NEURAL NETWORKS AND INVERSION OF SEISMIC DATA

Neural networks can be viewed as applications that map one space, the input space, into some output space. In order to simulate the desired mapping the network has to go through a learning process consisting of an iterative change of the internal parameters, through the presentation of many input patterns and their corresponding output patterns. The training process is accomplished if the error between the computed output and the desired output pattern is minimal for all examples in the training set. The network will then simulate the desired mapping on the restricted domain of the training examples. We describe an experiment where a neural network is designed to accept a synthetic common shot gather (i.e., a set of seismograms obtained from a single source), as its input pattern and to compute the corresponding one-dimensional large-scale velocity model as its output. The subsurface models are built up of eight layers with constant layer thickness over a homogeneous half-space, 450 examples are used to train the network. After the training process the network never computes a subsurface model which perfectly fits the desired one, but the approximation of the network is sufficient to take this model as starting model for further seismic imaging algorithms. The trained network computes satisfactory velocity profiles for 80% of the new seismic gathers not included in the training set. Although the network gives results that are stable when the input is contaminated with white noise, the network is not robust against strong, i.e., correlated, noise. This application proves that neural networks are able to solve nontrivial inverse problems.