Elastic Kirchhoff-Helmholtz Synthetic Seismograms

An approximate hybrid formulation of the elastic Kirchhoff-Helmholtz theory for numerical simulation of seismic wave propagation in multilayered inhomogeneous and transversely isotropic media is developed. The layer boundaries can be curved or irregular. We insert a general computational ansatz into the basic elastodynamic divergence theorem to express the unknown variables in terms of slowly varying amplitude and phase functions. In situations where the geometrical optics approximation becomes invalid, more accurate methods can be applied to compute these functions. In particular, the kernel remains regular when rays have caustics on the target integral surface. Branch points are taken into account to include head waves. Both elementary solutions and WKBJ expansion are employed to compute the Green’s function. To reduce the resulting integral to a numerical form, the surface is divided into a set of segments and the above functions are replaced by their local polynomial series in the vicinity of each segment. It allows us to construct an error-predictive numerical algorithm in which the truncation error is prescribed via the higher order terms of such series. We show, using geologically relevant synthetic models, the performance of the proposed technique.