Missing:
Appendix A
RES2DINV Inversion Parameters
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix A 40
Thesis inversion parameters
The following list shows the inversion parameters chosen for the software used in this study. Software: RES2DINV ver. 3.51z
References: Loke & Barker, 1996; Loke, 2002.
Initial damping factor is 0.1600. Minimum damping factor is 0.0150. Line search is always used. Convergence limit is 1.0000. Minimum change in RMS error is 0.4000. Number of iterations is 20. Vertical to horizontal flatness filter ratio is 1.0000. User defined increase in layer thickness. Number of nodes between adjacent electrodes is 4. Smoothness constrain is only used directly on model resistivity values. Number of topographical datum points is not reduced. Topographical modeling is to be carried out. Least-squares linear topographical trend to be removed. Jacobian matrix is recalculated for first two iterations. Increase of damping factor with depth is 1.0500. Topographic modeling is not carried out. Robust data inversion constrain is used with cutoff factor 0.0500. Robust model inversion constrain is used with cutoff factor 0.0050. Extended model is used. Effect of side blocks is not reduced. Normal mesh is used. Damping factor is not optimized at each iteration. No inter-model constrain is used in time-lapse inversion. Simultaneous time-lapse inversion is used. Thickness of first layer is 0.2500. Factor to increase layer thickness with depth varies by array. Finite element method is used. Width of blocks used is 1 times the unit electrode spacing. Model blocks can have different widths. RMS convergence limit is 1.0 percent. Logarithms of apparent resistivity values are used for the inversion. Resistivity/IP data are inverted sequentially. Do not proceed automatically in sequential IP inversion. IP damping factor is 0.1500. Automatic IP damping factor is not used. Cutoff factor for borehole data is 0.00100. Range of resistivity values are limited. Upper resistivity cutoff limit is 20.00000. Lower resistivity cutoff limit is 0.05000. Average resistivity used. ______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix A 41
Appendix B
Graphs of Resistivity Mismatch as a Function of Depth For All Twelve Models
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix B 42
Vertical Boundary Model RMS % Mismatch 0
5
10
15
20
25
30
35
40
45
50
55
0 -2 -4 -6
Depth
-8 -10 -12 -14 -16 -18 -20
Vertical Layer Low
Vertical Layer High
RMS % Mismatch 0
20
40
60
RMS % Mismatch 80
100
0
0
0
-2
-2
-4
-4
-6
-6
40
-10
80
100
-10
-12
-12
-14
-14
-16
-16
-18
-18
-20
-20
Horizontal Boundary Model - Resistor
Horizontal Boundary Model - Conductor % RMS Error 0
10
20
30
40
50
% RMS Error 60
70
80
0
0
0
-2
-2
-4
-4
-6
-6
-8
5
10
15
20
25
30
35
40
45
50
-8 Depth
Depth
60
-8 Depth
Depth
-8
20
-10
-10
-12
-12
-14
-14
-16
-16
-18
-18
-20
-20
D ip o le -D ip o le
Po le -D ip o le
Po le -Po le
W enner
Sch lu mb erg er
Graphs of the layer-by-layer resistivity mismatch for the five DCR arrays for the vertical boundary, vertical conductor, vertical resistor, horizontal conductor over resistor, and horizontal resistor over conductor models. ______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix B 43
Undulating Boundary RMS % Mismatch 0
10
20
30
40
50
60
70
0 -2 -4 -6
Depth
-8 -10 -12 -14 -16 -18 -20
Horizontal Layer Low
Horizontal Layer High
RMS % Mismatch 0
20
40
RMS % Mismatch
60
80
100
0
0 -2
40
-4
-6
-6
80
100
Depth
-8
-10
-10
-12
-12
-14
-14
-16
-16
-18
-18
-20
-20
Dipping Layer High
D ipping Layer Low
RMS % Mismatch
R M S % M is m atc h 0
25
50
75
10 0
12 5
15 0
17 5
0
20 0
0
0
-2
-2
-4
-4
-6
-6
-8
-8 Depth
D ep th
60
-2
-4
-8 Depth
20
0
-10
20
40
60
80
100
120
140
160
-10
-12
-12
-14
-14
-16
-16 -18
-18
-20
-20
