Advanced empirical data analysis and numerical simulations for structure and soil dynamic behavior as contributions to seismic risk assessment

Seismic waves are elastic waves generated by a sudden disturbance in a medium that propagates in the ground and on the free surface with velocity, frequency, and amplitude dependent on the medium’s and the source’s elastic properties. As seismic waves propagate through the earth’s medium away from the source, they dissipate their energy. Three effects cause the attenuation of seismic wave energy: 1) geometrical spreading, which occurs as a result of the wave-front expanding with increasing distance from its source; 2) in- trinsic absorption, which converts kinetic energy into, for example, heat via internal friction due to the an-elasticity of the medium and 3) scattering, which redistributes kinetic energy due to random small-scale elastic heterogeneities in the medium. Intrinsic and scattering attenuation structures provide insights into the nature of the Earth’s interior and place constraints on seismic wave propagation. Therefore, the ability to separately estimate the spatial distributions of intrinsic (Qi ) and scatter- ing (Q−sc1) attenuation is crucial for improving our understanding of the wave propagation through near-surface geology and built-in structures. According to Aki (1969), seismic coda results from the scattering of seismic waves by random heterogeneity in the Earth’s lithosphere. Originally proposed by Wu et al. (1985), Hoshiba (1997) numerically (using a Monte Carlo approach) computed the theoretical energy envelopes for a stratified Earth model for his depth-dependent Multi-Lapse Time Window Analysis (MLTWA). MLTWA compares the seismic en- energy integrated from three consecutive seismograms windows starting from the S- wave arrival time and displayed against hypo-central distance, with the energy integrals predicted by a theoretical model suitable for the multiple-scattering problem. This study developed an innovative approach using the MLTWA method to esti- mate seismic wave attenuation through near-surface geology and built-in structures. Despite the common application of MLTWA used to estimate the attenuation of the crust and mantle, this study modified MLTWA to use a vertical array of seismo- grams for separately estimating the scattering and intrinsic seismic attenuation of depth-dependent near-surface media. The application of MLTWA, a depth-dependent media, might become computation- ally demanding. Therefore, to overcome this problem, an inversion strategy that combines grid search and simulated annealing is proposed. Grid search is used over an extensive range of parameter space but with a relatively wide grid spacing to find possible narrow parameter space with a potential solution. We use the narrowed parameter space identified with the grid search to constrain our area of search of the solution using simulated annealing (Kirkpatrick 1983). Simulated annealing con- verges toward the solution with a couple of hundred iterations or sometimes less. The method is applied to seismic data collected from sensors installed in a borehole and a nearby building test site at Atakoy, Istanbul, Turkey. An intrinsic and scattering shear wave attenuation is estimated for a building and two layers in the near-surface beneath the building. Frequency-dependent Qi, Qsc, and Qs values are estimated for frequencies 1 to 15 Hz. For example, at 5 Hz, estimated Qs values are 16, 23, and 83, are for the building, 50 m deep shallow layer, and the half-space below, respectively. Our results are comparable to previous studies on the same study site such as in Parolai et al.(2010). He estimated average Qs values of 30, 46, and 99 for the 0 - 50, 0 - 70, and 0 - 140 m depth ranges, respectively, using spectral fitting for the frequency band of 1-15 Hz. Our results also fit well within ranges of Qs values between 10 and 100 for near-surface geology estimated by Hutchings et al. (2012).

Seismic waves are elastic waves generated by a sudden disturbance in a medium that propagates in the ground and on the free surface with velocity, frequency, and amplitude dependent on the medium’s and the source’s elastic properties. As seismic waves propagate through the earth’s medium away from the source, they dissipate their energy. Three effects cause the attenuation of seismic wave energy: 1) geometrical spreading, which occurs as a result of the wave-front expanding with increasing distance from its source; 2) in- trinsic absorption, which converts kinetic energy into, for example, heat via internal friction due to the an-elasticity of the medium and 3) scattering, which redistributes kinetic energy due to random small-scale elastic heterogeneities in the medium. Intrinsic and scattering attenuation structures provide insights into the nature of the Earth’s interior and place constraints on seismic wave propagation. Therefore, the ability to separately estimate the spatial distributions of intrinsic (Qi ) and scatter- ing (Q−sc1) attenuation is crucial for improving our understanding of the wave propagation through near-surface geology and built-in structures. According to Aki (1969), seismic coda results from the scattering of seismic waves by random heterogeneity in the Earth’s lithosphere. Originally proposed by Wu et al. (1985), Hoshiba (1997) numerically (using a Monte Carlo approach) computed the theoretical energy envelopes for a stratified Earth model for his depth-dependent Multi-Lapse Time Window Analysis (MLTWA). MLTWA compares the seismic en- energy integrated from three consecutive seismograms windows starting from the S- wave arrival time and displayed against hypo-central distance, with the energy integrals predicted by a theoretical model suitable for the multiple-scattering problem. This study developed an innovative approach using the MLTWA method to esti- mate seismic wave attenuation through near-surface geology and built-in structures. Despite the common application of MLTWA used to estimate the attenuation of the crust and mantle, this study modified MLTWA to use a vertical array of seismo- grams for separately estimating the scattering and intrinsic seismic attenuation of depth-dependent near-surface media. The application of MLTWA, a depth-dependent media, might become computation- ally demanding. Therefore, to overcome this problem, an inversion strategy that combines grid search and simulated annealing is proposed. Grid search is used over an extensive range of parameter space but with a relatively wide grid spacing to find possible narrow parameter space with a potential solution. We use the narrowed parameter space identified with the grid search to constrain our area of search of the solution using simulated annealing (Kirkpatrick 1983). Simulated annealing con- verges toward the solution with a couple of hundred iterations or sometimes less. The method is applied to seismic data collected from sensors installed in a borehole and a nearby building test site at Atakoy, Istanbul, Turkey. An intrinsic and scattering shear wave attenuation is estimated for a building and two layers in the near-surface beneath the building. Frequency-dependent Qi, Qsc, and Qs values are estimated for frequencies 1 to 15 Hz. For example, at 5 Hz, estimated Qs values are 16, 23, and 83, are for the building, 50 m deep shallow layer, and the half-space below, respectively. Our results are comparable to previous studies on the same study site such as in Parolai et al.(2010). He estimated average Qs values of 30, 46, and 99 for the 0 - 50, 0 - 70, and 0 - 140 m depth ranges, respectively, using spectral fitting for the frequency band of 1-15 Hz. Our results also fit well within ranges of Qs values between 10 and 100 for near-surface geology estimated by Hutchings et al. (2012).