Sensitivity Densities for Rotational Ground-Motion Measurements

Abstract

We derive and analyze sensitivity densities for two quantities derived from rotational ground-motion measurements: the rms (root-mean-square) amplitude A ω of the rotation seismogram ![Graphic][1] and the apparent shear-wave speed ![Graphic][2] , 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, β a coincides with the true shear-wave speed β . Based on analytical and numerical examples, we demonstrate that the β 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 β 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 β 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 ω resemble those for the velocity amplitude measurements A v . It is, therefore, the combination of A ω with A v , and not one of them alone, that is likely to provide additional constraints on the Earth’s structure near the receiver. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif