Geology Reference
In-Depth Information
layered model derived by an approximate interpretat-
ion method in order to improve the correspondence
between observed and calculated functions.
In addition to this indirect modelling there are also a
number of direct methods of interpreting resistivity data
which derive the layer parameters directly from the field
profiles (e.g. Zohdy 1989). Such methods usually
involve the following steps:
1.
Determination of the resistivity transform of the field
data by direct filtering.
2.
Determination of the parameters of the upper layer
by fitting the early part of the resistivity transform curve
with a synthetic two-layer curve.
3.
Subtraction of the effects of the upper layer by reduc-
ing all observations to the base of the previously deter-
mined layer by the use of a
reduction equation
(the inverse
of a recurrence relationship).
Steps
2
and
3
are then repeated so that the parameters
of successively deeper layers are determined. Such
methods suffer from the drawback that errors increase
with depth so that any error made early in the interpre-
tation becomes magnified. The direct interpretation
methods consequently employ various techniques to
suppress such error magnification.
The indirect and direct methods described above have
now largely superseded curve-matching techniques and
provide considerably more accurate interpretations.
Interpretation of VES data suffers from non-
uniqueness arising from problems known as
equivalence
and
suppression
. The problem of equivalence (see e.g.
van Overmeeren 1989) is illustrated by the fact that
identical bell-shaped or basin-shaped resistivity curves
(Fig. 8.9(a)) can be obtained for different layered models.
Identical bell-shaped curves are obtained if the product
of the thickness
z
and resistivity
r
, known as the trans-
verse resistance, of the middle layer remains constant.
For basin-shaped curves the equivalence function of the
middle layer is
z/
r
, known as the longitudinal conduc-
tance. The problem of suppression applies to resistivity
curves in which apparent resistivity progressively in-
creases or decreases as a function of electrode spacing
(Fig. 8.9(b)). In such cases the addition of an extra inter-
mediate layer causes a slight horizontal shift of the curve
without altering its overall shape. In the interpretation of
relatively noisy field data such an intermediate layer may
not be detected.
It is the conventional practice in VES interpretation
to make the assumption that layers are horizontal and
isotropic. Deviations from these assumptions result in
errors in the final interpretation.
C
4
C
2
θ
C
0
C
1
C
3
C
5
Fig. 8.14
Apparent current sources caused by a dipping interface.
The sources C
1
-C
5
are successive images of the primary source C
0
in the interface and the surface.The sources lie on a circle centred
on the outcrop of the interface, and their number is dependent
upon the magnitude of the dip of the interface,
q
.
The assumption of isotropy can be incorrect for indi-
vidual layers. For example, in sediments such as clay or
shale the resistivity perpendicular to the layering is usu-
ally greater than parallel to the direction of the layering.
Anisotropy cannot be detected in subsurface layers dur-
ing vertical electrical sounding and normally results in
too large a thickness being assigned to the layers. Other
anisotropic effects are depth-dependent, for example the
reduction with depth of the degree of weathering, and
the increase with depth of both compaction of sediments
and salinity of pore fluids.The presence of a vertical con-
tact, such as a fault, gives rise to lateral inhomogeneity
which can greatly affect the interpretation of an electri-
cal sounding in its vicinity.
If the layers are dipping, the basic theory discussed
above is invalid. Using the optical analogue, the number
of images produced by a dipping interface is finite, the
images being arranged around a circle (Fig. 8.14). Be-
cause the intensity of the images progressively decreases,
only the first few need to be considered in deriving a
reasonable estimate of the resulting potential. Conse-
quently, the effect of dip can probably be ignored for in-
clinations up to about 20°, which provide a sufficient
number of images.
Topography can influence electrical surveys as
current flow lines tend to follow the ground surface.
Equipotential surfaces are thus distorted and anomalous
readings can result.
