Reciprocity and representation theorems for rotational seismology

SUMMARY Recently, there has been an increasing interest in employing rotational motion measurements for seismic source inversion, structural imaging and ambient noise analysis. We derive reciprocity and representation theorems for rotational motion. The representations express the rotational motion inside an inhomogeneous anisotropic earth in terms of translational and rotational motion at the surface. The theorems contribute to the theoretical basis for rotational seismology methodology, such as determining the moment tensor of earthquake sources.