Electrical Resistivity Techniques
- Unconsolidated formations: 5-50 ohm-meters
- Sedimentary rocks: 5-200 ohm-meters
- Extrusive rocks: 20-1000 ohm-meters
- Intrusive rocks: 50-10,000 ohm-meters.
General Resistivity Techniques
The electrical resistivity method measures the bulk resistance of earth materials to the passage of electricity. This measurement correlates most strongly with the electrical properties of the pore water, the amount of pore water, and the presence of clay materials in the matrix. The rare occurrence of metallic minerals can have a large influence on the resistivity of earth materials. Resistivity correlates very well with the geologic composition of rocks and unconsolidated materials.
As the ionic concentrations in the pore water and the other factors mentioned above can vary over several orders of magnitude, it is not surprising that the resistivity of rocks varies by more than five orders of magnitude. This variation implies that differentiation of geologic formations by the use of resistivity is a useful tool in determining the subsurface geometry of various rock boundaries.
Some representative resistivities are:
These ranges are should not be discouraging; any one formation will generally have only one characteristic resistivity. What it does tell us is that we may-or may not-have a contrast in physical properties, i.e. , resistivity. Thus, we may-or may not-have a reasonable geophysical target for a Micro Geophysics Corporation survey.
Many electrode configurations are used in geophysics to measure subsurface resistivity. A common factor in these configurations is a set of current input electrodes usually labeled A and B and a set of voltage measurement electrodes usually labeled M and N. The dipole-dipole method places the A and B electrodes to one side with a spacing between them denoted as "a". The M and N electrode pair with equal a-spacing are placed colinearly a distance "na" away from A and B. A distance equal to an integer multiple of a is denoted "na". The figure shows the electrode configuration.
As measurements are taken at various n's, that is, the pairs of electrodes are moved apart, a sounding is obtained. If the electrodes are moved across the surface, a profile of comparative values is generated. Thus the dipole-dipole method produces a combination sounding-profiling set of data ifmeasurements are taken at various values of n along a profile. The availability ofmodern high-powered sources and sensitive synchronous receivers allow the superior field efficiency and data density attributes of this technique to be exploited in preference to the older Wenner or Lee electrode configurations.
Basic Dipole-Dipole configuration:
Detailed Dipole-Dipole configuration, including electric field lines (solid) and resultant equopotential surfaces (dashed):
Most of the following discussion is taken from the reference given below.
A two-dimensional (pseudosection) format has been developed to present
dipole-dipole data with several values of n. If the results are plotted in
the two-dimensional array shown in the figure, the effects of along the line
variations in the earth's parameters can easily be separated from the effects
of vertical variations in the earth's parameters. The lateral position of
the apparent values is plotted in relationship to where the electrodes were
when that particular measurement was performed. The distance of the plotted
apparent value from the measurement line is related to the separation between
the electrodes when the measurement was made.
The 45-degree angle used to plot the data is entirely arbitrary. This process is shown in the figure to the right, where (a) through (d) demonstrate theplotting sequence. The pseudosection plots are contoured, and the resulting anomalous patterns can be recognized as being caused by a particularsource geometry and/or correlated from line to line. However, the contoured data are MOST EMPHATICALLY NOT meant to represent sections of the electrical parameters of the subsurface. The relationship of the plotted, contoured pseudosection and the actual section of the electrical parameter is a very complex mapping function. The pseudosection data plots aremerely a convenient method for showing all of the apparent resistivity data along one given line in one presentation. It cannot be overemphasized-THE PSEUDO SECTION PLOTS ARE NOT CROSS SECTIONS.
REFERENCE: Van Blaricom, Richard, 1980, Practical Geophysics for
the Exploration Geologist, Northwest Mining Association, Spokane, Washington,
99201, 303 p.
The Schlumberger sounding method refers to an electrical array illustrated in the figure. Advantages of this array include superior quanitative vertical resolution and a lack of sensitivity tolateral effects. Additionally, the equipment demands are reduced by the larger signals recorded between thecurrent electrodes. A brief description of the method is provided below.
Basic Schlumberger survey configuration:
Electrical resistivity utilizing the Schlumberger sounding method consists of a pair of current electrodes (shown as A and B in the figure). Current is passed between A and B and monitored by potential electrodes M and N. As the distance between A and B is increased, deeper horizons have more effect on the potential between M and N.
A plot of the apparent resistivity versus half the distance from A to B yields a curve indicative of the vertical resistivity distribution in the subsurface.
Geophysical Interpretation of Resistivity Surveys
The electrical resistivity data can interpreted using computer programs which invert the observed data to a model of the true resistivities of the subsurface. These programs accept the observed data and a starting model from the interpreter and invert the data to produce a layered or two-dimensional resistivity model. The following is excerpted from the program documentation as provided by Interpex, Ltd, the manufacturor of such programs:
"There are some parameters which affect the inversion. These are the parameter fixes, the convergence criteria and the weighting of errors by their reciprocal standard errors (error bars)."
"The parameter resolution matrix is calculated as a by-product of the inversion and is an indication of the resolvability and the interdependence of the parameters. In mathematical terms, it is a measure of the degree and nature of the singularity of the matrix which results from linearization of the nonlinear system. It can be "read" however, to give an indication of which layer parameters are well resolved, which are poorly resolved, and which groups of parameters are interdependent." "It is best to explain the resolution matrix by using examples. The first example is one in which resolution is perfect; that is, every parameter is resolved:
P2 0.00 1.00
P3 0.00 0.00 1.00
T1 0.00 0.00 0.00 1.00
T2 0.00 0.00 0.00 0.00 1.00
Notice that the triangular matrix we have shown here has ones along the diagonal, and zeros everywhere else. This triangle is just the nonrepetitive part of a symmetric matrix. This matrix shows the parameters which we have resolved as linear combinations of the parameters which we have used to specify our model, that is in terms of the layer resistivities and thicknesses. Since the resolution matrix is the identity matrix, we have perfect resolution.".
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