GREEN'S FUNCTIONS FOR THE VISCOELASTIC HALFSPACE: A CONVOLUTIONAL NEURAL NETWORK APPROACH

An identification problem in elastodynamics is addressed through the use of machine learning (ML) to recognize the presence of a free surface in a 3D viscoelastic continuum by measuring the dynamic response (displacements) at a receiver node due to an impulse at a source node. Specifically, a convolutional neural network (CNN) is constructed based on numerical solutions in the form of spectrograms, which are furnished through an implementation of the fundamental solutions of elastodynamics for both the full- and the half-spaces, while both frequency and time domains are considered. Following training of the CNN and its subsequent validation, data streams are evaluated and the results are given in the form 'confusion' matrices, which quantify the probability that a given displacement signal moves unimpeded or is being scattered. This in turn indicates the presence or absence of a free surface in the continuum. Furthermore, it is possible to re-train the CNN to estimate of the depth of the source point from the free surface, if such a surface exists. Finally, applications of this work are in areas ranging from geophysics to material science.