Chap 2 - Self Potential

7/30/2019 Chap 2 - Self Potential

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Chapter 2

Self Potential/Spontaneous Potential

2.1 Introduction

If two electrodes are buried in the ground and connected to a voltmeter a potential difference is usually

measured. Such electrical potentials can be very variable in amplitude and can show high values in regions

where sulfides are present. These potentials can be the result of a variety of phenomena the principal of which

involve oxidation and reduction reactions.

Self potentials can be divided into two main groups:

1. Background Potentials are generally of the order of mV and mainly arise due to water circulation, small

mineral quantities, biologic and topographic effects, however human activities may also produce SP signals.

2. Mineral Potentials occur in regions of anomalous concentrations of sulfide ores (also near graphite) and

can be of the order of hundreds of mV or even V.

Do not be misled by the name background potential as in many applications these are the signals of

interest; however, we will not explore all of the mechanisms which generate these potentials.

Surface

Water Table

Current

Flow Negative Ions

Ele

ctrons

+

Figure 2.1: A mechanism for mineral self-potential anomalies (adapted from Sato and Mooney (1960) via Keareyet al. (2002)).

Significant SP anomalies are associated with massive sulfide deposits, but how are they generated? Unfor-

tunately a definitive explanation does not exist and it may well be that multiple processes play a role depending

on the particular setting. A generally favoured explanation, proposed by Sato and Mooney (1960), applies to

ore bodies that straddle the water table (figure 2.1). Above the water table (in the incompletely saturated

10


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vadose zone) dissolved electrolytes gain electrons from the ore body and are reduced. At depth (in the fully

saturated phreatic zone) an oxidation reaction occurs transferring electrons back to the ore body. Electrons

are then conducted through the ore body completing the circuit. Unfortunately, this proposal can not explain

all SP observations; e.g. the large anomalies associated with poorly conductive sphalerite bodies and observed

anomalies in excess of their theoretical maximum.

Streaming or electrokinetic potentials are generated by the flow of an aqueous electrolyte through narrow

channels (pores). The amplitude of the resulting potential drop depends on both the electrical (e.g. resistivity)

and mechanical (e.g. viscosity) properties of the fluid and on the conditions driving the flow. The effect depends

on interaction between the liquid and the solid surface (an effect called the zeta potential). This potential can

be present (and significant) in situations involving groundwater flow, such as dam seepage, geothermal settings

or groundwater pulses following major storms. SP anomalies generated by this mechanism may be used to map

subsurface barriers to, or conduits of, flow.

2.2 SP in the Field

SP measurement is an electrochemical process, therefore contact with the ground must be adequate. In practice

non-polarizing electrodes are used otherwise the potentials generated by reactions between the ground and the

electrodes would mask the target signal. Porous-pot electrodes are one example of non-polarizing electrodes,

they consist of a metal strip (such as Cu or Ag) immersed in a saturated solution of the same metal (e.g.

CuSO4 or AgCl) within a porous pot (figure 2.2a). The solution slowly leaks through the porous pot creating

the contact with the ground.

To check for the non-polarization of the electrodes field measurements should also be made with the

electrode positions reversed. The two SP values obtained should have the same absolute value. It is also

important that the resistance of the voltmeter be sufficiently large that the equipment draws a minimal amount

of current from the ground (in practice this means a resistance of at least 108 ). To ensure good ground

contact of the electrodes should be kept wet and shaded when a fixed electrode is used; the initial potential

difference between the electrodes should be measured and the contact resistance kept to a minimum.

metal

saturated

solution

porousbottom

a)

!V

Rv

R1 R2

b)

Figure 2.2: a) Schematic of a porous-pot non-polarizing electrode for use in SP studies. b) The SP circuit, R vshould be large and R1 + R2 small.


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SP 12

2.2.1 Field measurements

There are different possible arrangements in which the equipment can be deployed.

Fixed Spacing In this approach the distance between the two electrodes is kept constant. A grid is established

and measurements are taken by moving both electrodes along the grid either maintaining (figure 2.3a) or

alternating (figure 2.3b) the electrode positions. If the electrode orientations are switched this must be recorded

as it will change the sign of the measured potential difference. Fixed orientation measurements requires that

both electrode positions are changed between each reading; only one electrode position is changed between

readings in the alternating orientation deployment.

