ACCURACY OF FINITE‐DIFFERENCE MODELING OF THE ACOUSTIC WAVE EQUATION

two methods rapidly deteriorates. This effect, known as “grid dispersion,” must be taken into account in order to avoid erroneous interpretation of seismograms obtained by finite-difference techniques. Both seconti-order accuracy and fourth-order accuracy finite-difference algorithms are considered. For the second-order scheme, a good rule of thumb is that the ratio of the upper half-power wavelength of the source to the grid interval should be of the order of ten or more. For the fourth-order scheme, it is found that the grid can be twice as coarse (five or more grid points per upper half-power wavelength) and good results are still obtained. Analytical predictions of the effect of grid dispersion are presented; these seem to be in agreement with the experimental results. ence methods to that obtained by classical analytical methods for the simple case of an infinite twodimensional 90.degree wedge (quarter space) in an otherwise infinite homogeneous medium. The source field was that due to a line source distribution located parallel to the corner of the wedge (see Figure I). For analytical simplicity, the acoustic velocity of the wedge medium is taken to be zero. This is equivalent to having a perfectlj “soft” wedge medium such as a vacuum.