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Low dispersive modeling of Rayleigh waves on partly staggered grids |
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| Authors: | O Rojas B Otero J E Castillo S M Day |
| Institution: | 1. Universidad Central de Venezuela, Caracas, Venezuela 2. Universitat Politécnica de Catalunya-TECH, Barcelona, Spain 3. San Diego State University, San Diego, CA, USA |
| Abstract: | In elastic media, finite-difference (FD) implementations of free-surface (FS) boundary conditions on partly staggered grid (PSG) use the highly dispersive vacuum formulation (VPSG). The FS boundary is embedded into a “vacuum” grid layer (null Lame’s constants and negligible density values) where the discretized equations of motion allow computing surface displacements. We place a new set of compound (stress-displacement) nodes along a planar FS and use unilateral mimetic FD discretization of the zero-traction conditions for displacement computation (MPSG). At interior nodes, MPSG reduces to standard VPSG methods and applies fourth-order centered FD along cell diagonals for staggered differentiation combined with nodal second-order FD in time. We perform a dispersion analysis of these methods on a Lamb’s problem and estimate dispersion curves from the phase difference of windowed numerical Rayleigh pulses at two FS receivers. For a given grid sampling criterion (e.g., six or ten nodes per reference S wavelength λ S), MPSG dispersion errors are only a quarter of the VPSG method. We also quantify root-mean-square (RMS) misfits of numerical time series relative to analytical waveforms. MPSG RMS misfits barely exceed 10 % when nine nodes sample the minimum S wavelength $\lambda _{\text {MIN}}^{\mathrm {S}}$ in transit (along distances $\sim $ 145 $\lambda _{\text {MIN}}^{\mathrm {S}}$ ). In same tests, VPSG RMS misfits exceed 70 %. We additionally compare MPSG to a consistently fourth-order mimetic method designed on a standard staggered grid. The latter equates the former’s dispersion errors on grids twice denser and shows higher RMS precision only on grids with six or less nodes per $\lambda _{\text {MIN}}^{\mathrm {S}}$ . |
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