Rigid boundary conditions for staggered-grid modelling
Zaiming Jiang, John C. Bancroft, Laurence R. Lines
Staggered-grid modelling methods have been shown previously to be more accurate than non-staggered grid schemes when liquids are involved inside the subsurface models. This report shows that the staggered-grid modelling can also accurately simulate seismic activities when rigid boundaries are involved. The rigid boundary is discussed from both mathematical and numerical perspectives. First, formulas about rigid boundary reflections are mathematically derived and qualitatively interpreted. Specifically, seismic reflection amplitude and polarity changes at wide incident angles are discussed. Second, a finite-difference implementation of the rigid boundary conditions is designed within a staggered-grid modelling scheme and the modelling results are presented. It is shown that the numerical modelling results accurately match the mathematical derivations and qualitative interpretations. The validity of the implementation method of the rigid boundary conditions within a staggered-grid modelling scheme is also proven.