The gridded measurements should ultimately form a closed loop and the sum of all potentials within that

loop should equal zero (the potential at our starting point should be constant). If our potential loop does not

sum to zero, then the remainder represents an error that should be distributed among the readings. After checks

and correction the gridded potential measurements are used to draw maps of the equipotential lines as well as

profiles.

Advantages of the fixed spacing approach include the need for only a short wire and the reduced importance

of telluric currents (generally long-wavelength currents induced in the ground by geomagnetic fluctuations). A

disadvantage is that generally two operators are required to move the system.

!V1 !V2 !V3a) !V1 !V2 !V3b)

Figure 2.3: Segments of fixed spacing grids for SP deployment in which electrode orientation a) remains fixedand b) is alternated. In both cases three potential difference measurements are taken; the electrode movesbetween readings 1 and 2 are shown by the short-dashed arrows, the electrode moves between readings 2 and 3by the long-dashed arrows.

Fixed Electrode In this approach one electrode is kept at a single position and the other moved through

the grid. An arbitrary value is assigned to the potential at the fixed electrode from which all others are

calculated. Advantages of this system include generally reduced measurement errors and that it can be more

easily performed by a single operator. However a longer wire is required and the larger separation between

electrodes may allow telluric currents to influence the results.

!V1

!V2

!V3

Figure 2.4: Segment of fixed electrode grid for SP deployment. Three potential difference measurements aretaken; the electrode moves between readings 1 and 2 are shown by the short-dashed arrows, the electrode movesbetween readings 2 and 3 by the long-dashed arrows.


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2.2.2 Applications

Self potential measurements are used in sulfide exploration, geothermal exploration, to locate faults or springs

in groundwater studies, and in geotechnical monitoring of leakage of water from dams or canals, or of leachate

from landfills. SP can also be used to search for pipelines, monitor pipeline corrosion, check for electrical powerleakage and in well logging (one electrode is kept at the surface and the other lowered into the borehole).

Downhole SP measurements of streaming potential can be used in reservoir monitoring to track the process of

injected water towards the oil extraction well.

In general, SP is employed in small areas for certain specific problems. Conducting ground is essential -

ice is no good. Practical problems to keep an eye out for include electrode polarization; rain, which changes the

contact strength and ground conductivity; telluric variations which can have daily drifts; artificial sources of

electricity in the vicinity; and a shift in the equipotential lines in relation to an ore body lying at the boundary

between units of vastly different resistivity since current will flow preferentially in the less resistive unit.

2.3 SP Anomaly Theory

2.3.1 A Linear Conductor

l

A

I

V1 V2

Figure 2.5: A current I flows through a linear conductor of length and cross sectional area A. The potentialat the ends of the linear conductor are V1 and V2.

Consider a linear conductor (figure 2.5); from Ohms law we can relate the potential drop to the resistance

and current

V1 V2 = RI (2.1)

where R is the resistance of the conductor. Recall from equation (1.1) that the total resistance of the conductor

depends on its resistivity as well as and A; therefore

V1 V2 = (V2 V1) =

AI

or I = A

(V2 V1)

(2.2)

In the limit of a vanishingly small element ( d) we obtain

I= A

dV

d(2.3)

The current density is defined as (j = I/A) so that

j = 1

dV

d(2.4)


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2.3.2 Current Point Source - Infinite Medium

For a point source of electric current in an homogeneous, isotropic and infinite medium the equipotential surfaces

are spheres centred on the point source (figure 2.6). From the definition of current density we have

j = 1dVdr

(2.5)

where dV/dr is the potential gradient in the r direction. Or, if we prefer

dV

dr= j

= I4r2

(2.6)

where we have used A = 4r2. The potential at a given point can therefore be found by integration

V = I

4r2dr (2.7)

We are free to take any point as our zero potential (i.e. as our reference); however, we note that dV/dr as r 0. Therefore, we take infinity as our reference so that we can evaluate equation (2.7); our integralbecomes

V(r) =

r

I4r2

dr =I

4r(2.8)

If we had a sink instead of a source, then the direction of current flow would be reversed (I I) and thepotential will be

V(r) = I4r

(2.9)

RdrA

I

+

Figure 2.6: An electric current point source

2.3.3 Point Source in a Half Space

Measurements are carried out on the Earth - which is not infinite! At the surface of the Earth there is a very

large jump in resistivity (air is an excellent insulator) so that the correct geometry is closer to that of the

semi-infinite half-space.


