Methodology for Analytic Estimation of Fast Shear Polarization Direction in HTI Formations

Abstract

Abstract A new algorithm for processing cross-dipole acoustic log waveforms in formations with horizontal transverse anisotropy (HTI) has been developed. Conventional algorithms for anisotropy processing of cross-dipole acoustic waveforms minimize an objective function whose parameters are the azimuth angle of a reference (usually X-dipole) transmitter relative to the fast principal flexural-wave axis of the HTI formation and the fast and slow shear wave slowness. Minimizing the objective function with respect to all the parameters provides the desired anisotropy angle and the amount of anisotropy. It is common to minimize the objective function over all the parameters using a numerical search method (such as very fast simulated annealing) or by evaluating the objective function on a fine grid in the parameter space (i.e., brute force); however, this is never necessary with cross-dipole waveforms. It is possible to derive equations for the angle of the X-dipole relative to the fast principal flexural-wave axis that can be solved analytically as a function of the other parameters. Analytic computation relative to numerical computation provides several advantages. First, the angle found at any given point in the auxiliary parameter space is a mathematically exact global minimum (up to computer precision) with respect to the angle of the objective function at that point in the auxiliary parameter space. This is not guaranteed with a numerical-search algorithm. In addition, studying the objective function at the minimizing angle with respect to the remaining auxiliary parameters can provide insight as to the best means of minimizing the objective function with respect to the remaining parameters. This paper uses synthetic and field data to demonstrate the advantages of this new algorithm.