# Saturation Effect on the Coherency Loss of Spatially Varying Vertical Ground Motions
## 1 Introduction  
The simulation technology of SVEGMs greatly facilitates the seismic study of extended structures, e.g., tunnels, dams, and bridges [1; 2; 3; 4; 5; 6]. For the seismic analysis and earthquake-resistant design of offshore platforms and sea-crossing bridges etc., onshore earthquake records or artificial waves are usually used as inputs due to the lack of offshore records and seismic motions simulation methods applicable to offshore sites. However, the pore-water saturation of the soil layer and the seawater layer may strongly affect the amplitudes of vertical in-plane motions [7]. Thus, many researchers have studied the influence of the surface water layer, or site saturation, on the ground motions and proposed several methods to generate offshore SVEGMs. [PERSON] [8] and [PERSON] [9] indicated that the depth of the seawater is significant to the offshore vertical response. [PERSON] and [PERSON] [10] explained why the water layer can greatly suppress the vertical site response at the resonant frequencies of P-waves in the water layer. [PERSON] and [PERSON] [11] found that the water layer does not have a significant effect on the horizontal components of motion, but will produce a significant reduction in the vertical components of motion near the resonant frequencies of the P-waves in the water layer. [PERSON] et al. [12] conducted a theoretical analysis of the effect of seawater on incident plane P-and SV-waves at the ocean bottom. [PERSON] et al. [13] derived an offshore transfer function model and then developed a method simulate seafloor seismic motions. Considering the effect of the soft soil layer and soil saturation on site transfer function, [PERSON] et al. [7] presented a new method to study the effect of the seawater layer on vertical in-plane motions. [PERSON] et al. [14] proposed a new method of modeling spatially varying ground motion due to the ice-seawater layer, where the effects of water saturation on vertical ground motion were considered. [PERSON] et al. [15] presented a comprehensive and rational approach of synthesizing three directional spatially correlated earthquake ground motions, which took into consideration the effect of Poisson's ratio ofwater saturation on soil. [PERSON] et al. [PERSON] et al. (2016) established a modeling and simulation method for three-dimensional spatially correlated ground motion at multiple onshore and offshore sites in which hydrodynamics and one-dimensional wave propagation theory were utilized to construct the transfer function. [PERSON] et al. [PERSON] et al. (2017) reported a simulation method of spatially variable seismic underground motions in saturated double-phase media with overlying water excited by an SV-wave. Considering a saturated alluvial valley site, [PERSON] et al. [PERSON] et al. (2018) developed an effective simulation method for multiple-station spatially correlated ground motions on both the bedrock and the surface. The achievements in this scientific field have contributed to the seismic analysis or earthquake-resistant design of many important large scale offshore structures (e.g., Unocal Platform Irene, Southern California, USA; Hong Kong-Zhuhai-Macao Bridge, Southern Guangdong, China). However, the influence regularity study of the saturation and the surface water layer on the coherency loss between vertical SVEGMs is not included in the abovementioned works and has not received wide attention, and the understanding level of this effect is low. Revealing the effect of the influence regularity of saturation and the surface water layer on the coherency loss function can strengthen the understanding of hazards resulting from SVEGMs, and, for a certain project, the influence regularity study of saturation and surface water layer can contribute to summarizing the coherency loss model. It can then facilitate the fast generation of numerous SVEGMs, generating significant meaning for the three-dimensional seismic analysis, reliability analysis, and earthquake-resistant design of large off-coast structures.