A number of recent studies have analyzed seismic rotational data using a relationship between transverse acceleration and rotation rate derived for a homogeneous full space. In this study we explore this relationship further theoretically by presenting a full ray theory (FRT) method to simulate rotational motions of fundamental mode seismic surface waves in smooth, laterally heterogeneous Earth models. In the ray picture of wave propagation the vertical component of the rotational rate motion of fundamental mode Love waves is obtained by dividing the transverse component of ground acceleration by the Love-wave local phase velocity beneath the seismic recording station. We illustrate the method with examples of theoretical calculations of T≈40 sec rotational rate ground motions of fundamental Love waves using the crust model CRUST2.0 combined with the mantle model S20RTS for the 25 September 2003 M 8.1 Tokachi-oki earthquake, Japan. FRT rotation synthetics match complete calculations using the spectral-element method very well and fit real data reasonably well. Furthermore, we show that the effect of realistic local structure beneath receivers on rotational motions is strong enough to be observable. FRT calculations could potentially help to determine Love-wave local dispersion curves and, thus, to estimate the 1D local shear velocity structure beneath seismic stations from point measurements of rotational rate and acceleration ground motions.

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