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Joint Inversion of Vertical Electrical Sounding
and Dipole Induction Sounding
Justyna Bala, Grzegorz Pszczola Department of
Geoinformatics and Applied Computer
Science Faculty of Geology, Geophysics and
Environmental Protection AGH University of
Science and Technology
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Plan of the Presentation

• Non-uniqueness of the inverse problem
• The geolelectrical methods for which
• we were solving invers problem
• The used algorithm
• The results of our computing
• Conclusions

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Forward and inverse problems
MODELING
INVERSION
model parameters gt observed data
Forward problem
observed data gt model parameters
Inverse problem
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Non-uniqueness of the inverse problem

• The existence of many competitive solutions
• It may happen that it will be impossible to
  perform measurement again
• Restricted possibilites of measurement (i.e.
  the surface of the area)
• Imperfect geological model
• Computational limitations (the lack of
  possibilites to construct
• the complicated geological models)
• Typical measurement errors

One of the ways of better information analysis
included in the measured data is joining
inversion for different methods.
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Geoelectrical Measurements

• The purpose of geoelectrical surveys is to
  determine the subsurface resistivity distribution
  by making measurements on the ground surface.
• The geoelectrical methods are used in two
  different modes profiling and sounding.
• Profiling is used to detect lateral variations
  across a site by taking
• series of readings along a line using a
  fixed configuration of coils
• or electrodes. 
• Soundings are used to estimate vertical
  variations in electrical
• conductivity or resistivity.

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Vertical Electrical Sounding
The resistivity measurments are made by injecting
current into the ground through two current
electrodes (A and B), and measuring the resulting
voltage difference at two potential electrodes (M
and N). From the current and voltage, an apparent
resistivity value is calculated.
In vertical electrical sounding, the distance
between the current electrodes and the
potential electrodes is systematically
increased, thereby we can receive the
information on subsurface resistivity from
successively greater depths.
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Dipole Induction Sounding
(electromagnetic terrain conductivity measurement)
An alternating current in the EM transmitter coil
creates a magnetic field which induces electrical
current loops within the ground the current
loops, in turn, create a secondary magnetic
field.  Both the primary magnetic field (produced
by the transmitter coil) and the secondary field
induce a corresponding alternating current in the
EM receiver coil.
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The Model Parameters

• For the test computing the model data were
  generated for the 1D two layered medium having
  the parameters
• The resistivity of the upper layer ?1 10
  ohm,
• the thickness of the upper layer h1 10 m.
• The resistivity of the lower layer ?2 100
  ohm,
• the thickness of the lower layer h2 ?.

?1
h1
?2

• The measurment system
• Vertical Electrical Sounding 12 electrode
  separations
• (from 1.0 m to 68.13 m)
• Dipole Induction Sounding 3 coil separations
  (10m, 20m, 40m).

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The Idea of the Algorithm

• From each of the points from the parameters
  grid the local minimalization
• function is started.
• We can choose the density of this grid.
• The obtained local minimum result depends on
  the starting point.

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Result 1
Vertical Electrical Sounding
Basins of attractions
The function value in found local minimum
The thickness of the upper layer h1
The resistivity of the lower layer ?2
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Result 2
Dipole Induction Sounding
Basins of attractions
The function value in found local minimum
The thickness of the upper layer h1
The resistivity of the lower layer ?2
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The Computations
A client receives the task (a starting point)
from Task Server and returns the result (a local
minimum and the function value in found local
minimum) to Result Server. Our computations were
possible only in the computer room where the
lectures for students are usually held. The
created program had to be resistant for shutting
down or restarting of the clients.
Task server
Client
Result server
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Conclusions

• We were solving the global optimization problem
• The analysis of the basins of attractions
  should allow to examine the practical
  features as

• Non-uniqueness of the inverse problem
• The influence of different parameters on
  the interpretation result
• Creating the optimum algorithms solving these
  problems

• As every optimization problem, this one also
  requires
• a lot of computing time

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The created computing environment allows

• Monte-Carlo sampling
• Grid Search
• Basins of Attractions
• Multistart

In the future we would like to

• Evaluate more complex geological models
• Join the different geoelectrical methods (such
  as
• Vertical Electrical Sounding and Dipole
  Induction
• Sounding )
• Create the objective function for joint
  inversion
• for these methods

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Thank you for your attention !
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References
1 MENKE W., Geophysical Data Analysis
Discrete Inverse Theory. Academic Press
Inc., Orlando, Florida, 1984. 2 PRESS W.
H., FLANNERY B. P., TEUKOLSKY S. A. i VETTERLING
W. T., Numerical recipes in C. The art of
scientific computing, Cambridge University Press,
Cambridge 1986. 3 PSZCZOLA G.,
LESNIAK A., WIT R. Algorytm genetyczny z
klasteryzacja w zagadnieniu lokalizacji
hipocentrum, Prace Naukowe Instytutu Górnictwa
Politechniki Wroclawskiej, 2004, Vol. 107,
No. 39, ss. 123133. 4 ZDANOV M. S., The
geoelectrical methods in geophysical exploration,
Elsevier, Amsterdam 1994.