Definition 31.10University Earth and Space Sciences — Year 3 · অধ্যায় 31 — Field and Lab Methods III
The apparent resistivity of a four-electrode measurement is ρa=KΔVMN/I, with the geometric factor K=2π/(1/AM−1/BM−1/AN+1/BN): the resistivity of the uniform ground that would give the same reading.
An electrode array is a rule that places the four electrodes: the Wenner array puts them equally spaced, a apart, in the order AMNB; the Schlumberger array puts M and N, 2l apart, at the centre of a much longer AB, of half-length s; dipole–dipole, pole–dipole and pole–pole arrays separate the current pair from the potential pair or send one electrode far away.
A vertical electrical sounding expands an array about a fixed centre and plots ρa against the spacing on logarithmic scales: the larger the spacing, the deeper the current flows.
Electrical resistivity tomography plants many electrodes along a line, measures many four-electrode combinations, and inverts them together for a section of resistivity.
The two sounding arrays. Current enters at A and leaves at B (red); the potential difference is measured between M and N (blue); the faint lines are lines of current. The Wenner array keeps the three spacings equal; the Schlumberger array keeps MN short and expands AB.
Left: Schlumberger curves over two layers, for reflection factors k from 0.9 (resistive base, blue, top) to −0.9 (conductive base, red, bottom). Right: the sounding on the Varden valley floor, its readings and the model that produced them (dry alluvium over saturated alluvium over granite), with the line ρa=s/S of the whole alluvium.
Coach
