Coherency model for dense seismic array

The recorded translational motions represent characteristics of the seismic excitation at one single point. Most foundation systems have finite, but considerable dimension, and it may offer rigidity constraint over the underlying soil. However, the extent of rigidity depends on the foundation footprint. Therefore, free-field ground motions are in general preferred in seismic design and effect of foundation flexibility is separately accounted for in a case-by-case. Hence, information about the spatial variability of translational motion is needed for seismic design of structures. Coherency is the best descriptor of spatial variability quantitatively. Moreover, description of the ground motion input cannot be completed without specifying the rotational ground motion. Since direct measurement of the rotational excitations is not feasible, these components must be extracted from the recorded translational data under suitable assumptions so as to account for their effects in an approximate sense in seismic design. Once the coherency is estimated, a number of procedures are available to generate spatially varying ground motion conditioned upon a seed event and coherency model. Objectives of this study are to obtain a coherency model for translational and rotational motion to completely specify the appropriate ground motion fields.