A comparison of geophysical inversion and machine learning in inverse problems

Geophysical inversion and machine learning both provide solutions of inverse problems in which we estimate model parameters from observations. In this study, we compare geophysical inversion and machine learning approaches in an aspect of solving inverse problems and show similarities and differences of these approaches in a mathematical form and numerical tests. We take reflectivity inversion as an example of the inverse problem. We apply geophysical inversion based on the least-squares method and artificial neural network (ANN) as a machine learning approach to solve reflectivity inversion using 2D synthetic data sets and 3D field data sets. Neural network with multiple hidden layers successfully generates the non-linear mapping function to predict reflectivity. The different levels of noise were applied to data to examine noise sensitivity of each method. Also we test different L1 regularizers to investigate how regularizers affect on inverting clean or noisy data for both approaches. L1 regularization alleviate effect of noise in seismic traces and enhance sparsity, especially in leastsquares method. The 2D synthetic model and field data examples show neural network yield high spatial resolution.