Stability and Grid Dispersion of the P-SV 4th-Order Staggered-Grid Finite-Difference Schemes

Stability and grid dispersion in the P-SV 4th-order in space, 2nd-order in time, displacement-stress staggered-grid finite-difference scheme is investigated in the case of a homogeneous unbounded medium. All results, however, also apply to the velocity-stress and displacement- velocity-stress finite-difference schemes. Independent stability conditions for the P and S waves are obtained by exact separation of equations for the two types of waves. Since the S-wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5, commonly used in numerical modelling, the sampling of the minimum S wavelength by 6 grid spacings (with the velocity difference not larger than 2.5%) is recommended. Grid dispersion is strongest for a wave propagating in a direction of a coordinate axis and weakest for a wave propagating along a plane diagonal. Grid dispersion in the 4 ^th -order scheme for the sampling ratios s = 1/5 and s = 1/6 is smaller than grid dispersion in the 2 ^nd -order scheme for s = 1/10 and s = 1/12, respectively.