A new insight into the reciprocity principle

Reciprocity is usually applied to wavefields associated with concentrated p oint forces and point receivers, but, reciprocity has a much wider applicat ion 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, viscoelasti c solids and for distributed sources and receivers, and test these relation s with a full-wave numerical modeling algorithm. The theory and the numeric al experiments show that, in addition to the usual relations involving dire ctional forces (1) the diagonal components of the strain tensor an reciproc al for dipole sources (single couple without moment), (2) the off-diagonal components of the stress tensor are reciprocal for double couples with mome nts (3) the dilatation due to a directional force is reciprocal to the part icle velocity due to a dilatational source, and (4) some combinations of th e off-diagonal strains are reciprocal for single couples with moments.