Gain compensated directional propagation measurements
A method for obtaining gain compensated electromagnetic logging while drilling propagation measurements includes rotating an electromagnetic logging while drilling tool having first and second transverse transmitter antennas whose moments are orthogonal to one another and first and second transverse receiver antennas whose moments are orthogonal to one another in a subterranean wellbore. Electromagnetic voltage measurements are acquired from the first and second transverse receiver antennas while rotating. The acquired voltage measurements are processed to compute harmonic voltage coefficients. Ratios of selected ones of the harmonic voltage coefficients are in turn processed to compute a gain compensated quantity including a transverse term.
1. A method for making downhole electromagnetic logging while drilling measurements, the method comprising
(a) rotating an electromagnetic logging while drilling tool in a subterranean wellbore, the logging tool including first and second transverse transmitter antennas whose moments are orthogonal to one another and first and second transverse receiver antennas whose moments are orthogonal to one another;
(b) acquiring a plurality of electromagnetic voltage measurements from the first and second transverse receiver antennas while rotating in (a);
(c) processing the voltage measurements acquired in (b) to compute harmonic voltage coefficients;
(d) processing a ratio of the harmonic voltage coefficients to compute a gain compensated quantity including a transverse term, wherein the transverse term is one an xx direct coupling impedance, a yy direct coupling impedance, an xy cross coupling impedance and yx cross coupling impedance or a combination thereof.
2. The method of claim 1 , wherein the processing in (d) is performed by a downhole processor.
3. The method of claim 2 , further comprising:
(e) transmitting the gain compensated quantity to a surface location; and
(f) causing a surface computer to invert the gain compensated quantity to obtain one or more properties of a subterranean formation.
4. The method of claim 1 , further comprising:
(e) processing the gain compensated quantity to compute a gain compensated phase shift and a gain compensated attenuation.
5. The method of claim 1 , wherein the harmonic voltage coefficients computed in (c) comprise DC, first order harmonic sine, first order harmonic cosine, second order harmonic sine, and second order harmonic cosine voltage coefficients.
6. The method of claim 1 , wherein the gain compensated quantity computed in (d) comprises at least one proportional to an xx coupling or a yy coupling.
7. The method of claim 6 , wherein the gain compensated quantity is computed using at least one of the following mathematical equations:
CXX
xx
=
(
V
D
C
_
12
xx
+
V
SHC
_
12
xx
)
(
V
D
C
_
21
xx
+
V
SHC
_
21
xx
)
(
V
D
C_
11
xx
+
V
SHC
_
11
xx
)
(
V
D
C
_
22
xx
+
V
SHC
_
22
xx
)
CXX
yy
=
(
V
D
C
_
12
yy
+
V
SHC
_
12
yy
)
(
V
D
C
_
21
yy
+
V
SHC
_
21
yy
)
(
V
D
C
_
11
yy
+
V
SHC
_
11
yy
)
(
V
D
C
_
22
yy
+
V
SHC
_
22
yy
)
CYY
xx
=
(
V
D
C
_
12
xx
-
V
SHC
_
12
xx
)
(
V
D
C
_
21
xx
-
V
SHC
_
21
xx
)
(
V
D
C
_
11
xx
-
V
SHC
_
11
xx
)
(
V
D
C
_
22
xx
-
V
SHC
_
22
xx
)
CYY
yy
=
(
V
D
C
_
12
yy
-
V
SHC
_
12
yy
)
(
V
D
C
_
21
yy
-
V
SHC
_
21
yy
)
(
V
D
C
_
11
yy
-
V
SHC
_
11
yy
)
(
V
D
C
_
22
yy
-
V
SHC
_
22
yy
)
wherein CXX xx and CXX yy represent the quantities proportional to the xx coupling, CYY xx and CYY yy represent the quantities proportional to the yy coupling, V DC _ 11xx , V DC _ 12xx , V DC _ 21xx , V DC _ 22xx , V DC _ 11yy , V DC _ 12yy , V DC _ 21yy , and V DC _ 22yy represent DC harmonic voltage coefficients, and V SHC _ 11xx , V SHC _ 12xx , V SHC _ 21xx , V SHC _ 22xx , V SHC _ 11yy , V SHC _ 12yy , V SHC _ 21yy , and V SHC _ 22yy represent second harmonic cosine voltage coefficients.
