Stoneley wave generation by an incident P-wave propagating in the surrounding formation across a horizontal fluid-filled fracture

This study investigates the generation of the low-frequency borehole Stoneley wave (tube wave) by a plane P-wave propagating through the surrounding elastic formation, which is intersected by a fluid-filled fracture. A model is constructed taking into account the dynamic fluid coupling between the borehole interior and the fluid-filled fracture of infinite extent with parallel walls. The basic mechanism of such coupling is due to the contraction of the fracture walls by the incident P-wave, leading to seismic radiation into the fracture. The dynamic fluid flux from the fracture into the borehole interior, and vice versa, is the source of the low-frequency Stoneley wave. An expression for the monopole pressure source, exciting the tube wave, is obtained. The tube-wave equation in the long-wave approximation is derived in the presence of a fluid-filled fracture of infinite extent. Amplitudes and waveforms of Stoneley waves are analysed in the seismic wavelength range for P-wave pulses of various shapes. It is shown that the amplitude and waveform of the Stoneley wave depends significantly on the two dimensionless parameters of the problem: (1) the ratio of the borehole radius to the dominant wavelength of the incident pulse; (2) the ratio of the fracture width to the borehole radius. It is found that the amplitude of the generated Stoneley wave can be of the order of the P-wave amplitude in the borehole fluid. Stoneley waveforms are found to be completely different from those of the incident pulse.