D ip o le -D ip o le
Po le -D ip o le
Po le -Po le
W enner
Sch lu mb erg er
Graphs of the layer-by-layer resistivity mismatch for the five DCR arrays for the undulating boundary, horizontal conductive layer in a resistor, horizontal resistive layer in a conductor, dipping conductive layer and dipping resistive layer models.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix B 44
Block Model Low
Block Model High
RMS % Mistatch 5
10
15
20
25
30
35
RMS % Mismatch 40
45
50
55
0
0
0
-2
-2
-4
-4
-6
-6
-8
-8 Depth
Depth
0
-10
-12
-14
-14
-16
-16
-18
-18
-20
-20
Po le -D ip o le
10
15
20
25
30
35
40
45
50
55
-10
-12
D ip o le -D ip o le
5
Po le -Po le
W enner
Sch lu mb erg er
Graphs of the layer-by-layer resistivity mismatch for the five DCR arrays for the conductive block and resistive models.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix B 45
Appendix C
Tables of Resistivity Mismatch and Array Performance Grades For the Shallow, Intermediate, and Deep Portions of All Twelve Models, And Overall Array Performance Grades For All Twelve Models
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix C 46
VB Array DD PD PP WN SC
Resistivity Mismatch S I D 3.34 2.20 6.67 4.66 6.54 25.75 3.50 12.50 32.65 3.77 17.33 42.56 2.61 2.18 26.73
Performance Grade S I D A A A A A B A A B A A C A A B
Overall Grade A A A B A
VLL Array DD PD PP WN SC
Resistivity Mismatch S I D 4.93 18.06 55.56 6.78 38.11 83.71 4.37 35.57 59.05 109.04 176.77 209.31 9.99 151.60 217.01
Performance Grade S I D A A C A B E A B C E E E A E E
Overall Grade B C B E D
VLH Array DD PD PP WN SC
Resistivity Mismatch S I D 6.53 22.90 37.66 5.75 38.89 61.73 5.90 39.45 61.76 4.33 39.36 65.74 3.80 31.75 75.01
Performance Grade S I D A B B A B D A B D A B D A B D
Overall Grade B B B B B
Resistivity mismatches and array performance grades for the S, I, and D portions of the VB, VLL, and VLH models, and overall array performance grade for all arrays. Depth acronyms from Table 4. Model acronyms from Table 1. Array acronyms from Figure 1.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix C 47
HBL Array DD PD PP WN SC
Resistivity Mismatch S I D 22.39 25.41 5.65 23.95 28.34 8.34 29.84 36.46 5.46 29.00 37.34 20.55 29.16 37.00 21.10
Performance Grade S I D B B A B B A B B A B B B B B B
Overall Grade B B B B B
HBH Array DD PD PP WN SC
Resistivity Mismatch S I D 60.44 62.67 4.38 45.27 46.18 7.30 31.78 34.24 6.70 40.97 42.64 4.35 38.33 39.17 3.66
Performance Grade S I D C C A C C A B B A C C A B B A
Overall Grade B B B B B
UB Array DD PD PP WN SC
Resistivity Mismatch S I D 25.90 30.27 8.16 25.88 32.73 8.40 32.39 42.19 7.02 34.24 57.47 18.50 23.85 33.56 11.70
Performance Grade S I D B B A B B A B C A B C A B B A
Overall Grade B B B B B
HLL Array DD PD PP WN SC
Resistivity Mismatch S I D 38.61 47.78 4.86 46.30 56.22 12.85 76.62 79.57 17.50 61.16 69.37 24.66 50.62 62.18 29.13
Performance Grade S I D B C A C C A D D A D D B C D B
Overall Grade B B C C C
HLH Array DD PD PP WN SC
Resistivity Mismatch S I D 39.34 202.60 10.90 43.81 211.74 10.73 73.55 189.25 94.81 45.44 203.30 31.30 48.00 209.94 16.52
Performance Grade S I D B E A C E A D E E C E B C E A
Overall Grade C C E C C
Resistivity mismatches and array performance grades for the S, I, and D portions of the HBL, HBH, UB, HLL, and HLH models, and overall array performance grade for all arrays. Depth acronyms from Table 4. Model acronyms from Table 1. Array acronyms from Figure 1. ______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix C 48
DLL Array DD PD PP WN SC
Resistivity Mismatch S I D 30.40 33.59 72.57 28.74 50.23 111.43 35.55 56.98 98.16 34.64 71.17 126.76 19.17 49.16 116.42
Performance Grade S I D B B D B C E B C E B D E B C E
Overall Grade C C C D C
DLH Array DD PD PP WN SC
