Acoustic field in a borehole within fluid formations with a horizontal interface

Abstract

The acoustic field in a cylindrical borehole embedded in a horizontally layered infinite medium is studied. The modes in each layer are found to consist of continuous as well as discrete ones, the orthogonality and completeness of which are proven. The relevant weights associated with the two kinds of modes are determined by solving a set of integral equations deduced from the boundary conditions at the layer interface. This technique is not limited to low frequencies, but applies well to frequencies prevailing in typical logging environment. Reflection, transmission and coupling coefficients of different modes are evaluated. The numerical results are verified by comparison with the method of real axis integration (RAI) and the hybrid mehtod proposed by Tsang [“Transient acoustic waves in a fluid-filled borehole with a horizontal bed boundary separating two solid formations”, J. Acoust. Soc. Am. 81, 844–853 (1987)]. The scaled laboratory experiments are carried out and the corresponding results are presented for comparison with the numerical computation.