DC resistivity surveys

Introduction

This resource provides conceptual and theoretical background about DC resistivity surveying. It does notgo into interpretation or inversion of data, although a subsequent version of the resource will coverinterpretation in more detail. However, two activities provide an introduction to working with rawsounding and profiling data.

The content is structured so that essentials about this method are provided on one page (Measurementsand data), while more advanced background physics and mathematics are presented on a second page (Principles). Severalappendicies are included with additional information. Activities are included for self-testing, and for instructor-assigned markedexercises.

DC resistivity surveys

In resistivity surveying, information about the subsurface distribution of electrical conductivity is obtained by examining howcurrents flow in the earth. DC (direct current) resistivity methods involve injecting a steady state electrical current into the groundand observing the resulting distribution of potentials (voltages) at the surface or within boreholes.

Like all geophysical processes, DC surveys can be described in terms of input energy, the earth's physical properties, and signalsor data that are measured.

Using the same colour scheme as the flow diagram above, Figure 2 shows how this conceptual framework applies for DC methods.The energy source is a pair of electrodes that inject a well-known current into the ground at known locations (Fig. 2a). The earth affects this energy because variations in the electrical conductivity of subsurface structures will bend the current flow lines (Fig. 2b). The measured signals or data (Fig. 2c) will involve measurements of voltage at the earth's surface or within boreholes. Thistype of data contains information about how charges become distributed at boundaries where electrical conductivity changes.

2a. The energy source is a controlled DC electrical current injected into the

ground.

2b. Increases and decreases in electrical conductivity cause current paths to converge

and diverge respectively.

2c. Data are voltages caused by charges accumulating due to current

flow.

For each placement of the transmitting electrodes, several voltages will often be measured at different locations. Therefore, thecomplete data set includes measured voltages with known currents and electrode geometries. In order to create maps or graphsof raw data for quality assessment or for direct interpretations, it is usual to convert the data into a form that has units ofresistivity. Such results are most commonly used as the input for DC resistivity inversions, in which the results will be 1D, 2D or3D models of how subsurface conductivity is distributed.

The physical property - electrical conductivity

Electrical conductivity (or resistivity) is a bulk property of material describing how well that material allowselectric currents to flow through it. Consider current flowing through the unit cube of material shown to the

right:

Resistance is simply the measured voltage over the measured (known) current (which is Ohm'sLaw). Resistance will change if the measurement geometry or if the volume of material changes.Therefore, it is NOT a physical property.Resistivity is basically the resistance per unit volume. It is defined as the voltage measured across a unit cube's length(volts per metre, or V/m) divided by the current flowing through the unit cube's cross sectional area (Amps per metresquared, or A/m2). This results in units of Ohm-m2/m or Ohm-m. The greek symbol rho, , is often used to represent resistivity. Conductivity, often represented using sigma, , is the inverse of resistivity: = 1/ . Conductivity is given in units ofSiemens per metre, or S/m. Millisiemens per metre (mS/m) are often used; 1000 mS/m = 1 S/m. So 1 mS/m = 1000Ohm-m.

The electrical conductivity of Earth's materials varies over many orders of magnitude. It depends upon many factors, including:rock type, porosity, connectivity of pores, nature of the fluid, and metallic content of the solid matrix. A very rough indication ofthe range of conductivity for rocks and minerals is in the figure here.

Soils and rocks are composed mostly of silicate minerals, which are essentially insulators. Exceptions include magnetite, specularhematite, carbon, graphite, pyrite, and pyrrhotite. Therefore conduction is largely electrolytic, so conductivity depends mainlyupon:

porosity;hydraulic permeability, which describes how pores are interconnected;moisture content; concentration of dissolved electrolytes; temperature and phase of pore fluid;amount and composition of colloids (clay content).

Detailed discussion of geologic factors affecting this important physical property are provided in a separate location.

F. Jones, UBC Earth and Ocean Sciences, 03/14/2007 20:28:30

DC resistivity: measurements and data

On this page:| Introduction | Current in the ground | Sources

| Measurements: voltage | Data: apparent resistivity| Survey configurations

| Plotting raw data | Processing options | Interpretation

Introduction

All geophysical surveys involve energizing the earth in order to generate signals, which will contain information about the types and distributions of subsurface physical properties.

For DC resistivity surveys, the energy source is a generator which injects a constant current into the ground using two electrodes. The "signals out" (data) are voltages measured at various places on the surface, along with strength of the known current source (in Amperes) and details about relative geometry of the four electrodes.

In order to create maps or graphs of raw data for quality assessment or for direct interpretations, measurements are converted into a form that is related to the relevant physical property. For each measurement, a 3D version of Ohm's Law is used to generate a datum with units of resistivity (or condutivity). These transformed data are called apparent resistivities because they represent the earth's true resistivity only if the ground is uniform within range of the measurement. When subsurface resistivity varies, interpretation must be based upon the way in which apparent resistivity varies as a function of electrode geometry and position. The commonly used survey procedures are explained later on this page, after discussions about current flow, sources, measurements, and conversion to apparent resistivities.

