lecture 15 resistivity-gpr
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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