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

Dept. of Electrical and Comput. Eng., Univ. of Illinois, Urbana, IL 61801

Qing-Huo Liu

Schlumberger-Doll Res., Old Quarry Rd., Ridgefield, CT 06877

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.