3D BASEMENT FOCUSING EFFECTS ON GROUND MOTION CHARACTERISTICS

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1 ISET GOLDEN JUBILEE SYMPOSIUM Indian Society of Earthquake Technology Department of Earthquake Engineering Building IIT Roorkee, Roorkee October 20-21, 2012 Paper No. A018 3D BASEMENT FOCUSING EFFECTS ON GROUND MOTION CHARACTERISTICS Darakhshan Sahar 1, Vinay Kumar 2 and J.P. Narayan 3 Department of Earthquake Engineering, Indian Institute of Technology, Roorkee 1 dakshi_sahar@yahoo.com, 2 vinaytomar23@gmail.com, 3 jaypnfeq@iitr.ernet.in ABSTRACT This paper presents the effects of hemi-spherical synclinal basement topography (HSBT) on the ground motion characteristics. A comparison of spectral amplification along the focal length caused by cylindrical synclinal basement topography (CSBT) and HSBT is also documented in this paper. 2D and 3D Finite difference algorithms have been used in order to simulate the seismic responses of models corresponding to CSBT and HSBT. The simulated results revealed HSBT focusing, intense mode conversion from the upper part of the HSBT and diffraction of incident waves from the top corners of the HSBT. Frequency dependent spectral amplification was inferred and an increase in this phenomenon was noticed towards the focus of HSBT and CSBT. An analysis of simulated results revealed that spectral amplification caused by HSBT is too large as compared to the same caused by CSBT. Key words: 3D Finite difference simulation, fourth order spatial accuracy, basement topography effects 1. INTRODUCTION It is usually expected that damage to buildings from an earthquake will be greatest near the epicenter and will decrease steadily with increasing distance. But sometimes very peculiar damage pattern occur in a basin which cannot be explained using simple soil amplification and resonance effects as was reported in Santa Monica area, Los Angeles basin during Northridge earthquake of 1994 (Gao et al., 1996; Hartzell, 1997; Alex and Olsen, 1998; Davis et al., 2000). Gao et al. (1996) proposed that the amplification in Santa Monica area was due to basement focusing from a lens shaped structure of the deep Los Angeles basin sediments based on the analysis of recorded data. Davis et al. (2000) carried out inversion of aftershock records using SH-wave FD simulations and inferred that the damage in Santa Monica occurred due to the focusing caused by the presence of several underground acoustic lenses at depths of around 3 km in Los Angeles basin.

2 They also reported frequency dependent amplification of ground motion due to basement focusing based on analytical solutions. Basement focusing effects on the ground motion characteristics was also observed in the form of consistent anomalous damage to unreinforced brick chimneys in west Seattle, Washington during 1949 Olympia earthquake of magnitude 7.1, 1965 Tacoma earthquake of magnitude 6.5 and 2001 Nisqually earthquake of magnitude 6.8 (Ihnen and Hadley, 1986; Booth et al., 2004; Frankel et al., 2002; Stephenson et al., 2006). In order to simulate the seismic responses of models corresponding to CSBT and HSBT, 3D finite difference algorithm developed by Narayan and Sahar (2012) and 2D finite difference algorithm developed by Narayan and Vinay (2012) have been used. Both the elastic and visco-elastic seismic responses of an unbounded HSBT and CSBTmodels on the vertical array along the focal length have been computed to study the combined effects of sediment damping, basement focusing and mode conversion. Snapshots in a rectangular area are also computed to identify the different seismic phases developed at the base of HSBT. The spectral amplification caused by HSBT and CSBT along the focal length and the effect of soil damping is computed just by taking the spectral ratio of responses with and without HSBT and CSBT in the models. 2. HSBT AND CSBT MODELS AND PARAMETERS In order to study the combined effects of rheology of sedimentary deposit and hemispherical and cylindrical synclinal basement topographies on the ground motion characteristics, seismic responses of an unbounded CSBT and HSBT models consisting of a single sedimentary layer are simulated using S-wave incident plane wave front. Figure 1 show the north-south cross-section of the HSBT (3D model) and CSBT (2D model) models (CSBT is infinitely extending in east-west direction). Figure 1. North-south cross section of HSBT and CSBTmodels with a vertical array passing along the focal length (Note: The distances of receivers points from the tip of HSBT/CSBT are normalized with the focal length of synclical basement topographies (SBT) mentioned as NDTSBT in the manuscript).

