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CSIR-NET 2019 DEC 101

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101) An MT Survey was conducted over a fault. If one of the axis of measurement coincides with the fault extension, then the impedance elements Zxx, Zyy, Zxy and Zyx are 

(Thanks to Chandrasekhar, ANU)


 Solution:

As we all know that the impedance can be defines as the ratio of electric field intensity to the magnetic field intensity.

 

                                                      Z=\frac{E}{H}

 

 In the presence of the 2-D or 3-D structures the impedance is not invariant but it depends on the distance of the point of measurement from the structure and the angle between the strike and the co-ordinate axis.

 

After getting  the four tensor components from the processing the data they align the components parallel and perpendicular to the structure. This procedure is known as ‘”location of Principle axes” and the relations are as follows

 

Z_{xx}=\frac{1}{2}[Z_{xy}^{'}+Z_{yx}^{'}]\sin2\theta

 

Z_{yy}=-\frac{1}{2}[Z_{xy}^{'}+Z_{yx}^{'}]\sin2\theta

 

Z_{xy}=Z_{xy}^{'}-[Z_{xy}^{'}+Z_{yx}^{'}]\sin^{2}\theta

 

Z_{yx}=Z_{yx}^{'}-[Z_{xy}^{'}+Z_{yx}^{'}]\sin^{2}\theta

 

 

 Where \theta is the clockwise rotation angle between the survey and the principle axes.

 

·      During the rotation of 1800 the off diagonal elements Z_{xy} and Z_{yx} have two maximas(00, 1800) and one minimum(900).

 

·      Where as the diagonal elements Z_{xx} has two minima(-450,1350) with a maximum at 450 where as Z_{yy} is the exact convers

 

 

·      If the ground is isotropic Z_{xx}=Z_{yy}=0  and Z_{xy} = -Z_{yx}

 

·      If the ground is anisotropic Z_{xx}=-Z_{yy}  and Z_{xy}≠Z_{yx}

 

 

·      If the axes of measurements are parallel and normal to strike then the condition is

Z_{xx}=Z_{yy}=0 

 

 

In the given problem the axes of measurements are parallel then the relation between the impedance tensor is as follows

     Z_{xx}=Z_{yy}=0    and Z_{xy}=-Z_{yx}

 

 Reference: Applied Geophysics by W.M.Telford, L.P.Geldart and R.E.Sheriff.


 


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