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I

air !!"

!1

+

Figure 2.7: An electric current point source in a half space

In this geometry the equipotential surfaces are half spheres A = 2r2 and the potential for a source is

V(r) =I

2r(2.10)

and for a sink

V(r) = I2r

(2.11)

Another way of thinking about the half-space problem is to consider that since the current can not flow up

through the surface and enter the air any current that would have done so must flow into the ground instead.

That is, although the source produces the same total current, the current flow in the ground is doubled; replacing

I with 2I in equations (2.8, 2.9) gives the half-space potentials. From the point of view of an observer below

the surface it is as if the source was doubled. The infinite resistivity contrast at the surface acts somewhat like

a mirror, reflecting any current that approaches it. This remains true if the source is located at depth and

leads to the method of images; the potential within the half-space is the same as that in an infinite space with

a second point source (the source image) located above the surface, like a reflection in a mirror (see figure 2.8).

Rather than consider one source in a half-space it is equivalent to consider two sources in an infinite space.

surface

+

+

h

h

r1

r2

S

SI

P

Figure 2.8: A source (S) located a depth h below the surface. In the method of images we reflect the lowerhalf-space in the surface, resulting in a second source, the source image (SI). The potential is calculated at pointP as if both sources were located in an infinite medium.

To calculate the potential within the half-space we consider an observation point (P) located at depth and

find

VP = VS + VSI =I

4r1+

I

4r2(2.12)

Note that we are using the potential formula for point sources in an infinite medium, due to the perfectly

reflective surface causing us to see what appears to be two sources in an infinite space. Less colloquially,


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the observed current and potential due to a single source in a half space is identical to that from the method of

images inspired model of two sources in an infinite space. If we move either the observation point or the source

to the surface, then r1 = r2 = r and we find

VP = VS + VSI =

I

2r (2.13)

2.3.4 Multiple Poles

The method of images effectively turns the single source problem into a multiple source problem. In geologic

settings there will often be multiple sources and/or sinks and there may be non-point sources. As we saw

above, determining the potential from multiple sources is relatively straightforward, electric potential is a scalar

quantity and thus the individual potentials can be summed in the familiar algebraic fashion. Determining the

net current flow is more complicated as current (or current density) is a vectorquantity having both a magnitude

and direction and it must be added using the rules for vector algebra (see figure 2.9).Assuming for the moment that the source and sink are in an infinite medium and are of equal strength,

the potential is

V = VS+ + VS =I

4r1 I

4r2(2.14)

Note that at any point that is equidistant from the two sources ( r1 = r2) the net potential is zero.

+

!

r1

r2S+

S!

j+

j!

jR

Figure 2.9: An electric current point source (S+) and point sink (S) produce current densities j+ and j at agiven point. The total, resultant current density (jR) is found through vector addition.

The magnitude of the current densities for the source and sink are found from equation (2.4) and theamplitude of the resultant current density is

|jR| =I

4

1

r14+

1

r24(2.15)

If the source and sink are of equal strength all current lines will begin and end at S+ and S.

For multiple poles (i.e. point source and sinks) distributed in three dimensions the potential or current

density is found by extending the procedure above to sum over all poles. For non-point sources (or sinks)

the summation becomes an integral. In a semi-infinite half-space the procedure is the same except that the

half-space potential formula (or the method of images) is used.


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2.3.5 Potential of an Ore Body

Suppose that we are doing an SP survey near a buried sulfide ore body, what sort of signal should we expect?

