### ASA 125th Meeting Ottawa 1993 May

## 2aEA10. Improved integration methods for poles in transfer functions.

**Daniel Zwillinger
**

**
Paul Jameson
**

**
**
*BBN, 70 Fawcett St., Cambridge, MA 02138
*

*
*
When analyzing stress transmission in layered media as a function of
in-plane wave number, the transfer function may exhibit pole-like behavior.
These poles are associated with trace matching to bending waves in high
stiffness layers. However, the exact interrelationship of multiple poles for
the case of multiple various layers is not well understood. This condition
presents difficulties to routines that integrate over the wave number. Hence,
most users employ adaptive integration schemes that compensate for the poles by
increasing the number of points at which the transfer function is evaluated. An
improved approach, which involves singularity isolation, is being used in
software being developed at BBN. This approach is to describe the pole in an
analytical form and perform the integral analytically in the region in which
the pole occurs. In this presentation, how to construct the analytic function
for a single layer is illustrated, and the generalization to multiple layers is
described. This approach leads to a reduction in computer processing time.