Machine learning and geophysical inversion — A numerical study

Abstract

As geophysicists, we are trained to conceptualize geophysical problems in detail. However, machine learning algorithms are more difficult to understand and are often thought of as simply “black boxes.” A numerical example is used here to illustrate the difference between geophysical inversion and inversion by machine learning. In doing so, an attempt is made to demystify machine learning algorithms and show that, like inverse problems, they have a definite mathematical structure that can be written down and understood. The example used is the extraction of the underlying reflection coefficients from a synthetic seismic response that was created by convolving a reflection coefficient dipole with a symmetric wavelet. Because the dipole is below the seismic tuning frequency, the overlapping wavelets create both an amplitude increase and extra nonphysical reflection coefficients in the synthetic seismic data. This is a common problem in real seismic data. In discussing the solution to this problem, the topics of deconvolution, recursive inversion, linear regression, and nonlinear regression using a feedforward neural network are covered. It is shown that if the inputs to the deconvolution problem are fully understood, this is the optimal way to extract the true reflection coefficients. However, if the geophysics is not fully understood and large amounts of data are available, machine learning can provide a viable alternative to geophysical inversion.