Spectral-element and adjoint methods for structural tomography and seismic source parameters inversion

The development of high-performance computing and numerical techniques has enabled global and regional tomography to reach high levels of precision, and seismic adjoint tomography has become a state-of-the-art tomographic technique.
Adjoint tomography uses full waveform simulations and back projection to compute finite frequency sensitivity kernels. These kernels describe the variation of the discrepancy (or misfit) between observed seismic data and modeled synthetics as a function of the model parameters. They are used in an iterative inversion aiming at minimizing the misfit function, thereby recovering model parameters.

This inverse approach benefits from an accurate numerical technique to solve the seismic wave equation in complex 3D media, in the first place. Here I use a spectral-element method, which contrary to finite-element methods (FEM), uses high degree Lagrange polynomials, allowing the technique to not only handle complex geometries, like the FEM, but also to retain the strength of exponential convergence and accuracy due to the use of high degree polynomials.

After describing spectral-element and adjoint methods, I will discuss two applications: (1) a 3D adjoint tomography for the Middle East to improve seismic waveform predictions in the area, and (2) results on seismic source parameters inversion for seismic monitoring.