Correcting shale volume and measuring anisotropy in invaded zone

1. A method of estimating a parameter of interest of an earth formation, comprising:

estimating a continuous radial profile of anisotropy of an invaded zone of the earth formation using an estimated continuous radial profile of horizontal resistivity in the invaded zone, an estimated shale volume, and an estimated continuous radial profile of vertical resistivity in the invaded zone; and

using at least one processor to estimate the parameter of interest by using the estimated continuous radial profile of anisotropy of the invaded zone of the earth formation.

2. The method of claim 1 , wherein the continuous radial profile of horizontal resistivity in the invaded zone is estimated by modeling a hydrodynamic evolution of the invaded zone using:

(a) a step-wise radial profile of horizontal resistivity in the invaded zone as an initial estimate of horizontal resistivity in the invaded zone;

(b) an estimated shallow resistivity at a borehole wall; and

(c) an estimated longitudinal conductivity of the formation at an outer boundary from the borehole wall estimated using multi-component induction logging information.

3. The method of claim 2 , wherein:

the estimated shale volume is estimated using gamma ray information;

the shallow resistivity at the borehole wall is estimated using shallow resistivity logging information;

the estimated vertical resistivity is estimated using multi-component induction logging information;

the continuous radial profile of anisotropy is further estimated using an estimated resistivity of shale; and

the estimated resistivity of shale is estimated using multi-component induction logging information and the estimated shale volume.

4. The method of claim 2 , wherein the step-wise radial profile of horizontal resistivity is estimated using an inversion of induction logging information based on a cylindrical model of the earth formation.

5. The method of claim 1 , wherein the earth formation includes thinly laminated layers.

6. The method of claim 1 , wherein the continuous radial profile of vertical resistivity is estimated by an expression given by:

Rxo

v

=

(

1

-

V

sh

)

2

1

/

Rxo

h

-

V

sh

/

R

sh

+

V

sh

·

R

sh

where Rxo v is the vertical resistivity profile in the invaded zone, V sh is the estimated shale volume, R sh is a resistivity of shale, Rxo h is the continuous radial profile of horizontal resistivity in the invaded zone estimated using a step-wise radial profile of horizontal resistivity and hydrodynamic modeling.

7. The method of claim 1 , wherein the continuous radial profile of anisotropy is estimated by an expression given by:

λ

=

R

y

R

h

where λ is the anisotropy profile, R v is a vertical resistivity of the invaded zone estimated using the continuous radial profile of vertical resistivity, and R h is the continuous radial profile of horizontal resistivity estimated using a step-wise radial profile of horizontal resistivity and hydrodynamic modeling.

8. The method of claim 1 , wherein the parameter of interest includes a value of shale volume of the earth formation.

9. The method of claim 1 , wherein the parameter of interest includes shale volume of the earth formation, and further comprising:

estimating a shale resistivity;

estimating a minimum horizontal resistivity and a maximum horizontal resistivity using the estimated anisotropy; and

correcting the estimated shale volume if at least one of (a) an estimated horizontal resistivity of the borehole wall and (b) an estimated horizontal resistivity of the earth formation is not between about the minimum horizontal resistivity and about the maximum horizontal resistivity.

10. An apparatus for estimating a parameter of interest of an earth formation, comprising:

an instrument disposed on a carrier, wherein the instrument comprises:

a radiation source;

a first gamma ray detector;

at least one second gamma ray detector;

at least one transmitter configured to apply electromagnetic signals to the earth formation;

at least one receiver configured to be responsive to the electromagnetic signals applied to the earth formation by the at least one transmitter; and

at least one processor configured to:

estimate a continuous radial profile anisotropy of an invaded zone of the earth formation using an estimated continuous radial profile of horizontal resistivity in the invaded zone, an estimated shale volume, and an estimated continuous radial profile of vertical resistivity in the invaded zone; and

estimate the parameter of interest by using the estimated anisotropy of the invaded zone of the earth formation.

11. The apparatus of claim 10 , wherein the continuous radial profile of horizontal resistivity in the invaded zone is estimated by modeling a hydrodynamic evolution of the invaded zone using:

(a) a step-wise radial profile of horizontal resistivity in the invaded zone as an initial estimate of horizontal resistivity in the invaded zone;

(b) an estimated shallow resistivity at a borehole wall; and

(c) an estimated longitudinal conductivity of the formation at an outer boundary from the borehole wall estimated using multi-component induction logging information.

12. The apparatus of claim 11 , wherein:

the estimated shale volume is estimated using gamma ray information;

the shallow resistivity at the borehole wall is estimated using shallow resistivity logging information;

the estimated vertical resistivity is estimated using multi-component induction logging information;

the continuous radial profile of anisotropy is further estimated using an estimated resistivity of shale; and

the estimated resistivity of shale is estimated using multi-component induction logging information and the estimated shale volume.

13. The apparatus of claim 11 , wherein the step-wise radial profile of horizontal resistivity is estimated using an inversion of induction logging information based on a cylindrical model of the earth formation.

14. The apparatus of claim 10 , wherein the earth formation includes thinly laminated layers.

15. The apparatus of claim 10 , wherein the continuous radial profile of vertical resistivity is estimated by an expression given by:

Rxo

v

=

(

1

-

V

sh

)

2

1

/

Rxo

h

-

V

sh

/

R

sh

+

V

sh

·

R

sh

where Rxo v is the vertical resistivity profile in the invaded zone, V sh is the estimated shale volume, R sh is a resistivity of shale, Rxo h is the continuous radial profile of horizontal resistivity in the invaded zone estimated using a step-wise radial profile of horizontal resistivity and hydrodynamic modeling.

16. The apparatus of claim 10 , wherein the parameter of interest includes a value of shale volume of the earth formation.

17. The apparatus of claim 10 , wherein the parameter of interest includes shale volume of the earth formation, and further comprising:

estimating a shale resistivity;

estimating a minimum horizontal resistivity and a maximum horizontal resistivity using the estimated anisotropy; and

correcting the estimated shale volume if at least one of (a) an estimated horizontal resistivity of the borehole wall and (b) an estimated horizontal resistivity of the earth formation is not between about the minimum horizontal resistivity and about the maximum horizontal resistivity.

18. A non-transitory computer-readable medium product having stored thereon instructions that, when read by at least one processor, causes the at least one processor to execute a method of estimating a parameter of interest of an earth formation comprising thinly laminated layers, the method comprising:

estimating a continuous radial profile anisotropy of an invaded zone of the earth formation using an estimated continuous radial profile of horizontal resistivity in the invaded zone, an estimated shale volume, and an estimated continuous radial profile of vertical resistivity in the invaded zone; and

using at least one processor to estimate the parameter of interest by using the estimated anisotropy of the invaded zone of the earth formation.

19. The non-transitory computer-readable medium product of claim 18 , further comprising at least one of: (i) a ROM, (ii) an EPROM, (iii) an EEPROM, (iv) a flash memory, and (v) an optical disk.