12. Apparent resistivity sounding data for
Schlumberger array is theoretically generated by the teacher for the following
4-layer model as \rho_1=100Ωm, \rho_2=20Ωm, \rho_3=500Ωm, \rho_4=10Ωm
and the layer thicknesses h_1=50m, h_2=20m, h_3=50m. If the student
interprets this theoretical sounding data for \rho_3 as 750Ωm, then according
to the Principle of Equivalence, the thickness h_3 would be __________m (round
off to 2 decimal places)
Solution:
Principle of equivalence: It is impossible to distinguish between
two highly resistive beds of different "h" and "\rho"
values if the product "h*\rho" is the same.
So,
Apparent
resistivity sounding data for Schlumberger array is theoretically generated by Teacher
h_3=50m
and \rho_3 =500 ohm m
If the student interprets this theoretical sounding data,
\rho_3 =750 ohm m
And what is the h_3 = ?
h_3*\rho_3 =h_3*\rho_3
50*500 =h_3*750
h_3*750=50*500
h_3=\frac{50*500}{750}
h_3=33.33 m
Reference: Applied Geophysics by W.M. Telford , L.P.
Geldart and R.E.Sheriff.
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