Many recent studies have attempted to predict surface ground motions recorded at downhole array sites using 1D ground response analyses (GRAs) and have highlighted the often-poor agreement between the simulated (i.e., theoretical) and recorded (i.e., empirical) ground motions. The Delaney Park Downhole Array (DPDA) is an example of a site where 1D analyses have consistently resulted in over-estimation of amplification when attempting to replicate empirical small-strain ground motions, and researchers have hypothesized that subsurface spatial variability is to blame for the mismatch. In this study, we first update a large-scale (1.6 km × 1.6 km × 80 m), site-specific, pseudo-3D shear wave velocity (Vs) model of the DPDA site using a geostatistical approach based on 108 horizontal-to-vertical spectral ratio (H/V) of noise measurements. We then perform 2D GRAs on cross-sections extracted from the updated pseudo3D Vs model with various lateral extents and with various azimuths. By using cross-sections along different lateral extents and azimuths, we show that 2D GRAs can result in either higher or lower amplifications relative to 1D GRAs, depending on how the simulated waves constructively or destructively interfere. Regardless, 2D GRAs remained ineffective at matching the recorded ground motions, potentially due to the complex 3D spatial variability around the downhole array, and which cannot be effectively captured by individual 2D cross-sections at certain azimuths. It is hoped that future 3D GRAs will be able to better capture the effects of wave scattering and other complex wave propagation patterns required to match the recorded ground motions at the DPDA site.

The first computational model of elastic wave propagation in horizontally layered media was proposed 70 years ago by Thomson and Haskell. Later, ground motion modelers further simplified the horizontally layered model for vertical wave propagation by assuming deep seismic sources and low-velocity near-surface layers. These simplifications reduce the governing 3D vector wave equation, which involves diffraction, reflection-transmission, and conversion of P and S body and surface waves, to a 1D scalar wave equation that only contains the reflection-transmission of vertically propagating S waves. Such 1D models continue to be utilized as “reasonable” tools for ground response analyses. However, recent studies at borehole array sites have revealed that 1D analyses may only be reasonable in about 50% of cases. Despite the known limitations of 1D models, 2D/3D models are not widely used in practice because of the higher computational costs and the lack of adequate subsurface data. Recent advancements in computational science and non-invasive site characterization, however, are trying to alleviate these limitations and

make 2D/3D ground response analyses more feasible. In this study, we use the finite volume code FLAC to model seismic wave propagation at the Treasure Island Downhole Array (TIDA) site using 1D and 2D subsurface models and discuss the inherent limitations of 1D analyses. The 3D subsurface model shows a relatively flat bedrock layer beneath the site that begins to slope upward approximately 500 m away from the TIDA borehole. This dipping bedrock layer has been found to substantially influence the recorded ground motions at the borehole array. We use a high-frequency input motion at the base of our model to “decouple” various components of the scattered wavefield and reveal their interactions in forming the observed ground response. Part of the vertically propagating shear wave is diffracted at the tip and toe of the slopping bedrock and further propagates toward the ground surface as cylindrical P and S body waves. Reverberations of these obliquely incident body waves within the soft dipping layer lead to surface projections that

travel in the down-slope direction. While these 2D surface waves give rise to a better match between field recordings and numerical simulations, we still need to consider 3D out-of-plane effects and non-vertical excitations to adequately capture the true response. Overall, the seismic wave propagation in each site is inherently a 3D phenomenon; while it is possible to capture some characteristics of its response at lower dimensions, adequately modeling the true response, especially at higher frequencies, may require 3D analyses.

