Parametric estimation of phase and group slownesses from sonic logging waveforms

Abstract

Sonic logging waveforms consist of a mixture of nondispersive waves, such as the P‐ and S‐headwaves, and dispersive waves, such as the Stoneley and pseudo‐Rayleigh waves in monopole logging and the flexural wave in dipole logging. Conventionally, slowness dispersion curves of various waves are estimated at each frequency, independent of data at other frequencies. This approach does not account for the fact that slowness dispersion functions in sonic logging are continuous and, in most cases, smooth functions of frequency. We describe a parametric slowness estimation method that uses this property by locally approximating the wavenumber of each wave as a linear function of frequency. This provides a parametric model for the phase and group slownesses of the waves propagating across the receiver array. The estimation of phase and group slownesses is then carried out by minimizing the squared difference between the predicted and observed waveforms. The minimization problem is nonlinear and is solved by an iterative algorithm. Examples using synthetic and field data are shown and the results are compared with those obtained by the conventional Prony method. Based on the comparison, we conclude that the parametric method is better than the conventional Prony method in providing robust and stable slowness estimates.