### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 5aPAb6. Acoustic field in a borehole within a layered formation.

**Xiuming Wang
**

**
Hailan Zhang
**

**
Congfu Ying
**

**
**
*Inst. of Acoust., Academia Sinica, Beijing 100080, People's Republic of
China
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*
*
In acoustic well logging, the borehole may be considered as a vertical
waveguide of infinite cross section with horizontal discontinuities, and the
conventional mode expansion cannot be applied. Some authors introduced an
artificial large coaxial cylindrical boundary, transforming the problem into one
with finite cross section. However, this approach is limited to low frequency.
Based on the theory of generalized function, the mixed spectrum of the infinite
cross-section waveguide is analyzed and a new hybrid method is proposed in which
the acoustic field is expressed as a sum of several discrete modes and an
integral of continuous modes with unknown weight functions which are obtained by
numerically solving a group of integral equations deduced from the boundary
conditions at discontinuities. It is shown that this method makes it possible to
calculate up to the frequency for a typical logging environment. Laboratory
experiments have been conducted in which a specific method was adopted to form a
liquid cylinder surrounded by fluid layers. Both studies reveal that the
reflection of the guided wave at the discontinuity is strongly dependent on the
wave frequency. When the frequency is low the reflection is prominent, but at a
high frequency the reflection is much weaker.