In this study, we want to show that the use of the first-order additional components of the ray method in the seismic wavefield modeling is feasible and can bring a substantial improvement to the standard ray results obtained with the zero-order ray approximation only. For the calculation of a first-order additional component, spatial derivatives of the parameters of the medium and of the zero-order ray amplitude term are necessary. We calculate the latter derivative approximately from neighboring rays by substituting the derivative by a finite differences.
In order to test the accuracy of the calculations with first-order additional components, we study situations, in which exact solutions are known and in which the zero-order ray theory gives incomplete results. One such situation is a vicinity of nodal lines of a single force point source in a homogeneous medium. We study in detail the effects of incorporating individual higher-order ray terms on the accuracy of the ray calculations. Another situation, in which the calculations with first-order additional components are tested against the exact solution is nearly normal PS reflection. In both cases, the use of first-order additional components substantially improves the fit with the exact solution.
Finally, we show the effects of the first-order additional terms in the VSP modeling. They include such phenomena like elliptical polarization of P waves or their transverse polarization and longitudinal polarization of S waves, unknown in the zero-order approximation of the ray method.
Eisner, L. & Psencik, I.: Computation of additional components of the first-order ray approximation in isotropic media. PAGEOPH, 148 (1996), 227-253.