Sensitivity Densities for Rotational Ground-Motion Measurements

We derive and analyze sensitivity densities for two quantities derived from rotational ground-motion measurements: the rms (root-mean-square) amplitude A(omega) of the rotation seismogram omega = 1/2 del x u and the apparent shear-wave speed beta(a) = 1/2A(v)/A(omega), where A(v) denotes the rms amplitude of the velocity seismogram. In the case of a plane S wave in a homogeneous and isotropic medium, beta(a) coincides with the true shear-wave speed beta. Based on analytical and numerical examples, we demonstrate that the beta(a) kernels attain large absolute values only in the vicinity of the receiver but not in the vicinity of the source. This effect is pronounced in the case of both body S waves and surface waves (Love + Rayleigh). Moreover, the beta(a) kernels are dominated by the higher Fresnel zones while reaching only small absolute values in the first Fresnel zone. This implies (1) that measurements of beta(a) are to the first order independent of the Earth structure near the source, (2) that such measurements may be used for one-station local shear-wave speed tomography, and (3) that comparatively low-frequency signals can be used in order to invert for small-scale structures. The sensitivity densities corresponding to the rotation amplitude measurement A(omega) resemble those for the velocity amplitude measurements A(v). It is, therefore, the combination of A(omega) with A(v), and not one of them alone, that is likely to provide additional constraints on the Earth's structure near the receiver.