Resistivity Mismatch S I D 35.34 73.22 53.09 40.46 95.40 74.85 48.94 121.32 80.24 46.46 76.22 38.53 41.47 79.29 46.18
Performance Grade S I D B D C C E D C E E C D B C D C
Overall Grade C C C D C
BL Array DD PD PP WN SC
Resistivity Mismatch S I D 14.96 20.44 14.29 15.96 17.60 11.78 29.48 56.95 37.65 6.40 11.08 10.94 11.62 15.02 12.30
Performance Grade S I D A B A A A A B C B A A A A A A
Overall Grade A A B A A
BH Array DD PD PP WN SC
Resistivity Mismatch S I D 10.72 16.54 9.66 16.45 23.66 17.36 18.96 36.04 29.98 20.13 28.19 23.05 18.02 26.67 19.15
Performance Grade S I D A A A A B A A B B B B B A B A
Overall Grade A A B B A
Resistivity mismatches and array performance grades for the S, I, and D portions of the DLL, DLH, BL and BH models, and overall array performance grade for all arrays. Depth acronyms from Table 4. Model acronyms from Table 1. Array acronyms from Figure 1.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix C 49
Appendix D
Inversion Results For All Twelve Models
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 50
dipole-dipole 1
9
17
1.19 3.25
distance (-) 25 distance (-)
pole-dipole 33
41
1
49
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
pole-pole 17
9
distance (-) 25
33
41
1
49
1.19 3.25
1.19 3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1 1.19
9
17
distance (-) 25 distance (-)
17
1.19 3.25
5.63
1
9
33
41
Wenner 9
17
distance (-) 25 distance (-)
distance (-) 25
33
41
49
33
41
49
49
3.25 5.63 9.00 11.00
Vertical Boundary
13.80 16.80
Inversion results for the VB model using the data from the DD, PD, PP, WN, and SC. Model acronyms from Table 1. Array acronyms from Figure 1. Distance and depth are dimensionless.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 51
dipole-dipole 1
9
17
1.19
distance (-) 25 distance (-)
pole-dipole 33
41
49
1
17
9
1.19
3.25
distance (-) 25 (-) distance
33
41
49
33
41
49
33
41
49
33
41
49
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
pole-pole 1
9
17
distance (-) 25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
9
17
1.19
distance (-) 25 distance (-)
33
41
Wenner
17
9
distance (-) 25
49
3.25
Vertical Layer Low
5.63 9.00 11.00 13.80 16.80
dipole-dipole 1
9
17
1.19
distance (-) 25 distance (-)
pole-dipole 33
41
1
49
17
1.19
distance (-) 25 distance (-)
3.25
3.25 5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
pole-pole 1
9
17
distance (-) 25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1 1.19
9
9
17
distance (-) 25 distance (-)
33
41
Wenner 9
17
distance (-) 25
49
3.25 5.63 9.00 11.00
Vertical Layer High
13.80 16.80
Inversion results for the VLL and VLH models using the data from the DD, PD, PP, WN, and SC. Model acronyms from Table 1. Array acronyms from Figure 1. Distance and depth are dimensionless.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 52
dipole-dipole 1
17
9
distance (-) 25 (-) distance
pole-dipole 33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
Wenner
distance (-) 17
9
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
distance (-) 17
25 (-) distance
33
41
49
33
41
49
33
41
49
33
41
49
16.80
pole-pole 1
9
17
9
1.19
distance (-) 25 distance (-)
33
41
9
distance (-) 17
25
49
3.25
Horizontal Boundary Low
5.63 9.00 11.00 13.80 16.80
dipole-dipole 1
9
17
distance (-) 25 (-) distance
pole-dipole 33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
9
Wenner
distance (-) 17
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
9
distance (-) 17
25 (-) distance
16.80
pole-pole 1
9
17
distance (-) 25 (-) distance
33
41
9
distance (-) 17
25
49
1.19 3.25 5.63
Horizontal Boundary High
9.00 11.00 13.80 16.80
Inversion results for the HBL and HBH models using the data from the DD, PD, PP, WN, and SC. Model acronyms from Table 1. Array acronyms from Figure 1. Distance and depth are dimensionless.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 53
