A new insight into the reciprocity principle

Reciprocity is usually applied to wavefields associated with concentrated point forces and point receivers, but, reciprocity has a much wider application potential. In many cases, however, it is not used at its full potential because (1) a variety of source and receiver types are not considered or (2) its implementation is not well understood. We obtain reciprocity relations for inhomogeneous, anisotropic, viscoelastic solids and for distributed sources and receivers, and test these relations with a full-wave numerical modeling algorithm. The theory and the numerical experiments show that, in addition to the usual relations involving directional forces (1) the diagonal components of the strain tensor an reciprocal for dipole sources (single couple without moment), (2) the off-diagonal components of the stress tensor are reciprocal for double couples with moments (3) the dilatation due to a directional force is reciprocal to the particle velocity due to a dilatational source, and (4) some combinations of the off-diagonal strains are reciprocal for single couples with moments.