Insights on Numerical Damping Formulations Gained From Calibrating 2D Ground Response Analyses at Downhole Array Sites

Appropriately modeling seismic wave attenuation is critical for ground response analyses (GRAs), which aim to replicate local site effects observed in ground motions. Accurately predicting even small‐strain site effects remains challenging because theoretical transfer functions (TTFs) from GRAs often overestimate empirical transfer functions (ETFs) when the small‐strain damping ratio ( D min ) is set equal to laboratory‐obtained values. Previous studies addressed this by increasing D min in 1D GRAs to account for apparent damping mechanisms that cannot be inherently modeled in 1D. These attempts have improved predictions of fundamental‐mode amplitudes, but often result in overdamping at higher modes. This study investigates more direct modeling of apparent damping using 2D GRAs at four downhole array sites: Delaney Park (DPDA), I‐15 (I15DA), Treasure Island (TIDA), and Garner Valley (GVDA). At each site, three numerical damping formulations were evaluated: Full Rayleigh, Maxwell, and Rayleigh Mass, each implemented with both a conventional D min and an inflated D min (ⴜ × D min ) obtained from site‐specific calibration. Results show that the appropriate D min multiplier (ⴜ) correlates well with the velocity contrast of a site. When applied with inflated D min , Full Rayleigh and Maxwell damping systematically overdamped higher modes, and Maxwell damping also shifted modal peaks, particularly at higher frequencies. In contrast, Rayleigh Mass damping provided the closest match to ETFs at three sites, reducing transfer function misfit by 27%–44% relative to Full Rayleigh and 44%–49% relative to Maxwell. Rayleigh Mass damping was also computationally efficient, allowing average timesteps more than eight times larger than those with Full Rayleigh. These findings demonstrate that inflated D min can account for unmodeled attenuation in 2D GRAs, particularly at sites with low velocity contrast, and that frequency‐dependent formulations such as Rayleigh Mass damping can more effectively capture site response than traditional frequency‐independent approaches, underscoring the need to re‐evaluate the long‐standing practice.