Finite aperture multipole sources, radiation, and impedance loading in fluid-filled boreholes

Multipole borehole acoustic source output and frequency content is strongly influenced by borehole fluid, tool and formation loading effects. An extra complication arises from the fact that multipole sources act in tandem and therefore the action of one source influences the other and vice versa (mutually induced impedance loading). In this paper we present a general theory that allows for swift wave field computation in and away from the fluid-filled borehole while incorporating the earlier mentioned loading effects. We compare our dimensionless impedance results with Finite Element Modeling (FEM) for a fast and slow formation while incorporating a Logging While Drilling (LWD) tool. The theoretical results are in good agreement with FEM results.