Modeling and imaging of multiply generated and scattered tube waves due to multiple hydraulic fractures

Although tube-wave generation and tube-wave scattering in VSP experiments are extensively used to detect and characterize subsurface hydraulic fractures (i.e., open fractures and/or permeable layers), the majority of the earlier studies consider only single generation and single scattering (reflection and transmission) responses. We formulate a new integral equation which represents total tube wavefield including multiple reflection, transmission and generation due to multiple fractures. The accurate prediction of the complex signatures of total tube wavefield is crucial for further characterizing the hydraulic properties of highly-fractured areas, such as a fault-damaged zone. Deriving the integral equation further enables us to develop a new approach to imaging and characterizing hydraulic fractures. We numerically show that the proposed integral equation can be used to predict the total tube wavefield. A spatial-focusing analysis is useful to identify the positions of the hydraulic fractures. We applied the developed theory to field VSP data obtained at a fault-damaged zone in the Median Tectonic Line, Shikoku, Japan. Our preliminary result shows evidence that tube waves are generated and scattered at open fractures and thin layers of the cataclasites at this field.