The derivation of the coupled elastic wave equations is similar to that of the uncoupled equations. In an elastic medium forces have to be in balance. This implies that the divergence of the elastic stress tensor has to equal the product of mass density and the second temporal derivative of the particle displacement . We can also include a forcing term and get

(5) |

The elastic strain can be calculated by taking spatial derivatives of the displacement , as follows:

(6) |

Next we relate the components of the elastic stress to the components of the elastic strain , the electric displacement and the first temporal derivative of the thermal displacement in the following equation:

(7) |

(8) |

1/13/1998