Simple elastic finite-difference scheme

This article investigates which features of the elastic finite-difference schemes are essential for their accuracy and which ones allow simplifications. It is shown that the schemes employing the geometrically averaged parameters are more accurate than those using local material parameters, mainly when a discontinuity passes between the grid lines. It is also shown that the accuracy of the mixed spatial derivatives at the internal grid points does not degrade when the number of the implicitly employed stress values and the geometrically averaged material parameters decreases from four to two (the so-called full and short forms, respectively), The shea and full forms give the same numerical results, while 50% of the arithmetic operations are saved with the short one. However, at the free-surface points, such a simplification is not permitted, and the full form should be used. Based on these results, a new simple elastic scheme (called PS2) is suggested.