Characterization of hydraulic properties of a dipping permeable layer using the amplitude of the generated tube wave

Low-frequency Stoneley waves in a fluid-filled borehole (tube waves) have been extensively studied in order to estimate the hydraulic properties of fractures intersecting a borehole. We present a new model for tube-wave generation in a borehole (VSP) intersected by a dipping, permeable layer characterized by certain values of porosity and permeability. The new model accounts for the layer stiffness in the deformation process, and it considers realistic boundary conditions. We show a clear connection between the permeable-layer model and the multiple, parallel-wall open fracture model developed earlier. The effect of large dip angles is investigated in detail using numerical modeling (FEM). The approximate solution (the Mathieu functions) and the results of FEM reveal that the effect of the dip angle is significant for a thick permeable layer and large dip angles. We also develop an inversion method to estimate the tube to P-wave amplitude ratio using multiple receivers, whose performance is numerically tested. The preliminary results of field data application at Nojima fault in Japan show the estimated permeability to be similar to that in a foregoing study. The developed theory is crucial in evaluating field data at fault-damaged zones where steeply-dipping, cataclasite layers and fault gouges are dominant.