Electrical methods

Methods

Applied source

Natural source

Archaeology and Electrical Methods

Some Equipment     A Geophysical Contractor

Basic electricitycircuit.gif (4012 bytes)ohmslaw.gif (1624 bytes)

Ohm's law:

eq1.gif (1019 bytes)

In circuit diagrams, lump resistance, capacitance, inductance, etc. into discrete components; in Earth, these properties are distributed, although not necessarily uniformly, throughout Earth.

eq2.gif (1001 bytes) [amps m-2]

eq3.gif (1082 bytes) or eq4.gif (1081 bytes) [ohm m or Wm] ohmslaw2.gif (1678 bytes)

Current flow: homogeneous, isotropic Earthequipot_surface.gif (4073 bytes)

current flux, j, at distance r:

eq7.gif (1081 bytes)

by ohm's law:

 eq8.gif (1155 bytes) or: eq9.gif (1433 bytes)

Integrating this expression, gives eq10.gif (1139 bytes)

This gives the potential around a single current electrode. For 2 current electrodes (positive and negative) , just add the potentials due to the individual current electrodes:

eq11.gif (1422 bytes)

We know the current we are putting into the ground (i), so we could theoretically measure V at some point (r1 and r2, our distance from the 2 current electrodes would be known), so we could solve for r. our ultimate goal.

array.gif (3683 bytes)

However, we really must measure a potential difference, so we use two potential electrodes. At the second potential electrode,

eq12.gif (1430 bytes)

The potential difference between electrodes C and D is Vc - Vd. Solving for r gives the fundamental equation of the resistivity method:

eq13.gif (1723 bytes)

Since this holds only for homogeneous half-space, this equation gives the apparent resistivity for the "real" Earth. Sometimes the quantity V/I above is replaced by "R".

Wenner array

Probably the most common arrangement of electrodes is the Wenner array:

wenner.gif (2675 bytes)

To calculate the apparent resistivity for this array:

eq14.gif (1641 bytes)
eq15.gif (1666 bytes)
eq16.gif (1328 bytes), so
eq17.gif (1139 bytes)

The other configuration is the Schlumberger array. I'll let you look that up...

Field Methods

General

Typical Resistivities

Material

Resistivity W-m

Wet to moist clayey soil and wet clay

1s to 10s

Wet to moist silty soil and silty clay

Low 10s

Wet to moist silty and sandy soils

10s to 100s

Sand and gravel with layers of silt

Low 1000s

Coarse dry sand and gravel deposits

High 1000s

Well-fractured to slightly fractured rock with moist-soil-filled cracks

100s

Slightly fractured rock with dry, soil-filled cracks

Low 1000s

Massively bedded rock

High 1000s


Material Electric Resistivities
(room temperature)

Material

Resistivity W-m

Silver

1.6x10-8

Copper

1.7x10-8

Aluminum

2.7x10-8

Carbon (graphite)

1.4x10-5

Germanium*

4.7x10-1

Silicon*

2x103

Carbon (diamond)

5x1012

Polyethylene

1x1017

Fused quartz

>1x1019

*Values very sensitive to purity.


Geological Material Resistivities

material resistivity (ohm-centimetre)
Seawater (18oC) 21
Uncontaminated surface water 2x104
Distilled water 0.2 - 1x106
Water (4oC) 9x106
Ice 3x108
Rocks (in situ)
Sedimentary
   Clay, soft shale 100 - 5x103
   Hard shale 7 - 50x103
   Sand 5 - 40x103
   Sandstone 104 - 105
   Glacial moraine 1 - 500x103
   Porous limestone 1 - 30x104
   Dense limestone >106
   Rock salt 108 - 109
Igneous 5x104 - 108
Metamorphic 5x104 - 5x109
Rocks (laboratory)
Dry granite 1012
Minerals
Copper (18oC) 1.7x10-6
Graphite 5 - 500x10-4
Pyrrhotite 0.1-0.6
Magnetite crystals 0.6 - 0.8
Pyrite ore 1 - 105
Magnetite ore 102 - 5x105
Chromite ore >106
Quartz (18oC) 1014 - 1016

