The existence of local soft interlayer can significantly amplify or attenuate the ground motion and thus might influence the lagged spatial coherency between spatially varying earthquake ground motions. A target site with a local soft interlayer was assumed first, and then two numerical examples were set. In example 1, linear soil behavior was considered and a large amount of quasi-stationary spatially varying earthquake ground motions were generated by combining the one-dimensional wave propagation theory and the classical spectral representation method. The influence regularity of varying shear wave velocity, buried depth, and thickness of the soft interlayer on the characteristics of lagged spatial coherency was investigated. In example 2, non-linear soil behavior was taken into account and fully non-stationary spatially varying earthquake ground motions were thus generated by using time-varying transfer function and spectral representation method. An overall evaluation was carried out to shed light on the differences of characteristics of spatial coherency between non-linear soil and linear soil cases. It showed that: (i) As the shear wave velocity of interlayer declines and as the buried depth and thickness increase, remarkable reduction of spatial coherency showed up; (ii) the reduction of lagged spatial coherency caused by varying buried depth may be more inclined to concentrate in the lower frequency range; (iii) the non-linear soil behavior can cause greater further reduction of lagged spatial coherency in comparison with linear soil behavior, especially in the higher frequency range; (iv) the troughs of lagged spatial coherency curve tend to be located in the variation range of vibration frequency of time-varying spectral ratio.

The effect of the influence regularity of site saturation and water level on the coherency loss between spatially varying earthquake ground motions (SVEGMs) in a vertical direction is not yet clear. Therefore, taking an onshore-offshore site as an example, the influence regularity of site saturation and water level on the coherency loss of SVEGMs in a vertical direction was studied, in which the saturation degree of the whole site (SD), the groundwater level (GWL), and the thickness of the surface water layer (WLT) were considered. Under each case mentioned above, a large number of vertical in-plane SVEGMs were synthesized and then correspondingly, the mean lagged coherency loss and phase angle of coherence function were obtained, and a series of comparisons were carried out to shed light on the varying trend of the value of lagged coherency loss and phase angle, with predefined parameters. The results showed that SD, GWL, and WLT possess significant effects on the varying trend of the coherence function of vertical SVEGMs.