Simulation of full-waveform log in saturated cracked formations using Hudson's approach

We study the propagation of elastic waves that are generated in a fluid‐filled borehole surrounded by a cracked transversely isotropic medium. In the model studied the anisotropy and borehole axes coincide. To obtain the effective elastic moduli of a cracked medium we have applied Hudson's theory that enables the determination of the overall properties as a function of the crack orientation in relation to the symmetry axis of the anisotropic medium. This theory takes into account the hydrodynamic mechanism of the elastic‐wave attenuation caused by fluid filtration from the cracks into a porous matrix. We have simulated the full waveforms generated by an impulse source of finite length placed on the borehole axis. The kinematic and dynamic parameters of the compressional, shear and Stoneley waves as functions of the matrix permeability, crack orientation and porosity were studied. The modelling results demonstrated the influence of the crack‐system parameters (orientation and porosity) on the velocities and amplitudes of all wave types. The horizontally orientated cracks result in maximal decrease of the elastic‐wave parameters (velocities and amplitudes). Based on the fact that the shear‐ and Stoneley‐wave velocities in a transversely isotropic medium are determined by different shear moduli, we demonstrate the feasibility of the acoustic log to identify formations with close to horizontal crack orientations.