Tube-wave Generation Due to Permeable Layers in a VSP Experiment: A New Model Elucidating the Effect of Dip Angles

The hydraulic properties of subsurface fractures are critically important in the exploration of geothermal and hydrocarbon reservoirs. The analysis of tube waves (low-frequency Stoneley waves propagating along a fluidfilled borehole) is a promising approach to estimate the hydraulic properties of fractures intersecting a borehole. We present a new model for tube-wave generation in a borehole (VSP) by a permeable structure characterized by certain values of porosity and permeability. Contrary to the conventional theory, the new model accounts for the layer stiffness in the deformation process and it is valid for the large tube-wave amplitude. For the first time, it was possible to show a clear connection between the permeable-layer model and the parallel-wall open fracture model developed earlier. The generated tube-wave amplitudes well correspond to those of the multiple open fractures. Furthermore, the effect of large dip angles is extensively discussed. The approximate solution (the Mathieu functions) and the numerical modeling results (FEM) reveal that the effect of the dip angle is significant for a thick structure and large dip angles. The developed theory is important to evaluate field data which contain the effects of tube waves due to dipping permeable layers, e.g., cataclasite layers and fault gouges