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[pic]



119899, Russia, Moscow, Moscow State University,

Geological Faculty, Department of Geophysics,

tel. & fax: (7-095) 939-49-63,

E-mail: Sh@geophys.geol.msu.su

WEB site: www.geol.msu.ru/deps/geophys/rec_labe.htm

A.A.Bobachev, I.N.Modin, E.V.Pervago, V.A.Shevnin

Manual.


IE2DP1 - software for 2D forward resistivity.

1. Introduction.
The name IE2DP1 means: Integral Equation (method of decision), 2D
(dimension), P (point current electrodes), 1 - across inhomogeneities.
IE2DP1 program fulfills two dimensional (2D) electric field modeling for
different modifications of resistivity and induced polarization (IP) field
techniques. The line of measurements is directed across inhomogeneities.


2. Technical part.

2.1 Brief notes about method of solution
Forward problem is solved by integral equation method. Under the
influence of primary current sources at the boundaries between media with
different electric properties the secondary current sources appear. These
secondary sources create surface electric layer. Total (resulting) electric
field may be calculated as superposition of primary (E0) and secondary
fields of all current sources (ES):[pic]
Apparent resistivity (ra) is calculated by formula:
[pic]
where r0 - resistivity of medium included inhomogeneities.
All region of modeling is consider divided on blocks (bodies) with
different resistivities and chargeabilities. Blocks boundaries are divided
into cells of small size considered as secondary current sources. On this
way inhomogeneous medium is similar to homogeneous one, but with
additional (secondary) current sources on block boundaries. The size of
cell is selected in such way that the distance from it to nearest boundary,
including earth surface, is less then its size.

Details of mathematical algorithm can be found in the first part of
book [1], pp.69-75 (in Russian) or in articles [3,4].

2.2. Possibilities of IE2DP1 program

Program IE2DP1 may be used for calculation of listed below arrays and
technologies, depending on Key_of_Array value (from 15 to 18). All arrays
are calculated for ideal (infinite small) MN dipole. The time of
calculation is proportional to a number of current electrode positions,
therefore only sounding array with minimal number of them are recommended.
Together with ra the apparent chargeability ha can be also calculated for
each array. Apparent chargeability is saved always in the file "IE2DP1.RES"
and reference point is in current electrode location.


List of arrays Key_of_Array value
1. 3-electrodes pole-dipole AMN sounding array (A - is fixed)
15
A electrode is on the left of MN and fixed. In the process of
sounding MN is moved on the right from A. Point of reference is in A
electrode location. For the set of sounding - A is moved along profile with
step = Step. Distances AO could be anywhere (O-point is the center of MN
dipole). The output file is "IE2DP.RES".
2. 3-electrodes pole-dipole MNB sounding array (B - is fixed)
16
B electrode is on the right of MN and fixed. In the process of
sounding MN is moved on the left from B. Point of reference is in B
electrode location. For the set of sounding - B is moved along profile with
step = Step. Distances BO could be anywhere. The output file is
"IE2DP.RES".
3. Arbitrary four-electrodes gradient array Afix__MN__Bfix 17
Current electrodes A & B are fixed and MN is moved along the profile
with step=Step from point with coordinates (X0, 0). Depth and position of
current electrodes could be arbitrary. Point of reference is in the centre
of MN. The output file is "IE2DP1.RES".
4. Combined 3-electrodes pole-dipole AMN sounding array, which is
used often for multi-electrodes soundings equipment
18
[pic]
The position of current electrode A is fixed, and MN dipole moves on the
both side from A-electrode. The point of reference is in the centre of MN
dipole location. For the set of sounding - A is moved along profile with
the step = Step. The distances AO is for i-th spacing is calculated in the
next way
[pic]
where Step is the distantce between current electrodes.
The first and the last MN dipole location is calculated by:
[pic][pic]
where nSteps is a number of current electrodes.

