Parametrization for 2-D SH full waveform inversion

Abstract

With single-parameter full waveform inversion, estimating the inverse of the Hessian matrix will accelerate the convergence, but is computationally expensive. Therefore, an approximate Hessian, which is easier to compute, is often used. Similarly, in the case of multi-parameter full waveform inversion, the computation of the Hessian terms that contain derivatives with respect to more than one type of parameter, called cross-parameter Hessian terms, is not usually feasible. If the nonlin- ear inverse problem is well-posed, then the result should be independent of the parametrization choice provided we start close to the global minimum. However, the choice of parametrization will affect the rate of convergence to the exact solution and the “best” choice of parametrization is the one with the fastest rate. If the inverse problem is ill-posed the choice of parametrization introduces a bias towards a particular solution among the non-unique ones that explain the data. This obfuscates the search for the “best” parametrization. We investigated parametrization choices for a 2-D SH experiment where only the reflected wavefield is recorded. Our numerical examples suggest that certain type of scatterers are better inverted by one parametrization choice than another due to the parametrization bias. Therefore, there is nothing like a “best” parametrization in these single-component SH examples.Geoscience & EngineeringCivil Engineering and Geoscience