Accurately modeling seismic wave attenuation is critical for ground response analyses (GRAs), which aim to replicate local site effects in ground motions. However, theoretical transfer functions (TTFs) from GRAs often overestimate empirical transfer functions (ETFs) when the small-strain damping ratio (Dmin) is set equal to laboratory measurements. Prior studies addressed this by inflating Dmin in one-dimensional (1D) GRAs to account for apparent damping mechanisms such as diffraction and mode conversions that cannot be captured in 1D. Although this approach improved fundamental-mode predictions, it often overdamped higher modes. This study explores more direct modeling of apparent damping using two-dimensional (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, Full Rayleigh, Maxwell, and Rayleigh Mass, were implemented using both conventional
Nearby in the stack
Dmin
and an inflated
Dmin
(
m×Dmin
) obtained from site-specific calibration. Results show that the appropriate
Dmin
multiplier (
m
) correlates with the site's velocity contrast. Using inflated
Dmin
, Full Rayleigh and Maxwell damping systematically overdamped higher modes, with Maxwell damping also shifting modal peaks. In contrast, Rayleigh Mass damping consistently achieved the closest match to ETFs at three of the four sites while offering faster computational performance. These findings demonstrate that inflated
Dmin
can represent unmodeled attenuation in 2D GRAs, particularly at sites with low velocity contrast, and that frequency-dependent formulations such as Rayleigh Mass damping can more accurately predict site response than traditional frequency-independent approaches.