Hydraulic fracture characterization using borehole sonic data

1. A method for assessing induced fractures in a subterranean formation, comprising:

providing a sonic tool in a borehole surrounded by the subterranean formation, wherein the sonic tool comprises an acoustic source and a plurality of receivers;

transmitting a sonic signal by the acoustic source before and after a hydraulic fracturing operation;

acquiring sonic data by the plurality of receivers before and after the hydraulic fracturing operation, wherein the sonic data comprises Stoneley data and cross dipole data;

calculating a shear modulus in a borehole cross-sectional plane from the Stoneley data;

calculating two shear moduli in two orthogonal borehole axial planes from the cross dipole data;

estimating changes in the shear modulus and the two shear moduli; and

outputting the changes in the shear modulus and the two shear moduli to assess the induced fractures,

wherein the borehore is a cased hole, and

wherein the method further comprises using an algorithm that accounts for a distortion of a steel casing that is bonded with the formation through a cement annulus.

2. The method of claim 1 , further comprising using an algorithm that accounts for a distortion of a sonic tool structure.

3. The method of claim 1 , further comprising converting the moduli into a compressional modulus along the borehole axis.

4. The method of claim 1 , further comprising converting the moduli into three shear moduli in the two orthogonal borehole axial planes and the borehole cross-sectional plane.

5. A method for assessing induced fractures in a subterranean formation, comprising:

providing a sonic tool in a borehole surrounded by the subterranean formation, the sonic tool comprising an acoustic source and a plurality of receivers;

transmitting a sonic signal by the acoustic source before and after fracturing;

collecting sonic data before and after fracturing the formation wherein the sonic data comprises Stoneley data and cross dipole data;

calculating a far-field shear modulus in a borehole cross-sectional plane and a far-field shear moduli in two orthogonal borehole axial planes from the Stoneley data and the cross dipole data;

inferring open or closed status of a fracture from the far-field shear moduli in the borehole cross-sectional plane and two orthogonal borehole axial planes;

estimating a radial width or height or both of a vertical fracture from the Stoneley data and the cross dipole data; and

outputting the radial width or height or both of the vertical fracture to assess the induced fractures.

6. The method of claim 5 , wherein the collecting comprises recording low-frequency monopole waveforms to obtain a borehole Stoneley dispersion.

7. The method of claim 5 , wherein the collecting comprises recording high-frequency monopole waveforms to obtain a far-field compressional slowness.

8. The method of claim 5 , wherein the collecting comprises recording cross-dipole waveforms and processing them to obtain the fast-shear azimuth.

9. The method of claim 5 , wherein the calculating comprises rotating cross-dipole waveforms to obtain the fast-dipole and slow-dipole dispersions.

10. The method of claim 5 , wherein the calculating comprises processing the borehole Stoneley dispersion to obtain the far-field shear modulus in the borehole cross-sectional plane.

11. The method of claim 5 , wherein the calculating comprises processing the fast- and slow-dipole dispersions to obtain the far-field shear moduli in the two orthogonal borehole axial planes.

12. The method of claim 5 , wherein the calculating comprises estimating differences in the far-field compressional and the three shear moduli between the pre-frac and post-frac acquisitions.

13. The method of claim 5 , wherein the calculating comprises estimating the dominant fracture orientation in terms of relative magnitude of changes in the three shear moduli.

14. The method of claim 5 , wherein the calculating comprises estimating the fracture parameters in terms of the normal and tangential compliances.

15. The method of claim 5 , wherein the calculating comprises comparing radial profiles of cross-dipole shear slownesses before and after fracturing.

16. The method of claim 5 , wherein the calculating comprises estimating an increase in the radial alteration after fracturing as an indicator of radial extent of vertically aligned fractures.

17. The method of claim 5 , wherein the estimating comprises an axial extent of increase in the cross-dipole shear slowness dispersion.

18. The method of claim 5 , wherein the sonic data is open hole sonic data or cased hole sonic data.