Partial derivatives of surface wave phase velocity with respect to physical parameter changes within the Earth

Abstract

By using energy equations, which are equivalent to fundamental equations and boundary conditions in surface wave problems, we can get analytical expressions for partial derivatives of phase velocity with respect to changes of physical parameters within the earth. These derivatives can be calculated by knowing only the eigenfunction corresponding to the phase velocity. Numerical examples are worked out for CANSD (a model proposed by Brune and Dorman for the Canadian shield), the Jeffreys model, and the Gutenberg model for crustmantle structure. An application of the present result to numerical inversion of surface wave data is demonstrated by an example.