5. Arbitrary four-electrodes gradient array Afix__MN__Bfix 19
[pic]
Current electrodes A & B are fixed and MN is moved along any
direction. The direction of measurements profile is defined by Step and
StepZ from point with coordinates (X0,Z0). Depth and position of current
electrodes could be arbitrary. Point of reference is in the centre of MN.
The result of calculation is electrical field along MN profile, because the
normal field could be equal to zero, so it is impossible to use
conventional apparent resistivity. The output file is "IE2DP1.txt".

There are some output files for 18-th array.. Therefore it is
possible to use different programs for results' presentation.

1.The ASCII files are "A_MN.txt" (the current electrode is moved on the
left from MN dipole) and "MN_B.txt" (the current electrode is moved on the
right from MN dipole). The files contains three columns: MN center
position, AO distance and corresponding value of synthetic apparent
resistivity. This format is suitable for "Surfer" program.

2. The ASCII files "FORWARD.RS2" and "REVERSE.RS2" are compatible with
ASCI data files of "Resix" programs. The files contains three columns: TX
index, RX index and app. resistivity value for AMN or MNB array. TX index
defines the position of reference point and TR index - the spacing number.

In "FORWARD.RS2" file positions the current electrode position (XA) and MN
dipole center (O) are calculated by next formulas:
XA=XO+Step*(TX-1),
O=XO+Step*(TX+RX-0.5).
In "REVERSE.RS2" file the next formulas are used:
O=XO+Step*(TX-0.5),
XA=XO+Step*(TX+RX).

For work with result of calculation with IPI-software it is necessary to
convert this files into IPI format. Use program RES2IPI for this. You could
use "Convert.bat" bath file to covert results into IPI format.
rxi2ipi forward.rs2 /A
copy forward.dat a_mn.dat
del forward.dat
rxi2ipi reverse.rs2 /B
copy reverse.dat mn_b.dat
del reverse.dat

The apparent chargeability can be also calculated for each array but app.
resistivity. Apparent chargeability is saved always in the file
"IE2DP1.RES" and reference point is in current electrode location.

3. Recommendation and file description

Principal restrictions on resistivities values for bodies don't exist in
this program. Accuracy is usually good enough, if conductive blocks of
great dimensions and resistivity less then 1/50 from one of cross-section
are absent. Form of boundaries also can be arbitrary. We recommend to use
the distances in range from 0.5 to 1000 m.

3.1. Work with IE2DP1 program is not allowed to use:
1. Number of cells more than 800
2. Number of bodies more than 50
3. Number of angular points more than 100
4. Number of angular points for one body more than 40
5. Number of sounding or profiling points more than 101
6. Number of VES distances more than. 30
[pic]
Fig.3.
Legend for fig.3:
1 - true resistivity of outer body;
2 - true resistivity of inner body;
real boundaries: 4-5, 5-6, 6-7, 7-4
fictitious boundaries: 3-4, 1-2, 2-3, 3-8, 8-1
These bodies should be round by the next rule:
1-st body: 1 2 3 4 5 6 7 4 3 8,
2-nd body: 7 6 5 4
7. One body is almost inside the other one. To avoid this problem you
should do fictitious lines, which connect inner body and outer space. Along
these lines one should go twice. Firstly in one direction and then, after
round of inner body counter-clock-wise, - in opposite direction. In this
way the additional boundary for inner body does its boundary closed and at
the same time connected with outer space. This way of description is given
as example in data file and also at the fig. 3.
Legend for fig. 4:
1 - true resistivity of outer body;
2 - true resistivity of inner body;
3 - true resistivity of outer body;
real boundaries: 7-6, 6-5, 5-4, 4-7;
fictitious boundaries - others.
These bodies should be round by the next rule:
1-st body: 1 2 3 4 5 6 7 8,
2-nd body: 7 6 5 4,
3-rd body: 8 7 4 3 9 10.

[pic]
Fig. 4..
For such case it may be simpler to divide modeling region into three
parts: inner body, which is laying on the boundary between two outer blocks
with equal resistivities. And in this case only contrasting boundaries
(which have contrast in resistivity) should be divided into sells. See fig.
4.

