Journal
STUDIA GEOPHYSICA ET GEODAETICA
Volume 46, Issue 2, Pages 355-381Publisher
SPRINGER
DOI: 10.1023/A:1019866422821
Keywords
Free Surface; Grid Spacing; Rayleigh Wave; Epicentral Distance; Stress Imaging
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Funding
- VEGA, Slovak Republic [1/1090/21]
- European Commission [EVG1-CT-2000-00026 SESAME]
- National Science Foundation [CDA96-01954]
- Silicon Graphics Inc.
- Institute for Crustal Studies, University of California at Santa Barbara
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We numerically tested accuracy of two formulations of Levander's (1988) stress-imaging technique for simulating a planar free surface in the 4(th)-order staggered-grid finite-difference schemes. We have found that both formulations (one with normal stress-tensor components at the surface, the other with shear stress-tensor components at the surface) require at least 10 grid spacings per minimum wavelength (lambda(min)/h = 10) if Rayleigh waves are to be propagated without significant grid dispersion in the range of epicentral distances up to 15 lambda(S)(dom). Because interior 4(th)-order staggered-grid schemes usually do not require more than 6 grid spacings per minimum wavelength, in the considered range of epicentral distances, it was desirable to find alternative techniques to simulate a planar free surface, which would not require denser spatial sampling than lambda(min)/h = 6. Therefore, we have developed and tested new techniques: 1. Combination of the stress imaging (with the shear stress-tensor components at the surface) with Rodrigues' (1993) vertically refined grid near the free surface. 2. Application of the adjusted finite-difference approximations to the z-derivatives at the grid points at and below the surface that uses no virtual values above the surface and no stress imaging. The normal stress-tensor components are at the surface in one formulation, while the shear stress-tensor components are at the surface in the other formulation. The three developed formulations give for the spatial sampling lambda(min)/h = 6 results very close to those obtained by the discrete-wavenumber method. Because, however, the technique with the vertically refined grid near the free surface requires 3 times smaller time step (due to the refined grid), the technique with adjusted finite-difference approximations is the most accurate and efficient technique from the examined formulations in the homogeneous halfspace.
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