Geology 228/378Applied and

Environmental GeophysicsLecture 6

DC resistivity Surveys

Direct current (DC) Resistivity

1. Introduction 2. Current flow in the ground 3. Schlumberger, Wenner, dipole-dipole,

pole-dipole arrays 4. Field methods and instrumentation 5. Data interpretation 6. Field Examples

Ohms Law (discovered in 1827)

IRV = Georg Simon Ohm (1787-1854)

It's Resistivity, NOT Resistance

LRA

ALR

=

=

So the unit for resistivity is ohm-meter

For a point source in an infinity medium, we have the resistance R and potential V expressed as

====

===

S

jdsIrI

rIIRV

rrr

ALR

44

44 2

Furthermore

rVIor

IrV

44

==

This resistivity is called the apparent resistivity. Only when the material is uniform, the apparent resisitivityis equal to the constant, real resistivity.

jrV

rV

Ir

rIVr

IrV

a ====22 444

Most geophysical resistivity surveys have the measurements occurred at the surface of the earth. The air above the ground is literally an insulator (zero conductivity) and the current only flows in the ground. Thus, for calculating the current density on an equal-potential sphere, the surface area becomes from the closed spherical surface to the surface of the lower-hemisphere, and the potential changes to

rIV

2

=Electric field and current

VgradV ==EV== EJ

r

I

V

In practice, the field surveys usually measure the Voltage V, other than the potential itself. This voltage V is the difference of potential between 2 points. IN DC resistivity surveys the voltage is usually measured by two electrodes planted on the surface.

3131 22 r

IrIVVV

==

r1

r3

I

V3V1

For the current can be physically flowing through the ground, wehave to have 2 poles: one for current injected in (source) and one for the current flow out (sink). Thus, both the source and sink will generate an electric potential, but with opposite polarity.

22

11

2

2

rIV

andrIV

=

=

r1r2

Dipole

And the total potential for the two poles is

)11(222 2121

21 rrI

rI

rIVVV ==+=

And the total voltage between two points generated by the two poles is

)1111(2

)22

()22

(

4321

4231

21

rrrrI

rI

rI

rI

rI

VVV

+=

=

+=

APPARENT RESISTIVITY

because

)1111(2 4321 rrrr

IV a +=

IVk

IV

rrrra

=

+= 1

4321

)1111(2then

GEOMETRIC FACTOR

K is the geometric factor that describes the geometry of the electrode configuration being used:

A B

M NV

I

1

4321

11112

+=

rrrrK

111112

+=

NBANMBAMK

IV

rrrr

a

= )(2

13

31 Pole-Dipole array

Schlumberger Array

1

22211211

11112

+=

PCPCPCPCK

2l 2l(n-1) 2l

IVnnnla

+= )1)(1(2

Data plotting

Dipole-Dipole Array

path gpropagatin :couplingreceiver pattern,radiation :,

spreading lgeometrica :signals source received, :,

LPP

GSR

RS

Pole pole Pole - dipole

Dipole - dipole

Wenner Schlumberger

ELECTRODE ARRAYS

CHOICE OF THE BEST ARRAY

Depends on:1) type of structure to be mapped2) sensitivity of the resistivity meter 3) background noise level

Things to be considered:1) depth of investigation2) sensitivity of the array to vertical and horizontal structures 3) horizontal data coverage4) signal strength.

DIPOLE-DIPOLE ADVANTAGES

Low EM coupling between current and potential circuits

Good for depth penetration

High resolution and is sensitive to vertical resistivity boundaries (e.g. dykes and cavities)

DIPOLE-DIPOLE DISADVANTAGES

Poor for vertical resolution of horizontal structures (e.g. sills or sedimentary layers)

Data collected from dipole-dipole array are easily affected by near-surface resistivity variations and therefore can produce noisy data at sites with cultural relics

