RegSEM: a versatile code based on the spectral element method to compute seismic wave propagation at the regional scale

The spectral element method, which provides an accurate solution of the elastodynamic problem in heterogeneous media, is implemented in a code, called RegSEM, to compute seismic wave propagation at the regional scale. By regional scale we here mean distances ranging from about 1 km (local scale) to 90 • (continental scale). The advantage of RegSEM resides in its ability to accurately take into account 3-D discontinuities such as the sediment-rock interface and the Moho. For this purpose, one version of the code handles local unstructured meshes and another version manages continental structured meshes. The wave equation can be solved in any velocity model, including anisotropy and intrinsic attenuation in the continental version. To validate the code, results from RegSEM are compared to analytical and semi-analytical solutions available in simple cases (e.g. explosion in PREM, plane wave in a hemispherical basin). In addition, realistic simulations of an earthquake in different tomographic models of Europe are performed. All these simulations show the great flexibility of the code and point out the large influence of the shallow layers on the propagation of seismic waves at the regional scale. RegSEM is written in Fortran 90 but it also contains a couple of C routines. It is an open-source software which runs on distributed memory architectures. It can give rise to interesting applications, such as testing regional tomographic models, developing tomography using either passive (i.e. noise correlations) or active (i.e. earthquakes) data, or improving our knowledge on effects linked with sedimentary basins.

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

[2]  K. Marfurt Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations , 1984 .

[3]  P. Lognonné Normal modes and seismograms in an anelastic rotating Earth , 1991 .

[4]  G. A. Baker Error Estimates for Finite Element Methods for Second Order Hyperbolic Equations , 1976 .

[5]  Jean-Pierre Vilotte,et al.  Solving elastodynamics in a fluid-solid heterogeneous sphere: a parallel spectral element approximation on non-conforming grids , 2003 .

[6]  Jean Virieux,et al.  SH-wave propagation in heterogeneous media; velocity-stress finite-difference method , 1984 .

[7]  Paul Christiano,et al.  On the effective seismic input for non-linear soil-structure interaction systems , 1984 .

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

[9]  J. Virieux P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method , 1986 .

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

[11]  A. Tarantola Inversion of seismic reflection data in the acoustic approximation , 1984 .

[12]  Emanuele Casarotti,et al.  CUBIT and Seismic Wave Propagation Based Upon the Spectral-Element Method: An Advanced Unstructured Mesher for Complex 3D Geological Media , 2008, IMR.

[13]  Carl Tape,et al.  Seismic tomography of the southern California crust based on spectral‐element and adjoint methods , 2010 .

[14]  Qinya Liu,et al.  Tomography, Adjoint Methods, Time-Reversal, and Banana-Doughnut Kernels , 2004 .

[15]  D. Komatitsch,et al.  Spectral-element simulations of global seismic wave propagation: II. Three-dimensional models, oceans, rotation and self-gravitation , 2002 .

[16]  A. Fichtner,et al.  Efficient numerical surface wave propagation through the optimization of discrete crustal models—a technique based on non-linear dispersion curve matching (DCM) , 2008 .

[17]  Andreas Fichtner,et al.  Full waveform tomography for radially anisotropic structure: New insights into present and past states of the Australasian upper mantle , 2009 .

[18]  C. Bassin,et al.  The Current Limits of resolution for surface wave tomography in North America , 2000 .

[19]  Roberto Paolucci,et al.  Near-Fault Earthquake Ground-Motion Simulation in the Grenoble Valley by a High-Performance Spectral Element Code , 2009 .

[20]  B. Romanowicz,et al.  Towards improving ambient noise tomography using simultaneously curvelet denoising filters and SEM simulations of seismic ambient noise , 2011 .

[21]  M. Ritzwoller,et al.  Monte-Carlo inversion for a global shear-velocity model of the crust and upper mantle , 2002 .

[22]  A. Tarantola,et al.  Two‐dimensional nonlinear inversion of seismic waveforms: Numerical results , 1986 .

[23]  K. R. Kelly,et al.  SYNTHETIC SEISMOGRAMS: A FINITE ‐DIFFERENCE APPROACH , 1976 .

[24]  John Lysmer,et al.  A Finite Element Method for Seismology , 1972 .

[25]  É. Delavaud,et al.  Interaction between surface waves and absorbing boundaries for wave propagation in geological basins: 2D numerical simulations , 2005 .

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

[27]  Jean-Pierre Vilotte,et al.  Triangular Spectral Element simulation of two-dimensional elastic wave propagation using unstructured triangular grids , 2006 .

[28]  Jean-Pierre Vilotte,et al.  Coupling the spectral element method with a modal solution for elastic wave propagation in global earth models , 2003 .

[29]  L. Pérez-Rocha,et al.  Diffraction of elastic waves by three-dimensional surface irregularities. Part II , 1989 .

[30]  M. Longuet-Higgins A theory of the origin of microseisms , 1950, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[31]  D. Boore,et al.  Finite Difference Methods for Seismic Wave Propagation in Heterogeneous Materials , 1972 .

[32]  Jean-Jacques Marigo,et al.  2-D non-periodic homogenization of the elastic wave equation: SH case , 2010 .

[33]  Jean Virieux,et al.  SH-wave propagation in heterogeneous media: velocity-stress finite-difference method , 1984 .

[34]  R. Sadourny Conservative Finite-Difference Approximations of the Primitive Equations on Quasi-Uniform Spherical Grids , 1972 .

[35]  Andreas Fichtner,et al.  The adjoint method in seismology – I. Theory , 2006 .

[36]  Jean-Jacques Marigo,et al.  2-D non-periodic homogenization to upscale elastic media for P–SV waves , 2010 .

