Accuracy of finite differences in smooth media

Ludek Klimes


Accuracy of finite-difference schemes of the 2nd and 4th order in 2-D and 3-D regular rectangular grids is studied. The method of designing the schemes and estimating their accuracy is proposed. Considered are the point schemes, expressed in terms of the values of the material parameters and of the wavefield at gridpoints. Only the common schemes applicable in smooth parts of seismic models, outside structural interfaces are taken into account. Finite differences at structural interfaces are studied in another paper.

The inaccuracy of finite-difference schemes is governed, above all, by the error in the propagation velocity, caused by the discretization. This error is estimated for several finite-difference schemes. It is explicitly dependent on the direction of propagation and on the wave polarization. The maximum propagation-velocity error over all directions of propagation enables to appreciate the accuracy of individual schemes in order to find the best one. The proposed approach is general, and applicable to other finite-difference schemes, for example, of the 6th and higher orders.


Seismic waves, finite differences of the 2nd and 4th order, 2-D and 3-D seismic modelling, elasticity.

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Revised version

Klimes, L.: Accuracy of finite differences in smooth media. PAGEOPH, 148 (1996), 39-76.

In: Seismic Waves in Complex 3-D Structures, Report 1, pp. 127-149, Dep. Geophys., Charles Univ., Prague, 1994.
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