Groundwater Geophysics Phần 3 docx

96 Kord Ernstson, Reinhard Kirsch

(layer i) with thickness hi in a sounding curve supplies a substitute resistiv￾ity ρ*i and substitute thickness h*

i:

i T ρL ρ = ρ ⋅ ∗ (3.6)

L

T hi hi

ρ

ρ = ⋅ ∗ (3.7)

While for the substitute resistivity ρL < ρ*i< ρT , the substitute thickness

h*i is larger than the true thickness hi by a multiplier of λ=(ρT/ρL)

1/2, λ be￾ing the coefficient of anisotropy (Fig. 3.9).

Fig. 3.9. Electrical anisotropy on different scales: a macroanisotropic resistivity

section with average transverse and longitudinal resistivities ρT and ρL (left) and a

single microanisotropic layer with transverse and longitudinal resistivities ρT and

ρL (right). Interpretation of the sounding curve leads to higher thickness of the mi￾croanisotropic layer (h3

*

) than in reality

Geoelectric anisotropy is a matter of scale and of the resolution of a ver￾tical resistivity section. While graphite, a slate or a lake sediment may be

termed microanisotropic, a sequence of well-defined electrically isotropic

beds can behave macroanisotropic if they are not resolved in a geoelectric

sounding curve (see, e.g., the ten-layer case in Fig. 3.8).

3 Geoelectrical methods 97

For a macroanisotropic section, average longitudinal and average trans￾verse resistivities can be calculated from the parameters of the single beds

(Fig. 3.9):

L i i i ρ = ∑h / ∑h /ρ ∗ (3.8)

ρ = ∑ ρ ∑ ∗

T i i i h / h (3.9)

Substitute resistivity and thickness as well as coefficient of anisotropy are

the same as for microanisotropic behavior (3.6, 3.7).

Equivalence between true resistivity sections and sections with substi￾tute layers due to anisotropy may cause serious modeling and interpreta￾tion errors if the anisotropy (both macro and micro) is not recognized. As

can be calculated from Eqs. 3.6 - 3.9, intermittently occurring high- and

low-resistivity beds may lead to large coefficients of anisotropy and, cor￾respondingly, to large errors in modeled thicknesses.

Anisotropy also leads to discrepancies between results of vertical elec￾trical soundings and electromagnetic induction measurements (horizontal

current flow-lines). Comparing VES date with data from resistivity bore￾hole logging (mostly horizontal flow lines), anisotropy must also be taken

into consideration.

3.2.5 Geological and hydrogeological interpretation

The discussion of the principle of equivalence shows that singular depth

soundings are in general little meaningful. Likewise, the sometimes used

term "electrical drilling" should basically be avoided, because VES is not

intended to and cannot replace boreholes but is methodically a different

complex. VES interpretation comprises the more or less synchronous han￾dling of measured sounding curves in the survey area and their modeling

results. Continuity of layers in the area should be checked as well as the

reality of obvious breaks in the geologic layering.

With regard to equivalence, reinterpretation of some soundings can be

necessary, and additional field measurements may be helpful. In areas of

young Cenozoic unconsolidated deposits (molasse, glacial sediments) with

rapidly changing thicknesses (Fig. 3.10A), data of a key borehole may be

required to fix modeling parameters and thus to get absolute depths inde￾pendent of equivalence. In hard sedimentary rocks where stratigraphic

standard thicknesses and rock resistivities are frequently well known and

constant over large areas, VES modeling and interpretation may be easier

leading to a detailed knowledge of the tectonics in many cases (Fig. 3.10B).

98 Kord Ernstson, Reinhard Kirsch

As the final result, a resistivity model of the project area which is geologi￾cally and hydrogeologically reasonable and without discrepancies with

drilling or other geophysical results should be obtained.

Fig. 3.10. Resistivity depth profiles from vertical electrical soundings. A: Quater￾nary sandy aquifer partly covered with till, B: tectonic graben as a fractured and

partially karstified limestone aquifer

3.3 Resistivity mapping

Targets of resistivity mapping (or profiling) are near surface resistivity

anomalies, caused by, e.g., fracture zones, cavities or waste deposits. Any

common electrode configuration (e.g., Wenner or Dipole-Dipole) can be

used for mapping purposes. In general, the chosen four-point configuration

3 Geoelectrical methods 99

is kept constant and moved along profiles, while apparent resistivity is

recorded (Fig. 3.11). Prior to the field works, optimum electrode spacing

of the configuration can be determined by model calculations, if assump￾tions on resistivity and depth of the target and on resistivity of the sur￾rounding material are possible.

I U

apparent resistivity

distance

Fig. 3.11. Resistivity mapping with a dipole-dipole configuration

Another common array is the gradient array (Fig. 3.12). Here electrodes A

and B are fixed and only electrodes M and N are moved, and a rectangular

area between the electrodes is mapped. The apparent resistivities are calcu￾lated from (3.1, 3.2) and plotted as a map of isoohms (Fig. 3.13). Instead

of point electrodes line electrodes may be used for current injection (e.g.

grounded cables or a number of lined-up connected steel rods).

Although the mapping response of an arbitrary resistivity distribution

can be calculated, interpretation is in general done qualitatively by locating

structures of interest and outlining their extension and strike. Nevertheless,

a study of resistivity mapping model curves (see, e.g., Keller & Frischknecht

1970, Schulz 1985) may be very useful to learn that even simple geometries

may produce complex apparent-resistivity profiles and that anomalies may

be quite different when measured with different electrode configurations.

100 Kord Ernstson, Reinhard Kirsch

Fig. 3.12. Gradient array for resistivity mapping

0 20 40 60 80 100 120 140

0

10

20

30

40

90

105

120

135

150

m

m Ohmm

Fig. 3.13. Apparent resistivities over fracture zones in limestone mapped by gra￾dient array

3.3.1 Square array configuration

The square array configuration is especially designed for the mapping of

resistivity anisotropy, caused by e.g. fracture zones. Fracture zones may

behave electrically anisotropic, because the resistivity parallel to strike is

in general lower than perpendicular. The electrodes are arranged to form a

square (Fig. 3.14) whose side length is a, and the apparent resistivity as￾signed to the midpoint is computed from

I

U

ρA = K ⋅ (3.10)

with the geometric factor of the square array defined by

2 2

2 a K −

π = (3.11)

At each location, the square is rotated by 45°, and four apparent resistivity

values ρA1 ... ρA4 are measured (Fig. 3.14). They depend on the resistivity