Current flow in the ground

The path of the current in the earth after it is injected with two electrodes depends upon the distribution of electrical resistivity. If the Earth is uniform, current flows in a regular three dimensional pattern under the electrodes as illustrated Figure 1. The north slice number 8 (flagged with a *) is similar to the type of image commonly shown in texts to indicate how current flows in two dimensions under a pair of source electrodes.

Figure 1. These figures show slices through a uniform Earth with current flowing out of the right-hand (near) electrode and back into the left-hand (far) electrode. A connecting red line substitudes for a real generator. Vectors with white dots for heads show the direction of current flow, while their colour indicates the strength (or current density) in units of Log10 Amperes per square

metre (A/m2); so the maximum shown is Log10(J)=-3.33, or J=0.000468 A/m2.

Topslice 1slice 2slice 3slice 4slice 5slice 6slice 7slice 8slice 9slice 10slice 11 slice 12slice 13

shell

Northslice 1slice 2slice 3slice 4slice 5slice 6slice 7slice 8 *slice 9slice 10slice 11 slice 12slice 13slice 14slice 15slice 16

Eastslice 1slice 2slice 3slice 4slice 5slice 6slice 7slice 8slice 9slice 10slice 11 slice 12slice 13slice 14slice 15slice 16

There is no need to click: moving your mouse over the links simulates animations.

Vector plots of current distribution were generatedusing 3D EM modeling code developed by the UBC Geophysical Inversion Facility.

Normally the earth is NOT uniform. Galvanic currents will flow towards regions of high conductivity and away from regions of high resistivity, as illustrated in Figure 2.

Figure 2. Click buttons for images a. through e.

a. The Elura ore body. Depth to top of gossan (in blue) is approximately 100 m.b. A DC resistivity survey involves injecting current at one location and measuring resulting

potentials at another location.c. Current will flow. Current density increases within conductive regions, and decreases within

resistive regions. d. Charges build up at interfaces between regions of different electrical conductivity.e. Variations in charge distribution are detected as variations in distribution of potential, or

voltage, at the surface.

Elura Orebody Electrical resistivities

Rock Type Ohm-m

Overburden 12

Host rocks 200

Gossan 420

Mineralization (pyritic) 0.6

Mineralization (pyrrhotite) 0.6

Figure 2. The Elura orebody (in New South Wales, Australia) is an example of a subsurface target with a range of electrical resistivities.

Details are from I.G. Hone, Geoelectric Properties of the Elura Prospect, Cobar, NSW, in "The Geophysics of the Elura Orebody, Cobar NSW,"

1980, Australian Society of Exploration Geophysicists.

The relation between charge distribution, current flow and resulting potentials is discussed more fully in the section on principles.

Sources

High power and reliable constant current are the primary requirements of DC resistivity transmitters. For small scale work (electrodes up to roughly 100 m apart), a transmitter capable of sourcing up to several hundred milliwatts of power might be adequate. For larger scale work (electrodes as much as 1000 m or more apart), it is possible to obtain transmitters that can source up to 30,000 watts. See the appendix called "Instruments" for more details.

Current is usually injected as a 50% duty cycle reversing square wave (Figure 3). That is, current is on for several seconds, off for several seconds, on with reversed polarity, off, etc. Voltages are recorded while current is on.

Figure 3.

This pattern for the current source is necessary because a voltage measured when the current is off will be non-zero in many situations. Naturally occuring potentials are called spontaneous or self potentials (SP), and they are usually caused by electrochemical activity in the ground. From the point of view of DC resistivity surveys, SP voltages are noise because measured voltages must be caused by the source current only. The 50% duty cycle reversing square wave is employed so as to remove the (poorly known) SP signals.

Measurements: potential difference

It is tempting to compare the earth to a resistor in an electric circuit (Figure 4a). However, it is important to recognize the difference between resistance and resistivity. If we apply Ohm's law, R=V/I, to the situation in Figure 4b, we will have a resistance, which is in units of Ohms. This is NOT the ground's resistivity, which has units of Ohm-m. We do not want the resistance of this circuit; we want a measure of the ground's resistance per unit volume, or resistivity.

Figures 4. a. b.

In order to derive the relation between measurments (I, V, geometry) and the required physical property (resistivity or ) we should start from first principles. This is done in detail in the section called principles. The derivation is a three step process:

First find a relation for potential due to a point source of current in a uniform medium with no boundaries (image to the right). The expression will look like Ohm's law with the addition of terms involving the distance between source and potential measurement location. Next, the potential due to two sources (actually, a source and a sink) is the superposition of potentials due to each one. Finally, since we must make potential measurements using two electrodes, an expression for potential difference can be derived as the difference between relations for potential at single electrodes.

The actual measurement configuration can be summarized as shown in Figure 5. This conceptualization is useful, regardless of the actual placement of electrodes on the surface.

