Three‐dimensional finite difference method and hybrid modeling of earthquake ground motion

Oprsal, Ivo; Zahradnı́k, Jiřı́

doi:10.1029/2000jb000082

Cited by 40 publications

(39 citation statements)

References 40 publications

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“…The accuracy of implementation of the realistic damping in the developed code is validated by comparing the numerically computed phase velocity, quality factors and spatial spectral damping with the same based on the GMB-EKmodel and Futterman's relations [16]. The developed 3D FD code has the provision of the use of continuous variable grid size in all the directions to reduce the computation memory and time [23,30,31,38,41,[43][44][45][46]. The second aspect of this paper deals with the study of the combined effects of the sediment damping and the focusing caused by the hemi-spherical (HS) and hemi-cylindrical (HC) unbounded SBT models on the ground motion amplification.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional viscoelastic finite-difference code and modelling of basement focusing effects on ground motion characteristics

Narayan

Sahar

2014

Comput Geosci

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This paper consists of two parts. The first part of the paper is concerned with developing a 3D staggered grid time-domain finite-difference (FD) code with fourth-order spatial accuracy for simulating the responses of viscoelastic geological models with a continuous variable grid size in all the directions. The 3D FD code is written in Fortran 90. In the developed code, the realistic damping in the timedomain simulation is incorporated based on the generalized Maxwell body rheological model proposed by Emmerich and Korn (GMB-EK) Geophysics 52,1252-1264, 1987 with improvements made by Kristeck and Moczo Bull Seism Soc Am 93, [2273][2274][2275][2276][2277][2278][2279][2280] 2003. The accuracy of implementation of the realistic damping is validated by comparing the numerically computed phase velocity, quality factors and spatial spectral damping with the same based on GMB-EK model and Futterman's relations. It is also concluded that the grid spacing ratio up to 5.0 can be used unharmed. The second part of the paper presents the application of the developed code to simulate the basement focusing effects on ground motion characteristics in an unbounded medium. The combined effects of sediment damping and the focusing caused by the hemi-spherical (HS) and hemicylindrical (HC) synclinal basement topography (SBT) on the ground motion characteristics are studied. The simulated responses and the computed snapshots revealed the SBT focusing and defocusing phenomenon, intense mode conversion and diffractions of the incident waves. A good match of the spectral amplifications caused by the HS and HC basement topography models at their focus with the same computed analytically also reveals the accuracy of the developed FD code. The response of elastic HS and HC basement topography models revealed an increase of spectral amplification with an increase of frequency. Further, an increase of rate of frequency-dependent amplification towards the focus was inferred. The average spectral amplification (ASA) caused by the elastic HS basement topography model at the focus is more than the square of the same caused by the elastic HC basement topography model, and this ratio of ASA is increasing with an increase of sediment damping.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional viscoelastic finite-difference code and modelling of basement focusing effects on ground motion characteristics

Narayan

Sahar

2014

Comput Geosci

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“…While the numerical simulation of earthquake wave generation and propagation has been significantly advanced in computational seismology, little attention is paid to it in the system of the earthquake hazard and disaster simulation; see [Fäh et al, 1994;Bao et al, 1996;Graves, 1996;Zahradník and Moczo, 1996;Faccioli et al, 1997;Moczo et al, 1997;Kamae et al, 1998;Komatitsch and Vilotte, 1998;Furumura and Koketsu, 1998;Ortiz-Aleman et al, 1998;Aoi and Fujiwara, 1999;Pitarka, 1999;Fujiwara, 2000;Moczo et al, 2002;Oprsal and Zahradník, 2002;Kim et al, 2003;Kristek and Moczo, 2003;Bielak et al, 2003;Komatitsch et al, 2004] for the use of finite difference method of seismic ground motion simulation; see also [Zienkiewicz et al, 1999;Koketsu et al, 2004;Kaeser and Dumbser, 2006] for the use of finite element method. This is mainly because the length scale of the system is much smaller than that of computational seismology.…”

