Nonlinear inversion of correlation waveforms with hierarchical reconstructions

Introduction

Waves propagating through a complex medium provide a non-invasive way to probe its interior structures. In ambient noise imaging, the input data are the cross-correlation of the stochastic wavefields.

Optimization Problem

To reconstruct the properties of the medium, the waveform inversion is formulated as an optimization problem involving a misfit function whose convexity plays a critical role in the achievable spatial resolution of the inversion results, especially in the absence of a priori information about the medium.

Current Limitations

Current inversions are often limited by:

• Computational cost
• Cross-talk between the physical quantities
• The use of single-scattering approximations

Project Overview

Project INCORWAVE proposes to create a new mathematical and computational framework for nonlinear inversion of full waveform cross-correlation. Two specific problems are considered:

1. Reconstruction of geophysical visco-elasticity tensors with applications to Earth's subsurface monitoring.
2. Reconstruction of three-dimensional flows in the Sun to characterize the poorly understood properties of deep solar convection.

Inversion Procedure

To improve the convexity of misfit functions, the inversion procedure of project INCORWAVE will follow a hierarchical progression which is established by selecting subsets of input data, unknown parameters, and frequencies.

Selection Criteria

The choice of each of these subsets, as well as the associated misfit function, is controlled by criteria in the form of convergence estimates.

Modeling Operators

Indispensable to meaningful inversion is accurate modeling operators that describe the physics under consideration and that are adapted to the treatment of real data.

Development of Solvers

For the reconstruction of the elasticity tensor, the project will develop a solver in terms of P- and S-potentials for heterogeneous media. A 3D global Sun vector-wave solver is created for the inversion of the convection component of the solar flow that does not bear symmetry.