Bayesian eikonal tomography using Gaussian processes

TL;DR

This paper introduces a Bayesian approach to eikonal tomography using Gaussian processes, providing a rigorous interpolation method that includes uncertainty quantification for phase velocity maps from surface wave data.

Contribution

It formulates eikonal tomography within a Gaussian process framework, enabling analytical derivation of phase delay gradients and a fully Bayesian estimation of phase velocities.

Findings

Uncertainty estimates in traditional eikonal tomography are often underestimated.

The Gaussian process approach improves interpolation accuracy and uncertainty quantification.

The method allows for analytical solutions without sampling, enhancing efficiency.

Abstract

Eikonal tomography has become a popular methodology for deriving phase velocity maps from surface wave phase delay measurements. Its high efficiency makes it popular for handling datasets deriving from large-N arrays, in particular in the ambient-noise tomography setting. However, the results of eikonal tomography are crucially dependent on the way in which phase delay measurements are interpolated, a point which has not been thoroughly investigated. In this work, I provide a rigorous formulation for eikonal tomography using Gaussian processes (GPs) to interpolate phase delay measurements, including uncertainties. GPs allow the posterior phase delay gradient to be analytically derived. From the phase delay gradient, an excellent approximate solution for phase velocities can be obtained using the saddlepoint method. The result is a fully Bayesian result for phase velocities of surface waves, incorporating the nonlinear wavefront bending inherent in eikonal tomography, with no sampling required. The results of this analysis imply that the uncertainties reported for eikonal tomography are often underestimated.