Geological constraints in velocity inversion
, by Jos van Trier

The result of velocty-inversion methods depends on the parametrization of the velocity
model an dthe way it is constrained during the inversion. When a smooth-velocity model
is chosen, the velocity inversion can often be performed efficiently, but the risk of
finding a non-geological model is severe.
In this paper geological information is used to parametrize the velocity model and to
constrain the velocity inversion, leading to a more realistic velocity model. An important
part of the geological information comes from interpreting the seismic image of the
subsurface. The image is obtained by migration-velocity optimization with a smooth velocity
model. The smooth, resulting from the optimization, correctly models cumulative traveltimes
to reflectors.
Structural boundaries are picked from the image, where the boundaries are given a certain
width, corresponding to the seismic resolution in the image. The picked boundaries are
used to parametrize the velocity model in several structures, each with a velocity function
independent of the others. The velocity functions are modeled by splines.
A second optimization determines the velocities inside the structures (the boundaries
themselves are kept fixed). The data used in the optimization are the traveltimes of rays
traveling from reflectors to the surface through the smooth model. The optimization is
damped by geological constraints, coming from well logs and general geological information.