Methods and systems for determining fast and slow shear directions in an anisotropic formation using a logging while drilling tool
Methods are provided for determining properties of an anisotropic formation (including both fast and slow formations) surrounding a borehole. A logging-while-drilling tool is provided that is moveable through the borehole. The logging-while drilling tool has at least one dipole acoustic source spaced from an array of receivers. During movement of the logging-while-drilling tool, the at least one dipole acoustic source is operated to excite a time-varying pressure field in the anisotropic formation surrounding the borehole. The array of receivers is used to measure waveforms arising from the time-varying pressure field in the anisotropic formation surrounding the borehole. The waveforms are processed to determine a parameter value that represents shear directionality of the anisotropic formation surrounding the borehole.
1. A method of determining properties of an anisotropic formation surrounding a borehole, comprising:
providing a logging-while-drilling tool that is moveable through the borehole, the logging-while-drilling tool having at least one dipole acoustic source spaced from an array of receivers;
during movement of the logging-while-drilling tool, operating the at least one dipole acoustic source to excite a time-varying pressure field in the anisotropic formation surrounding the borehole, wherein the at least one dipole acoustic source produces a predefined excitation of an oriented dipole transmitter wavefield in the borehole at a particular azimuthal direction;
during the movement of the logging-while-drilling tool, using the array of receivers to measure waveforms arising from the time-varying pressure field in the anisotropic formation surrounding the borehole; and
processing the waveforms measured by the array of receivers to determine a parameter value that represents shear directionality of the anisotropic formation surrounding the borehole, wherein:
the processing involves processing waveforms measured by the array of receivers in the frequency domain for the predefined excitation to evaluate a cost function which is based on a propagation model of dispersion extracted from the waveforms, and
the cost function is evaluated to maximize energy projected onto a signal subspace defined by two Bessel functions J(w) and Y(w) along fast and slow flexural dispersions of the waveforms.
2. A method according to claim 1 , wherein the movement of the logging-while-drilling tool involves at least one of rotation and sliding motion of the logging-while-drilling tool.
3. A method according to claim 1 , wherein the parameter value represents a fast shear direction of the anisotropic formation.
4. A method according to claim 1 , wherein the parameter value represents a slow shear direction of the anisotropic formation.
5. A method according to claim 1 , wherein the parameter that represents shear directionality of the anisotropic formation is used to generate synthetically-rotated waveforms, and the synthetically-rotated waveforms are used to estimate dipole shear slowness of the formation.
6. A method according to claim 1 , wherein:
the movement of the logging-while-drilling tool involves rotation of the logging-while-drilling tool;
the Bessel function J(w) is configured to account for flexural mode of the formation; and
the Bessel function Y(w) is configured to account for propagation of a drill-collar flexural wave in an annulus between the rotating logging-while-drilling tool and the formation as well as coupling between the moving logging-while-drilling tool and the formation.
7. A method according to claim 1 , wherein:
the cost function involves a set of frequency points that are selected based on estimated dispersion of fast and slow flexural modes.
8. A method according to claim 1 , wherein:
the propagation model is determined by rotating two-component data vectors over a set of one or more predetermined rotation angles.
9. A method according to claim 8 , wherein:
the two-component data vectors are defined by inline and crossline waveforms received by the array of receivers that correspond to the predefined excitation.
10. A method according to claim 8 , wherein:
the propagation model is determined by rotating two-component data vectors over a plurality of predetermined rotation angles, and selecting rotated two-component data vectors that show largest flexural dispersion splitting.
11. A method according to claim 10 , wherein:
the set of one or more predetermined rotation angles is configured to cover fast shear direction of the formation based on fast shear directions acquired from other depths in the formation.
12. A method according to claim 8 , wherein:
the rotated two-component data vectors are used to estimate dispersion of fast and slow flexural modes arising from the predefined excitation of the sonic dipole transmitter; and
the estimated dispersion of fast and slow flexural modes is used to define the propagation model.