Ambient-noise methods, and the horizontal-to-vertical spectral ratio (HVSR), whether from earthquakes (eHVSR) or mircrotremors (mHVSR), have gained much popularity in the field of site response over the last decade. These methods can be used either for direct prediction or to inform the velocity structure utilized in more conventional site response analyses. This paper describes a field study and subsequent analyses undertaken in the Lower Hutt sedimentary basin of New Zealand. The field study involved collecting 50 ambient-noise or microtremor measurements across the entire basin over the same time window that microtremor measurements were being recorded at strong-motion stations in the basin for use as reference stations. Additionally, microtremor array measurements (MAM; involving ~24 ambient-noise measurements per site) and multi-channel analysis of surface waves (MASW) were conducted at five sites to better quantify deep and shallow velocity structure of the basin. In total, microtremor data were collected at 154 locations. This paper focuses on the use of the microtremor data collected for direct prediction of site response in the sedimentary basin. The hybrid standard spectral ratio approach is tested in this region. A rigorous validation study was performed at strong motion stations at which microtremor measurements were made for use as reference basin sites in the hybrid spectral ratio method. The prediction accuracy and uncertainty of the method, when using synchronized versus unsynchronized data between the reference basin sites and temporary target sites, are compared. The hybrid spectral ratio method predicts well the observed site amplification between nearby, deep basin sites for f < 5 Hz, when synchronized data are used. Predictions around the fundamental frequency of the basin (corresponding to periods of 1- 2 seconds) worsen when unsynchronized data are used due the influence from environmental and anthropogenic factors on microtremor amplitudes. Finally, the method is used to predict the site response, relative to a rock reference site, at all basin sites at which synchronized temporary microtremor data were collected. Early efforts to spatially interpolate the observations and predictions are discussed.

This paper presents a study on 3D ground motion simulation-based site amplification using the Wellington region of New Zealand as a case study. Several recent models of the Wellington sedimentary basin have been developed and are used in the simulations conducted as a part of this study to investigate the influence of basin geometry on site amplification. Location-specific site amplification factors for acceleration response spectra are presented at key locations throughout the Wellington CBD to illustrate how the simulated site amplification compare with observations. The simulations are found to produce amplification factors that have comparable level of amplification to observed amplification factors at deeper basin locations. Several limitations are also highlighted in this comparison. At shallow basin locations, the spatial resolution of the simulations conducted are not able to properly capture the basin response. Due to an enforced minimum S-wave velocity of 500 m/s in the simulations, the periods of spectral peaks are not accurately matched between simulation and observation. This provides motivation for further research into improvement and advancements in the simulations.

The seismic design of typical structures in Taiwan is performed by using the design ground motions with return period of 475 years. For critical infrastructure such as nuclear power plant and major transportation hub, design ground motions with longer return period should be used. In addition, site-specific ground response analyses would be performed to obtain the input ground motion histories for the subsequent dynamic time history analyses of the foundations and the super-structures at the same site. Due to the simplicity in code usage and input parameter specification, 1D ground response analysis is preferred in lieu of multi-dimensional ground response analysis. However, for sites with high lateral variability, 1D ground response analysis may not be sufficient in capturing the real ground response. In this study, we explore the difference in the 1D and 3D ground response analysis results when subjected to long-return period seismic motions. Two target sites are considered. Based on thorough geotechnical and geophysical investigation, detailed 3D velocity models would be constructed for both sites. A series of 1D and 3D ground response analyses are performed with several long-return period motions. The modeling results would be compared to identify the conditions under which the 3D analysis results are significantly different.

In this study, the seismic ground motion incoherency evaluation and numerical simulation based on spatial variability of rock site was performed using numerical analysis. To conduct this research, an inhomogeneous rock numerical models of 300 m x 150 m were generated using Finite Element Method (FEM) software, OpenSees. A case matrix based on the coefficient of variation and correlation length, a representative parameters indicating spatial variability, was generated. Through the dynamic numerical analysis, ground motions were obtained for each case, and the ground motion coherency functions were calculated. The empirical coherency function of the Pinyon-Flat site in the western United States was reproduced using numerical analysis, which showed the possibility of developing a coherency function of actual rock site using numerical simulation. And, as a result of the case study analysis, it was found that the spatial variability of the rock mass has a very large effect on the seismic ground motion coherency.