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

Abstract

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.

Quantification of focusing effects of the semi-spherical and semi-cylindrical synclinal basement topography on ground motion characteristics

“…This may be the reason behind the observed mysterious damage to only unreinforced brick chimneys in western Seattle during the Nisqually earthquake Kumar 2012, 2014). Recently, Narayan and Sahar (2014) studied the basement focusing caused by the unbounded hemi-spherical (HSBT) and hemi-cylindrical (HCBT) models considering the existence of both the 2D and 3D basement topography in nature. Narayan and Sahar (2014) also validated the accuracy of simulated responses of the HSBT and HCBT models by comparing the same with the analytical solutions (Born and Wolf 1980;Marcuse 1982;Davis et al 2000).…”

“…Recently, Narayan and Sahar (2014) studied the basement focusing caused by the unbounded hemi-spherical (HSBT) and hemi-cylindrical (HCBT) models considering the existence of both the 2D and 3D basement topography in nature. Narayan and Sahar (2014) also validated the accuracy of simulated responses of the HSBT and HCBT models by comparing the same with the analytical solutions (Born and Wolf 1980;Marcuse 1982;Davis et al 2000). They reported an increase of differences in ground motion amplification due to the focusing towards the focus points.…”

Quantification of effects of geometry of sediment bedrock interface on ground motion in 3D basin with circular free surface

“…The modified version of forth-order accurate 3D viscoelastic FD program of Narayan and Sahar (2014) for displacement-stress relation is used for the simulations. The frequency-dependent damping in the FD simulations is incorporated based on the GMB-EK rheological model.…”

“…The effective values of the unrelaxed Lame's parameters and density at the desired location in the staggered-grid are obtained using the harmonic and arithmetic means, respectively to incorporate the material discontinuity (Moczo et al, 2002). The details of computation of unrelaxed moduli, anelastic coefficients and anelastic functions at four relaxation frequencies and the validation of incorporation of frequency dependent damping in the time domain FD algorithm are given in Narayan and Sahar (2014). In order to increase the speed of numerical computations, the programs was optimized and auto-parallelized using PGI Cuda-Fortran compiler.…”

“…The considered four SS-, CN-, TR45 and TR20-basin models have GSBI as semi-spherical (SSbasin), conal (CN-basin), trapezoidal with edge-slope 45° (TR45-basin) and trapezoidal with edge-slope 20° (TR20-basin), respectively. The seismic responses were computed using a 3D staggered-grid finite-difference (FD) algorithm capable of simulating the seismic response in the time-domain with frequencydependent damping (Narayan and Sahar, 2014;Kamal and Narayan, 2015). The developed maps for the spatial variation of amplitude amplification, ASA and AAF in the basins are analyzed to infer the effects of GSBI on the amplitude and focusing of the BGS-waves.…”