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Interferometry by deconvolution
Content:
         Interferometry allows us to synthesize data recorded at any two receivers into
waves that propagate between these receivers as if one of them behaves as a
source. This is typically accomplished by cross-correlations. Based on perturba-
tion theory and representation theorems, we show that interferometry can also
be done by deconvolutions for arbitrary media and multidimensional experi-
ments. 
          This is important for interferometry applications where the excitation
is described by a complicated function. First, we derive a series expansion that
proves that interferometry can be accomplished by deconvolution before source
integration. This method, unlike using cross-correlations, yields only causal scat-
tered waves that propagate between the receivers. We provide an analysis in
terms of singly and multiply scattered waves. Because deconvolution interfer-
ometry shapes the zero-offset trace in the interferometric shot gather into a
band limited spike centered at time equal zero, spurious arrivals are generated
by the method.
         Here, we explain the physics behind these spurious arrivals and
demonstrate the they usually do not map onto coherent structures in the im-
age domain. We also derive an interferometry method that does deconvolution
after source integration that is associated with existing interferometry tech-
niques. Deconvolution after source integration yields both causal and acausal
scattering responses, and it also introduces spurious events. Finally, we illus-
trate the main concepts of deconvolution interferometry and its differences with
the correlation-based approach through stationary-phase analysis and with nu-
merical examples.