Borehole Stoneley Wave Propagation across Heterogeneous and Permeable Structures

This study investigates the propagation of borehole Stoneley waves across heterogeneous and permeable structures. By modeling the structure as a zone intersecting the borehole, a simple one-dimensional theory is formulated to treat the interaction of the Stoneley wave with the structure. This is possible because the Stoneley wave is a guided wave, with no geometric spreading as it propagates along the borehole. The interaction occurs because the zone and the surrounding formation possess different Stoneley wavenumbers. Given appropriate representations of the wavenumber, the theory can be applied to treat a variety of structures. Specifically, four types of such structures are studied, a fluidfilled fracture (horizontal or inclined), an elastic layer of different properties, a permeable porous layer, and a layer with permeable fractures. The application to the fluid-filled planar fracture shows that the present theory is fully consistent with the existing theory and accounts for the effect of the vertical extent of an inclined fracture. In the case of an elastic layer, the predicted multiple reflections show that the theory captures the wave phenomena of a layer structure. Of special interest are the cases of permeable porous zones and fracture zones. The results show that, while Stoneley reflection is generated, strong Stoneley wave attenuation is produced across a very permeable zone. This result is particularly important in explaining the observed strong Stoneley attenuation at major fractures, while it has been a difficulty to explain the attenuation in terms of the