Non-linear avo inversion using support vector machines
Heidi Anderson Kuzma, James W. Rector · 2004
Model/data pairs, computed using known geophysical forward relationships, can be used to train Support Vector Machines to approximate inverse relationships. Given appropriate training data, a Support Vector Machine statistically reproduces the results of non-linear inversion. Inversion of the non-linear Zoeppritz equations is an ill-posed problem. The results of an inversion depend heavily on the a priori assumptions used to regularize it. If an SVM is trained using data that contains the same assumptions, it will get the same answer. It captures non-linear relationships as easily as linear ones by employing a kernel function. A naive SVM can usually be trained using fewer calculations of a forward model than are necessary in an equally naive inversion. Since an SVM only needs to be trained once whereas an inversion needs to be repeated on each new data set, procedures which require multiple inversions of the same data become available. The Jackknife method uses multiple inversions to calculate error bars and improve a model estimate.