One- and Two-Dimensional Ground Response Analyses: What They Do/Don’t Tell about the Site

Abstract

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.