Lecture 15 Resistivity-GPR

Death Valley Basin

Furnace Creek Fault

Resistivity

• SYSCAL R1 Plus – resistivity meter for medium-depth exploration

• can be used for:– geological mapping– groundwater exploration

Put 48 stainless steel electrodes in the ground every five meters

Attach the electrodes to the cable with clips

Press start on the box

Ohm’s Law

(12.1)

V=voltage (volts)

I=current (amps)

R=resistance (ohms)

V IR

+ -

Battery

current

resistance + -

V

R

I

Resistivity

Double length double RDouble area halve R

R proportional to length/area

(12.2a)

R esistivity

R area=

1Conductivity= (12.2b)

lengthR

area

length

current

length

Area

Archie’s law

3

resistivity of water

= porosity

S is fraction of pores containing water 1

, , , constants

a 0.5-2.5

n 2

m 1.3 to 2 depending on age larger numbers older rock

1 10 ohm-m

m nt w w

w

w

a s

a m n

2t

4t

. .,suppose 1, 1.5, 2,

then

1.5/

for =0.01, 0.1, 0.3, 0.5

1.5 10 ,150,17,and 6

if 1ohm-m

w

w

e g S a m

Wenner ArrayOhm’s law V=IR

Voltage (V)

Current (I)

Resistance (R)

a=2πa ΔV/I

Apparent resistivity

Electric Sounding

Shallowest = a

Deepest = spacing*(round down((number of electrodes -1) /3))

Field Data

Theory 1 (Telford et al., page 523)

4

buried source

1 surface source

2

IV

r

IV

r

r1 r2

V

I

r3 r4

V1+V2

I2

1r1−1r2

⎛

⎝⎜⎞

⎠⎟

V3 +V4 I2

1r3−1r4

⎛

⎝⎜⎞

⎠⎟

ΔV (V1 +V2 )−(V3 +V4 )I2

1r1−1r2

⎛

⎝⎜⎞

⎠⎟−1r3−1r4

⎛

⎝⎜⎞

⎠⎟⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

Wenner array

1 2 3 4

1

2

3

4

2 1

(1/ 1/ ) (1/ 1/ )

2

2

2

V

I r r r r

r a

r a

r a

r a

Va

I

Δ

Δ

Two Layer Model Wenner Spread

1

1/ 2 1/ 22 21

2 1

2 1

(1 4 )

where

1 1

1 (2 / ) 4 (2 / )

where

a w

mw

m

D

D kmz a mz a

k

+

+ +

+

%Resistivity function from Pages 529 Telford et al., Applied Geophysics%Second Editionclear faarray=x; %metersrho1=a(1);rho2=a(2);z=a(3);k=(rho2-rho1)/(rho2+rho1);

%Equation 8.38for i=1:length(aarray);aa=aarray(i); m=1:10000;D=sum( k.^m./((1+(2*m*z./aa).^2).^0.5) )-sum( k.^m./((4+(2*m*z./aa).^2).^0.5) );rhoa=rho1*(1+4*D);f(i)=rhoa;end

figure(1)plot(log10(aarray),log10(f),log10(aarray), log10(y),'*')

Mtlab Program for 2 Layer Resistivity

2

1

2

1

Pseudosections

Roughly how resistivity varies vertically and laterally

Electrical imaging creates ‘true’ section using tomographic theory

Turkey Flat Modeled Resistivity

Line 1

Line 2

• Two resistivity lines were laid out for Middle Mountain • The anomaly colored yellow is most likely the water table dammed

by the faults• From the 1st line to the 2nd line the water table increases in size

likely due to the increase in distance between the fault splays

Middle Mountain Resistivity

Furnace Creek Fault

Map view

SAF Splay

Model to explain increase in size of water table