A parallel evolution strategy for an earth imaging problem in geophysics

Abstract

In this paper we propose a new way to compute a rough approximation solution, to be later used as a warm starting point in a more refined optimization process, for a challenging global optimization problem related to Earth imaging in geophysics. The warm start consists of a velocity model that approximately solves a full-waveform inverse problem at low frequency. Our motivation arises from the availability of massively parallel computing platforms and the natural parallelization of evolution strategies as global optimization methods for continuous variables.Our first contribution consists of developing a new and efficient parametrization of the velocity models to significantly reduce the dimension of the original optimization space. Our second contribution is to adapt a class of evolution strategies to the specificity of the physical problem at hands where the objective function evaluation is known to be the most expensive computational part. A third contribution is the development of a parallel evolution strategy solver, taking advantage of a recently proposed modification of these class of evolutionary methods that ensures convergence and promotes better performance under moderate budgets.The numerical results presented demonstrate the effectiveness of the algorithm on a realistic 3D full-waveform inverse problem in geophysics. The developed numerical approach allows us to successfully solve an acoustic full-waveform inversion problem at low frequencies on a reasonable number of cores of a distributed memory computer.

On the Use of Adjoint Methods for Refractivity Estimation in the Troposphere

“…In future work, we will aim at improving our results by combining multiscale parametrization [9] and different regularization methods [8]. More realistic ducts will be analysed and robustness tests with respect to noise will be executed.…”

A Multiscale Parametrization for Refractivity Estimation in the Troposphere

“…Solving ( 2) for high-dimensional m is a highly ill-posed problem even in the absence of modeling or measurement errors and noise [4]. In the next section, we explain how to apply the search space reduction technique to reduce the complexity of (2), referring the works in [6], [7].…”

“…Besides, the interest can be to restrict the search direction such that some nonphysical local minima are avoided, or inversion parameters are polished (e.g. filtered, regularized) [6]. The reader is referred to [6] for further information about these ideas.…”

“…in geophysics (e.g., [6]). In this paper, we apply the multiscale strategy in the parametrization, being inspired from the ideas in [7].…”

“…Our objective is to investigate the potential of MPT to mitigate the nonlinearity of the problem in our context, prior to curing the ill-posedness using regularization [6], [7]. In this work, we propose the recipe for multiscale least-squares inverse problem using adjoint state method for wide-angle parabolic equation.…”