Coherency model for translational and rotational ground motions

Spatial variability of the translational ground motion may influence the seismic design of certain civil engineering structures with spatially extended foundations. Lagged coherency is usually considered to be the best descriptor of the spatial variability. Most coherency models developed to date do not consider the spatial variability of the spectral shape of auto-spectral density (ASD), which is expected to be critical. This paper proposes a coherency model that accounts for the variability in spectral shape of ASD. Numerical results illustrate that the effect is not that critical for a dense array but can be significant in case of large array. Rotational ground motions on the other hand are not measured by the accelerograph deployed in the free-field owing to the unavailability of appropriate instruments and rather extracted from the recorded three-component translational data. Previous studies [e.g., Basu et al. (Eng Struct 99:685–707, 2015)] reported the spatial variability of extracted rotational components, even over a dimension within the span of most civil engineering structures, for example, tens of metres. Since rotation does not propagate like a plane wave, coherency model based on plane wave propagation does not apply to address the spatial variability of rotational components. This paper also proposes an alternative to address the spatial variability of rotational components. Illustrations based on relatively short separation distance confirm the expectation.