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1. WO2020142057 - SHEAR VELOCITY RADIAL PROFILING BASED ON FLEXURAL MODE DISPERSION

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[ EN ]

WHAT IS CLAIMED IS:

1. A method for profiling acoustic shear velocities in a borehole, said method comprising:

generating a measured flexural wave velocity dispersion based on measured flexural wave velocities: determining formation properties including determining a far-field shear velocity based, at least in part, on the measured flexural wave velocity dispersion;

generating a reference flexural wave velocity dispersion based on the determined formation

properties;

generating a linear approximation model for an alteration zone having multiple layers, said generating a linear approximation model including:

generating a set of wavelength dependent perturbation values based on differences between wavelength-correspondent velocities in the measured flexural wave dispersion curve and the reference flexural wave dispersion curve; and

generating a respective sensitivity kernel for each of the multiple layers based on ratios between each of a set of wavelength dependent and layer dependent flexural wave pertuibation values and an approximated shear velocity perturbation value; processing the linear approximation model to determine a set of shear velocity pertuibation values based on the wavelength dependent pertuibation values and the sensitivity kernels; and determining a respective shear velocity for each of the multiple layers based on the far-field shear velocity and the shear velocity perturbation values.

2. The method of claim 1, wherein said generating a linear approximation model includes selecting a first number of layers and a first approximated shear velocity value, said method further comprising: applying a linearity constraint to the generation of sensitivity kernels including,

determining whether a first set of generated sensitivity kernels satisfy a linearity threshold; in response to the first set of sensitivity kernels not satisfy ing the linearity threshold, selecting at least one of a second number of layers and a second approximated shear velocity perturbation value; and

re-generating the linear approximation model using at least one of the second number of layers and the second approximated shear velocity perturbation value.

3. The method of claim 1, further comprising:

generating predicted flexural wave phase velocities resulting from the determined radially shear wave velocity profiles;

comparing the predicted flexural wave phase velocities with the measured flexural wave

velocities; and

in response to differences between the predicted flexural wave velocities and the measured flexural wave velocities exceeding a threshold, generating the linear approximation model using another reference flexural w ave velocity dispersion.

4. The method of claim 1, wherein said determining the far-field shear velocity comprises generating a low-frequency asymptote of the measured flexural wave velocity dispersion and determining the far-field shear velocity as corresponding to an asymptotic limit of the low-frequency asymptote.

5. The method of claim 1, wherein said generating a measured flexural wav e velocity dispersion and said generating a reference flexural wave velocity dispersion comprise:

determining frequency dependent dispersions of the measured flexural wave velocities and the

reference flexural wave velocities; and

normalizing the frequency dependent dispersions based on a ratio of flexural wave wavelength and a borehole radius value.

6. The method of claim 1, wherein said generating a set of wavelength dependent perturbation values comprises applying a flexural mode perturbation function to the measured flexural wave velocity dispersion and the reference flexural wave velocity dispersion, wherein the flexural mode perturbation function specifies flexural mode perturbation values, m, in accordance with the relation,


where sd represents measured flexural wave velocity, so represents reference flexural wave velocity , and h represents wavelength normalized by a specified radial distance.

7. The method of claim 1, wherein said generating a respective sensitivity kernel for each of the multiple layers comprises:

for each of the multiple layers,

generating a flexural mode perturbation dispersion as a function of normalized wavelength; and

for each of a selected sampling range of normalized wavelength values, computing a

sensitivity kernel as the ratio between a flexural mode perturbation value and the approximated shear velocity perturbation value.

8. The method of claim 1, wherein said processing the linear approximation model to determine a set of shear velocity perturbation values comprises determining the set of shear velocity perturbation values as an inversion function of the wavelength dependent perturbation values and the shear velocity sensitivity kernels.

9. The method of claim 1, wherein said determining a set of shear velocities comprises for each of a respective one of the multiple layers, computing a shear velocity in accordance with the relation,

where Vi represents the shear velocity of the ith annular layer, u, represents the shear velocity perturbation of the ith annular layer, and V0 represents the far-field shear velocity.

10. The method of claim 1, further comprising:

emitting, by a dipole acoustic source within a borehole, acoustic energy into a formation; and measuring, by an acoustic receiver, velocities of flexural waves generated by the acoustic energy.

11. An apparatus comprising:

a processor, and

a machine-readable medium having program code executable by the processor to cause the apparatus to,

generate measured flexural wave velocity dispersion based on measured flexural wave velocities; determine formation properties including determining a far-field shear velocity based, at least in part, on the measured flexural wave velocity dispersion;

generate a reference flexural wave velocity dispersion based on the determined formation

properties;

generate a linear approximation model for an alteration zone having multiple layers, said

generating a linear approximation model including:

generating a set of wavelength dependent perturbation values based on differences between wavelength-correspondent velocities in the measured flexural wave dispersion curve and the reference flexural wave dispersion curve; and

generating a respective sensitivity kernel for each of the multiple layers based on ratios between each of a set of wavelength dependent and layer dependent flexural wave perturbation values and an approximated shear velocity perturbation value; process the linear approximation model to determine a set of shear velocity perturbation values based on the wavelength dependent perturbation values and the sensitivity kernels; and

determine a respective shear velocity for each of the multiple layers based on the far-field shear velocity and the shear velocity perturbation values.