Electrical profiling

el-surv1.gif (8261 bytes)

el-surv2.gif (25984 bytes)

el-surv3.gif (55243 bytes)

Barnes Method for 2 layers, 2 electrode spacings

A

B

C

D

E

F

G

Electrode Interval, ft

R (W) (V/I, measured)

2pAR (W-ft)

2pAR (W-cm)

1/R (1/W)

Layer (1/W)

W-cm k=957.5

Station 1

 

 

 

 

 

 

30

13.9

2618

79796

0.072

 

 

35

3.1

683

20816

0.322

0.250

3830

Station 2

 

 

 

 

 

 

30

13.9

2618

79796

0.072

 

 

35

13.5

2972

90580

0.074

0.002

478750

 

 

 

 

 

 

 

Modified from "Earth Resistivity Manual," Soiltest, Inc., 1968, p. 8.

Explanation of table above

Electric Sounding

Flow lines for layer on half-space; different resistivity contrasts

Increasing the electrode spacing samples deeper:

el-soun1.gif (61531 bytes)

For the two cases of higher resistivity layer at depth, and lower resistivity layer at depth, apparent resistivity varies with electrode spacing like so:

el-soun2.gif (26946 bytes)

Data collected for such a survey might look like this:

Spacing,
m

 V    I 

Apparent
Resistivity,
W-m

1.0

   

50.0

2.0

   

50.0

5.0

   

49.0

10.0

   

38.0

20.0

   

21.0

50.0

   

10.0

100.0

   

9.0

Notice that the spacing is basically logarithmic.

Burger's Table 5-4 allows you to calculate the variation of apparent resistivity with electrode spacing for a layer-on-a-halfspace model.  Notice that when the electrode spacing is a fraction of the depth to the interface, the apparent resistivity is essentially that of the upper layer. When the electrode spacing is many times the depth to the interface, the apparent resistivity approaches the resistivity of the lower layer.

Schlumberger array

schlumberger.gif (1810 bytes)

Case Histories

Whately, MA: (Burger, p. 122-3, 302) Rural community in west-central MA.   In 1983 and 1984, pesticide contamination found in many homeowners' wells. Because water derived from shallow wells penetrating unconfined aquifer, contamination viewed with great alarm, resulting in state funding for study and possible remediation. Soon obvious that alternate water source necessary. Well logs indicated sand and gravel layer sandwiched between thick sequence of glacial-lake clays above and compacted glacial till and /or arkosic bedrock below. Clay layer forms impermeable between the deeper sands and gravels and the contaminated surface sands. It was reasoned that deeper sands and gravels might constitute a confined aquifer if areas of sufficient thickness could be discovered.   Preliminary geophysical investigations suggested the presence of anomalously deep bedrock areas which might be a prime location for the aquifer thicknesses required. Ultimately, seismic refraction and electrical resistivity supplemented by selected drilling sites delineated a buried river valley filled with the sands and gravels to extent sufficient to develop as community water source.

Resistivity effectively mapped bedrock depths which tended to correlate with location of buried aquifer.  Fig. 5-35(a) is a typical apparent resistivity curve. Steep downward segment is due to thick clay layer (about 50 m), and last upward segment reveals the presence of bedrock.  Analysis of curve yields bedrock depth of 71 m, which is abnormally deep for local area, but agrees with 75 m depth to bedrock determined from a well less than 1 km away. Gravel aquifer cannot be detected but is inferred from increased depth of bedrock (channel).

Fig_5-35a.gif (10241 bytes)

Easthampton, MA: (Burger, p. 303) This town also depends on confined aquifer, a glacial sand and gravel deposit resting on Triassic sedimentary rocks. It is overlain by glacial lake clays which vary in thickness, thinning to zero in recharge area, where the aquifer is exposed to the surface. The profile below was part of a study to determine the thickness and extent of the aquifer.  From this sounding, the clay layer thickness was estimated to be about 31 m.

Fig_5-35b.gif (10486 bytes)