Small signal strength for large values of n

Apparent Resistivity Pseudo-section for a Block model

Wenner

Pole-pole

Dipole - dipole

Pole-dipole

Block model response

Near Surface Layer

Near Surface Layer Response, Plan View

Near Surface Layer Response, Pseudosection

Buried Vertical Contact

Buried Vertical Contact Response, Plan View

Buried Vertical Contact Response, Pseudosection

3D Prism

3D Prism Response, Plan View

3D Prism Response, Pseudosection

Pole-pole array sensitivity

Pole-dipole array sensitivity

Dipole-dipole array sensitivity

Wenner array sensitivity

Schlumberger array sensitivity

Resistivity Surveys

AGI Sting R-1 and the Swift automotive switchbox

DC Resistivity Interpretation

path gpropagatin :couplingreceiver pattern,radiation :,

spreading lgeometrica :signals source received, :,

LPP

GSR

RS

Electric current in layered media

The current flow in the layered media deviates from that observed in the homogeneous media. In particular, notice that in the layered media the current flow lines are distorted in such a way that current preferentially seems to be attracted to the lower-resistivity portion of the layered media. In the model on the left, current appears to be pulled downward into the 50 ohm-m layer. In the model on the right, current appears to be bent upward, trying to remain within the lower resistivity layer at the top of the model. This shouldn't be surprising. What we are observing is the current's preference toward flowing through the path of least resistance. For the model on the left, that path is through the deep layer. For the model on the right, that path is through the shallow layer.

Sting/Swift prg: DIP-DIP title2 unit electrode spacing3 array No. dip-dip=3193 No. of data points1 1-middle point used0 0-no IP1st: apparent rho-location 2nd: P1P2 spacing3rd: dipole separation factor n4th: apparent resistivity3.000 2.000 1 2961.0005.000 2.000 1 2769.0007.000 2.000 1 1040.3009.000 2.000 1 2994.30011.000 2.000 1 779.580

.45.000 2.000 1 10305.00047.000 2.000 1 6955.20049.000 2.000 1 5515.00051.000 2.000 1 4435.9004.000 2.000 2 2168.8006.000 2.000 2 1696.4008.000 2.000 2 1233.200

DC Resistivity Interpretation

path gpropagatin :couplingreceiver pattern,radiation :,

spreading lgeometrica :signals source received, :,

LPP

GSR

RS

CURRENT CONDUCTION IN ROCKS

Electrolytic conduction occurs by the relatively slow movement of ions within an electrolyte

Electronic conduction is the process by which metals, for example, allow electrons to move rapidly, so carrying the charge

This is applicable in zero and low frequency case

crystalline rock can lead to low resistivities if they are filled with fluids.

The resistivities of various earth materials are shown below.

Material Resistivity (Ohm-meter)Air Pyrite 3 x 10^-1Galena 2 x 10^-3Quartz 4 x 10^10 - 2 x 10^14Calcite 1 x 10^12 - 1 x 10^13Rock Salt 30 - 1 x 10^13Mica 9 x 10^12 - 1 x 10^14Granite 100 - 1 x 10^6Gabbro 1 x 10^3 - 1 x 10^6Basalt 10 - 1 x 10^7Limestones 50 - 1 x 10^7Sandstones 1 - 1 x 10^8Shales 20 - 2 x 10^3Dolomite 100 - 10,000Sand 1 - 1,000Clay 1 - 100Ground Water 0.5 - 300Sea Water 0.2

Archies law:In the ground, and in low frequencies, electricity is essentially conducted through the interstitial water in pores by ionic transport

wnmSa =

effective formation resistivity;wpore water resistivity; porosity;S saturation;a 0.5-2.5;m 1.3-2.5;n ~2.

E C V ar i at i on wi t h Dept h

0

5

1 0

1 5

2 0

2 5

5 0 1 0 0 1 5 0

E C ( mi cr omhos/ cm)

EC Variation w ith Depth

0

5

10

15

20

25

50 100 150

EC (micromhos/cm)

Dept

h (f

t)

Cr Variation with Depth

0

5

10

15

20

25

0 5 10 15 20

Cr (mg/l)

Dept

h (f

t)

EC vs Cr

y = 0.2827x - 19.9R2 = 0.8969

0

5

10

15

20

0 50 100 150

EC ( micromhos/cm)

Cr

( mg/

l)

DC Resistivity Case Studies

=

L

ds

RS ePPGSR)(

)()(

path gpropagatin :couplingreceiver pattern,radiation :,

spreading lgeometrica :signals source received, :,

LPP

GSR

RS

Detection of Saltwater Intrusion along the Noyo

River, California

Resistivity and Seismic Survey Results

N

NEX Gas Station Site

ESTCP LTM Test Cell

GeoVIS/Piezocone Facility

Plume Control and Containment System NVBC Port Hueneme In-Situ BioBarrier

(Leading Edge)

ESTCP NFESC/ASU In-Situ BioBarrier

NVBC Port Hueneme In-Situ BioBarrier

(Mid Plume)

Patterson Rd.

