Download DC Resistivity: Modeling

Geology 5660/6660
Applied Geophysics
6 Apr 2016
Last Time: Intro to DC Electrical Resistivity
• DC Resistivity: inject electrical current across two (source
& sink) electrodes, measure voltage across two others.
• Governing equation derives from Maxwell’s equations
to get Ohm’s Law:
• Material property imaged is rock resistivity:
 Low for clays, shales, graphite; intermediate for soils/
unconsolidated seds; high for consolidated seds and
crystalline rocks
 Sensitive to sulfides, temperature, pore fluids
• Apparent resistivity
(1&2 current; a&b voltage
electrodes)
For Wed 6 Apr: Burger 265-301 (§5.1-5.4)
© A.R. Lowry 2016
Geology 5660/6660
Applied Geophysics
Last Time Cont’d: DC Electrical Resistivity
• Electrode Arrays:
 Wenner (constant spacing):
 Wenner-Lee (local voltage measurements)
 Schlumberger (move only current
electrodes):
 Dipole-dipole
 Pole-dipole (simple approach for tunnels/karst)
Modeling:
1
2
Current penetration for a layer over half-space:
Fraction of total current that penetrates below depth
of an interface, z, is
a is current electrode spacing,
r2 - r1
k=
r2 + r1
1
2
1.00
Fraction of Current
0.90
0.80
z=a
0.70
0.60
0.50
r2 - r1
k=
r2 + r1
z = 3a/2
0.40
0.30
z = 3a
0.20
0.10
0.00
-1.00 -0.80 -0.60 -0.40 -0.20
0.00
0.20
Resistivity Ratio k
0.40
0.60
0.80
1.00
Apparent resistivity for a layer over halfspace: For Wenner
array, given by:
array
Apparent resistivity for the two-layer over half-space case:
for various half-space resistivity values.
Apparent resistivity for the two-layer over halfspace case:
Dependence of apparent resistivity on thickness of middle layer
“Universal Curves"
Wenner array app depends only on 2/1, a/d1 for layer over a
halfspace
For 3+ layers:
• Rule of thumb: if layer thickness < 0.1 the depth to top of
layer, it cannot be resolved
• But also depends on resistivity contrast (thicker layers may
not be resolved if contrast is too small; transition of
apparent resistivity versus a-spacing is much sharper for
a resistive layer over a conductive layer than for the
opposite).
• When layer thickness is small relative to depth-to-top,
solution from sounding can be highly non-unique
Resist does either Wenner or Schlumberger array for
vertical sounding only (horizontal layers); and is
somewhat less adaptable than the other Burger programs
 = 100  m
 = 10  m
 = 500  m
 = 10000  m
10 m (Particularly because of
10 m forced logarithmic
10 m variation of a-spacing)