a new Adaptive Minimum Prediction-Error Deconvolution procedure. The first neural network is developed to detect the reflectivity sequence. The second neural network is developed to determine the magnitudes of the detected reflections. The third neural network is developed to estimate the seismic wavelet. A Block-Component Method is proposed for simultaneous reflectivity estimation and wavelet extraction based on these three neural networks. These three neural networks and the Block-Component Method are simulated for broad-band and narrow-band wavelets. Real seismic data are processed using the Block-Component Method, and the results are compared with those using the MVD Filter and the maximum-likelihood based SMLR Detector [8,9].

Compared with existing deconvolution methods, the Neural Network Adaptive Minimum Prediction-Error Deconvolution method of this report has the following advantages: (1) it is totally realized by standard Hopfield neural networks which are suitable for hardware implementation; (2) the new Block-Component Method gives better results for real seismic data processing than the MLD-based Block Component Method; (3) the Neural Reflectivity Estimator gives much better results than the SMLR Detector in the case of a narrow-band wavelet and low signal-to-noise ratio; and, (4) it needs very weak assumptions about the wavelet and the reflectivity sequence, i.e., it is suitable for a nonminimum-phase wavelet, non-Gaussian or colored measurement noise, and, the reflectivity sequence can be random or deterministic.

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