Abstract:

Propagating modes often appear in borehole acoustical measurements, providing information about the surrounding formation. A dipole source, for example, excites borehole flexural waves, whose low-frequency slowness asymptote is the formation shear slowness. However, because the flexural mode may be highly dispersive, and its spectral amplitude is small in the low-frequency regime, the shear slowness is difficult to estimate. Monopole sources excite Stoneley waves whose slowness is dispersive and a complex function of formation properties, likewise making formation slowness estimation problematical. Theoretical modal dispersion characteristics may be predicted over a prescribed frequency range by finding the poles of a simplified analytical borehole reponse function [Kurkjian, Geophysics 50, 852--866 (1985)]. This model is used to estimate formation parameters based on nonlinear optimization. A new spectral estimator (frequency-wave number) is first used to estimate the slowness dispersion for a measured array dataset [M. P. Ekstrom and C. J. Randall, J. Acoust. Soc. Am. 98, 2867 (1995)]. The parameters of an analytical model are then iteratively adjusted via a nonlinear optimization algorithm to minimize the error between model and estimated slownesses. Optimizer performance depends on the error function construct, constraints imposed, and variational knowledge of the forward model. Results of using monopole and dipole field data sets will be shown.