[37]  M. Korn,et al.  Incorporation of attenuation into time-domain computations of seismic wave fields , 1987 .

[38]  Emanuele Casarotti,et al.  Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes , 2011 .

[39]  Error Estimates for the Finite Element Method , 2002 .

[40]  Albert Tarantola,et al.  Theoretical background for the inversion of seismic waveforms including elasticity and attenuation , 1988 .

[41]  Carl Tape,et al.  Adjoint Tomography of the Southern California Crust , 2009, Science.

[42]  Jeroen Tromp,et al.  Three-Dimensional Simulations of Seismic-Wave Propagation in the Taipei Basin with Realistic Topography Based upon the Spectral-Element Method , 2008 .

[43]  T. Dupont $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations , 1973 .

[44]  Andreas Fichtner,et al.  Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods , 2009 .

[45]  D. Komatitsch,et al.  Introduction to the spectral element method for three-dimensional seismic wave propagation , 1999 .

[46]  T. Jordan,et al.  FAST TRACK PAPER: Full three-dimensional tomography: a comparison between the scattering-integral and adjoint-wavefield methods , 2007 .

[47]  James F. Doyle,et al.  The Spectral Element Method , 2020, Wave Propagation in Structures.

[48]  P. Lognonné,et al.  Fréchet derivatives of coupled seismograms with respect to an anelastic rotating earth , 1996 .

[49]  D. Komatitsch,et al.  The Spectral-Element Method, Beowulf Computing, and Global Seismology , 2002, Science.

[50]  Roland Martin,et al.  An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation , 2009 .

[51]  V. Červený,et al.  Seismic Ray Theory , 2001, Encyclopedia of Solid Earth Geophysics.

[52]  R. Snieder,et al.  Eurasian fundamental mode surface wave phase velocities and their relationship with tectonic structures , 1998 .

[53]  H. Kanamori,et al.  Waveform modeling of the slab beneath Japan , 2007 .

[54]  Andreas Fichtner,et al.  The adjoint method in seismology—: II. Applications: traveltimes and sensitivity functionals , 2006 .

[55]  B. Romanowicz,et al.  Modelling of coupled normal modes of the Earth: the spectral method , 1990 .

[56]  Andreas Fichtner,et al.  Simulation and Inversion of Seismic Wave Propagation on Continental Scales Based on a Spectral - Element Method , 2009 .

[57]  J. Tromp,et al.  Theoretical Global Seismology , 1998 .

[58]  E. Bozdağ,et al.  On crustal corrections in surface wave tomography , 2008 .

[59]  Martin Käser,et al.  Regular versus irregular meshing for complicated models and their effect on synthetic seismograms , 2010 .

[60]  Emmanuel Chaljub,et al.  Spectral element modelling of three-dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core , 2003, physics/0308102.

[61]  S. P. Oliveira,et al.  EFFECT OF ELEMENT DISTORTION ON THE NUMERICAL DISPERSION OF SPECTRAL ELEMENT METHODS , 2011 .

[62]  Kim B. Olsen,et al.  Site Amplification in the Los Angeles Basin from Three-Dimensional Modeling of Ground Motion , 2000 .

[63]  Jeannot Trampert,et al.  Assessment of tomographic mantle models using spectral element seismograms , 2010 .

[64]  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.

[65]  Géza Seriani,et al.  Spectral element method for acoustic wave simulation in heterogeneous media , 1994 .

[66]  Jean-Paul Montagner,et al.  Reliability of mantle tomography models assessed by spectral element simulation , 2009 .

[67]  P. Moczo,et al.  The finite-difference time-domain method for modeling of seismic wave propagation , 2007 .

[68]  D. Komatitsch,et al.  Simulations of Ground Motion in the Los Angeles Basin Based upon the Spectral-Element Method , 2004 .

[69]  Yvon Maday,et al.  Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries , 1990 .

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

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

[72]  Z. Alterman,et al.  Propagation of elastic waves in layered media by finite difference methods , 1968 .

[73]  Jean-Paul Montagner,et al.  SPICE benchmark for global tomographic methods , 2008 .

[74]  J. Tromp,et al.  Noise cross-correlation sensitivity kernels , 2010 .

[75]  F. Marone,et al.  Non-linear crustal corrections in high-resolution regional waveform seismic tomography , 2007 .

[76]  D. L. Anderson,et al.  Preliminary reference earth model , 1981 .

[77]  P. Paolucci,et al.  The “Cubed Sphere” , 1996 .

[78]  Michel Campillo,et al.  Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise , 2004 .

[79]  B. Romanowicz,et al.  A simple method for improving crustal corrections in waveform tomography , 2010 .

[80]  J. Marigo,et al.  Shallow layer correction for Spectral Element like methods , 2008 .

[81]  F. Gilbert Excitation of the Normal Modes of the Earth by Earthquake Sources , 1971 .

[82]  Jean-Paul Montagner,et al.  Global upper mantle tomography of seismic velocities and anisotropies , 1991 .

[83]  J. Vilotte,et al.  The Newmark scheme as velocity–stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics , 2005 .

[84]  Pierre-Yves Bard,et al.  Quantitative Comparison of Four Numerical Predictions of 3D Ground Motion in the Grenoble Valley, France , 2010 .

[85]  A. Patera,et al.  Spectral element methods for the incompressible Navier-Stokes equations , 1989 .

[86]  Tatsuo Ohmachi,et al.  Love-wave propagation in a three-dimensional sedimentary basin , 1992, Bulletin of the Seismological Society of America.

[87]  J. Trampert,et al.  On the robustness of global radially anisotropic surface wave tomography , 2010 .