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It is now presumed that the reader has a general knowledge
of classical elasticity theory.
Few textbooks, if any, develop the special subject of stratified media
which is so important in seismology.
Many papers on that subject may be found in the
*Bulletin of the Seismological Society of America (BSSA)*.
For those readers unfamiliar with the *BSSA*,
we now present the results of applying the general methods of this chapter
to the equations of isotropic elasticity.

The conventions in elasticity are (*u*, *w*) displacements
in *x* and *z* directions,
is the stress matrix,
and are Lame's constants and is density.
Hooke's law and Newton's law with time dependence leads to

| |
(1) |

where
| |
(2) |

Define also
| |
(3) |

If material properties do not vary in the *x* direction,
we have the row eigenvector transformation
to up- and downgoing wave variables.
| |
(4) |

and the column eigenvector inverse transform
| |
(5) |

where
The matrices partition nicely into blocks.
The reader may verify
that and .

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** Up:** Mathematical physics in stratified
** Previous:** CONSERVATION PRINCIPLES AND MODE
Stanford Exploration Project

10/30/1997