8. The method of claim 1 , wherein the gain compensated quantity computed in (d) comprises at least one quantity proportional to an xx coupling plus a yy coupling or an xx coupling minus a yy coupling.
9. The method of claim 8 , wherein processing the ratio in (d) comprises computing a ratio of a first product of DC voltage coefficients to a second product of DC voltage coefficients to compute the gain compensated quantity.
10. The method of claim 9 , wherein the gain compensated quantity is computed using at least one of the following mathematical equations:
CXXplusYY
xx
=
V
D
C
_
12
xx
V
D
C
_
21
xx
V
D
C
_
11
xx
V
D
C
_
22
xx
CXXplusYY
yy
=
V
D
C
_
12
yy
V
D
C
_
21
yy
V
D
C
_
11
yy
V
D
C
_
22
yy
wherein CXXplusYY xx and CXXplusYY yy represent the quantities proportional to an xx coupling plus a yy coupling and V DC _ 11xx , V DC _ 12xx , V DC _ 21xx , V DC _ 22xx , V DC _ 11yy , V DC _ 12yy , V DC _ 21yy , and V DC _ 22yy represent the DC voltage coefficients.
11. The method of claim 8 , wherein processing the ratio in (d) comprises computing a ratio of a first product of second harmonic cosine voltage coefficients to a second product of DC voltage coefficients to compute the gain compensated quantity.
12. The method of claim 11 , wherein the gain compensated quantity is computed using at least one of the following mathematical equations:
CXXminusYY
xx
=
V
SHC
_
12
xx
V
SHC
_
21
xx
V
D
C
_
11
xx
V
D
C
_
22
xx
CXXminusYY
yy
=
V
SHC
_
12
yy
V
SHC
_
21
yy
V
D
C
_
11
yy
V
D
C
_
22
yy
wherein CXXminusYY xx and CXXminusYY yy represent the quantities proportional to an xx coupling minus a yy coupling, V DC _ 11xx , V DC _ 22XX , V DC _ 11yy , and V DC _ 22yy represent the DC voltage coefficients, and V SHC _ 12xx , V SHC _ 21xx , V SHC _ 12yy , and V SHC _ 21yy represent the second harmonic cosine voltage coefficients.
13. The method of claim 8 , wherein processing the ratio in (d) comprises computing a ratio of a second harmonic cosine voltage coefficient to a DC voltage coefficient to compute the gain compensated quantity.
14. The method of claim 13 , wherein the gain compensated quantity is computed using at least one of the following mathematical equations:
CXXminusYY
ijxx
=
V
SHC
_
ijxx
V
D
C
ijxx
CXXminusYY
ijyy
=
-
V
SHC
_
ijyy
V
D
C
_
ijyy
wherein CXXminusYY ijxx and CXXminusYY ijyy represent the quantities proportional to an xx coupling minus a yy coupling, V DC _ ijxx and V DC _ ijyy represent the DC voltage coefficients, and V SHC _ ijxx and V SHC _ ijyy represent the second harmonic cosine voltage coefficients.
15. The method of claim 1 , wherein the gain compensated quantity computed in (d) comprises at least one measurement proportional to an xy coupling plus a yx coupling or an xy coupling minus a yx coupling.
16. The method of claim 15 , wherein processing the ratio in (d) comprises computing a ratio of a second harmonic sine voltage coefficient to a DC voltage coefficient to compute the gain compensated quantity.