3 The positive X and Y-coordinates are pointing towards north and west directions, respectively. The positive Z-coordinate is pointing upward from the tip of the synclinal basement topography (SBT). All the distances are measured with respect to the tip of SBT. The shape of considered HSBT and CSBT models is hemispherical and half-circular, respectively and has radius of curvature 3000 m for both 3D and 2D synclinal models. The P-wave and S-wave velocities and quality factors at reference frequency, density and unrelaxed moduli of sedimentary deposit and basement rock are given in table 1 for elastic and viscoelastic rheological models. A plane front for S-wave was generated at a depth of 1000 m below the tip of SBT (means at a depth of 4000 m with respect to top-flat part of the SBT). Seismic responses were computed at 24 equidistant (300 m apart) receiver points on a vertical array extending from 240 m below the tip of SBT to 6600 m above the same. Both the elastic and viscoelastic seismic responses of SBT models were computed for quantification of combined effects of sediment rheology and SBT on ground motion characteristics. The time step was taken as Seismic response at the receiver just above the tip of SBT (at 60 m from tip of SBT) is considered as reference in order to exclude the effects of impedance contrast between SBT and overlying sedimentary deposit from the combined effects of SBT and sediment rheology on the ground motion characteristics. Table 1: Rheological parameters for sedimentary deposit above basement for different basement topography models SBT Models Velocity at F R (m/sec) Density (kg/m 3 ) QF at F R Unrelaxed Moduli (GPa) Sediment Deposits S-wave P-wave S-wave P-wave Elastic viscoelastic Basement Rock Elastic Viscoelastic SEISMIC RESPONSES ON A VERTICAL ARRAY Seismic responses of both the HSBT and CSBT models have been computed on the vertical arrays along the focal length to study the effect of focusing of incident plane wave front. Figures 2a & 2b show the horizontal components of ground motion for elastic and viscoelastic 2D (CSBT) and 3D (HSBT) models respectively. Both the horizontal components (u and v) in the 3D case have almost the same amplitude, hence only one component is shown in figure The amplitude in the vertical components is almost negligible as compared to the horizontal component. The focal length (F L ) of SBT of the order of 6600 m was obtained using the following equation. Where r is the radius of circular SBT (3000 m) and is the ratio of S-wave velocity of sediment to that of basement rock.

4 (a) (b) Figure 2. (a) Elastic and viscoelastic seismic responses for an incident horizontal SV-wave front, on a vertical array for 2D model (b) Seismic responses for an incident horizontal S-wave front, on a vertical array for 3D model (Note: Different normalization factors are used for 2D and 3D responses). Figure 2 depicts that there is tremendous increase of amplitude of transmitted S-wave in the horizontal component in the basin towards the focus of the SBT, due to SBT-focusing effects. Diffracted body waves from the top corners of the SBT are very clearly visible on receivers R2-R14 in horizontal component.

