Zonge GDP-32 - 3-Point Decoupling

MATHEMATICAL ALGORITHMS
Section 15, Page 3 October 2002
15.2 3-POINT DECOUPLING
QUADRATIC DECOUPLING EQUATIONS
Harmonic Frequencies
1. First, third, fifth harmonics (0.1,0.3,0.5 Hz; 0.125,0.375,0.625 Hz; etc)
φ
c
= ( 15 φ
1
- 10 φ
3
+ 3 φ
5
) / 8
2. Third, fifth, seventh harmonics (0.3,0.5,0.7 Hz; 0.375,0.625,0.875 Hz; etc)
φ
c
= ( 35 φ
3
- 42 φ
5
+ 15 φ
7
) / 8
3. 0.1, 0.3, 1.0 Hz (0.1, 0.3, 1.0 Hz)
φ
c
= ( 35 φ
1
- 15 φ
3
+ φ
10
) / 21
4. First, third, fifth, seventh harmonics (.1,.3,.5,.7 Hz; .125,.375,.625,.875 Hz; etc)
φ
c
= ( 35 φ
1
- 35 φ
3
+ 21 φ
5
- 5 φ
7
) / 16
Binary Frequencies
5. Three sequential binary frequencies (0.125,0.250,0.5 Hz; 8,16,32 Hz; etc)
φ
c
= ( 8 φ
1
- 6 φ
2
+ φ
3
) / 3
6. First, second, and fourth sequential binary frequencies (0.125,0.250,1.0 Hz)
φ
c
= ( 48 φ
1
- 28 φ
2
+ φ
4
) / 21
7. Four sequential binary frequencies (0.125,0.250,0.5,1.0 Hz; 4,8,16,32 Hz; etc)
φ
c
= ( 8 φ
1
+ 2 φ
2
- 5 φ
3
+ φ
4
) / 6
When operating in low resistivity environments with large dipole spacings, as is common with
dipole-dipole or pole-dipole surveys, electromagnetic coupling is often an overwhelming factor
in IP measurements. The Complex Resistivity (CR) program provides for automatic removal of
electromagnetic effects by using a 3-point decoupling algorithm, which assumes that the IP
effect at very low frequencies is relatively independent of frequency. This routine works well in
moderately coupled environments. For extreme coupling environments (e.g., 10 ohm-meter
ground and using 300 m dipoles), we recommend that full frequency CR be used to permit more
precise coupling removal.
The formula used for 3-point decoupling in the GDP-32
II
is as follows:
φ
3pt
= 1.875 φ
1
- 1.25 φ
3
+ 0.375 φ
5
φ
1
= phase at the fundamental frequency
φ
3
= phase at the third harmonic
φ
5
= phase at the fifth harmonic