### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 5aPA9. Three-dimensional dyadic Green's function for elastic waves in
multilayer cylindrical structures.

**Cai-Cheng Lu
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*Dept. of Electrical and Comput. Eng., Univ. of Illinois, Urbana, IL 61801
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**Qing-Huo Liu
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*Schlumberger-Doll Res., Old Quarry Rd., Ridgefield, CT 06877
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Multilayer cylindrical structures are encountered in many applications.
Elastic waves generated by an arbitrary source in such a structure can be found
by using the corresponding three-dimensional dyadic Green's function. In this
work, a 3-D dyadic Green's function for the displacement field is derived for
elastic wave propagation in coaxial cylindrical structures with an arbitrary
number of layers. The primary and reflection parts of the dyadic Green's
function are first written in terms of the Fourier transform of z (axial
coordinate) and Fourier series of (theta) (azimuthal coordinate). In this
transform domain, the boundary conditions are then imposed so that the
reflection coefficients can be calculated for each k[sub z] and n, which are,
respectively, the transform variables of z and (theta). The spatial dyadic
Green's function is then obtained by inverse transforming this solution in
k[sub z]-n domain. Once this dyadic Green's function is found, elastic waves
due to any source in the cylindrical structure can be obtained by integrating
the Green's function with the source. The numerical results are validated
against previous results for special geometries. Several applications of this
dyadic Green's function will be shown for layered structures commonly used in
acoustic well logging.