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GATE-2021(12) Apparent resistivity (Expected answer)

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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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