Radial Profiles of Formation Mass Density, Bulk and Shear Moduli From Borehole Flexural and Stoneley Dispersions

Exploration wells are liquid-filled boreholes drilled into formations with different geophysical and petrophysical properties. These boreholes support axisymmetric, flexural, and quadrupole family of guided modes that can probe radially varying formation properties at different frequencies. Radially varying formation properties are caused by drilling-induced fractures or near-wellbore stress concentrations. This work describes a novel workflow that inverts borehole flexural and Stoneley dispersions to obtain radially varying formation mass density and shear and bulk moduli away from the borehole surface. An integral equation relates fractional changes in guided mode velocities at different frequencies caused by fractional changes in radially varying mass density and shear and bulk moduli from a radially uniform reference state. A solution of this integral equation is based on extending the Backus–Gilbert (B–G) method for obtaining radial profile of a single to radial profiles of three formation properties away from the borehole surface. Inverted radial profiles from synthetic flexural and Stoneley dispersions have been validated against input formation parameters used to generate synthetic (measured) dispersions.