Generic Gradient Expression for Robust FWI of Surface Waves

Abstract

A key feature of FWI is the misfit function that considers the point-to-point difference between the observed data and the calculated data, to provide high-resolution imaging using a local optimization approach. However, in the case of slow surface waves propagating in the low velocity medium of the near surface, cycle-skipping can occur, and the optimization may be locked in a local minimum. More robust misfit functions have recently been proposed with the aim of mitigating this problem for surface waves, integrating recipes used for 1D surface wave analysis in FWI and moving to misfit functions in alternative domains. The aim of this study is to define the gradient expression of such misfit functions through a generic adjoint formalism and to present a simple synthetic example showing the more robust behavior of these approaches compared to the classical FWI approach.

Wave equation dispersion inversion of surface waves recorded on irregular topography

“…Li and Schuster (2016) developed a method for inverting dispersion curves associated with surface waves. This method is denoted as wave equation dispersion inversion (WD) and has the benefit of robust convergence compared to the tendency of full waveform inversion (FWI) to getting stuck in local minima (Masoni et al, 2014;Solano et al, 2014;Yuan et al, 2015;Köhn et al, 2016). It has the advantage over the traditional inversion of dispersion curves (Xia et al, 1999;Socco et al, 2010;Maraschini et al, 2010) in that is does not assume a layered model and is valid for arbitrary 2D or 3D media.…”

Full waveform inversion of SH‐ and Love‐wave data in near‐surface prospecting

“…(), Masoni et al . () and Pérez Solano, Donno and Chauris () increased the robustness of 2D surface wave inversion by defining new cost functions in different data domains. Apart from methodical developments and synthetic inversion tests, the number of 2D surface wave field data applications are currently very limited.…”

“…However, the extension of this concept to 2D surface wave inversion using local optimisation methods is a challenging task, due to potential cycle-skipping problems in case of the strongly dispersive surface wavefield. Masoni et al (2013), Masoni et al (2014a), Masoni et al (2014b) and Pérez Solano, Donno and Chauris (2014) increased the robustness of 2D surface wave inversion by defining new cost functions in different data domains. Apart from methodical developments and synthetic inversion tests, the number of 2D surface wave field data applications are currently very limited.…”