On the structure of one-way elastic-wave propagation and exact solutions to the elastodynamic equations : theory for 2-dimensional SH waves

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Haines, A.J. 1995 On the structure of one-way elastic-wave propagation and exact solutions to the elastodynamic equations : theory for 2-dimensional SH waves . Lower Hutt: Institute of Geological & Nuclear Sciences Institute of Geological & Nuclear Sciences science report 95/08 261 p.

Abstract: A one-way wave propagation theory is developed to generate exact solutions to the elastodynamic equations in any heterogeneous media. The new approach is radically different from traditional one-way wave propagation techniques. It is based on a reappraisal of the physical foundations of one-way propagation and avoids practical problems and philosophical inconsistencies inherent in the traditional approach. In particular, the new approach is completely consistent with the simple idea that forward- and backward-propagating waves involve forward and backward propagation of energy. The mathematical basis of the new approach is a generally-applicable class of exact factorizations of the elastodynamic equations. These factorizations result in separate one-way wave equations for forward- and backward-going waves involving only the first spatial derivatives of the wavefields with respect to a range variable. (auth.)