Seismic waves estimation and wave field decomposition with factor graphs

Physical wave fields are often described by means of a vector field. Advances in sensor technology enable us to collect an increasing number of measurement at the same location (e.g. direction, polarization, translation, and rotation). One question arising naturally is how to properly process such large and diverse information, possibly from sensors of different kinds. In this paper we propose a technique for the analysis of vector wave fields and show an application to the seismic wave field. The contributions of this paper are the following: i) We provide a framework to perform maximum likelihood parameter estimation of any wave type, modeling jointly all the measurements and parameters; ii) In the same framework, we address wave superposition by gradually decomposing the wave field; iii) We also propose an iterative algorithm for noise variance estimation. Index Terms — Array signal processing, factor graph, seismic waves