5 Figure 3. Snapshots of horizontal component in a rectangular area at different times.

6 The amplitude of diffracted waves was highly variable due to divergence, damping and the interference effects. Diffracted waves are merged with the transmitted S-wave on receivers R15-R24. A decrease of amplitude of S-wave at R22-R24, in the horizontal component, very near the focus can be inferred. The maximum amplitude of S-wave in horizontal component was obtained at receiver R21 at a distance of 5700 m from the tip of SBT, instead of at the focus. Finally, the analysis of figure 2 reveals tremendous effects of SBT focusing and rheology of sediments on the ground motion characteristics but it is larger in case of 3D basement focusing as compared to 2D. 3.1 Snapshots In order to further demonstrate the HSBT-focusing effects, mode conversion and development of diffractions from the top corners of HSBT, snapshots for the horizontal component were computed in a rectangular area at different times. Snapshots were computed in an area extending from 240 m down to 6600 m up of the tip of HSBT and 3000 m south to 3000 m north of tip of HSBT. The snapshots at different times for horizontal are shown in figures 3. The snapshot at time 1.0 sec depict just entered S- wave into the synclinal part of HSBT. The focusing of transmitted S-wave towards the focus is very much clear in the snapshots at times 2.0 sec, 2.5 sec, 3.0 sec and 3.5 sec. The diffracted S-waves are also visible in horizontal component of snapshots at different times. The maximum focusing effects is visible in horizontal component of snapshot at time 3.5 sec. Figure 4. Spectral amplification factors for horizontal component of S-wave at different NDTSBT values caused by SBT focusing for 2D and 3D elastic Models.

7 4. SPECTRAL AMPLIFICATION To study the effects of basement focusing and sediment rheology on the ground motion characteristics quantitatively, spectral amplitude amplification of S-wave in each trace recorded above the SBT on a vertical array along the focal length is computed for both 2D and 3D models with respect to the trace recorded just above the tip of SBT. The spectral amplitude amplifications at different normalized distances with respect to the focal length (6600 m) from the tip of SBT (mentioned as NDTSBT in the manuscript) is shown in figures 4 and 5. Diffracted waves have been removed purposely from the traces where it was possible during the computation of amplitude spectra. Figure 4 shows the spectral amplification in case of elastic responses of HSBT and CSBT models. Similarly, figure 5 shows the spectral amplification in case of viscoelastic responses. Analysis of figure 4 depicts an increase of spectral amplification with increase of NDTSBT value. It can also be inferred that spectral amplification is increasing with the increase of frequency. Further, it is noted that the rate of increase of spectral amplification with frequency is increasing with an increase of NDTSBT value. Figure 5. Spectral amplification factors for horizontal component of S-wave at different NDTSBT values caused by SBT focusing for 2D and 3D viscoelastic medels.

8 But, the spectral amplification is very much affected by the presence of diffracted waves in the traces, where it was not possible to remove. The largest spectral amplification of the order of 5.38 and 27 were obtained for CSBT (2D) and HSBT (3D), respectively for frequency 7.0 Hz at NDTSBT value of On the basis of analysis of figures 4 and 5, a decrease in the spectral amplification can be inferred due to sediment damping. Further, the higher frequencies are damped more as compared to the lower frequencies, even higher frequencies were more amplified due to the SBT-focusing as was inferred from the analysis of elastic models. The amplitude amplification in time domain is computed at different NDTSBT positions and shown in figure 6(a). It was computed just by taking the ratio of the maximum amplitude at different NDTSBT positions and the maximum amplitude in the second trace of response. There is an increase of amplitude amplification in time domain with the increase of NDTSBT value. The maximum amplitude amplification was obtained at NDTSBT value equal to around 0.87 for both CSBT and HSBT models. (a) Figure 6. (a)amplitude amplification of horizontal component of S-wave in time domain (shown by triangles for 3D and circles for 2D). (b) Average spectral amplification factors at different NDTSBT values (shown by triangles for 3D and circles for 2D). (b)