dipole-dipole 1
9
17
distance (-) 25 (-) distance
pole-dipole 33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
9
Wenner
distance (-) 17
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1 1.19
9
distance (-) 17
25 (-) distance
33
41
49
33
41
49
16.80
pole-pole 1
9
17
distance (-) 25 distance (-)
33
41
9
distance (-) 17
25
49
3.25 5.63 9.00 11.00
Undulating Boundary
13.80 16.80
Inversion results for the UB model using the data from the DD, PD, PP, WN, and SC. Model acronyms from Table 1. Array acronyms from Figure 1. Distance and depth are dimensionless.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 54
dipole-dipole 1
pole-dipole
distance (-) 17
9
25 (-) distance
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
Wenner
distance (-) 17
9
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
25 (-) distance
33
41
49
33
41
49
16.80
pole-pole 1
distance (-) 17
9
17
9
distance (-) 25 (-) distance
33
41
distance (-) 17
9
25
49
1.19 3.25
Horizontal Layer Low
5.63 9.00 11.00 13.80 16.80
dipole-dipole 1
9
17
distance (-) 25 (-) distance
pole-dipole 33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
9
Wenner
distance (-) 17
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
9
25 (-) distance
33
41
49
33
41
49
16.80
pole-pole 1
distance (-) 17
9
17
9
distance (-) 17
25
distance (-) 25 (-) distance
33
41
49
1.19 3.25 5.63 9.00 11.00
Horizontal Layer High
13.80 16.80
Inversion results for the HLL and HLH models using the data from the DD, PD, PP, WN, and SC. Model acronyms from Table 1. Array acronyms from Figure 1. Distance and depth are dimensionless.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 55
dipole-dipole 1
17
9
1.19
distance (-) 25 distance (-)
pole-dipole 33
41
49
1
17
9
distance (-) 25 (-) distance
33
41
49
33
41
49
33
41
49
33
41
49
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
pole-pole 1
17
9
distance (-) 25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
17
9
1.19
distance (-) 25 distance (-)
33
41
Wenner 9
17
distance (-) 25
49
3.25
Dipping Layer Low
5.63 9.00 11.00 13.80 16.80
dipole-dipole 1
9
pole-dipole
distance (-) 17
25 (-) distance
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
9
Wenner
distance (-) 17
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
9
25 (-) distance
16.80
pole-pole 1
distance (-) 17
9
17
9
distance (-) 17
25
distance (-) 25 (-) distance
33
41
49
1.19 3.25 5.63 9.00 11.00
Dipping Layer High
13.80 16.80
Inversion results for the DLL and DLH models using the data from the DD, PD, PP, WN, and SC. Model acronyms from Table 1. Array acronyms from Figure 1. Distance and depth are dimensionless.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 56
dipole-dipole 1
pole-dipole
distance (-) 17
9
25 (-) distance
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
Wenner
distance (-) 17
9
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1
25 (-) distance
33
41
49
33
41
49
16.80
pole-pole 1
distance (-) 17
9
17
9
distance (-) 17
9
25
distance (-) 25 (-) distance
33
41
49
1.19 3.25 5.63
Block Model Low
9.00 11.00 13.80 16.80
dipole-dipole 1
9
17
1.19
distance (-) 25 distance (-)
pole-dipole 33
41
49
1
17
distance (-) 25 (-) distance
33
41
49
33
41
49
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
pole-pole 1
9
distance (-) 17
25
33
41
49
1
1.19
1.19
3.25
3.25
5.63
5.63
9.00 11.00
9.00 11.00
13.80
13.80
16.80
16.80
Schlumberger 1 1.19
9
9
17
distance (-) 25 distance (-)
33
41
Wenner 9
distance (-) 17
25
49
3.25 5.63 9.00 11.00
Block Model High
13.80 16.80
Inversion results for the BL and BH models using the data from the DD, PD, PP, WN, and SC. Model acronyms from Table 1. Array acronyms from Figure 1. Distance and depth are dimensionless.
