Wavefield inversion and tomography using the energy norm

Abstract

Wavefield migration and tomography are the most precise methods for subsurface imaging and characterization in complex settings. Tomography provides an accurate earth model of physical properties, usually seismic wave velocities, so that migration can deliver an image with the correct position of geological interfaces. Although these methods, which are based on robust wavefield extrapolation, are considered to be state-of-art technology, both suffer from large computational cost, slow convergence to accurate earth models, ambiguity and crosstalk contamination between model parameters, and imaging artifacts caused by improper correlation between wavefields, among other problems. Considering the interest of the geophysical community in improving these methods and the theoretical framework already developed in wave physics, I propose solutions to wavefield imaging problems based on a powerful measure of wavefield energy called{\it energy norm}. Since this measure emerges from the differential equations that govern wave propagation, it naturally leads to computational tools that can exploit important wavefield features, such as propagation and polarization directions. Using the energy norm, I propose techniques to attenuate spurious artifacts and expedite convergence to more geologically-plausible earth models, as well as to improve source location estimation for passive seismic methods. The energy norm also enables us to implement correlation of different wave modes without computationally intensive wave-mode separation. Overall, the energy norm facilitates a whole range of techniques suited for wavefield imaging, since it is a general concept applicable to various problems involving acoustic or elastic propagation in isotropic or anisotropic media. Here, I present solutions to these problems persistent in exploration seismology, including passive- and active-source seismic experiments. Numerical experiments show the efficacy of these applications for models that emulate complex subsurface structures, such as salt bodies, diffractors, dipping layers and faults. With available field datasets, I validate the methodology for various challenging scenarios currently employed in exploration seismology: 3D, multicomponent, active or passive acquisition, ocean-bottom nodes, etc. Developing novel, accurate and efficient techniques for wavefield imaging, as well as their validation with field data, serves as my main contribution for improving seismic exploration efficiency. The techniques developed in this thesis can potentially be applied to non-exploration problems that involve other types of wave phenomena different from seismic.