Theory of traveltime shifts around compacting reservoirs

Time-lapse traveltime shifts of reflection events recorded above hydrocarbon
reservoirs can be used to monitor production-related compaction and pore-
pressure changes. Existing methodology, however, is limited to zero-offset rays
and cannot be applied to traveltime shifts measured on prestack seismic data.
Here, we give an analytic 3D description of stress-related traveltime shifts for
rays propagating along arbitrary trajectories in heterogeneous anisotropic me-
dia.
The nonlinear theory of elasticity helps to express the velocity changes in
and around the reservoir through the excess stresses associated with reservoir
compaction. Since this stress-induced velocity field is both heterogeneous and
anisotropic, it should be studied using prestack traveltimes or amplitudes. Then
we obtain the traveltime shifts by first-order perturbation of traveltimes that
accounts not only for the velocity changes, but also for 3D deformation of reflec-
tors. The resulting closed-form expression can be efficiently used for numerical
modeling of traveltime shifts and, ultimately, for reconstructing the stress dis-
tribution around compacting reservoirs.
The analytic results are applied to a 2D model that includes a compacting rect-
angular resevoir embedded in an initially homogeneous and isotropic medium.
The computed velocity changes around the reservoir are primarily caused by
deviatoric stresses and produce an anisotropic medium with substantial values
of the Thomsen parameters ǫ and δ and variable orientation of the symmetry
axis. The offset dependence of the traveltime shifts should play a crucial role
in estimating the anisotropy parameters and the compaction-related deviatoric
stress components.