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix D 57
Appendix E
Plots of 2D Spatial Gradient and 2D Spatial Laplacian Of the Inversion Results For All Twelve Models
______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix E 58
dipole-dipole array
distance (-)
dipole-dipole array ) (* ()
distance (-)
pole-dipole array() ) (*
distance (-)
pole-pole array ) (*
distance (-)
+ *
, *
, )
-*
-)
, *
, )
-*
-)
, *
, )
-*
-)
Schlumberger array distance (-) ) (* () + * + )
, *
, )
-*
-)
Wenner array ) (*
()
, *
, )
-*
-)
True) Model (*
()
,*
, )
-*
-)
distance (-)
+ )
distance (-)
')
' (*
' ()
pole-dipole array
distance (-) distance (-)
+ *
+ )
distance (-)
')
' (*
' ()
pole-pole array
distance (-) distance (-)
!"
! #
$%
$&
')
')
' (*
' (*
' ()
' ()
distance (-) Schlumberger array ) (* ( ) + * + ) distance (-)
,*
, )
-*
-)
')
' (*
' (*
' ()
' ()
()
distance (-) + *
+ )
distance (-)
,*
,)
-*
-)
')
')
' ( *
' (*
' ( )
' ()
True ) Model(*
( )
distance (-) +*
+)
distance (-)
,*
, )
-*
-)
')
')
' (*
' (*
' ()
' ()
.
/010
24343
+ *
+ )
distance (-)
distance (-)
')
Wenner array ) (*
()
54646
79848
:1>
?4@4@
A1B4B
C4D1D
distance (-) + *
+ )
distance (-)
distance (-) + *
+)
distance (-)
EFD4D4D
Apparent resistivity in Ω -m Plots of the spatial gradient (left) and spatial Laplacian (right) of the inversion results of VB model for the five DCR arrays and the true model. Model acronym from Table 1. Distance and depth are dimensionless. ______________________________________________________________________________________ Investigating the Performance of Electrical Resistivity Arrays - Appendix E 59
dipole-dipole array Q RS RQ
T S T Q (-) distance
US
UQ
VS
dipole-dipole array Q RS RQ
VQ
WQ
WQ
W RS
W RS
W RQ
W RQ
distanceT Q (-)
T S
US
U Q
VS
pole-dipole Q RS array RQ
VQ
WQ
WQ
W RS
W RS
W RQ
W RQ
RQ
distance T S T Q (-)
US
U Q
VS
pole-pole Q Rarray S
VQ
RQ
distance (-) WQ
W RS
W RS
W RQ
W RQ
US
UQ
VS
WQ
W RS
W RS
W RQ
W RQ
distance T S T Q (-)
US
UQ
VS
Wenner array Q RS
VQ
RQ
distance (-) WQ
W RS
W RS
W RQ
W RQ
RQ
distance T S T Q (-)
U S
U Q
VS
VQ
distance T S T Q (-)
U S
U Q
VS
VQ
US
UQ
V S
V Q
distance T S T Q (-)
U S
U Q
VS
VQ
US
UQ
V S
V Q
distance (-)
WQ
TrueQ Model RS
VQ
distance (-)
WQ
RQ
distance T S T Q (-)
Schlumberger array distance Q RS RQ TS TQ (-)
VQ
distance (-)
Wenner array Q RS
VS
distance (-)
WQ
distance Schlumberger array Q RS RQ T S T Q (-)
U Q
distance (-)
distance (-)
pole-pole array Q RS
U S
distance (-)
distance (-)
pole-dipole Q RS array RQ
distance T S T Q (-)
US
UQ
VS
TrueQ Model RS
VQ
distance (-)
RQ
distance TS TQ (-) distance (-)
WQ
WQ
W RS
W RS
W RQ
W RQ G
HG4G
I
