Acoustic field in a borehole within a horizontally layered formation

The acoustic field in a cylindrical borehole embedded in a horizontally layered infinite fluid medium is studied. The system exhibits both continuous and discrete modes, 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. It as shown that the results are effective up to frequencies prevailing in a typical well logging environment. The theoretical results are verified by scaled laboratory experiments.