THE RECIPROCITY PROPERTIES OF GEOMETRICAL SPREADING

Reciprocity is an important property of acoustic and elastic waves, In this work it is explicity verified that acoustic waves also satisfy t he reciprocity theorem in a ray-geometric approximation, This is achie ved by deriving a reciprocity relation for the geometric spreading. Th e analysis is based on integrating the equations of dynamic ray tracin g from the source to a receiver and in the reverse direction. It is sh own that for a point source the geometric spreading for rays travellin g in opposite directions differs by a factor depending on the velociti es at the endpoints of the ray. This factor depends on the number of d imensions that one considers, Since the equations of kinematic and dyn amic ray tracing are the same for elastic waves and acoustic waves, th e derived reciprocity relations for the geometrical spreading hold for elastic waves as well, The results obtained are used to correct some errors in the derivation of an averaging theorem by Snieder & Lomax (1 996).