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Ray methods usually give very accurate traveltimes and accurate amplitudes for geometric arrivals if the model is sufficiently smooth. These methods are efficient, and computing time is low to moderate. Diffractions and multiple reflections can be added, though at high computing times and never with complete accuracy. Ray methods are the methods of choice for many structural verification problems and are quite useful for stratigraphic problems if the interfaces are reasonably smoothly varying.

Ray methods usually give very accurate traveltimes and accurate amplitudes for geometric arrivals if the model is sufficiently smooth. These methods are efficient, and computing time is low to moderate. Diffractions and multiple reflections can be added, though at high computing times and never with complete accuracy. Ray methods are the methods of choice for many structural verification problems and are quite useful for stratigraphic problems if the interfaces are reasonably smoothly varying.

Wave equation methods solve the propagation problem over the entire model, rather than performing local solutions as in ray methods. Two commonly used wave methods are the Kirkhhoff<ref name=pt07r18>Hilterman, F. J., 1970, Three-dimensional seismic modeling: Geophysics, v. 35, p. 1020–1037., 10., 1190/1., 1440140</ref> method and the finite difference method.<ref name=pt07r28>Kelley, K. R., Ward, R. W., Treitel, S., Alford, R. M., 1976, Synthetic seismograms—a finite difference approach: Geophysics, v. 41, p. 2–27., 10., 1190/1., 1440605</ref> Kirkhhoff methods use a local approximation to obtain a reflected wave field at an interface. These methods can provide accurate traveltimes for geometric and diffracted arrivals and accurate amplitudes for geometric arrivals, even in complex media. Diffraction amplitudes are usually not very accurate for these methods, and multiples are usually absent. Computing time is moderate.

Wave equation methods solve the propagation problem over the entire model, rather than performing local solutions as in ray methods. Two commonly used wave methods are the Kirkhhoff<ref name=pt07r18>Hilterman, F. J., 1970, Three-dimensional seismic modeling: Geophysics, v. 35, p. 1020–1037., 10., 1190/1., 1440140</ref> method and the finite difference method.<ref name=pt07r28>Kelley, K. R., R. W. Ward, S. Treitel, and R. M. Alford, 1976, Synthetic seismograms—a finite difference approach: Geophysics, v. 41, p. 2–27., 10., 1190/1., 1440605</ref> Kirkhhoff methods use a local approximation to obtain a reflected wave field at an interface. These methods can provide accurate traveltimes for geometric and diffracted arrivals and accurate amplitudes for geometric arrivals, even in complex media. Diffraction amplitudes are usually not very accurate for these methods, and multiples are usually absent. Computing time is moderate.

Finite difference methods can provide very accurate results even in the most complex media. These methods provide exact numerical solutions and can include all wave phenomena, such as diffractions, multiples, and ground roll. The only limitations on finite difference methods are imposed by computing time, which is high in two dimensions and very high in three dimensions. This effectively limits grid size and hence the resolution obtainable. However, these are still the methods of choice for highly faulted complex models for which amplitude accuracy is important.

Finite difference methods can provide very accurate results even in the most complex media. These methods provide exact numerical solutions and can include all wave phenomena, such as diffractions, multiples, and ground roll. The only limitations on finite difference methods are imposed by computing time, which is high in two dimensions and very high in three dimensions. This effectively limits grid size and hence the resolution obtainable. However, these are still the methods of choice for highly faulted complex models for which amplitude accuracy is important.