A comparison of standard inversion, neural networks and support vector machines
Karl N. Kappler, Heidi Anderson Kuzma, James W. Rector · 2005
The object of geophysical inversion is to recover earth parameters from measured data. If the relationship between an earth model and the data is linear, then three different methods of data interpretation, linear inversion, Neural Networks and Support Vector Machines, arrive at the same model from different paradigms. Linear inversion finds a model by minimizing a least squares objective function to which there is a closed form solution. NNs and SVMs use training data to approximate a functional inverse. If the relationship between models and data is non-linear, there is no longer a closed form solution to the inversion objective function, and a model is found by iterative guessing. An NN finds non-linear relationships by adopting a more complicated architecture. A SVM is rendered non-linear by changing a single parameter. All three approaches can be used independently or in combination. This tutorial explains the differences and relationships between them.