Section: Introductionmentioning

confidence: 99%

Integrated Simulation for Earthquake Hazard and Disaster Prediction

Hori

Oguni

Ichimura

2009

J. Earthquake and Tsunami

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This paper presents the integrated simulation for earthquake hazard and disaster prediction. The earthquake hazard simulation takes advantage of the macro-micro analysis method which estimates strong ground motion with high spatial and temporal resolution. The earthquake disaster simulation calculates seismic responses for all structures in a target area by inputting synthesized strong ground motion to a structure analysis method which is plugged into the system; a suitable analysis method, linear or nonlinear, is chosen depending on the type of the structure. The results of all simulations are visualized so that government officials and residents can share common recognition of possible earthquake hazard and disaster. Two examples of this integrated earthquake simulations are presented; one is made by plugging nonlinear structure analysis methods into the system, and the other is made for an actual city, the computer model of which is constructed with the help of available geographical information systems.

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“…The accuracy of the FD method very much depends on the implementation of the boundary condition at the free-surface. A free surface boundary condition can be achieved using either the stress imaging technique (LEVANDER, 1988;GRAVES, 1996;GOTTSCHAMMER and OLSEN, 2001) or the vacuum formulation (BOORE, 1972;ZAHRADNIK et al, 1993;OPRSAL and ZAHRADNIK, 2002). The well-known stress imaging technique was first proposed by LEVANDER (1988) in his P-SV wave fourth order spatially accurate staggered grid FD scheme.…”

Section: Introductionmentioning

confidence: 99%

“…We have used a continuous grid mesh with variable grid size which was initially proposed by MIYATAKE (1980). It has been used by MOCZO (1989), OPRSAL and ZAHRADNIK (1999), Pitarka (1999) and OPRSAL and ZAHRADNIK (2002) for 2D and 3D simulations. Maximum grid spacing ratio up to 4.0 was used by PITARKA (1999) in a 3D simulation.…”

Section: Introductionmentioning

confidence: 99%

A Fourth Order Accurate SH-Wave Staggered Grid Finite-difference Algorithm with Variable Grid Size and VGR-Stress Imaging Technique

Narayan

Kumar

2008

Pure Appl. Geophys.

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This article presents a new approach for the implementation of a planar-free surface boundary condition. It is based on a vertical grid-size reduction above the free surface during the explicit computation of a free surface boundary condition. This technique is very much similar to the well-known stress imaging technique. VGR-stress imaging technique name is proposed for this new free surface boundary condition (VGR stands for 'vertical grid-size reduction'). To study the performance of the proposed VGR-stress imaging technique, it was implemented in a newly developed second order accurate in time and fourth-order accurate in space (2, 4) staggered grid SH-wave finite-difference (FD) algorithm with variable grid size. It was confirmed that the effective thickness (ETH) of first soil layer becomes less by one-half of vertical grid size than the assigned thickness (ATH), if stress imaging technique is used as a free surface boundary condition. The qualitative and quantitative results of various numerical experiments revealed that the proposed VGR-stress imaging technique is better than the stress imaging technique since it is free from the thickness discrepancy arising due to the use of images of stress components across the free surface. On the basis of iterative numerical experiments, it was confirmed that the stability condition for this FD scheme with variable grid size is VSDt minðDx;DzÞ 0:71: It was also inferred that at least five to six grid points per shortest wavelength are required to avoid the grid dispersion. The maximum grid-spacing ratio up to 12.5 or even more did not affect the accuracy of (2,4) SH-wave algorithm. The obtained reduction of 10.46 and 5.38 folds in the requirement of computational memory and time for a particular basin-edge model, as compared with the homogeneous grid size, reflects the efficacy of the new FD algorithm.

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Three‐dimensional finite difference method and hybrid modeling of earthquake ground motion

Cited by 40 publications

References 40 publications

Three-dimensional viscoelastic finite-difference code and modelling of basement focusing effects on ground motion characteristics

Three-dimensional viscoelastic finite-difference code and modelling of basement focusing effects on ground motion characteristics

Integrated Simulation for Earthquake Hazard and Disaster Prediction

A Fourth Order Accurate SH-Wave Staggered Grid Finite-difference Algorithm with Variable Grid Size and VGR-Stress Imaging Technique

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