The Sacramento-San Joaquin Delta, herein referred to as the Delta, is located in California’s Central Valley, roughly 50 km east of the San Francisco Bay area. Roughly 700,000 acres of land within the Delta are protected by more than 1,770 km of levees, which also serve as a conduit for approximately two-thirds of the State’s drinking water supply. Vital transportation, utility, and communication lifelines cross the patchwork of subsided islands, which are protected by the levees.

Before the lands were reclaimed, the area was a great tidal freshwater marsh. As the wetland vegetation died, the plant matter was only able to partially decay before the material became submerged and/or overgrown leaving organic deposits known as peat. The thickness of these organic deposits vary across the Delta, reaching up to 15 m in some areas. Many of the Delta levees were constructed atop these peaty deposits, as illustrated schematically in Figure 1.

In 2009 the Delta Risk Management Strategy (DRMS) conducted a probabilistic seismic hazard analysis (PSHA) for the Delta and concluded that seismic events pose a significant hazard to the Delta levees; this conclusion has since been reinforced by recent research efforts (Wong et al. 2021). The peaty soils affect risk in two ways: (1) seismic demand as a result of site amplification of ground motions and (2) ground motion deformation potential associated with permanent shear and/or volumetric deformations. Sites with peat may be characterized as having 30-m time-averaged shear wave velocities, *V _{S30}*, in the range of 100 to 200 m/s, which is softer than the lower limit for NGA-West2 ergodic site response models. We suspect these models to poorly capture the true behavior of such soft soil sites, therefore this work is concerned with investigating the (linear) site response of soft peaty organic soil sites in the Delta region.

We assembled a ground motion database that significantly expands upon the NGA-West2 database for California events and sites. From this larger database we extracted 526 ground motions recorded by 45 seismic instruments located within the Delta jurisdictional boundaries corresponding to 68 events with a wide range of source-to-site azimuths (shown in Figure 2). We only consider motions produced by events with moment magnitudes **M**>4 to avoid difficulties that may be encountered in the analysis of site terms using smaller magnitude data. Additionally, magnitude-distance cutoffs suggested by (Boore et al. 2014; BSSA14) were considered during record selection, horizontal components are combined to median-component (RotD50) intensity measures, and a lowest usable frequencies are enforced.

Site-specific *V _{S30}* were computed at sites with a measured

\begin{equation} \ln{(\bar{V}_{S30})} = \mu_{\ln{V_{S30}}} + C(t_p -\mu_{t_p}) \pm \epsilon_n \sigma \label{(1)} \end{equation}

where *μ _{lnVS30}* and

**Table 1**. *V _{S30}*-peat thickness proxy model coefficients.

Site Condition | μ_{lnVS30} |
C (m^{-1}) |
μ (m)_{tp} |
σ |
---|---|---|---|---|

Free-Field | 5.0095 | 0.0881 | 3.5098 | 0.2886 |

Levee | 5.0974 | 0.0281 | 2.6280 | 0.3035 |

Our aim is to evaluate site response in the Bay-Delta region from empirical data, and then use the observed site response effects to investigate its dependence on readily available site parameters (e.g., *V _{S30}*, peat thickness, etc.). We apply procedures for evaluating non-ergodic site response effects from ground motion recordings (Stewart et al. 2017), which utilize residuals analyses. We begin by computing total residuals,

\begin{equation} R_{ij} = c_k + \eta_{Ei} + \eta_{Sj} + \epsilon_{ij} \label{(2)} \end{equation}

Non-ergodic site response is computed using *η _{Sj}*. To minimize bias for each site we use only data from sites with more than four observations and whose

We compute the observed linear site response for each site, *f _{1}*, as the sum of

To this point, we have only investigated the dependence of site response in the region with *V _{S30}*. We adopt a mulit-linear functional form to capture the observed

\begin{equation} F_{lin}(V_{S30}) = \begin{cases} c_{low} \ln{(\frac{V_{S30}}{V_1})} + Δc \ln{(\frac{V_1}{V_{ref}})} + A, \text{ }\text{ }\text{ } V_{S30} \leq V_1 \\ Δc \ln{(\frac{V_{S30}}{V_{ref}})} + A, \quad\qquad\qquad\qquad V_1 < V_{S30} \leq 400 \text{ m/s} \\ m \log_{10}(V_{S30}) + b, \qquad\qquad\quad\quad\text{ }\text{ } 400 \text{ m/s} < V_{S30} \leq V_{ref} \\ c\ln{(\frac{V_{S30}}{V_{ref}})}, \quad\qquad\qquad\qquad\qquad\text{ }\text{ }\text{ } V_{ref} < V_{S30} \leq V_2 \\ c\ln{(\frac{V_2}{V_{ref}})}, \quad\qquad\qquad\qquad\qquad\text{ }\text{ }\text{ } V_2 \leq V_{S30} \end{cases} \label{(3)} \end{equation}

where *V _{1}* and

Coefficients in the first two terms of Eq. (3) are obtained by regressing *f _{1}* on

*V*-scaling predicted by SS14 does not accurately capture the site response observed in the Delta over a wide frequency range._{30}- There is a relatively large scatter in the data, however some trends are consistent:
- Short periods (0.01-0.22 s): lower amplification than SS14.
- Moderate periods (0.9-3 s): soft soils (
*V*< 200 m/s) exhibit less_{S30}*V*-scaling than SS14._{S30} - Long periods (3-10 s): Delta sites amplify more than what SS14 predicts with soft soild having less
*V*-scaling._{S30} - Implementation of our local Delta-specific linear site response model leads to improved ground motion predictions and a reduction of epistemic uncertainty, however more work is needed before the model can be used in engineering applications.
- The long-period site response observed from empirical data cannot be captured by ground response analyses, which has been the basis for site response estimation in prior work. This distinction is one example of the value of the present approach.
- Nonlinear site response effects in the region are expected to be significant, and are being evaluated using ground response analyses with regionally-customized nonlinear dynamic properties of the peat and other soils. The final site response will combine an empirical site amplification model with a simulation-based nonlinear model.

- Our proposed model generally captures the observed site response, reducing uncertainty, however the functional form needs refinment which can be achieved using advanced regression methods (e.g., non-linear mixed-effects).
- Even with local
*V*-scaling, the linear site response model still has room for improvement. We intend to investigate the correlation between_{S30}*f*and additional site parameters (such as site fundamental period and peat thickness) to develop more sophisitcated model variants._{1} - To produce a comprehensive local site response model applicable to hazard level conditions (i.e., strong motions) we must develop a local non-linear model (in progress; discussed elsewhere).
- Lastly, we plan to run PSHA incorporating regional path (discussed elsewhere) and local site effects for the Delta region.

Funding for this study provided by California Department of Water Resources (DWR), Agreement 4600012415. We gratefully acknowledge this support. We want to particularly acknowledge Mike Driller (DWR), Tim Wheling (DWR), and Nick Novoa (DWR) for their assistance and support. Lastly, we want to acknowledge Ariya Balakrishnan (Division of Safety of Dams), Albert Kottke (Pacific Gas & Electric), Jamie Steidl (University of California, Santa Barbra and United States Geological Survey), and Ivan Wong (Lettis Consultants International) for their participation and guidance serving as advisory personnel.

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