Formation nonlinear constants from sonic measurements at two borehole pressures

Granular structure and microcracks in rocks cause large nonlinearities in the constitutive relations that result in the stress dependence of acoustic‐wave velocities. The nonlinear constitutive relations of isotropic materials are described in terms of two linear and three nonlinear elastic constants. For nonhyperelastic materials such as rocks, these constants are defined in terms of strain derivatives of stresses for either the load or unload cycle. Acoustic waveforms at an array of receivers recorded at two different borehole pressures can be used to estimate two of the three formation nonlinear constants. Processing of these time waveforms produced by a monopole or dipole source yields the Stoneley or flexural dispersions, respectively. The differences in the Stoneley and flexural dispersions caused by a known change in the borehole pressure are then utilized in a multifrequency inversion model that yields two of the three independent nonlinear constants of the formation. These two nonlinear constants...