Geology Reference
In-Depth Information
Ω
m
400
5.0
Field
curve
300
4.0
3.0
200
ρ
a
150
2.0
1.5
100
Fig. 8.11
The interpretation of a two-layer
apparent resistivity graph by comparison
with a set of master curves.The upper layer
resistivity
r
1
is 68 W m and its thickness
z
1
is
19.5 m. (After Griffiths & King 1981.)
ρ
1
1.0
0.2
0.3
0.4
0.6
0.8
1.0
2.0
3.0
4.0 5.0
a/z
10
z
1
20
30
40 50 60
80 100
150 200 m
dimensionless form for a number of values of the reflec-
tion coefficient
k
by dividing the calculated apparent re-
sistivity values
r
a
by the upper layer resistivity
r
1
(the
latter derived from the field curve at electrode spacings
approaching zero), and by dividing the electrode spacings
a
by the upper layer thickness
z
1
.The curves are plotted
on logarithmic paper, which has the effect of producing a
more regular appearance as the fluctuations of resistivity
then tend to be of similar wavelength over the entire
length of the curves.The field curve to be interpreted is
plotted on transparent logarithmic paper with the same
modulus as the master curves. It is then shifted over the
master curves, keeping the coordinate axes parallel, until
a reasonable match is obtained with one of the master
curves or with an interpolated curve.The point at which
r
a
/
r
1
=
a/z
= 1 on the master sheet gives the true values
of
r
1
and
z
1
on the relevant axes.
r
2
is obtained from the
k
-
value of the best-fitting curve.
Curve matching is simple for the two-layer case since
only a single sheet of master curves is required. When
three layers are present much larger sets of curves are
required to represent the increased number of possible
combinations of resistivities and layer thicknesses. Curve
matching is simplified if the master curves are arranged
according to curve type (Fig. 8.9), and sets of master
curves for both Wenner and Schlumberger electrode
configurations are available (Orellana & Mooney 1966,
1972).The number of master curves required for full in-
terpretation of a four-layer field curve is prohibitively
large although limited sets have been published.
The interpretation of resistivity curves over multilay-
ered structures may alternatively be performed by
partial
curve matching
(Bhattacharya & Patra 1968).The method
ρ
a
Master 2
Master 1
Master 3
a
1
2
ρ
1
z
1
ρ
e
z
e
ρ
2
ρ
3
Fig. 8.12
The technique of partial curve matching. A two-layer
curve is fitted to the early part of the graph and the resistivities
r
1
and
r
2
and thickness
z
1
of the upper layer determined.
r
1
,
r
2
and
z
1
are combined into a single equivalent layer of resistivity
r
e
and
thickness
z
e
, which then forms the upper layer in the
interpretation of the next segment of the graph with a second
two-layer curve.
involves the matching of successive portions of the field
curve by a set of two-layer curves. After each segment is
fitted the interpreted resistivities and layer thickness are
combined by use of auxiliary curves into a single layer
with an equivalent thickness
z
e
and resistivity
r
e
. This
equivalent layer then forms the upper layer in the inter-
pretation of the next segment of the field curve with an-
other two-layer curve (Fig. 8.12). Similar techniques are
available in which successive use is made of three-layer
master curves.
