Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures

A new hybrid two-step method for computation of P-SV seismic motion at inhomogeneous viscoelastic topographic structure is presented. The method is based on a combination of the discrete-wavenumber (DW), finite-difference (FD), and finite-element (FE) methods. In the first step, the DW method is used to calculate the source radiation and wave propagation in the background 1D medium. In the second step, the FD-FE algorithm is used to compute the wave propagation along the topographic structure. The accuracy of the method has been separately tested for inclusion of the attenuation and for inclusion of the free-surface topography through numerical comparisons with analytical and independent numerical methods. The method is a generalization of the hybrid DW-FD method of Zahradnik and Moczo (1996) for localized structures with a flat free surface. Numerical computations for a ridge, sediment valley, and the ridge neighboring the sediment valley show that a ridge can considerably influence the response of the neighboring sediment valley. This means that the neighboring topographic feature should be taken into account even when we are only interested in the valley response.

[1]  S. T. Harding,et al.  WAVE SCATTERING FROM A STEP CHANGE IN SURFACE TOPOGRAPHY , 1981 .

[2]  Masahiko Fuyuki,et al.  Finite difference analysis of Rayleigh wave scattering at a trench , 1980 .

[3]  Helga Emmerich.  PSV-wave propagation in a medium with local heterogeneities: a hybrid formulation and its application , 1992 .

[4]  A. Rovelli,et al.  Seismic response of the geologic structure underlying the Roman Colosseum and a 2-D resonance of a sediment valley , 1995 .

[5]  Eli Turkel,et al.  A fourth-order accurate finite-difference scheme for the computation of elastic waves , 1986 .

[6]  J. Z. Zhu,et al.  The finite element method , 1977 .

[7]  Francisco J. Serón,et al.  FINITE-ELEMENT METHOD FOR ELASTIC WAVE PROPAGATION , 1990 .

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

[9]  Peter Moczo,et al.  Hybrid Seismic Modeling Based on Discrete-wave Number and Finite-difference Methods , 1996 .

[10]  Dan Loewenthal,et al.  Seismic Waves in a Quarter and Three-Quarter Plane , 1970 .

[11]  A. Ungar,et al.  An Improved Representation of Boundary Conditions in Finite Difference Schemes for Seismological Problems , 1975 .

[12]  Luca Malagnini,et al.  Assessment of potential strong ground motions in the city of Rome , 1994 .

[13]  Gerard T. Schuster,et al.  Parsimonious staggered grid finite‐differencing of the wave equation , 1990 .

[14]  Evaluation of topographic effects on P and S-waves of explosions at the northern Novaya Zemlya Test Site using 3-D numerical simulations , 1992 .

[15]  Giuliano F. Panza,et al.  A hybrid method for the estimation of ground motion in sedimentary basins: Quantitative modeling for Mexico city , 1994 .

[16]  M. Bouchon,et al.  Effects of two-dimensional topographies using the discrete wavenumber-boundary integral equation method in P-SV cases , 1989 .

[17]  M. D. Trifunac,et al.  Erratum to surface motion of a semi-cylindrical alluvial valley for incident plane SH waves , 1972, Bulletin of the Seismological Society of America.

[18]  Dan Loewenthal,et al.  INSTABILITY OF FINITE DIFFERENCE SCHEMES DUE TO BOUNDARY CONDITIONS IN ELASTIC MEDIA , 1976 .

[19]  Peter Moczo,et al.  Testing four elastic finite-difference schemes for behavior at discontinuities , 1993 .

[20]  Application of the finite difference method in seismic source and wave diffraction simulation , 1986 .

[21]  Zoltan A. Der,et al.  Free-boundary conditions of arbitrary polygonal topography in a two-dimensional explicit elastic finite-difference scheme , 1988 .

[22]  A. Rotenberg,et al.  Seismic waves in a quarter plane , 1969 .

[23]  G. W. Farnell,et al.  Finite Difference Analysis of Rayleigh Wave Scattering at Vertical Discontinuities , 1973 .