Figure 5.

The measured voltage for any arrangement of electrodes can be derived from Figure 5 as follows (again, details are in the principles section):

G is a geometric factor (including the factor 1/2 ), which depends upon the locations of electrodes.

Data: Apparent resistivity

We are finally in a position to express the thing we want (a physical property) in terms of parameters we either know or measure (current, voltage and geometry). Rearranging the last expression above, we can define apparent resistivity as the halfspace resistivity which produces the observed potential from a particular electrode geometry:

. Similarily the apparent conductivity is .

We have the following important definition: Apparent resistivity is the resistivity derived using only the known current, measured voltage, and array geometry. It is the earth's true resistivity only when the earth (within range of the measurements) is a uniform halfspace. When the earth is more complicated, the measured apparent resistivity will be less than the maximum and more than the minimum true (or intrinsic) resistivities that are within range.

The essence of interpreting resistivity surveys is to find the true distribution of intrinsic resistivities by interpreting the pattern of apparent resistivities that were measured.

Now we can find simple relations between all our known and measured quantities and a useful physical property, namely the apparent resistivity. We only need expressions for the geometric factor based upon electrode geometry. G is easily found if the four distances take on convenient values. For example, if electrodes are spaced equally by a distance a, then, using the figure and relation for V above,

G = (1/a - 1/2a - 1/2a + 1/a)/2 = 1/2 a.

This is the case for the "Wenner" array shown in Figure 6, which summariz es the geometric factor for a variety of commonelectrode configurations. Note that in this figure, k=1/G . Usage of the various arrays is illustrated in the next section.

Figure 6. Survey configurations for DC resistivity surveying.

Survey configurations

There is a wide assortment of configurations commonly used for gathering DC resistivity (and induced polarization) data. In the field, the choice of array depends upon:

The type of information needed. For example, the location of a target may be all that is needed, or it may be necessary to characterize the details of the target.

1.

The most likely type of model (1D, 2D, or 3D) that will be used for interpretation. 2.The economics of the situation. Since wires must be placed to all electrode locations, and electrodes must be planted in the ground, surveys covering large areas in difficult terrain with hard or gravelly surface materials can rapidly become very expensive.

3.

The most common specific arrays are detailed in Figure 7, but there are several general types of surveys conducted on the surface.

Soundings provide 1D solutions, or vertical structure under one surface location. Electrode geometry is varied symmetrically about a single measurement location. The most common configurations for soundings are the Wenner and Schulmberger arrays.

Profiling provides information about lateral variations, usually with some information about vertical variations. Most profiles involve placing all electrodes on survey lines so that 2D models of the earth's electrical structure can be found. All seven types shown in the interactive figure below (Figure 7) can be used for profiling.

Three dimensional configurations of several types exist, in which electrodes are not in line. Examples include:

Equatorial dipole-dipole array (Figure 6 above), which is used primarily for very shallow work such as archeological investigations.Twin Probe configuration (basically a Wenner Gamma in Figure 6 above, but with spacing more like dipole-dipole) is also used mainly for very shallow investigations such as archeological work.The so-called E-Scan technique is a pole-pole configuration. However, it is organized by planting a large number of electrodes all over the area of interest, without trying to stay on a grid or on lines. Potentials are recorded at all electrodes and one is used for a current source. Then a new electrode becomes a current source, and all potentials are recorded. Once an electrode has been used as a source, it is never used again. This large data set must be inverted in order to obtain interpretable information. The E-Scan technique is expensive but it has been used in the exploration for geothermal energy and minerals.Off-line profiling involves moving the sources along one survey line and recording potentials using electrodes planted along a different (usually parallel) line. There are also numerous other proprietary or experimental electrode configurations designed for 3D interpretation.

Azimuthal arrays are used to investigate the horizontal electrical anisotropy near the surface. Electrode configurations are usually one of the linear arrays (Wenner, dipole-dipole, etc.). However, instead of moving the array along a line (profiling), or expanding it about a central point (sounding), the array is rotated about a central point so that resistivity as a function of azimuthal direction can be plotted. Further details about the use of azimuthal arrays are given in an appendix III.

Borehole work often involves conceptually similar arrays with sources and receivers in various combinations of surface and down-hole locations. These are not discussed further here.

The following images show how electrodes are placed for the various named arrays. Electrodes placed on lines imply that the array is usually used for profiling. A circle at the array's centre implies that the array is generally expanded symmetrically about its centre for acquiring sounding data.

Figure 7. DC resistivity arrays

a. dipole-dipole (dpdp) Most common profiling configuration.

b. Several potential measurements are taken for each transmitter station.

c. pole-dipole (pldp) Compared to dpdp, more efficient (move only one source electrode), deeper penetration, but lower spatial resolution.

d. pole-pole (plpl) Compared to pldp, more efficient, deeper penetration, but lower spatial resolution.

e. gradient array Poor depth information but rapid reconnaissance of large areas.

f. Real section Potential electrodes move along lines between current source electrodes.

g. Schlumberger sounding

Distance "a" is on the order of one tenth of distance "b".

h. For soundings, "b" can remain unchanged, as long as a << b, and measured potentials are strong enough to record.

i. Wenner sounding The three spacings between electrodes are kept equal for all measurements.

j. For soundings all electrodes must be moved for each new datum.

