Radial profiling of formation shear velocity from borehole flexural dispersions

Many formations surrounding a wellbore exhibit radial heterogeneity that can be caused by stress concentrations, mechanical damage, or fluid invasion. Optimal completions of wells require estimates of both the radial extent and magnitude of mechanical damage that might be present. The radial heterogeneity can be expressed in terms of variations in the compressional and shear velocities as a function of radial position. Both the lowest-order axisymmetric Stoneley and flexural mode dispersions are significantly perturbed in the presence of such radial heterogeneities. This paper describes results from a forward model for computing synthetic waveforms at an array of receivers produced by either a monopole or dipole source placed on the borehole axis. These waveforms are then processed by a modified matrix pencil algorithm for isolating both non-dispersive and dispersive arrivals in the wavetrain. The Backus-Gilbert technique is then used for the inversion of flexural dispersions over bandwidths ranging from about 2 to 6 kHz for estimating radial variations in formation shear velocity. Radial variations in the inverted shear velocity is essentially uniform in the case of a homogeneous formation and agrees remarkably well with the assumed radial profile of the shear velocity in the case of radially heterogeneous formation. Agreement has been obtained to within 2% between the inverted shear velocities and the assumed shear profile in generating the synthetic data. This technique has thus been validated against synthetic data and can have a variety of applications for probing materials with varying properties using wideband dispersive signals