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EQUIVALENT DIPOLES APPROACH TO THE ELECTRICAL FIELD VECTOR MEASUREMENTS
DATA INTERPRETING
Aleksandr A. Gorbunov, Igor. N. Modin
Moscow State University, Geological Faculty, Dept. of Geophysics, 119899
Moscow, Russia
E-mail: gorb@geophys.geol.msu.ru
INTRODUCTION
Estimating construction conditions is an important problem facing those
engaged in construction protection against corrosion to prevent their
destruction which is likely to result in severe economical losses and
environmental damage. The constructions, contacting the ground or buried
under the ground surface, reveal themselves as anomalous objects in the
layered medium or on its surface. If the metal of the construction is in
the galvanic contact with the embedding rock, the object appears to be
highly conductive. Concrete or covered with water-proof coating
constructions appear as the objects of high resistivity. Thus the ability
appears to use resistivity techniques for estimating the conditions of the
constructions.
Commonly used techniques of resistivity prospecting suppose that the
target object is crossed by the observation line. Sometimes it is
impossible to apply such techniques as there is no direct access to the
place. So a technique is needed capable of investigating the objects aside
the observation line.
Besides that, traditional techniques involve, generally, only one
component of the electric field, precisely, that in the observation line
direction. Using two orthogonal components, i. e. taking the vector
properties of the electric field into consideration, is likely to provide
additional information concerning 3D inhomogenities in the layered cross-
section.
ELECTRICAL FIELD VECTOR MEASUREMENTS (EFVM) TECHNIQUE
The EFVM technique (Fig.1) was introduced in 1992 by the MSU team
(Modin, Shevnin et al., 1992; Modin, Ignatova, 1995), implementing the
above mentioned approach. Two values of the potential difference DUx and
DUy are measured with orthogonal positions of the measurement line MN are
measured at a number of points O (center of MN) along the observation line
encircling the supposed location of the target object. The measurement are
implemented at the same points with several locations of the single current
electrode A introducing the electric current I into the cross-section. The
current electrode locations surround the object location as well. The
second current electrode B is placed in the «infinity». The measurements
are implemented taking the sign of the potential difference value into
consideration.
Generalizing the traditional apparent resistivity [pic] for the pole-
dipole (half-Schlumberger) array, the apparent resistivity vector [pic]
with components [pic] is introduced.
The field theory says, that the electrical field in the inhomogeneious
cross-section can be presented as the sum of the normal field and anomalous
field. The normal field is the field of the current source in the embedding
cross-section without inhomogenities. The anomalous field is the field of
the secondary sources induced by the normal field at the boundaries of the
inhomogeneities. Considering the layered cross-section as the embedding
medium, apparent resistivity vector can be presented as [pic] - the sum of
the normal and the anomalous apparent resistivity. The value of [pic] is
the traditional apparent resistivity for the embedding layered cross-
section, and its direction is the direction of the AO radius-vector. Thus
the anomalous apparent resistivity vector [pic] can be estimated,
representing the effect of the inhomogeneity as if in the semi-space. The
[pic] vector is oriented in the same way as the anomalous electric field
and brings the information concerning the inhomogeneity.
EQUIVALENT DIPOLES APPROACH TO EFVM DATA INTERPRETING
The anomalous field of the secondary sources representing the isolated
inhomogeneity in the primary field of the point current source can be
approximated with the field of dipole or so called 'real dipole' - a system
of two point sources of opposite signs separated by certain distance. The
properties of this dipole - its position in the cross-section and the
dipole moment vector value and direction - are connected with the
properties of the corresponding object. The EFVM inverse problem can be
thus posed as follows: to derive the properties of the dipole in the semi-
space from the observed vector of the dipole's electric field on the
surface of the semi-space (equivalent dipoles approach).
Wide-spread approach of minimizing the fitting error between the measured
and calculated electric field values by varying, within certain limits, the
dipole's properties is applied. Various dipole's properties sets, though
physically equivalent, are different regarding the calculational
effectiveness of the minimizing process. These sets are: dipoles'
coordinates and dipole moment vector components; 'real dipole's'
coordinates, intensity, length, dip angle and dip direction; poles'
coordinates and intensities separately. The latest approach proved to be
the most effective one. Solving the inverse problem for the data gained
with several current electrode location, a set of dipoles is obtained. The
spatial area occupied by this set marks the boundaries of the anomalous
object (Fig. 2).
REFERENCES
Modin I. N., Shevnin V. A. et al. Vector measurements in resistivity
prospecting. EAEG 56th Ann. Meeting, Vienna, Austria, 1994.
Modin I. N., Ignatova I. D. Coal layer inhomogeneities investigations by
vector resistivity measurements in mines. EAGE 57th Ann. Meeting, Glasgo,
UK, 1995.
[pic]
Fig. 1.The EFVM technique: current electrode (1), - Fig. 2. EFVM data
intrepreting using equivalent dipoles
positive (2) and negative (3) secondary sources, approach: current
electrode (1) and positive (2) and
primary (4), secondary (5) and total (6) field, negative (3) poles of
the equivalent dipoles, obtained
measured field components (7). for different current electrodes
position.