Interferometry in Perturbed Media

Interferometry recovers the impulse response of waves propagating between two sensors as if one of them acts as a source. The primary focus of this thesis is on providing a framework for interferometry based on perturbation theory that can be used for the direct reconstruction of the portion of the data that is of interest for imaging and inversion methodologies. I derive general reciprocity theorems in perturbed acoustic media. These theorems show that the wavefield perturbations are extracted from cross-correlating the perturbations detected by one receiver with unperturbed waves sensed by another. Apart from applications to interferometry, the representation theorems presented here can also be used for inverse-scattering and time-lapse monitoring. I also present a theory describing interferometry by deconvolution, based on a series expansion of deconvolved waves in the wavefield perturbations. This expansion is used to give a scattering-based interpretation of the physics of deconvolution interferometry. Deconvolution interferometry, like its correlation counterpart, also retrieves the impulse response between the receivers, but with boundary conditions that are different than those of the original measurement. Interferometry by deconvolution is particularly important for recovering the impulse response from noise records excited by a long and complicated source-time function. As an application of deconvolution interferometry in exploration geophysics, I elaborate on the use of this method for processing seismic-while-drilling data, while comparing to more standard practices. Interferometry by deconvolution yields wide-band images from drilling noise without requiring an independent estimate of the drill-bit excitation. This concept is applied to borehole measurements of drilling noise at the San Andreas Fault Observatory at Depth (SAFOD) to provide a broadside depth image of the San Andreas Fault system. This image displays the localized subsurface structure of the San Andreas Fault and of another major blind fault. Finally, the representation theorems in perturbed media are used to develop an interferometry method that targets the interference of specific arrivals in the data. This target-oriented interferometry method can be used to reconstruct primary reflections from internal multiples. The interference of internal multiples can be used to image subsalt structures using borehole receiver arrays placed beneath salt. I test this method both on numerical experiments and on field data from deep-water Gulf of Mexico.