8. To place current electrodes and measuring points close then 0.3 m to the
inner boundaries.

9. To describe body using smaller than 3 and more than 40 points. More
complicated bodies should be divided into parts. The boundaries without
electric properties contrast do not increase number of cells considerably.
10. To place the current electrodes closer to boundaries of modeling region
then maximal distance of sounding .

3.2. The rules to describe model

1. Angular points for each body should be described in counter-
clockwise direction. It is better to begin description of the first body
from right upper angle of it at the earth surface and then in clockwise
direction.
2. The lower boundary of modeling region should be deeper than maximal
depth of investigation for this array.
3. Total size and complexity of modeling region affect on time of
calculation and number of sells in the model. Common recommendations for
composition of models are the next:
- model should be as simple as possible, and remember that maximal
number of cells shouldn't be more than 800 (unfortunately, the program does
not show a number of cell, if it more then maximal). Try to remove extra
boundaries, it is possible to make by change resistivity of body on the
same like closest body.
- avoid layers with small thickness, if they affect weak on 2D part of
the model, because they add maximal numbers of cells. For example: the
layer with thickness 3 m for modeling area with width 500 m gives more then
250 cells.
- diminish, if it is possible, the total number of sounding points and
number of VES distances.
4. Cells' number is proportional to the "PrecisionFactror"
coefficient in model's file. It must be more or equal of one. The value "2"
is suitable for most of models. You could use the "1" to calculate complex
and uncontrast model. The value more then "2" leads to increasing of
accuracy of calculation. We recommend to check the accuracy of calculation
on close 1D model.

3.3. The order of operations to construct model of geoelectrical cross-
section.

1. Take the sheet of coordinated paper, select the scale and draw the
simplest model.
2. Select the beginning of coordinate axis over centre of model (X axis to
the right, Z axis - downward); put sounding points beginning from X0 and
then with step "Step".
[pic]
3. Draw boundaries of the model as strait lines with their number NB,
angular points - NP, number of bodies NT. Enumerate all angular points and
bodies, better with pencils of different colour.
4. Write all model parameters into data file.

4. Information about IE2DP1 package.
IE2DP1 package consist of two executable programs:
- "ie2_4" - program for model pre-processing and 2D modeling with linear
electrodes.
- "ie2dp_99" - program for 2D modeling with point electrodes.

They are united in one command file "start.bat"

5. How to operate with program IE2DP1.

1. Create Data-file (*.ie2) with model description using instructions and
some old data-file as example.
2. Create "ie2dp.arr".
3. Change the name of data file in the file "filename". Don not forget to
add new line after name of input file. Some FORTRAN compiler generates run-
time error if the end of line sign is absent.
4. Run file "start.bat".
5. If resulting number of cells in the model is more then maximal, "ie2_4"
program writes a message and "ie2dp_99" will not started.
6. If some angular point situated closer that 0.2 meter to current
electrode position or center MN dipole, then these points will be moved on
0.4 meter to the right and message about this appears.

6. How create initial model file for IE2DP1.

Input file can have any extension and *.ie2 is only recommended extension:
Format is fluent, figures in any line should have one ore more spaces
between figures.
1-st & 2-nd lines
Text of commentary for input file. Two lines with 60 characters in each.
3-rd line
NT, NP, KVP, PF, Key_grid - where
NT - number of bodies, NP-number of angular points,
KVP - Key IP (if KVP=0 IP is not calculated, and if KVP=1 - IP regime is
on).
PF - precision factor (Ordinary PF value is 1.0, 1.5 or 2. Precision at 3%
is guaranteed when PF>=2). If model is complicated we recommend to begin
with PF=0.8. We need that for the first estimation of elements number.
Precision of calculation is better if PF is more, but the total volume of
elements is restricted by limit of 800.
Key_grid - is a key.
if Key_Grid = -1 then the program creates the input file for 2D modeling
"ie2dp.xy".
if Key_Grid = 1 then the program creates the file "xz.txt", which is used
for plotting of cells' centres and grid analysis.
if Key_Grid = 2 then the program creates the file "ie.bin", which is used
for current lines drawing. In this case You should use Key_Array=12, for
definition of current electrodes position (see manual for IE2DL)
4-th group of lines ...(total Nt pairs! of lines)
R, IP, nV, NC, NH -Body's resistivity, chargeability (used for IP
calculation), number of angular points in the body, NC and NH are
reserved,
Nover(J) - The numbers of angular points numbers in count-clockwise
direction around this body.
5-th group of lines: ....(total Np lines )
Xp(i),Zp(i) - Coordinates X & Z of all angular points.
All other groups are used for 2D modeling with linear electrodes.