Let us approximate the ore body as some sort of lens with a current point sink at its top and a point source at

its bottom (figure 2.10). We will set our coordinates such that the surface is the xy-plane, and the current poleslie in the xz-plane (note that we have taken z to be positive down). The position ofS is therefore (0, 0, h1)

and that ofS+ is (a, 0, h2). Our measurement point is on the surface P(x,y, 0).

+

r1

r2

S+

S!

!

h1

h2

a

P

x

y

z

Figure 2.10: A buried ore body that is generating an electric current point source (S+) and point sink (S).SP measurements will be taken on the surface at point P.

The potential at P is the sum of the potentials from the sink and source which are

VS = I2r1 =I2

1x2 + y2 + h1

21/2 (2.16)

VS+ =I

2r2=

I

2

1

(x a)2 + y2 + h221/2

(2.17)

so that

VT(x, y) =I

2

1

(x a)2 + y2 + h221/2 1

x2 + y2 + h121/2

(2.18)

If a profile is taken directly over the body parallel to its length (i.e. along the x-axis) we have

VT(x) = I2

1(x a)2 + h22

1/2 1x2 + h1

21/2 (2.19)

An example contour map and profile are given in figure 2.11 for a dipping ore body characterised by a = 10,

h1 = 10, h2 = 15 (arbitrary units). Note that the anomaly peaks are not simply located above the poles and

that the negative anomaly associated with the shallower, negative pole is much more pronounced even for this

relatively shallowly dipping body ( 26.5). A vertically body will have no positive anomaly and the negativeanomaly will be centered on the negative pole (in an homogeneous medium).

2.3.6 Depth Calculation

The shape of the SP anomaly can be used to estimate the depth of the ore body. Let us first consider a body

with infinite length, in this case the anomaly is caused by the sink point only (figure 2.12a). The potential


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SP 18

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!"#$

!"#%

!"#&

!"#'

"

"#'

"#&

(!)*+,-

./0120345+67

-

(!)*+,-

8!9*+

:-

*

*

!!" " !"!%"

!&"

!'"

"

'"

&"

%"

!"#$

!"#%!

!"#%

!"#&!

!"#&

!"#'!

!"#'

!"#"!

"

"#"!

a) b)

Figure 2.11: The SP anomaly of an ore body shown by a) contours in plan view, b) a profile along the x-axis.

associated with this pole is

V = I2

1

(x2 + h2)1/2(2.20)

This function (which is plotted in figure 2.12b) goes to zero as x and has a minimum at x = 0 with

Vmin = I

2h(2.21)

!!" !# !$ !% !& " & % $ # !"!!

!"'(

!"'#

!"')

!"'$

!"'*

!"'%

!"'+

!"'&

!"'!

" x

V

Vmin

V1/2

-x1/2 x1/2

b)

x

!

S!

hr

"

P

a)

Figure 2.12: a) Geometry for the problem of calculating depth to an infinite body. b) The SP anomaly profile.

We can calculate the value of V that is one half ofVmin and which will occur at a x1/2. This leads to

V1/2 = I

4h

V1/2 = I

2x21/2

+ h21/2

i.e. I2h

= I

2 x21/2 + h21/2

1

2h=

1x21/2

+ h21/2


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!!" !# !$ !% !& " & % $ # !"!!

!"'(

!"'#

!"')

!"'$

!"'*

!"'%

!"'+

!"'&

!"'!

"

x

V

Vmin

V1/2

-x1/2 x1/2

b)

x

!S!

h

r

"

P

a)

+S+

r2

r1

l

#

Figure 2.14: a) Geometry for the problem of calculating depth to a vertical, finite body. b) The SP anomaly

profile.

will again provide a set of intersecting rays.

Both of the approximations we have considered provide estimates of the maximum depth to the current

sink (i.e. the top of the body) and the true position is often somewhat shallower. One major issue is the choice

of the zero level which must be selected correctly to determine the value of Vmin. When the profile is drawn the

reference (zero) potential needs to be set as the value for which the potential becomes constant far from the

body, this process is helped by a good lateral extent of measurements and a low level of noise.

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Chap 2 - Self Potential