17. The method of claim 16 , wherein the gain compensated quantity is computed using at least one of the following mathematical equations:
CXYplusYX
ijxx
=
-
V
SHC
_
ijxx
V
D
C
_
ijxx
CXYplusYX
ijyy
=
-
V
SHC
ijyy
V
D
C
ijyy
wherein CXYplusYX ijxx and CXYplusYX ijyy represent the quantities proportional to an xy coupling plus yx coupling, V DC _ ijxx and V DC _ ijyy represent the DC voltage coefficients, and V SHS _ ijxx and V SHC _ ijyy represent the second harmonic sine voltage coefficients.
18. The method of claim 15 , wherein processing the ratio in (d) comprises computing a ratio of a first product of DC voltage coefficients to a second product of DC voltage coefficients to compute the gain compensated quantity.
19. The method of claim 18 , wherein the gain compensated quantity is computed using at least one of the following mathematical equations:
CXXminusYX
ij
=
-
V
D
C
_
ijxy
V
D
C
_
ijyx
V
D
C
_
ijxx
V
D
C
_
ijyy
CXXminusYX
=
-
V
D
C
_
12
xy
V
D
C
_
21
yx
V
D
C
_
11
xx
V
D
C
_
22
yy
wherein CXYminusYX ij and CXYminusYX represent the quantities proportional to an xy coupling minus yx coupling and V DC _ ijxy , V DC _ ijyx , V DC _ ijxx , V DC _ ijyy , V DC _ 11xx , V DC _ 12xy , V DC _ 21yx , and V DC _ 22yy , represent the DC voltage coefficients.
20. The method of claim 15 , wherein the gain compensated quantity computed in (d) further comprises at least one measurement proportional to a xy coupling or a yx coupling.
21. The method of claim 20 , wherein the gain compensated quantity is computed using at least one of the following mathematical equations:
CXY
ij
=
CXYplusYX
ijxx
+
CXYminusYX
ij
2
CXY
ij
=
CXYplusYX
ijyy
+
CXYminusYX
ij
2
CYX
ij
=
CXYplusYX
ijxx
-
CXYminusYX
ij
2
CYX
ij
=
CXYplusYX
ijyy
-
CXYminusYX
ij
2
wherein CXY ij and CYX ij represent the quantities proportional to the xy coupling and the yx coupling, CXYplusYX ijxx and CXYplusYX ijyy represent quantities proportional to an xy coupling plus a yx coupling, and CXYminusYX ij represents a quantity proportional to an xy coupling minus a yx coupling.
22. The logging while drilling tool of claim 20 , wherein the first and second transmitter antennas are non-collocated and the first and second receiver antennas are non-collocated.
23. The logging while drilling tool of claim 20 , wherein the first transmitter antenna has a moment that is rotationally aligned with a moment of the first receiver antenna.
24. The method of claim 1 , wherein (d) further comprises computing a square root of the ratio.
25. An electromagnetic logging while drilling tool comprising:
a logging while drilling tool body;
first and second transverse transmitter antennas whose moments are orthogonal to one another deployed on the tool body;
first and second transverse receiver antennas whose moments are orthogonal to one another deployed on the tool body;
a controller configured to (i) cause the first and second transverse transmitter antennas antenna to transmit corresponding electromagnetic waves; (ii) acquire electromagnetic voltage measurements from the first and second transverse receiver antennas while the first and second transverse transmitter antennas are transmitting; (iii) process the electromagnetic voltage measurements to compute harmonic voltage coefficients; and (iv) process a ratio of the harmonic voltage coefficients to compute at least one gain compensated quantity including a transverse term, wherein the transverse term is one an xx direct coupling impedance, a yy direct coupling impedance, an xy cross coupling impedance and yx cross coupling impedance.
26. The logging while drilling tool of claim 25 , wherein the first and second transmitter antennas are collocated with one another.
27. The logging while drilling tool of claim 25 , wherein the first and second receiver antennas are collocated with one another.