Plotting raw data

How are apparent resistivities (calculated from measured potentials, currents and geometries) displayed for direct interpretation or for quality assessment? There is one conventional plotting scheme for soundings, while plotting of profiles depends upon the survey configuration.

Soundings

Soundings are used when the earth's electrical structure needs to be interpreted in terms of layers under a single location at the surface. The electrode spacings are varied symmetrically about a central location.

Therefore, data must be plotted as a function of electrode spacing rather than as a function of location. The resulting plot is called a sounding curve, and it arises as shown in this interactive figure (Figure 8). Only current electrodes are shown. Potentials would be measured inside current electrodes using either the Wenner or Schulmberger configurations.

At small electrode spacings current flows only in near-surface regions. Apparentresistivities look similar to the true resistivity of overburden.

As current flows deeper, apparent resistivities are influenced by the true resistivitiesof deeper materials.

The sounding curve begins to indicate that there are at least 2 layers under thislocation.

At very large electrode spacings most of the information reflects deeper groundbecause that is where most of the current is flowing.

The completed sounding curve.

Figure 8.

Profiling

Simple profiling involves moving a fixed array of four electrodes along a survey line. If there are no changes of spacing, then a simple graph of apparent resistivity versus line position would be adequate. A contour plot could be created if there is suitable

coverage of the area.

Pseudosections: When profiling, potentials are usually measured at several positions for every current source location. Results at wider separations between the potential pair and the transmitter pair provide some information about deeper structures. The conventional method of plotting such results is the pseudosection, so called because it is not a true geological cross-section. Values of apparent resistivity are plotted on the graph as shown in Figures 9 and 10. The vertical axis represents separation distance, NOT depth. When all values are plotted, the result is contoured. Interpretation is tricky and requires some experience.

Figure 9. Plotting a pseudosection of dipole-dipole data: current electrodes are spaced a metres apart (same for potential

electrodes), and current-voltage separation is n×a metres (n is an integer).

In the animation in Figure 10, the process of gathering and plotting profiling data is illustrated. The survey illustrated involves a dipole-dipole array with a = 2 metres, and n = 4.

Figure 10. For each measurement, notice the positions of current electrodes (left pair) and potential electrodes (right pair). Vertical axis of the plotted data is NOT depth; it is the value n, from 1 to 4 in this case.

1. Display the finished contoured pseudosection.

2. Return to the animation.

Gradient array: Large scale reconnaissance surveys are sometimes done using the gradient array (Figure 7e above). If the current sources are not moved, then the energizing field is the same for all measurements. There is, therefore, no inherent information about variations with depth, just like the case of gravity and magnetic surveys. Gradient array surveys are often displayed simply by contour plotting the results.

Real Sections: There is one variation of the gradient array that provides limited information about structures at depth. It is run under the trade name "real-section," but the plot is still a "pseudosection" because apparent resistivity data are plotted with no attempt to convert apparent (measured) resistivities into true (intrinsic) resistivities. In the following figures, red electrodes are the current source, and blue electrodes are the potential measurement electrodes. A row of potential measurements at fixed "a" spacing is gathered for each pair of current electrode placements. This is basically a set of seven (in this case) gradient surveys along the same line. At four stages in acquisition, the data look like the following:

Figure 11. Although the result is not a "real" section at all, data can be inverted as for any other pseudosection to provide a more legitimate estimate of the true Earth resistivity structure. This example shows data gathered over the San Nicolas deposit in Mexico.

After several measurements at one current source spacing.

After changing to narrower current spacing and re-doingpotential measurements.

Over halfway completed.

The completed "real-section" pseudosection.

Choice of array: Does the choice of array type matter for profiling? Appendix II has a brief comparison of pseudosections and the results of inverting data gathered using the arrays.

Processing options

Very little processing is applied to most raw resistivity data, other than to convert from apparent resistivities to potentials if that is needed for input to inversion programs. This is accomplished by using the apparent resistivity formula for the array in use, and the known geometric factor. If the current, I, is taken to be 1 (even if it was not 1 Amp in the field), then the result is a normalized potential in units of volts.

Interpretation of soundings and profiles

Interpretation of data is not part of this first version of the AGLO module on DC resistivity. Version 2 will explain current standard interpretation procedures.

For soundings, the earth is usually modeled as a sequence of layers. Forward modeling procedures are common and efficient. They involve estimating an initial simple model (a few layers) based on raw data, entering the estimated thicknesses and resistivities into a computer program that calculates data for the model, comparing these calculations to measurements, and adjusting the model until there is a good correspondance between calculated data and measured data. Some programs will perform parameteric inversion, in which the number of parameters is set (number of layers), and the code determines values for these parameters such that calculated and measured data are as similar as possible.

