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

Author： Moczo P. Kristek J. Bystrický E.

ISSN： 0039-3169

Source： Studia Geophysica et Geodaetica, Vol.44, Iss.3, 2000-07, pp. : 381-402

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Abstract

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.