7. Example of initial file.

The test. Jan 1998.
Model A. Variant 1. H=20, h=70, a=200, b=200.
3 10 0 1 -1 - Num. of bodies & points, KeyIP, PF, Key_grid.
300.0 0.0 6 0 0 - 1-st body: r, , num. of points, reserved,
reserved
1 2 3 4 5 6 - enumeration of angular points
100.0 0.0 8 0 0 - 2-nd body: r, , num. of pnts, reserved, reserved
6 5 7 8 4 3 9 10 - enumeration of angular points
10.0 0.0 4 0 0 - 3-rd body: r, , num. of pnts, reserved, reserved
7 5 4 8 - enumeration of angular points
-600.0 0.0 - X & Z 1-st point
600.0 0.0 - X & Z 2-nd point
600.0 20.0 - X & Z 3-rd point
99.8 20.0 - X & Z 4-th point
-99.8 20.0 - X & Z 5-th point
-600.0 20.0 - X & Z 6-th point
-99.8 90.4 - X & Z 7-th point
99.8 90.4 - X & Z 8-th point
600.0 100.0 - X & Z 9-th point
-600.0 100.0 - X & Z 10-th point

8. Model of geoelectrical cross-section for this example.
Legend:
1 - resistivity of the 1-st layer (1-st body);
2 - resistivity of the lower (2-nd) body;
3 - resistivity of inhomogeneity (3-rd body);
real boundaries: 3-4, 4-5, 5-6, 5-4, 4-8, 8-7, 7-5.
fictitious boundaries - others.
[pic]
Fig.5.



9. How create the file "ie2dp.arr" with array desription.

Format is fluent, figures in any line should have one ore more spaces
between figures.

1-st line
Step, StepZ, X0, Z0, nSteps, Ndistances
Step - the distance between VES point (Key_of_Array in [15,16,18]) or
between measurements points along X-axes (Key_of_Array in [17,19]).
StepZ - the distance between measurements points along Z-axes
(Key_of_Array =19).
X0 - X-coordinate of the fist measurements (or VES) point.
Z0 - the depth of the fist measurements points (Key_of_Array in [17,19]).
nSteps - a number of VES point (15,16) or current electrodes (if
Key_of_Array=18), or measurements points (17,19).
Ndistances - a number of AO distances. The maximal number of distances, if
Key_of_Array=18, is (nStep/2) - 1.

2-nd line
XA, ZA, XB, ZB, reserved, Key_of_Array, reserved
XA,ZA,XB,ZB - coordinates of current dipole are used if Key_of_Array in
[17,18]. The values -10000 for XA and 10000 for XB exclude corresponding
current electrodes from calculation.
Key_of_Array - see the list of arrays

3-rd line
AO - values, if Key_of_Array = 15 or 16.
For gradient array (17,19) the maximal distance (AO[Ndistances]) is used
for spatial frequency. It should be close to maximal distance between
current electrode and measurements point. Using this parameter helps
sometimes to improve calculations accuracy.

