Research Note: Internal/external seismic source wavefield separation and cancellation

A compact representation is obtained for the separation of a scalar wavefield on a closed surface into parts due to internal and external sources. The formula assumes that the total field and its gradients are known on the surface, as is the exact Green function of the medium. The derivation involves four rather straightforward applications of Green’s theorem or the representation theorem, though it is a remarkable result in that waves from either source that traverse the boundary many times are appropriately separated. The intermediate results at the four steps of the derivation also shed light on the possibility of acoustic shielding from unwanted sources without knowledge of the Green function for the medium.