Formation property determination apparatus, methods, and systems

A system, comprising:

• a down hole tool;
• azimuthally orthogonal dipole receiver arrays and azimuthally orthogonal transmitter arrays, each of the arrays attached to the down hole tool;
• logic to record a plurality of acoustic waveforms corresponding to acoustic waves received at the azimuthally orthogonal dipole receiver arrays, the acoustic waves being generated by the azimuthally orthogonal transmitter arrays;
• and
• a signal processor to estimate a global minimum of an objective function with respect to an azimuth angle and a set of auxiliary parameters, wherein the azimuth angle corresponds to an orientation of the transmitter arrays and the receiver arrays relative to fast and slow principal flexural wave axes, with the signal processor configured to estimate fast and slow principal flexural waves propagating along the axes and characterized by the waveforms as ordered complex eigenvalues of a waveform matrix diagonalized by a unitary similarity transformation at each data point of the waveforms, and the objective function depending on the waveforms, the ordered eigenvalues, the azimuth angle, and the set of auxiliary parameters, wherein the signal processor is also configured to remove existing ambiguities associated with the fast and slow principal flexural wave axes.

A processor-implemented method of estimating an azimuth angle, to execute on one or more processors that perform the method, comprising:

• recording a plurality of acoustic waveforms corresponding to acoustic waves received at azimuthally orthogonal dipole receiver arrays surrounded by a geological formation, the waves being generated by azimuthally orthogonal transmitter arrays, the azimuth angle corresponding to an orientation of the receiver arrays and the transmitter arrays relative to fast and slow principal flexural wave axes, wherein fast and slow principal flexural waves propagating along the axes and characterized by the waveforms being estimated as the ordered eigenvalues of a waveform matrix diagonalized by a unitary similarity transformation;
• defining an objective function dependent on the waveforms, the ordered eigenvalues, the azimuth angle, and a set of auxiliary parameters;
• minimizing the objective function with respect to the azimuth angle;
• and
• determining at least one anisotropy angle of the geological formation based on the global minimum.

An article including a machine-accessible medium having instructions stored therein, wherein the instructions, when accessed, result in a machine estimating an azimuth angle by performing:

• recording a plurality of acoustic waveforms corresponding to acoustic waves received at azimuthally orthogonal dipole receiver arrays surrounded by a geological formation, the waves being generated by azimuthally orthogonal transmitter arrays, the azimuth angle corresponding to an orientation of the receiver arrays and the transmitter arrays relative to fast and slow principal flexural wave axes, wherein fast and slow principal flexural waves propagating along the axes and characterized by the waveforms being estimated as the ordered eigenvalues of a waveform matrix diagonalized by a unitary similarity transformation;
• defining an objective function dependent on the waveforms, the ordered eigenvalues, the azimuth angle, and a set of auxiliary parameters;
• minimizing the objective function with respect to the azimuth angle;
• and
• determining at least one anisotropy angle of the geological formation based on the global minimum.