A CASE STUDY : VERTICAL ELECTRIC SOUNDINGS (VES)

VERTICAL ELECTRIC SOUNDINGS (VES)

In this section we show how the web services can solve a nonlinear inverse problem. Inverse problems are commonly found in geo-sciences. Specifically, we will provide solutions to the problem which arises when interpreting field data aquired through a method known as Vertical Electrical Soundings (VES).

For more details see: Versamedium-white-paper.pdf (PDF 842 KBytes)

Note I: You can run this demo also from a Windows NT based OS (32-bit), or from a computer with no OS at all . Go to the IN-WINDOWS-HOWTO for detailed instructions.

Note II: In order to visualize the results of the demo program in a graphical way, the PGPLOT graphic libraries should be installed. Install PGPLOT graphic libraries for C properly before attempting compilation, before proceeding. A small howto-guide can be found PGPLOT-HOWTO.

Download the distro_versa-ves-0.1.tar.gz (35.5 KBytes) program:

uncompress and unpack the compressed-package in some direcory

tar -zxvf distro_versa-ves-0.1.tar.gz

then cd (change directory) into the directory just created ./distro_versa-ves-0.1

cd distro_versa-ves-0.1

Compile the demo program as follows:

gcc -Wall -O2 -c -I/usr/local/pgplot versa-ves.c

then link the graphic libraries as follows:

gfortran -o versa-ves versa-ves.o -L/usr/local/pgplot/ -lcpgplot -lpgplot

-L/usr/X11R6/lib -lX11 -lm -lc

Finally, run program from command prompt:

``andlinux'' users might need to invoke the PGPLOT Server:

/usr/local/pgplot/pgxwin_server &

./versa-ves

EXAMPLE 1 : 100 Layers (under 10 seconds)

Parameters:
How many layers do you want in model (minimum 100)? : (default = 100):
Your number of layers are: 100
Regularization beta parameter? ( 0.0 <= beta <= 1.0 ) ?: (default = 1.000000):
Your beta parameter is: 1.000000
1-D regularization window size?: (default = 2):
1-D regularization window: 2
Solutions will have maximum=800.000000
Solutions will have minimum=0.100000
Type the number of nonlinear iterations? : (default = 5):
Number of nonlinear iterations: 5
Type the number of linear iterations? : (default = 10):
Number of linear iterations: 10
Wold you like to recycle a previous solution (1 = Yes)? : (default = 0 No):
Recycle: 0
Graphics device/type (? to see list, default /NULL): /xwin

If everything its right? you should see this output log:

Fig. 1 Initial arbitrary model (green), Synthetic Model (red) and Occam's Reference Model (yelllow).

Fig. 2 Response after 1 nonlinear times 10 linear iterations rms = 22.15 %(green) and Synthetic Data (red). Response of Occam's solution is not shown but fits the data to rms = 1 %, So you can think of the red dots as the Occam's response (yellow model in Fig. 1).

Fig. 3 Versamedium's model obtained after 1 nonlinear times 10 linear iterations (green), Synthetic Model (red) and Occam's Reference Model. Responses of this models are in Fig. 2

Fig. 4 Versamedium's model obtained after 5 nonlinear times 10 linear iterations (green), Synthetic Model (red) and Occam's Reference Model (yelllow).

Fig. 5 Versamedium's response obtained after 5 nonlinear times 10 linear iterations (green) rms = 5.83 %, Synthetic Data (red). For Models in Fig. 4.

Fig. 6 Credits.

Recycling previous solution (another 10 seconds)

Parameters:
How many layers do you want in model (minimum 100)? : (default = 100):
Your number of layers are: 100
Regulariz.......parameter?( 0.0 <= beta <= 1.0 ) ?:(default = 1.000000):0.9 <- Change
Your beta parameter is: 0.9
1-D regularization window size?:(default = 2):1 <---------------------------------Change
1-D regularization window: 1
Solutions will have maximum=800.000000
Solutions will have minimum=0.100000
Type the number of nonlinear iterations? : (default = 5):
Number of nonlinear iterations: 5
Type the number of linear iterations? : (default = 10):
Number of linear iterations: 10
Wold you like to recycle a previous solution (1 = Yes)? :(default = 0 No):1 <-----Change
Recycle: 1
Graphics device/type (? to see list, default /NULL): /xwin

Fig. 7 Versamedium's model obtained after another 5 nonlinear times 10 linear iterations (green). The above responses were obtained using the new parameters. Synthetic Model (red) and Occam's Reference Model (yelllow).

Fig. 8 Versamedium's response obtained after another 5 nonlinear times 10 linear iterations (green) rms = 1.96 %, Synthetic Data (red). For Models in Fig. 7.

EXAMPLE 2 : 1000 Layers (under 80 seconds)

How many layers do you want in model (minimum 100)? : (default = 100): 1000
Your number of layers are: 1000
Regularization beta parameter? ( 0.0 <= beta <= 1.0 ) ?: (default = 1.000000):
Your beta parameter is: 1.000000
1-D regularization window size?: (default = 2): 10
1-D regularization window: 10
Solutions will have maximum=800.000000
Solutions will have minimum=0.100000
Type the number of nonlinear iterations? : (default = 5):
Number of nonlinear iterations: 5
Type the number of linear iterations? : (default = 10):
Number of linear iterations: 10
Wold you like to recycle a previous solution (1 = Yes)? : (default = 0 No):
Recycle: 0
Graphics device/type (? to see list, default /NULL): /gif

If everything its right? you should see this output log:

Fig. 9 Versamedium's model obtained after another 5 nonlinear times 10 linear iterations (green). The above responses were obtained using the new parameters. Synthetic Model (red) and Occam's Reference Model (yelllow).

Fig. 10 Versamedium's response obtained after another 5 nonlinear times 10 linear iterations (green) rms = 1.13 %, Synthetic Data (red). For Models in Fig. 9.

Recycling previous solution (another 80 seconds)

How many layers do you want in model (minimum 100)? : (default = 100): 1000
Your number of layers are: 1000
Regularization beta parameter? ( 0.0 <= beta <= 1.0 ) ?: (default = 1.000000): 0.9
Your beta parameter is: 0.900000
1-D regularization window size?: (default = 2):
1-D regularization window: 2
Solutions will have maximum=800.000000
Solutions will have minimum=0.100000
Type the number of nonlinear iterations? : (default = 5):
Number of nonlinear iterations: 5
Type the number of linear iterations? : (default = 10):
Number of linear iterations: 10
Wold you like to recycle a previous solution (1 = Yes)? : (default = 0 No): 1
Recycle: 1
Graphics device/type (? to see list, default /NULL): /gif

If everything its right? you should see this output log:

Fig. 11 Versamedium's model obtained after another 5 nonlinear times 10 linear iterations (green). The above responses were obtained using the new parameters. Synthetic Model (red) and Occam's Reference Model (yelllow).

Fig. 12 Versamedium's response obtained after another 5 nonlinear times 10 linear iterations (green) rms = 0.6 %, Synthetic Data (red). For Models in Fig. 11.

REFERENCES:

For more details see Versamedium Web Service: White Paper

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