Ha, Joseph2011-06-212022-10-262011-06-212022-10-2619781978https://ir.wgtn.ac.nz/handle/123456789/24884A propagation model is developed to describe the propagation of P wave signals through the subducted lithosphere. The P wave signals are precursory to second P arrivals which have Jeffrey-Bullen travel times. The model theory is based on an approximation of the complete Helmholtz wave equation; an approximation that may be termed parabolic. The model is formulated in terms of a correlation function between the disturbances at two points of the wave field; the two-point coherence function, from which the intensity may be derived. An algorithm restricted to media that can be termed locally quadratic is developed. The solution so obtained is improved by an integral relation between the solutions of the Helmholtz and parabolic equations. The algorithm suggests an interpretation of the radiation field in terms of sub-beams. The sub-beam may be regarded as the wave analogue of a ray. The prediction of the parabolic propagation model is compared to the propagation of the precursors by considering the amplitude distance curves of the precursor and the theory. The best-fitting linear amplitude-distance curve indicates the curvature of the quadratic profile of the subducted lithosphere to be 2.57 x 10-6 km-2.pdfen-NZParabolic differential equationsWave equationSeismic wavesText