A pattern recognition approach to geophysical inversion using neural nets

Abstract

Summary This paper is a philosophical exploration of adaptive pattern recognition paradigms for geophysical data inversion, aimed at overcoming many of the problems faced by current inversion methods. APR (adaptive pattern recognition) methods are based upon encoding exemplar patterns in such a way that their features can be used to classify subsequent test patterns. These paradigms are adaptive in that they learn from experience and are capable of inferring rules to deal with incomplete data. APR paradigms can also be highly effective in dealing with noise and other data distortions through the use of exemplars which characterize such distortions. Rather than merely seeking to reduce the point by point mismatch between data and model curves, effective APR paradigms would match patterns by establishing a feature vocabulary and inferring rules to weight the relative importance of these features in interpreting data. They have the advantage that prototype data sets can include analogue modelling data and field survey data rather than being restricted to models for which a numerical forward model can be calculated. The success of this approach to inversion will depend upon the effectiveness of replacing continuous parameter estimation with microclassification (discretized parameter estimation). Once the viability of APR schemes has been established for inverting data from individual geophysical methods, the task of joint interpretation of data from different geophysical survey methods could be accomplished in an optimum fashion by using hierarchical adaptive schemes. The application of APR to inversion is explored from the standpoint of neural net implementations. The foundations and properties of seven well-known neural net paradigms are examined in terms of several attributes necessary to build an effective inversion system. Different input space representation concepts for feature extraction and data compression are presented, including moment methods and a non-reversible, generalized Fourier transform method. Both parametric and non-parametric concepts for output space representation are explored as microclassification paradigms for quantitative estimation of Earth properties. The paper concludes that neural net paradigms have become sufficiently powerful to justify research programs aimed at implementing APR methods for geophysical inversion.