Ch 11 Homework Assignments

HOMEWORK ASSIGNMENTS
1. CONSIDER A VERTICAL CONTACT BETWEEN TWO GEOLOGIC UNITS OF GREATLY
DIFFERENT RESISTIVITIES P1 AND P2 .
A. CALCULA TE THE DIRECTION THAT ELECTRICAL CURRENT WILL LEAVE THE BOUNDARY
INTO P2 IF IT APPROACHES THE BOUNDARY AT AN ANGLE OF 45° TO THE NORMAL.

B. CALCULATE THE ELECTRICAL POTENTIAL AT POINT A FROM A SINGLE SOURGE OF
CURRENT ( +I ) A T POINT B. REMEMBER THAT THE BOUNDARY WILL CREATE A
REFLECTED IMAGE OF THE CURRENT SOURCE WITH MAGNITUDE KI. FOR P1 = 100 Ωm
AND P2 = 0.1 Ωm
C. REPEAT (A)

AND

(B)

FOR P1 = 100 Ωm AND P2 = 10000 Ωm

2. Determine the potential difference between the two potential electrodes for cases (a) and (b).
Assume a current of 0.5 ampere for (a) and 0.8 ampere for (b).

3. Construct the current-flow lines beneath the interface in (a) and (b).

4 - Interpret the following data, which were obtained with a Schlumberger traverse.

Electrode
Spacing (m)
I.00
1.47
2.15
3.16
4.64
6.81
10.00

ρ ( Ω . m)
108
121
I4X
191
244
295
323

Electrode
Spacing (m)
14.68
21.54

ρ ( Ω . m)

31.62
46.42
68.13
100
146.78

307
245
168
122
115
162
220

Electrode
Spacing (m)
215.44
316.23
464.16
681.29
1000.0

ρ ( Ω . m)
293

381
479
580

675

5- The following data were gathered with a Wenner, expanding-spread traverse in an area of thick deltaic sands. Bedrock depths are greater than 30 m. What is your best estimate of the depth to the water table in this area?
Electrode Spacing (m)

0.47

0.69
1.00
1.47
2.15
3.16
4.64

ρ ( Ω . m)
2590
3288
4421
5198
6055
6686
7782

Electrode Spacing (m)

ρ ( Ω . m)

6.81
10.00
14.68
21.54
31.62
46.42

8753
7630
4805
2160
995
584

6. The following data were gathered with a Wenner. expanding-spread traverse in an area of dune sands underlain by lake clays which in turn are underlain by Triassic sedimentary rocks.
Estimate a value for clay thickness.

Electrode Spacing (m) ρ ( Ω . m)
0.69
1298.90
1.00
1398.06
1.47
1306.98
2.15
1153.02
3.16
925.27
4.64
762.40
6.81
554.13

Electrode Spacing (m) ρ ( Ω . m)