For profiling, pseudosections are rarely interpreted directly. 2D inversion schemes are used to estimate 2D models of the earth that have pre-determined characteristics. Most commonly, models consist of many rectangular cells of fixed size (often half the minimum electrode spacing). The codes perform non-linear optimization calculations to determine models that are both "smooth" (adjacent cells are as similar as possible) and are capable of generating a data set that is within pre-assigned error specifications on measured data.

More details will be provided in a subsequent version of this AGLO resource on DC resistivity surveying.

F. Jones, UBC Earth and Ocean Sciences, 01/09/2007 11:42:16

Physical principles of DC resistivity

On this page:| Introduction | Currents and voltages in a uniform Earth| Practical surveys

| Apparent resistivity | Anisotropic ground | Charge distribution | Forward modelling equations

Introduction

This chapter presents the important phyiscal principles upon which DC resistivity methods are based. The relations between current flow, potentials and resistivity in uniform ground are explained. This forms the basis for the concept of apparent resistivity derived from practical survey arrangements (two current and two potential electrodes planted at the surface). The effect of anisotropic ground upon measured potentials is then described. Finally, charge distribution is explained because it is a useful way of understanding how potentials arise at the surface due to variations in electrical conductivity underground. The forward modeling relations are also based upon charge distribution.

Currents and voltages in a uniform Earth

In order to derive a relation between measurments (I, V and geometry) and the required physical property (resistivity or ), we must start by identifying how these parameters relate to electric field strength, E (Volts per meter), current density, J (Amps per unit area), and resistivity (Ohm-m) in the three dimensional situation of a field survey (the introduction defines resistivity and conductivity).

Consider first a uniform Earth and one electrode, which is pumping a current, I, into the ground. We want to find the electric potential within the ground at a distance, r, from the current source. The current density in the ground is related to source current injected, and the potential measured at a surface defined by, r, is related to the electric field that exists in the ground because of the current which flows radially outward from its point source. These two relations will be combined with the 3D form of Ohm's law to end up with an expression for conductivity (the physical property we want) in terms of the current source, measured potential, and the distance.

First, by symmetry the current density out of the hemisphere of radius, r, is

and the current is flowing in a radial direction. Since J= E (Ohm's Law), the electric field must also be pointing radially outward. The relationship between the electric field and the potential is

Combining the expression for E, Ohm's Law and equation 1, we have

If we intergrate,

So the potential due to a point current electrode at the surface is:

.

The electric potential inside the earth caused by the radial flow of current is illustrated in the diagram below.

At the surface, where measurements are made, the potential is infinite at the current electrode because r=0, and it decays with distance.

Two electrode current sources

In a geophysical survey, current is injected into the ground using two electrodes. It is convenient to label the electrodes as

A: positive current electrode (carries a current +I)B: negative current electrode (carries a current -I)

For a uniform Earth, lines of current flow are shown in red in the figure to the right, and corresponding lines of equal potential (equipotential lines) are shown in black. Instead of the current flowing radially out from the current electrodes, it now flows along curved paths connecting the two current electrodes. Six current paths are shown. Between the surface of the earth and any current path we can compute the total proportion of current encompassed. The table below shows the proportion for the six paths shown (current path 1 is the top-most path and 6 is the bottom-most path).

Current Path % of Total Current

1 17

2 32

3 43

4 49

5 51

6 57

From these calculations and the graph of the current flow shown above, notice that almost 50% of the current placed into the ground flows through rock at depths shallower than or equal to the current electrode spacing.

The graph shown below plots the potential that would be measured along the surface of the earth for a fixed 2-electrode source. The voltage we would observe with our voltmeter (between purple electrodes) is the difference in potential at the two voltage

electrodes, ∆V.

Practical surveys

If there are two current (source) electrodes, the potential is the superposition of the effects from both. In a practical experiment (figure below), one electrode, A, is the positive side of a current source, and the other electrode, B, is the negative side. The current into each electrode is equal, but of opposite sign. For a practical survey, we need two electrodes to measure a potential difference. These are M, the positive terminal of the voltmeter (the one closest to the A current electrode), and N, the negative terminal of the voltmeter.

The measured voltage is a potential difference (VM - VN) in which each potential is the superposition of the effects from both current sources:

... so ...

Apparent resistivity

In the final relation, G is a geometric factor which depends upon the geometry of all four electrodes. Finally, we can define apparent resistivity (discussed in the measurements section) by rearranging the last expression to give:

. Similarly, the apparent conductivity is, .

We use the term apparent resistivity because it is a true resistivity of materials, only if the Earth is a uniform halfspace within range of the survey. Otherwise, this number represents some complicated averaging of the resistivities of all materials encountered by the current field.

Anisotropic ground

Structural anisotropy (for example, layering or fracturing) causes the simple form of Ohm's law to break down because current flow is not necessarily parallel to the forcing electric field. Instead of simply writing , we have to write

.

