SME
Geophysics
Geophysical imaging
Use this for “A Wenner survey with electrodes 10 m apart passes 0.20 A and reads 0.30 V across the inner pair. Find the apparent resistivity.”
Diagram
R
=
V
I
=
0.3
0.2
=
1.5
Ω.
ρₐ
=
2πaR
=
2
×
π
×
10
×
1.5
=
94.25
Ω·m.
The
survey
reads
the
ground
down
to
about
a
2
=
5
m;
spread
the
electrodes
to
look
deeper.
This is an example. Type your own values to start a new problem.
ρₐ (Ω·m)
=
2π
×
a (m)
×
R (Ω)
V
Voltage
example
I
Current
example
Formulas
R
=
V
I
1.5
=
0.3
0.2
ρₐ
=
2π
×
a
×
R
94.2478 = 2π × 10 × 1.5
Assumptions
•
Four electrodes evenly spaced a apart in a line; the current goes in and out through the outer two, and the voltage is read across the inner two.
•
Wider spacing samples deeper ground, to about a ÷ 2.
•
ρₐ is the true resistivity only when the ground is uniform; layered ground gives a blend.
Step-by-step
WE KNOW
a = 10 m, V = 0.3 V, I = 0.2 A
FIND
resistance (R), apparent resistivity (ρₐ)
Step 1 · Find resistance (R)
Use R = V ÷ I
Ohm’s law: the voltage across the inner pair over the current through the outer pair.
R
=
0.3
0.2
R
=
1.5
Ω
Step 2 · Find apparent resistivity (ρₐ)
Use ρₐ = 2π × a × R
The Wenner geometric factor 2πa turns the resistance into a resistivity.
ρₐ = 2π × 10 × 1.5
ρₐ = 94.2478 Ω·m
Check
Put the numbers back in. Both sides should match.
1.5
=
0.3
0.2
✓
94.2478 = 2π × 10 × 1.5 ✓
Topic check
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