Inversion of borehole dispersions for formation elastic moduli

An inversion technique for the estimation of formation elastic parameters from measured sonic borehole Stoneley and flexural dispersions is described. The inversion technique consists of minimizing a cost function derived directly from the determinant of the boundary conditions at the fluid-solid interface. This inversion model allows the possibility of simultaneously using multiple dispersive arrivals for the estimation of some of the elements of a parameter vector containing the geometrical and material constants of the formation model. In the case of noise-free measured dispersions, convergence to the exact values of inverted elastic constants is rapid and independent of the bandwidth. Results from the parametric inversion with uncertain formation elastic parameters show the influence of bandwidth and noise in the measured dispersions on the accuracy of the inverted elastic moduli. In the presence of noise, the inversion accuracy is largely dependent on the intrinsic sensitivity of the measured dispersion and far less dependent on the dispersion bandwidth.