### ASA 126th Meeting Denver 1993 October 4-8

## 5aUW10. Factorization of propagator matrices for efficient computation of
wave-fields in horizontally layered fluid--solid media.

**Sven Ivansson
**

**
**
*[Dept. of Hydroacoust. and Seismol., Natl. Defence Res. Establishment FOA
260), S-172 90 Sundbyberg, Sweden]
*

*
*
The wave field is decomposed into its frequency--wave-number components.
Compound matrices for solid layers provide a convenient way of computing the
boundary values at a fluid--solid interface [M. B. Porter and E. L. Reiss, J.
Acoust. Soc. Am. 77, 1760--1767 1985)], with loss-of-precision control. A
certain vector is propagated through a sequence of multiplications with
compound matrices, one for each layer. It is shown that computations of this
kind can be performed more efficiently if each compound matrix is decomposed as
a product of sparse matrices that are applied in sequence. Two kinds of
compound-matrix factorizations are proposed. In connection with dispersion
computations, our first factorization gives a method that is related to the
``fast form'' of Knopoff's method [F. Schwab et al., Bull. Seismol. Soc. Am.
74, 1555--1578 1984)]. This algorithm is slightly more efficient, however, and
its range of applicability is wider. The second compound-matrix factorization
gives a method that is significantly faster than the ``fast form'' of Knopoff's
method. Very few arithmetic operations are needed. It also provides a good
basis for analyzing the numerical performance of compound-matrix propagation.
Finally, it is shown how propagator-matrix factorization can be used to enhance
the efficiency for multi-frequency computations and computation of full
wave-fields, by wave-number integration or modal synthesis.