In homogeneous ground with single current and potential electrodes, the expression for V (voltage) in terms of resistivity and distance from the current source is (which was shown above). In anisotropic ground, there are different values of

resistivity for the horizontal and a vertical directions. The expression for voltage in terms of the two resistivities and distance is

, where is called the coefficient of anisotropy. See the table below for some values of

λ encountered in common geological materials.

Charge distribution

One of the fundamental principles regarding current flow is that away from the current electrode, all the current that goes into a body must come out. There are no sources or sinks of current anywhere, except at the current electrode itself.

Because there are no sources or sinks of current in the earth (conservation of charge), the normal component of current density is constant across any boundary where conductivity changes. That is, all of the current that flows into one side of the boundary must flow out the other side. Also, since lines of equal potential in an electric field are perpendicular to current flow, the electric field perpendicular to the normal component of current at the boundaries must also be constant across the boundary. Therefore there are two boundary conditions that must hold across interfaces where conductivity changes:

the normal component of current density, J, must be continuous, andtangential components of electric field, E, must be continuous.

Now, recall that Ohm's law is J = E. Since the normal component of J is continuous across a boundary where conductivity changes, the normal component of the E-field must NOT be equal. If 2 > 1 then E2 < E1. The following figure should clarify:

The only way an electric field can change at a boundary is if there is a charge on the boundary. If the current is flowing from a resistive medium to a conductive medium, then the charge buildup will be negative. If the current flows from a conductive medium to a resistive medium, then the charge will be positive. This is illustrated in the diagram below-left, where the anomalous body (blue) is more conductive than the host (yellow). In the figure below-right, the change in E-field is illustrated for a field crossing from a resistive medium (yellow) into a more conductive zone (blue). Tangential components are unchanged, but normal components of E are different so that normal components of J can remain unchanged. This change in direction is the origin of the concept that current lines "converge" upon entering a conductor, and "diverge" upon entering a resistor (illustrated with cartoons of the ore body in this chapter's introduction).

In fact, the charge density that accumulates will be related to the ratio of the two conductivities:

How are charges on boundaries related to DC resistivity surveying? Any electric charge produces an

electric potential. The Coulomb electrostatic potential is given by . All charge on

the edges of a body produce their own electric potentials, and at the surface (or anywhere else), the total potential is the sum of the potentials due to the individual charges (principal of superposition). These potentials are what we measure as voltages, and they are caused by charges building up on boundaries where conductivity changes, which in turn are caused by the current being forced to flow by the transmitter. Of course we don't measure absolute potential; rather, we measure the potential difference between two locations (say r1 and r2).

Equations for calculating DC measurements

Using the physics and appropriate mathematics to calculate a set of measurements is called "forward modeling." The DC resistivity forward modeling problem involves describing potentials everywhere as a function of conductivity in the ground, geometry, and input current. It requires three fundamental relations:

(a) Ohm's law.

(b) Electric field is the gradient of a scalar potential.

(c) Divergence of current density equals the rate of change of free charge density.

We want to obtain a differential equation and boundary conditions to define the forward problem that will allow us to relate conductivity everywhere to potential everywhere. Start by combining (a) and (b) to say , then plug this into (c) to get

. (2)

This holds for steady state conditions everywhere, except at the source position (r = rs), where it equals the input current, I. In other words, charge does not accumulate under steady state conditions, except at the point of the source.

Equation (2) can be re-written as

.

The Dirac delta function is used here to indicate that charge density is varying only at the point source of current.

Boundary conditions that must hold are:

The change of potential across the free surface is zero , and1.

V approaches 0 as r - rs approaches infinity.2.

This differential equation (4) and the two boundary conditions define the forward problem that relates conductivity everywhere in the ground to potential measured anywhere within or on the surface of the ground.

The discrete form

The problem can be discretized for calculation on a computer using finite difference or finite element methods. One approach is given in Dey and Morrison, 1979 (with more details in McGillevry, 1992). Essential aspects of their approach can be summarised as follows:

Application of the vector relation results in an expression that involves the grad2

operator. This allows a finite difference formulation.The problem is solved after transforming this modified form of equation (4) into the Fourier domain because it turns out to be easier.It is not trivial, but at each node of the mesh used to define the earth model, a finite difference form of the grad2 operator can be built involving algebraic expressions in constant values of conductivity and position within the cells adjacent to the node.Using this method, inverting one matrix will find values of potential at all nodes of the mesh. Nodes at the surface are the ones desired if a surface survey is being simulated.The matrix equation looks like C V' = S , where C is a sparse, diagonal, and banded matrix made up of the grad2 terms, V'is the vector of Fourier transformed potentials at each node, and S is the source vector, which is zero, except at the node where current is injected. The size of this matrix equation is MN by MN, where M is the number of vertical nodes, and N is the number of lateral nodes.For 2D probelms, it is common to discretize the Earth under the survey line into roughly 2*m+10 lateral cells, by roughly 2*n+8 cells vertically, where m is the number of stations along the survey line and n is the number of potential measurements per station. A problem with m=20 and n=8 would, therefore, have a matrix equation that is approximately 1000 by 1000.