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

[25]  A. Ilan,et al.  Stability of finite difference schemes for the problem of elastic wave propagation in a quarter plane , 1978 .

[26]  Akira Ohtsuki,et al.  Effect of topography and subsurface inhomogeneities on seismic SV waves , 1983 .

[27]  G. Panza,et al.  Variability of seismic ground motion in complex media: the case of a sedimentary basin in the Friuli (Italy) area , 1993 .

[28]  Jiří Zahradník,et al.  Simple Elastic Finite-Difference Scheme , 1995 .

[29]  R. Madariaga.  Dynamics of an expanding circular fault , 1976, Bulletin of the Seismological Society of America.

[30]  Seismic waves in a wedge , 1975, Bulletin of the Seismological Society of America.

[31]  J. Carcione.  Modeling anelastic singular surface waves in the Earth , 1992 .

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

[33]  Craig A. Schultz,et al.  Effect of three‐dimensional topography on seismic motion , 1996 .

[34]  F. Muir,et al.  Modeling elastic fields across irregular boundaries , 1992 .

[35]  K. Mclaughlin,et al.  Scattering from near-source topography: Teleseismic observations and numerical simulations , 1988 .

[36]  Amplification and differential motion due to an antiplane 2D resonance in the sediment valleys embedded in a layer over the half-space , 1996, Bulletin of the Seismological Society of America.

[37]  Interaction of a compressional impulse with a slot normal to the surface of an elastic half space , 1979 .

[38]  Olivier Coutant,et al.  Calculation of synthetic seismograms in a laterally varying medium by the boundary element-discrete wavenumber method , 1994 .

[39]  H. L. Wong,et al.  Surface motion of a semi-elliptical alluvial valley for incident plane SH waves , 1974, Bulletin of the Seismological Society of America.

[40]  A hybrid solution for wave propagation problems in regular media with bounded irregular inclusions , 1984 .

[41]  P. Moczo,et al.  Absorption correction for computations of a seismic ground response , 1990, Bulletin of the Seismological Society of America.

[42]  Donat Fäh,et al.  A hybrid technique for the estimation of strong ground motion in sedimentary basins , 1992 .

[43]  Ronnie Kosloff,et al.  Wave propagation simulation in a linear viscoacoustic medium , 1988 .

[45]  Jiří Zahradník,et al.  Blind prediction of the site effects at Ashigara Valley, Japan, and its comparison with reality , 1994 .

[46]  A. Levander.  Fourth-order finite-difference P-SV seismograms , 1988 .

[47]  Hiroshi Kawase,et al.  Time-domain response of a semi-circular canyon for incident SV, P, and Rayleigh waves calculated by the discrete wavenumber boundary element method , 1988 .

[48]  A. S. Alekseev,et al.  The solution of dynamic problems of elastic wave propagation in inhomogeneous media by a combination of partial separation of variables and finite-difference methods , 1980 .

[49]  2-D wave propagation by a hybrid method , 1989 .

[50]  Bernd Kummer,et al.  Hybrid modeling of elastic-wave propagation in two-dimensional laterally inhomogeneous media , 1987 .

[51]  Comment on “A hybrid method for the estimation of ground motion in sedimentary basins: Quantitative modeling for Mexico City” by D. Fäh, P. Suhadolc, St. Mueller, and G. F. Panza , 1995, Bulletin of the Seismological Society of America.

[52]  Bernard A. Chouet,et al.  A free-surface boundary condition for including 3D topography in the finite-difference method , 1997, Bulletin of the Seismological Society of America.

[53]  J. Zahradník,et al.  Heterogeneous formulations of elastodynamic equations and finite-difference schemes , 1995 .

[54]  Francisco J. Sánchez-Sesma,et al.  Three-dimensional scattering by two-dimensional topographies , 1994 .

[55]  Wave diffraction, amplification and differential motion near strong lateral discontinuities , 1993 .

[56]  M. Bouchon.  A simple method to calculate Green's functions for elastic layered media , 1981 .

[57]  Z. Alterman,et al.  Computer Generated Seismograms , 1972 .