On the calculation of group velocity, attenuations, etc. in a normal mode description

Abstract

The fact that a normal mode's group velocity may be calculated, without invoking a finite difference approximation involving a second eigenmode computation, does not appear to be widely recognized. The reciprocity relation is typically employed in the derivation of a group velocity formula in a way analogous to the derivation of normal mode attenuations. This paper obtains these results easily using the adjointness property and inner product appropriate to the problem. The complementarity of the reciprocity and adjoint methods is discussed. [Work sponsored by Naval Ocean Research and Development Activity.]