Estimation of hydro-fracture parameters by analysis of tube waves at vertical seismic profiling

The problem on tube wave excitation in a well intersected by a finite-size fluid-filled crack under action of external seismic wave is considered. This situation appears at vertical seismic profiling (VSP) in the presence of hydro-fracture intersecting the borehole. A heterogeneous integral-differential equation for the fluid pressure field in fracture is derived in the long-wave approximation by the fracture opening. Stitching of the solution for pressure in fracture with that for tube waves in a well allows to calculate the amplitude and shape of generated tube waves. Numerical computations that under action of the external seismic field the crack edges excite a strongly dispersive mode of a thin fluid layer which can be used for estimation of linear fracture size on the basis of VSP technique.