Equation (4) can also be used directly, resulting in a finite element formulation, as opposed to the finite difference formulation just described. Transformation into the Fourier domain is used here as well.

Mesh of cells for 2D Discretization of the Earth

The following figure is a cartoon showing how one can consider the earth's subsurface under a survey line.

It is a 2D mesh of rectangular cells, each with constant resistivity.The source and measurement locations must be on nodes.The grid must extend beyond the region of interest so that boundary values can be reduced gradually to zero at the edges of the region where calculations are performed.The boundary value problem is solved using finite differences.The solution returns a potential at each node. For geophysical surveys carried out along lines, only surface nodes would be of interest for comparing to measured data.Superposition holds for potential differences.The same mesh would have to be used for forward calculations and for inversion.

References

Dey , A. and H.F. Morrison, 1979a, Resistivity modelling for arbitrarily shaped two-dimensional structures, Geophysical Prospecting, 27, 106-136.

1.

Dey, A. and H.F. Morrison, 1979b, Resistivity modeling for arbitrarily shaped three-dimensional structures: Geophysics, 2.

44, no. 4, 753-780McGillevry, P.R., 1992, Forward modelling and inversion of dc resistivity and mmr data., unpublished PhD. thesis, UBC.3.

F. Jones, UBC Earth and Ocean Sciences, 01/09/2007 11:43:54

DC resistivity instruments

Transmitters

High power and reliable constant current are the primary requirements. For small scale work, transmitters capable of sourcing up to several hundred milliwatts of power might be adequate. For larger scale work, it is possible to obtain transmitters that can source up to 30,000 watts. Current is usually injected as a 50% duty cycle reversing square wave; that is, current is on for several seconds, off for several seconds, on with reversed polarity, off, etc.

Sorting wire and equipment to begin a resistivity / IP survey for a mineral exploration target. The survey lines will be up to 2 kilometres long. Transmitter wire is on a back portable reel, and wiring for reading potentials is bundled around cans for generator fuel and water for the crew of 4 field operators.

A small transmitter for mineral exploration (2500 watts) sitting on the floor of the field van. A full-waveform receiving system's electronics and computer sit just behind. Power is supplied by portable generators placed some distance from the vehicle to

minimize the noise. (Midaas PCIP survey systems, 1994.)

Decay voltages in IP surveys (measured during a time domain transmitter's "off" stages) are often two orders of magnitude smaller than primary voltages. Therefore, very high-power transmitters are often desirable. For mineral exploration in conductive ground (where potentials will be small), it is possible to obtain transmitters capable of sourcing tens of kilowatts of power. Needless to say, these are rather dangerous systems, and definitely not portable! The figures below show several currently available transmitters.

Three transmitters and their power generators.

Images are from Zong Engineering and Research sales literature.

10 kW Scintrex resistivity-IP transmitter in use in the field.

The power generator is on the pickup truck.

Receivers

For DC resistivity sounding, a simple digital volt meter can be adequate. A more complex system may involve amplifiers, filters, transmitter synchronizing circuits, display, storage, many inputs for simultaneous recording of many potentials, and other features. Synchronization with the transmitter is essential if IP data are to be gathered, but it is not critical if resistivity information only is to be obtained. IP receivers also must be capable of recording several signal strengths covering several orders of magnitude because signals while the transmitter is on may be several volts, while decay voltages during the transmitter's "off" time may be only a few micro or millivolts.

Electrodes

In general, current injection and potential measurement electrodes are not interchangeable. However, automated acquisition

systems using smaller source currents do employ the same stainless steel electrodes, both for sourcing current and measuring potentials. This becomes more and more difficult as source currents increase because the ground can become altered by high current densities.

For injecting current, low impedance is required - i.e. good contact resistance is the primary concern. Stainless steel stakes, sheets of foil, wetted (and perhaps salted) ground, are all possible approaches to improving contact resistance.

For measuring potentials, low noise, non-polarizing (not necessarily low impedance) electrodes are the primary concern. Small lead plates buried in the soil will often do the trick. In more difficult situations, wet electrodes made from porous ceramic jars containing copper sulfate solution are required. See Corwin, 1990 for a good discussion of electrodes for this type of galvanic work.

Cables

Ordinary insulated wire on reels (possibly on a back-pack) for easy handling are most common (figure to the right).

For small scale work, some systems are available that use multiconductor cable, and possibly "smart" electrodes that can be switched between input and measurement functions by computer.For large scale work, this is not practical because of the large currents involved (up to a hundred Amps or so in some cases). Multiconductor cables with individual wires capable of carrying that current would be prohibitively heavy for mineral exploration surveys, which commonly involve profile lines several kilometres long.However, there are some systems that use multiconductor seismic cable for the potentials while requiring the normal single, heavy gauge wire for the current source.

