Reciprocity Theorems, Deconvolution Interferometry, and Imaging of Borehole Seismic Data

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.