Plea

sant

Val

ley

Rd.

23rd

Ave

.

Pacific Ave.

NN

NEX Gas Station Site

ESTCP LTM Test Cell

GeoVIS/Piezocone Facility

Plume Control and Containment System NVBC Port Hueneme In-Situ BioBarrier

(Leading Edge)

ESTCP NFESC/ASU In-Situ BioBarrier

NVBC Port Hueneme In-Situ BioBarrier

(Mid Plume)

Patterson Rd.

Plea

sant

Val

ley

Rd.

23rd

Ave

.

Pacific Ave.

Piezocone GeoVIS Demonstration

Utility PoleUtilityShed

WaterStorageTanks

20V

ehic

leG

ate

20V

ehic

leG

ate

4 Pe

rson

nel

Gat

e100

60

W1(Inject)

W3

W2

Utility PoleUtilityShed

WaterStorageTanks

20V

ehic

leG

ate

20V

ehic

leG

ate

4 Pe

rson

nel

Gat

e100100

60

W1(Inject)

W3

W2

N

Note: Layout displayed with 10 x 10 grid

NN

Note: Layout displayed with 10 x 10 grid

N

Electrode locations for DC resistivity Surveys

East of Building 401East of Building 401Lot

AGI

1

2

3

4

56

7

8

9

10

1112

13

14

15

16

1718

19

20

21

22

23

24

25

26

27

28

Wells from previous extraction systemHydraulic Test WellsWells from previous extraction systemHydraulic Test WellsWells from previous extraction systemHydraulic Test WellsProposed electrode location

2/28/2005

4/1/2005

4/1 - 2/28, 2005

Day 00Day 01Day 02Day 03Day 04Day 07Day 11Day 16Day 23Day 31Day 37Day 41

0 5 10 15 20 25 30 350

0.5

1

1.5

00 0000 00

0000

0000 00 00 00

0101

01

01

01

01

01

01

0101

01

0202 02 02

02

02

02

0202

02 02

0303

0303

03

03

03

0303 03 03

04 0404 04

04

04

04

04

0404

04

0707 07 07

0707

0707

07 07 07

1111 11

11 1111

1111

11 11 11

16 16 16 1616

1616 16 16

1616

2323

23 23 23 23 23 23 23 23 2331 31

31 31 31 31 31 3131

313137 37

3737

3737 37

3737

373741 41 41 41

4141 41 41 41

4141

Y distance (ft)

DEC

(S/m

)

Z=12 ft

0 5 10 15 20 25 30 350

0.5

1

1.5

00 0000 00 00

0000 00 00 00 00

0101

01

01

01

01

01

0101 01 01

0202 02 02

0202

02

0202

0202

03 03 0303

0303

0303

0303 03

04 0404 04

04

04

04

0404 04 04

07 0707 07 07

0707

0707 07 07

1111 11

11 1111

1111

11 11 11

16 1616 16 16 16 16 16 16 16

1623

2323 23 23 23 23 23 23 23 23

3131

31 3131 31

31 3131

3131

37 37 37 37 3737 37

3737

3737

4141

41 4141 41 41 41 41 41 41

Y distance (ft)

DEC

(S/m

)

Z=15 ft

Homework:

The averaged electric conductivity of the groundwater found at the National Chromium site is about 100 microSiemensper centimeter.It is equivalent to 10 milliSiemens per meter.The averaged formation conductivity found by the DC resistivity tomography is 1milliSiemens per meter.

By assuming the porosity is 35%, 100 % saturation, and a = 1.0, m=2.0 and by Archies law, what is the estimated formation conductivity?

Geology 228/378Applied and Environmental GeophysicsLecture 6Direct current (DC) ResistivityAPPARENT RESISTIVITYGEOMETRIC FACTORDIPOLE-DIPOLE ADVANTAGESDIPOLE-DIPOLE DISADVANTAGESResistivity SurveysCURRENT CONDUCTION IN ROCKSDetection of Saltwater Intrusion along the Noyo River, CaliforniaResistivity and Seismic Survey Results