Matrix approach of seismic imaging

This thesis investigates new imaging approaches to perform seismic exploration in complex geological environments. The standard way of exploring the Earth is to shake the ground and apply time delays to the backscattered seismic wavefield to retrieve a reflectivity map of the crust. For this strategy to yield efficient results, the time delays corresponding to each depth need to be accurately computed, hence paradoxically requiring prior knowledge on the smoothly varying part of the velocity distribution in the underground. Unexpected velocity variations lead to aberrations: wavefronts distortions that modify the time to depth relationship. When studying unknown media, this happens in a way that is hardly predictable and constitute a first limitation of this traditional imaging approach. Another limitation stems from the successive interactions of the seismic wavefield with the medium heterogeneities, which lead to multiple reflections and multiple scattering events in the recorded echoes where the time to depth relationship not even holds any more. These phenomena usually coexist with the single scattering component that conveys information on the reflectors positions, but overtake it for extreme heterogeneities densities and impair the subsequent images. Such challenging issues prevent efficient investigations of the subsoil. Ultrasound imaging relies on similar physical principles than seismic imaging, and hence encounters analogous hurdles when probing heterogeneous media. Matrix methods have been proposed to overcome them for non-destructive testing and medical imaging purposes, and are adapted to geophysics in the present thesis. The approach takes advantage of impulse responses between geophones measured by diffuse seismic field cross correlation. These have already been used in previous works for surface wave tomography. Here, their body wave component is leveraged for depth imaging purposes. To that aim, they are interpreted as a reflection matrix, which gathers all the available information on the medium and can thus undergo a series of mathematical operations to get rid of the wavefield distortions and incoherent noise that impede the imaging process. In a first part, the case of the Erebus volcano in Antarctica is studied, where the seismic wavefield suffers from a significantly high level of multiple scattering that makes conventional imaging methods fail. The reflection matrix measured at the surface is projected down to depth by applying time delays both at emission and reception. This process emulates virtual emitters and receivers inside the volcano and leads to a new matrix gathering the pairwise impulse responses between them. A confocal filter followed by an iterative time reversal analysis of this matrix makes it possible to selectively extract the single scattering contribution and use it for imaging purposes, unveiling the structure of the volcano’s chimney. In a second part, the aberrations issues are tackled by studying the San Jacinto Fault Zone, California. Because of the wavefront distortions induced by the sedimentary layers, the subsoil images suffer from a loss in contrast and resolution. The surface reflection matrix is again projected down to depth at both emission and reception, then a space-Fourier transform is performed at the output and the ballistic phase is subtracted. This leads to a new mathematical object, the distortion matrix, which allows to gain insight into the aberration contribution undergone by the wavefronts as travelling through the crust. A singular value analysis of this distortion matrix makes it possible to extract the phase law that, when conjugated and applied to the Earth’s reflection response both at emission and reception, cancels the aberrations effects in the seismic wavefield on its way down and back respectively. This enables to map the fault depth structure with near to diffraction resolution.