We consider the problem of determining earth properties from
seismic data, i.e. measurements with broadband acoustic waves
using sources and receivers at the surface. For current data
processing methods this is considered as a partially linearized
inverse problem, where data is modelled by linearization about a
smooth background medium, with a medium perturbation that contains
only high-frequency components. Both the background, and the
perturbation are to be estimated from the data. Reconstructing the
high-frequency perturbation is an imaging problem, for which so
called migration methods are used, that are based on geometrical
wave propagation in the background medium.
This talk is about establishing whether a choice of background
medium is consistent with the data. A criterion for this, needed
in the estimation of the background model, is given by the so
called semblance principle that must be satisfied by migrated
data, and that express internal consistency of redundant data,
given the background medium.
This talk focuses on the class of shot-geophone migration schemes. We show
that shot-geophone migrated data satisfies an appropriate semblance
principle, even in complex background velocities (that lead to the
presence of conjugate points). The latter is not the case for binwise
migration schemes, in particular Kirchhoff schemes, that form the
alternative to shot-geophone migration.