10. Example of the file "ie2dp.arr".
__________________________________________________
5.0 0.0 -125 0.0 51 20 Step, StepZ, X0, Z0, Nsteps,
Ndistances
0.0 120.0 10000.0 0.0 0.0 18 0 XA, ZA, XB, ZB, reserved,
Key_of_Array, reserved
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Distances
__________________________________________________


11. What can you do with the help of IE2DP1 package?
1. Calculate theoretical VES curves for typical models to create master
curves.
2. Control interpretation results by calculation 2D-model after 1D
interpretation of field data, if the model seems to be 2D.
3. Investigate the influence of nearsurface inhomogeneous for finding them
on field VES curves and for developing ways to diminish their distorting
effects of VES curves.
4. Investigate the influence of deep inhomogeneous (structures).
5. Select optimal way of finding inhomogeneous objects by on-land,
underground or aquatorial measurements.
6. Investigate geological possibilities of resistivity method for definite
models (structures).
7. The same as 1-6 items for IP (induced polarization) method.

References
1. Electrical sounding of geological medium. Moscow university (MSU)
edition, part 1, 1988, 176 pp., part 2, 1992, 200 pp. (In Russian).
2. Electrical prospecting by resistivity method. MSU edition, 1994, 160 pp.
(In Russian).

3. BarthesV., Vasseur G. Three-dimensional resistivity modeling by integral
equation method. Avr. Eur. Geoterm Res. Proc. 2-nd Int. Semin. Results EC
Geotherm Energy Res. Strasburg, 1980 Dardect e.a. - 1980. - P. 854-876.

4. Dey A. Morrison H.F. Resistivity modeling for arbitrary shaped three-
dimensional structures// Geophys. prospecting - 1979. - Vol. 27, N 1.- P.
106-136.

Hot-line support on E-mail: Sh@geophys.geol.msu.su

Appendix II.

The file "start.bat".

if (iedl&&test -f ie2dp.xy)
then
calc.out
else
echo " Error in input files"
fi

Some technical details about FORTRAN sources of programs

The prorgam "iedl" is the pre-processing module.

The list of units for program "iedl":
elem.for - the main unit,
vvod.for - the input unit,
ntel.for, old.for, amnb.for, drr.for, gauss.for, pri.for - additional
units.
Subroutine SaveIE2DP1 in the unit elem.for - the output of cells'
description for calculating module.
It is quite probably, that units [old.for, amnb.for, drr.for, gauss.for,
pri.for] are not used in pre-processing.

The prorgam "calc.out" is the calculating module.

The list of units for program "calc.out":
oldmap.for - the main unit,
new_inp.for - the input unit,
ie2dp5.for gauss1.for - additional units.
The output of results files subroutines are situated in the unit
ie2dp5.for:
subroutine outBinary - the output of results in binary files
"AMN.bin", "MNB.bin" and "DIF.bin" for "ximage" program,
subroutine outSurfer - the output of results in ASCII files "A_MN.RES"
and "MN_B.RES" for "Surfer" program,
subroutine outInterpex - the output of results in ASCII files
"FORWARD.RS2" and "REVERSE.RS2" for Resix set of programs,
subroutine PRIRES - the output of results in file "IE2DP1.RES",
subroutine PRI_SG - the output of results in file "IE2DP1.RES", in
case of Key_of_Array value is equal 17.

The results of calculation stored in arrays Rok(i,j) and Rok_b(i,j) for
left and right array correspondingly. The i-index is the number of current
electrode (1..nSteps) and the j-index is the number of spacing
(1..nDistances).

The selection and calculation of spacial frequencies (AKY) is situated in
the unit ie2dp5.for, subroutine KYY. The time of calculation is
proportional to number of spacial frequencies. The accuracy depend on it
also. The next selection of AKY guarantees the error of calculation less
then 1% for most of models:

KY=6 ,
KTM=5 ,
AKY(1)=0 ,
AKY(2)=1 / (KY * maximal_AO) ,
AKY_maximal=KY*24/minimal_AO ,
AKY(i)=AKY(i-1)* (10.**(1./KTM)) .

Thus the modification of KY value leads to new spacial frequencies' range,
and changing of KTM value results in new geometric step between
frequencies.