On extracting rotational components of ground motion using an empirical rotational window

Rotational ground motions are not being measured by the accelerographs deployed in the free-field, but rather extracted from the recorded three-component translation data, usually at one single station (single station procedure, SSP). These SSPs differ from one another in terms of approximating the underlying wave propagation scenario in the field. Increasing order of complexity does not always guarantee better product and may lead to unrealistic results because of the assumptions of compatibility. This paper aims to develop a simplified procedure for estimating rotational motion that may compete with far more rigorous approaches. The proposed procedure makes use of the existence of appropriate translational components (ATCs) and time derivatives that lead to the rotational motion with due scaling through apparent wave velocity. First, a spectral window is proposed and a set of invariant characteristics are identified (with respect to the limited studies carried out in this paper). Next, an empirical rotational window is derived that enables computation of the apparent wave velocity. Three seismic events recorded in a dense array comprising 15 surface-stations are considered for assessing the proposed simplified method.