Acoustic anisotropy using statistical analysis
Acoustic anisotropy of downhole formations is determined using statistical analysis. During operation of a downhole system, acoustic slowness measurements are acquired around a borehole extending along a formation. Statistical analysis is performed on the acquired slowness measurements, whereby the maximum and minimum slownesses of the formation are determined.
1. A method to determine acoustic anisotropy, comprising:
acquiring acoustic slowness measurements of a formation surrounding a borehole that extends through the formation;
performing statistical analysis on the slowness measurements, wherein performing the statistical analysis comprises:
grouping the slowness measurements into a plurality of bins, the plurality of bins being a multiple of four bins, with each bin representing an equal yet separate portion of a range of azimuthal angles from 0 to 180 degrees around the borehole axis; and
averaging the slowness measurements in each bin to determine a characteristic slowness for each bin;
determining a maximum slowness and a minimum slowness of the formation based upon the statistical analysis, wherein the characteristic slownesses are compared to one another in order to determine the maximum and minimum slownesses;
determining characteristic azimuthal angles of the maximum and minimum slownesses around the borehole axis, with the characteristic azimuthal angle of the maximum slowness being 90 degrees from the characteristic azimuthal angle of the minimum slowness;
utilizing the characteristic azimuthal angles to separate the slowness measurements into a maximum slowness first azimuthal angle range of 90 degrees and a minimum slowness second azimuthal angle range of 90 degrees;
averaging the slowness measurements in the maximum slowness first azimuthal angle range of 90 degrees to determine a characteristic maximum slowness measurement; and
averaging the slowness measurements in the minimum slowness second azimuthal angle range of 90 degrees to determine a characteristic minimum slowness measurement, thereby determining the maximum and minimum slownesses.
2. A method as defined in claim 1 , wherein determining the maximum and minimum slownesses further comprises determining a maximum and minimum slowness azimuthal angle around an axis of the borehole.
3. A method as defined in claim 1 , wherein separating the slowness measurements further comprises using a bifurcation line positioned at a defined degree from the slowness angles.
4. A method as defined in any one of claim 1 , 2 , or 3 , wherein the acoustic slowness measurements are acquired using a rotating acoustic interrogation tool.
5. A method as defined in any one of claim 1 , 2 , or 3 , wherein the acoustic slowness measurements are acquired using a stationary acoustic interrogation tool having azimuthally-positioned sensors.
6. A method as defined in any one of claim 1 , 2 , or 3 , wherein the acoustic slowness measurements are acquired using a compressional, shear, flexural, quadrupole or Stoneley propagation mode.
7. A system to determine acoustic anisotropy, comprising:
a downhole assembly comprising at least one transmitter and one receiver array; and
processing circuitry communicably coupled to the transmitter and the receiver array, the processing circuitry being configured to implement any of the methods of claim 1 , 2 , or 3 .
8. A system as defined in claim 7 , wherein the downhole assembly is a drilling or wireline assembly.
9. A computer-program product comprising instructions which, when executed by at least one processor, causes the processor to perform any of the methods of claim 1 , 2 , or 3 .
10. A method to determine acoustic anisotropy, comprising:
acquiring acoustic slowness measurements of a formation surrounding a borehole that extends through the formation;
performing statistical analysis on the slowness measurements, wherein performing the statistical analysis comprises:
grouping the slowness measurements into a plurality of bins, the plurality of bins being a multiple of four bins, with each bin representing an equal yet separate portion of a range of azimuthal angles from 0 to 180 degrees around the borehole axis; and
averaging the slowness measurements in each bin to determine a characteristic slowness for each bin,
wherein the characteristic slownesses are compared to one another in order to determine the maximum and minimum slownesses;
whereby grouping the slowness measurements into the plurality of bins comprises:
assigning a 360 degree reference azimuthal angle, around the borehole axis, to each slowness measurement;
for those slowness measurements having reference azimuthal angles in a 180-360 degree range, subtracting 180 degrees from the reference azimuthal angles to thereby reassign those slowness measurements into a 0-180 degree range; and
dividing the slowness measurements in the 0-180 degree range into the plurality of bins; and
averaging the slowness measurements in each bin further comprises:
selecting bin pairs such that each azimuthal angle in one of the bins of the bin pair is 90 degrees from a corresponding azimuthal angle in the other bin of the bin pair;
analyzing each bin pair to determine a largest absolute difference in the characteristic slowness measurements, thereby determining the maximum and minimum slownesses; and
determining a maximum slowness and a minimum slowness of the formation based upon the statistical analysis.
11. A method as defined in claim 10 , wherein determining the maximum and minimum slownesses further comprises determining a maximum and minimum slowness azimuthal angle around an axis of the borehole.
12. A method as defined in any one of claims 10 - 11 , wherein the acoustic slowness measurements are acquired using a rotating acoustic interrogation tool.
13. A method as defined in any one of claims 10 - 11 , wherein the acoustic slowness measurements are acquired using a stationary acoustic interrogation tool having azimuthally-positioned sensors.
14. A method as defined in any one of claims 10 - 11 , wherein the acoustic slowness measurements are acquired using a compressional, shear, flexural, quadrupole or Stoneley propagation mode.
15. A system to determine acoustic anisotropy, comprising:
a downhole assembly comprising at least one transmitter and one receiver array; and
processing circuitry communicably coupled to the transmitter and the receiver array, the processing circuitry being configured to implement any of the methods of claims 10 - 11 .
16. A system as defined in claim 15 , wherein the acoustic slowness measurements are acquired using a rotating acoustic interrogation tool.
17. A system as defined in claim 15 , wherein the acoustic slowness measurements are acquired using a stationary acoustic interrogation tool having azimuthally-positioned sensors.
18. A system as defined in claim 15 , wherein the acoustic slowness measurements are acquired using a compressional, shear, flexural, quadrupole or Stoneley propagation mode.
19. A system as defined in claim 15 , wherein the downhole assembly is a drilling or wireline assembly.
20. A non-transitory computer-program product comprising instructions which, when executed by at least one processor, causes the processor to perform any of the methods of claims 10 - 11 .
21. A computer-program product as defined in claim 20 , wherein the acoustic slowness measurements are acquired using a rotating acoustic interrogation tool.
22. A computer-program product as defined in claim 20 , wherein the acoustic slowness measurements are acquired using a stationary acoustic interrogation tool having azimuthally-positioned sensors.
23. A computer-program product as defined in claim 20 , wherein the acoustic slowness measurements are acquired using a compressional, shear, flexural, quadrupole or Stoneley propagation mode.