Broad band trajectory mechanics

Abstract

Author(s): Vasco, DW; Nihei, K | Abstract: We present a trajectory-based solution to the elastodynamic equation of motion that is valid across a wide range of seismic frequencies. That is, the derivation of the solution does not invoke a high-frequency assumption or require that the medium have smoothly varying properties. The approach, adopted from techniques used in quantum dynamics, produces a set of coupled ordinary differential equations for the trajectory, the slowness vector and the elastic wave amplitude along the ray path. The trajectories may be determined by a direct solution of the governing equations or derived as the by-product of a numerical wavefield simulation. Synthetic tests with interfaces and layers containing increasingly narrow transition zones indicate that the conventional high-frequency trajectories associated with the eikonal equation bend too sharply into high-velocity regions as the wavelength exceeds the transition zone width. Tests in a velocity model, based upon mapped structural surfaces from the Geysers geothermal field in California, indicate that discrepancies between high-frequency and broad-band trajectories can exceed several hundred metres at wavelengths of 1 Hz. An application to a crosswell tomographic imaging experiment demonstrates that the technique provides a basis for the seismic monitoring of fluid flow along narrow features such as fracture zones.