NDLI: Low dispersive modeling of Rayleigh waves on partly staggered grids

Content Provider	Springer Nature Link
Author	Rojas, O. Day, S. M. Otero, B. Castillo, J. E.
Copyright Year	2013
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 $\lambda _{\text {MIN}}^{\mathrm {S}}$ .
Ending Page	43
Page Count	15
Starting Page	29
File Format	PDF
ISSN	14200597
e-ISSN	15731499
Journal	Computational Geosciences
Issue Number	1
Volume Number	18
Language	English
Publisher	Springer International Publishing
Publisher Date	2013-10-27
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Staggered grid Wave equation Simulation and numerical modeling Earth Sciences Geotechnical Engineering & Applied Earth Sciences Methods of ordinary differential equations Hydrogeology Finite difference High-order modeling First-order hyperbolic equations Mathematical Modeling and Industrial Mathematics Finite difference methods Soil Science & Conservation
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications Computational Mathematics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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