Artificial neural networks for parameter estimation in geophysics

Artificial neural systems have been used in a variety of problems in the fields of science and engineering. Here we describe a study of the applicability of neural networks to solving some geophysical inverse problems. In particular, we study the problem of obtaining formation resistivities and layer thicknesses from vertical electrical sounding (VES) data and that of obtaining 1D velocity models from seismic waveform data. We use a two-layer feedforward neural network (FNN) that is trained to predict earth models from measured data. Part of the interest in using FNNs for geophysical inversion is that they are adaptive systems that perform a non-linear mapping between two sets of data from a given domain. In both of our applications, we train FNNs using synthetic data as input to the networks and a layer parametrization of the models as the network output. The earth models used for network training are drawn from an ensemble of random models within some prespecified parameter limits. For network training we use the back-propagation algorithm and a hybrid back-propagation-simulated-annealing method for the VES and seismic inverse problems, respectively. Other fundamental issues for obtaining accurate model parameter estimates using trained FNNs are the size of the training data, the network configuration, the description of the data and the model parametrization. Our simulations indicate that FNNs, if adequately trained, produce reasonably accurate earth models when observed data are input to the FNNs.