Surface wave dispersion curve inversion using mixture density networks

Abstract

SUMMARYIn many seismological, environmental and engineering applications a detailed S-wave velocity model of the shallow subsurface is required. This is generally achieved by the inversion of surface wave dispersion curves using various inversion methods. The classical inversion approaches suffer from several shortcomings, such as inaccurate solutions due to local minima or large computation times in case of a wide parameter space. A number of machine learning (ML) approaches have been suggested to tackle these problems, which however do not provide probabilistic solutions and/or constrain layer number and layer thickness to a fixed value. In this study, we develop a novel neural network (NN) approach in order to characterize the shallow velocity structure from Love and Rayleigh wave dispersion curves. The novelty of our method lies in the simultaneous estimation of layer numbers, layer depth and a complete probability distribution of the S-wave velocity structure. This is achieved by a two-step ML approach, where (1) a regular NN classifies the number of layers within the upper 100 m of the subsurface and (2) a mixture density network outputs the depth estimates together with a fully probabilistic solution of the S-wave velocity structure. We show the advantages of our ML approach compared to a conventional neighbourhood inversion and a Markov chain Monte Carlo algorithm. Our ML approach is then applied to dispersion curves extracted from recorded noise data in Munich, Germany. The resulting velocity profile is in accordance with lithologic information at the site, which highlights the potential of our approach.