Variations on the theme

Since the early 1990's manufacturers of instruments have been producing automated systems which permit the use of electrodes for either current source or potential measurements. Some systems involve planting a series of electrodes and wiring them together with a cable, which allows each electrode to be selected either as a potential electrode or as a current source. This procedure is being implemented in borehole projects, as well as surface surveys. Examples of systems that work in this manner are given in the following list (as of January 2007).

http://www.agiusa.com/index.shtml (images to the right) http://www.iris-instruments.com/Product/Brochure/syscal.htmlhttp://www.zonge.com/and others

Another arrangement involves a towed array system in which all potential and source electrodes are basically heavy metallic weights. This arrangement is efficient when the survey site is essentially flat and ground is relatively soft. Other similar systems used both for land and marine use use capacitively coupled electrodes rather than electrodes that make galvanic (direct) contact with earth materials. Two examples of this approach can be seen at at the Iris Instruments and Geometrics (image to the right) websites (as of January 2007), and others.

In the early 1990's receivers were developed that could record complete digitized potential waveforms rather than simply measuring voltages at specific times relative to the transmitted signal. These systems produce large data sets, but with field computers running the systems, storage is not a problem. Fully digitized waveforms have several potential advantages, including identification and removal of all types of noise, and interpretation of

subtle, 2nd and 3rd order effects caused by frequency dependant responses of subsurface materials. One example of a current full waveform system is the Titan 24 Deep Earth Imaging System of Quantec Geoscience (as of January 2007). An example of full waveform data gathered by MIDAAS Inc. in the early 1990's is shown to the right. The figure shows the "off-time" IP signals for 12 potential measurements taken using one current station. "On-time" signals are not shown.

References

Corwin, R.F., 1990, The self-potential method for environmental and engineering applications, in Geotechnical and environmental geophysics, Vol I: Review and Tutorial, (Ward, S.H. ed), Society of Exploration Geophysics, pg 127 - 146.

F. Jones, UBC Earth and Ocean Sciences, 01/09/2007 11:42:38

Does array type matter?

Click the buttons below to see the array sketch (top), data (middle) andinversion models (bottom) for four different survey array types over a syntheticmodel.

Pole-pole array

Dipole-dipole array

Pole-dipole left array

Pole-dipole right array

Evidently all surveys generate interpretable models, and geology interpreted from those models will likely be verysimilar. The differences are due to the changes in how currentflows in the ground. Zones with higher current densities will bemore reliably imaged. To analyze this issue a little morecarefully you could generate second models for each situationand create images with depth of investigation properlycharacterized.

Conventional wisdom is that of these arrays, the pole-pole tendsto illuminate more of the ground (to greater depths) but it hasthe lowest spatial resolution. It is also the most inexpensive toconduct in the field if survey lines are long and the survey area is rough. The dipole-dipole arrays have the highest resolution,shallowest depth of investigation, and are more expensive torun because four electrodes need moving instead of only two.The pole-dipole surveys are a compromise, which used to beharder to interpret, owing to assymetry of pseudosections, butnow inversion procedures remove this problem.

F. Jones, UBC Earth and Ocean Sciences, 01/05/2007 11:02:40

Azimuthal resistivity

Azimuthal resistivity surveys are designed to measure anisotropy caused by near-vertical dipping structure (due to bedding planeor to fracturing). The idea is to record resistivity at one location for a range of angular orientations of the array. In other wordsthe electrode array is rotated about a central point.

Data (apparent resistivities) are generally plotted on a rose diagram with resistivityincreasing outwards along the radius, and the angular position depending on the orientationof the array.

The method works well when there is little or no overburden, but the results tend to rotate asoverburden thickens. Eventually the rose diagram appears to be 90 degrees off what wouldbe expected when the direction of anisotropy in rocks below overburden is known. The effectappears to have been described well enough that results can be interpreted if overburdenthickness is known. See Sandberg and Jagel, 1996, Jansen and Taylor, 1996, and Carlson etal, 1996, all in the SAGEEP '96 proceedings.

The example shown here is from Sandberg and Jagel (1996). It indicates good correlationbetween the fracture orientation (and hence, hydraulic transmissivity) and apparentresistivity, which is higher in line with fractures, as predicted when the "anisotropy paradox"is accounted for.

Reference

Sauck and Zabik 1992 Azimuthal resistivity techniques and the directional variations of hydraulic conductivity in glacialsediments, Proceedings, Symposium on the Application of Geophysics for Engineering and Environmental Problems(SAGEEP) 1992, p 197.In the proceedings of the Symposium on the Application of Geophysics for Engineering and Environmental Problems(SAGEEP) 1996, there are three relevant papers between pages 31 and 61:

Sandberg and Jagel, 1996,Jansen and Taylor, 1996, andCarlson et al, 199

F. Jones, UBC Earth and Ocean Sciences, 01/05/2007 12:18:56