Revisiting Seismic Tomography Through Direct Methods and High Performance Computing

Abstract:

Over the last two decades, the rapid increase in data availability and computational power significantly increased the number of data and model parameters that can be investigated in seismic tomography problems. Often, the model space consists of 10⁵-10⁶ unknown parameters and there are comparable numbers of observations, making direct computational methods such as the singular value decomposition prohibitively expensive or impossible, leaving iterative solvers as the only alternative option. Among the disadvantages of the iterative algorithms is that the inverse of the matrix that defines the system is not explicitly formed. As a consequence, the model resolution and covariance matrices, that are crucial for the quantitative assessment of the uncertainty of the tomographic models, cannot be computed. Despite efforts in finding computationally affordable approximations of these matrices, challenges remain, and approaches such as the checkerboard resolution tests continue to be used. Based upon recent developments in sparse algorithms and high performance computing resources, we demonstrate that direct methods are becoming feasible for large seismic tomography problems, and apply the technique to obtain a regional P-wave tomography model and its full resolution matrix with 267,520 parameters. Furthermore, we show that the structural analysis of the forward operators of the seismic tomography problems can provide insights into the inverse problem, and allows us to determine and exploit approximations that yield accurate solutions.