The zoeppritz equations, information theory, and support vector machines
Heidi Anderson Kuzma, James W. Rector · 2005
Geophysical forward models can act as band-pass filters, allowing only some of the inherent structure of the earth to be reflected in geophysical data. Many geophysical modeling programs require an enormous number of parameters to describe a 2 or 3-dimensional earth. It would seem that, in order to use a computer learning algorithm such as a Support Vector Machine (SVM) to interpret data, it is necessary to train the SVM with a number of examples that is on the order of the number of model parameters. Actually, the SVM can to be trained with much smaller training set, the size of which is loosely determined the number of real degrees of freedom in a resolvable model. Information Theory, particularly the concept of channel capacity, can be used to establish intuition about resolvable models. In this example, a Least Squares SVM is trained using 200 examples to resolve 1000 parameter velocity models from synthetic Amplitude Variation with Offset (AVO) data.