12. The apparatus of claim 11, wherein said program code executable by the processor to cause the apparatus to generate a linear approximation model includes program code executable by the processor to cause the apparatus to select a first number of layers and a first approximated shear velocity value, said apparatus further comprising program code executable by the processor to cause the apparatus to:

apply a linearity constraint to the generation of sensitivity kernels including,

determining whether a first set of generated sensitivity kernels satisfy a linearity threshold; in response to the first set of sensitivity kernels not satisfying the linearity threshold, selecting at least one of a second number of layers and a second approximated shear velocity perturbation value; and

re-generating the linear approximation model using at least one of the second number of layers and the second approximated shear velocity perturbation value.

13. The apparatus of claim 11, further comprising program code executable by the processor to cause the apparatus to:

generate predicted flexural wave phase velocities resulting from the determined radially shear wave velocity profiles;

compare the predicted flexural wave phase velocities with the measured flexural wave velocities; and

in response to differences between the predicted flexural wave velocities and the measured

flexural wave velocities exceeding a threshold, generate the linear approximation model using another reference flexural wave velocity dispersion.

14. The apparatus of claim 11, wherein the program code executable by the processor to cause the apparatus to determine the far-field shear velocity comprises program code executable by the processor to cause the apparatus to generate a low-frequency asymptote of the measured flexural wave velocity dispersion and determining the far-field shear velocity as corresponding to an asymptotic limit of the low-frequency asymptote.

15. The apparatus of claim 11, wherein the program code executable by the processor to cause the apparatus to generate a measured flexural wave velocity dispersion and generate a reference flexural wave velocity dispersion comprises program code executable by the processor to cause the apparatus to: determine frequency dependent dispersions of the measured flexural wave velocities and the

reference flexural wave velocities; and

normalize the frequency dependent dispersions based on a ratio of flexural wave wavelength and a borehole radius value.

16. The apparatus of claim 11, wherein the program code executable by the processor to cause the apparatus to generate a set of wavelength dependent perturbation values comprises program code executable by the processor to cause the apparatus to apply a flexural mode perturbation function to the measured flexural wave velocity dispersion and the reference flexural wave velocity dispersion, wherein the flexural mode perturbation function specifies flexural mode perturbation values, m, in accordance with the relation,


where sd represents measured flexural wave velocity , s0 represents reference flexural wave velocity, and h represents wavelength normalized by a specified radial distance.

17. The apparatus of claim 11, wherein the program code executable by the processor to cause the apparatus to generate a respective sensitivity kernel for each of the multiple layers comprises program code executable by the processor to cause the apparatus to:

for each of the multiple lay ers,

generate a flexural mode perturbation dispersion as a function of normalized wavelength; and for each of a selected sampling range of normalized wavelength values, determine a sensitivity kernel as the ratio between a flexural mode perturbation value and the approximated shear velocity perturbation value.

18. The apparatus of claim 11, wherein the program code executable by the processor to cause the apparatus to process the linear approximation model to determine a set of shear velocity perturbation values comprises program code executable by the processor to cause the apparatus to determine the set of shear velocity perturbation values as an inversion function of the wavelength dependent perturbation values and the shear velocity sensitivity kernels.

19. The apparatus of claim 11, wherein the program code executable by the processor to cause the apparatus to determine a set of shear velocities comprises program code executable by the processor to cause the apparatus to, for each of a respective one of the multiple layers, compute a shear velocity in accordance with the relation,


where Vi represents the shear velocity of the ith annular layer, u, represents the shear velocity perturbation of the ith annular layer, and V0 represents the far-field shear velocity.

20. One or more non-transitory machine-readable media comprising program code for profiling acoustic shear velocities in a borehole, the program code to:

generate measured flexural wave velocity dispersion based on measured flexural wave velocities; determine formation properties including determining a far-field shear velocity based, at least in part, on the measured flexural wave velocity dispersion;

generate a reference flexural wave velocity dispersion based on the determined formation properties; generate a linear approximation model for an alteration zone having multiple layers, said generating a linear approximation model including:

generating a set of wavelength dependent perturbation values based on differences between wavelength-correspondent velocities in the measured flexural wave dispersion curve and the reference flexural wave dispersion curve; and

generating a respective sensitivity kernel for each of the multiple layers based on ratios between each of a set of wavelength dependent and layer dependent flexural wave perturbation values and an approximated shear velocity perturbation value; process the linear approximation model to determine a set of shear velocity perturbation values based on the wavelength dependent perturbation values and the sensitivity kernels; and

determine a respective shear velocity for each of the multiple layers based on the far-field shear velocity and the shear velocity perturbation values.