Abstract

The reflection and scattering of Stoneley guided waves at the tip of a crack filled with a viscous fluid was studied numerically in two dimensions using the finite-element method. The rock surrounding the crack is fully elastic and the fluid filling the crack is elastic in its bulk deformation behavior and viscous in its shear deformation behavior. The crack geometry, especially the crack tip, is resolved in detail by the unstructured finite-element mesh. At the tip of the crack, the Stoneley guided wave is reflected. The amplitude ratio between reflected and incident Stoneley guided wave is calculated from numerical simulations, which provide values ranging between 43% and close to 100% depending on the type of fluid filling the crack (water, oil or hydrocarbon gas), the crack geometry (elliptical or rectangular), and the presence of asmall gas cap at the cracktip. The interference of incident and reflected Stoneley guided waves leads to a node (zero amplitude) at the tip of the crack. At other positions along the crack, this interference increases the amplitude. However, the exponential decay away from the crack makes the Stoneley guided wave difficult to detect at a relatively short distance away from the crack. The part of the Stoneley guided wave that is not reflected is scattered at the crack tip and emitted into the surrounding elastic rock as body waves. For fully saturated cracks, the radiation pattern of these elastic body waves points in every direction from the crack tip. The emitted elastic body waves can allow the detection of Stoneley guided wave-related resonant signals at distances away from the crack where the amplitude of the Stoneley guided wave itself is too small to be detected.

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