Measurement of nonlinear properties of formation using sonic borehole

Abstract

A method of investigating a formation traversed by a borehole includes, measuring at a plurality of different static borehole pressures the acoustic Stoneley and/or flexural wave velocities of waves propagating through the borehole and formation, and generating an indication of the nonlinearity of the formation by processing the velocity measurements. The velocity measurements are processed either by determining a fractional change in the measured acoustic velocity and dividing that fractional change by the change in borehole pressure to provide frequency dependent acoustoelastic coefficients, or by determining the fractional change in the measured acoustic velocity, and subtracting from the fractional change a component generated by the borehole fluid and a component due to linear aspects of the formation to provide a nonlinear formation component. By processing the velocity measurements at a plurality of frequencies, the nonlinear formation components are used to find nonlinear parameters of the formations. The nonlinear parameters are then used in conjunction with shear wave velocity information and a database of experimental data, to determine the stress in the formation, the strength of the formation, and therefrom, the amount of additional stress required to fracture the formation.