Choosing two boundary conditions will be like obtaining two more rows.
Reciprocity does apply to most geophysical prospecting problems.
A simple physical situation in which reciprocity does not apply is sound waves in a windy atmosphere. Obviously, still another possibility is to let the angle variable be the eigenvalue for fixed . Let us computer the vertical derivative of the quadratic form . In the acoustic example, this quadratic invariant is proportional to the energy flux. In other problems the quadratic forms need not always turn out to involve energy.