A hybrid multiresolution meshing technique for finite element three‐dimensional earthquake ground motion modelling in basins including topography

SUMMARY This paper is concerned with a finite element method that uses hybrid meshes of multiresolution structured and unstructured meshes to simulate earthquake ground motion in large basins. While standard octree-based mesh methods use cubic elements and rely on mesh refinement to model topography, the present hybrid meshes use tetrahedral elements to model complicated layer interfaces and above-ground surfaces and to provide a transition between cubic elements of different sizes. The hybrid meshes avoid the step-like character inherent to the cubic meshes and the resulting concomitant loss of accuracy. Several numerical experiments of increasing complexity are carried out to verify and illustrate the proposed technique.

[1]  Arben Pitarka,et al.  3D Elastic Finite-Difference Modeling of Seismic Motion Using Staggered Grids with Nonuniform Spacing , 1999 .

[2]  Tsuyoshi Ichimura,et al.  Earthquake Motion Simulation with Multiscale Finite-Element Analysis on Hybrid Grid , 2007 .

[3]  J. Kristek,et al.  Seismic-Wave Propagation in Viscoelastic Media with Material Discontinuities: A 3D Fourth-Order Staggered-Grid Finite-Difference Modeling , 2003 .

[4]  Hiroyuki Fujiwara,et al.  Finite-element Simulation of Seismic Ground Motion with a Voxel Mesh , 2004 .

[5]  Ezio Faccioli,et al.  2d and 3D elastic wave propagation by a pseudo-spectral domain decomposition method , 1997 .

[6]  Arthur Frankel,et al.  Three-dimensional simulations of ground motions in the San Bernardino Valley, California, for hypothetical earthquakes on the San Andreas fault , 1993, Bulletin of the Seismological Society of America.

[7]  D. Komatitsch,et al.  The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures , 1998, Bulletin of the Seismological Society of America.

[8]  Kim B. Olsen,et al.  Three-dimensional simulation of earthquakes on the Los Angeles fault system , 1996, Bulletin of the Seismological Society of America.

[9]  D. P. Young,et al.  A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics , 1990 .

[10]  J. Sochacki Absorbing boundary conditions for the elastic wave equations , 1988 .

[11]  D. Komatitsch,et al.  Spectral-element simulations of global seismic wave propagation—I. Validation , 2002 .

[12]  O. Ghattas,et al.  Parallel Octree-Based Finite Element Method for Large-Scale Earthquake Ground Motion Simulation , 2005 .

[13]  J. Lysmer,et al.  Finite Dynamic Model for Infinite Media , 1969 .

[14]  M. Dumbser,et al.  An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes — II. The three-dimensional isotropic case , 2006 .

[15]  Géza Seriani,et al.  3-D large-scale wave propagation modeling by spectral element method on Cray T3E multiprocessor , 1998 .

[16]  K. Koketsu,et al.  Specific distribution of ground motion during the 1995 Kobe Earthquake and its generation mechanism , 1998 .

[17]  A. Patera A spectral element method for fluid dynamics: Laminar flow in a channel expansion , 1984 .

[18]  Jianlin Wang,et al.  Three-dimensional nonlinear seismic ground motion modeling in basins , 2003 .

[19]  Thomas H. Heaton,et al.  Characterization of Near-Source Ground Motions with Earthquake Simulations , 2001 .

[20]  Gerard T. Schuster,et al.  Simulation of 3D elastic wave propagation in the Salt Lake Basin , 1995, Bulletin of The Seismological Society of America (BSSA).

[21]  Thomas J. R. Hughes,et al.  Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies , 1985 .

[22]  José M. Carcione,et al.  Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures , 1997, Bulletin of the Seismological Society of America.

[23]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[24]  Hiroyuki Fujiwara,et al.  3D finite-difference method using discontinuous grids , 1999, Bulletin of the Seismological Society of America.

[25]  M. Dumbser,et al.  An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - I. The two-dimensional isotropic case with external source terms , 2006 .

[26]  Géza Seriani,et al.  Numerical simulation of interface waves by high‐order spectral modeling techniques , 1992 .

[27]  Shuo Ma,et al.  Modeling of the Perfectly Matched Layer Absorbing Boundaries and Intrinsic Attenuation in Explicit Finite-Element Methods , 2006 .

[28]  Shuo Ma,et al.  Hybrid Modeling of Elastic P-SV Wave Motion: A Combined Finite-Element and Staggered-Grid Finite-Difference Approach , 2004 .

[29]  Tiankai Tu,et al.  High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers , 2003, ACM/IEEE SC 2003 Conference (SC'03).

[30]  J. Kristek,et al.  3D Heterogeneous Staggered-grid Finite-difference Modeling of Seismic Motion with Volume Harmonic and Arithmetic Averaging of Elastic Moduli and Densities , 2002 .

[31]  Robert W. Graves,et al.  Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences , 1996, Bulletin of the Seismological Society of America.

[32]  David R. O'Hallaron,et al.  Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers , 1998 .