Research

Normal modes; Full-Waveform Inversion; High-Performance Computing; Scientific Computing

(Figure above comes from IRIS.)

1. Normal mode computation at planetary scales (on going)

We apply fully unstructured tetrahedral meshes to discretize planets (for example, please see the preliminary reference earth model (RREM) below). To resolve the eigenvalue pollution issue, following the analysis separating the seismic point spectrum, we utilize a representation of the displacement for describing the oscillations of the non-seismic modes in the fluid outer core explicitly. Effectively, we separate out the essential spectrum which is naturally related to the Brunt-Väisälä frequency.

We have developed and exploited a novel, highly parallel and memory efficient polynomial filtered Lanczos algorithm for solving such problems of much larger size than those solved by traditional approaches. To the best of our knowledge, this is the first time that the direct calculation of the normal modes of 3-D strongly heterogeneous planets, in particular, Earth, Moon and Mars, is made feasible via a combination of multiple matrix-free methods and a separation of the essential spectra.

2. Elastic full-waveform inversion (FWI)

Motivation: We consider seismic land acquisition where the forward modeling can be viewed as solving an elastic boundary value problem. Vibroseis data (omitting correlation in time) are modeled by the Neumann-to-Dirichlet map: the boundary values are given by the normal traction underneath the base plate of the vibroseis and are zero (free surface) elsewhere.

Using the conditional Lipschitz stability estimate, we design full waveform inversion (FWI), with iterative regularization. The iterative regularization is implemented by projecting misfit gradients, after scaling, onto subspaces associated with the mentioned parametrizations. Consistent with the iterative regularization, we model elastic waves with the continuous Galerkin finite element method relating computational to parameter unstructured tetrahedral meshes. We illustrate our multi-parameter, multi-level, multi-frequency (sweep) inversion procedure in computational experiments of recovering the rough shapes and wave speeds of geological bodies from simple starting models, near (next row) and far (second next row) from the boundary.

3. 3D shape optimization

This is now joint work with TOTAL to invert for the internal boundaries of salt bodies.

4. Anisotropic waveform inversion

The work was performed during my internships with PGS.