9 The average spectral amplifications in the considered frequency range are also computed at different NDTSBT positions as shown in figure 6(b). An increase in average spectral amplification is found with the increase of NDTSBT value. It is found to be linear at some extent of NDTSBT value. Thereafter, an increase in average spectral amplification with NDTSBT value is obsevered with a fast rate. The maximum average spectral amplification is obtained at NDTSBT value of 0.87 which is in agreement with the time domain amplitude amplification. Analysis of figure 6 depicts that both the amplitude amplification and average spectral amplification are larger in case of HSBT as compared to CSBT at the respective NDTSBT values. The maximum spectral amplification in case of HSBT is around square of that of CSBT. 5. CONCLUSIONS The analysis of simulated responses of 2D cylindrical synclinal basement topography (CSBT) and 3D hemispherical synclinal basement topograpgy (HSBT) alongwith snapshots revealed significant effect of focusing on ground motion characteristics. Synclinal basement topography (SBT) has also cause mode conversion and diffraction of waves from its top corners. The maximum SBT focusing effect was inferred at a distance of around 0.87 times the focal length. A good similarity in the increase of amplitude amplification in time domain and average spectral amplification towards the SBT-focus has been observed up to a certain distance. Thereafter, the amplitude amplification in time domain has been found larger than that of average spectral amplification. An increase of spectral amplification of S-wave in the horizontal component with the increase of frequency and distance from the tip of SBT towards the focus has been inferred. Furthermore, an increase of rate of spectral amplification with frequency has been obtained with the increase in distance from the tip of SBT. A similar effect has been reported by Davis et al. (2000) based on the analytical solutions.the analysis of maximum amplitude amplification and averaged spectral amplification for both elastic and viscoelastic case has revealed that the amplification in 3D focusing (HSBT) is too large as compared to the same in 2D focusing (CSBT). AKCNOWLEDGEMENT The third auther is grateful to the Ministry of Earth Sciences (MoES), New Delhi and Council of Scientific and Industrial Research (CSIR), New Delhi for financial assistance through Grant Numbers MES-484-EQD and CSR-569-EQD, respectively. REFERENCE 1. Alex, C. M. and K. B. Olsen (1998) Lens-effect in Santa Monica?, GRL, 25, Booth, D. B., R. E. Wells and R. W. Givler (2004) Chimney damage in the greater Seattle area from area from the Nisqually earthquake of 28 February 2001, Bull. Seis. Soc. Am., 94, Davis, P.M., L. Justin, K. H. Rubinstein, S. S. Liu and G. L. Knopoff (2000) Northridge earthquake damage caused by geologic focusing of seismic waves, Science, 289, Frankel, A., D. Carver and R. A. Williams (2002) Nonlinear and linear site response and basin effects in Seattle for the M6.8 Nisqually, Washington, earthquake, Bull. Seis. Soc. Am., 92, Frankel, A., W. Stephenson and D. Carver (2009) Sedimentary Basin Effects in Seattle, Washington: Ground-Motion Observations and 3D Simulations, Bull. Seis. Soc. Am. 99,

10 6. Gao, S., H. Liu, P.M. Davis and G.L. Knopoff (1996) Localized amplification of seismic waves and correlation with damage due to the Northridge earthquake, Bull. Seis. Soc. Am., 86, S Hartzell, S., E. Cranswick, A. Frankel, D. Carver and M. Meremonte (1997) Variability of site response in the Los Angeles urban area, Bull. Seis. Soc. Am., 87, Ihnen, S.M. and D.M. Hadley (1986) Prediction of strong ground motion in the Puget Sound region: the 1965 Seattle earthquake, Bull. Seis. Soc. Am. 76, Narayan, J.P. and D. Sahar (2012) Development of 3D staggered grid fourth order finite difference algorithm for strong ground motion, Proceeding of 15 WCEE. 10. Narayan, J.P. and K. Vinay (2012) P-SV wave time-domain finite-difference algorithm with realistic damping and a combined study of effects of sediment rheology and basement focusing (communicated). 11. Stephenson, W. J., A. Frankel, J. K. Odum, R. A. Williams and T. L. Pratt (2006) Towards resolving an earthquake ground motion mystery in west Seattle, Washington State: Shallow seismic focusing may cause anomalous chimney damage, GRL, 33, L06316, doi: /2005gl