On Obtaining Initial Approximation for the Full Wave Inversion Problem Using Convolutional Neural Network

The paper considers the problem of choosing an initial approximation for gradient optimization methods as applied to the inverse problem of restoring the velocity distribution in a heterogeneous continuous medium. The behavior of the medium is described by a system of acoustic equations, and the direct problem is solved by applying a finite-difference scheme. L-BFGS-B is used as a gradient optimization method. The gradient of the error functional with respect to the medium parameters is calculated by applying the adjoint state method. An initial approximation for the gradient method is obtained using a convolutional neural network trained to predict the velocity distribution in a medium from its wave response. It is shown that a neural network trained on responses of simple layered structures can be successfully used to solve the inverse problem for a much more complex Marmousi model.