Difference between revisions of "Dictionary:Dar Zarrouk"

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{{lowercase}}{{#category_index:D|dar Zarrouk}}
 
{{lowercase}}{{#category_index:D|dar Zarrouk}}
(dar zar ruk&#x2019;) The name given by Maillet to resistivity parameters or curves that deal with layered anisotropic materials. The <b>dar Zarrouk variable</b> is the <b>transversal unit resistance</b> (&#x03C1;<sub>''T''</sub>), the depth integral of the transverse resistivity perpendicular to the strata; the <b>dar Zarrouk function</b> is the <b>longitudinal unit conductance</b> (1/&#x03C1;<sub>''L''</sub>), the depth integral of the conductivity parallel to the strata; and the <b>dar Zarrouk curve</b> is a plot of the mean resistivity (&#x03C1;<sub>''T''</sub>) of the formation down to the depth ''z'', plotted versus the anisotropy coefficient times ''z''(&#x03C1;<sub>''T''</sub>&#x03C1;<sub>''L''</sub>)<sup>1/2</sup>:  
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(dar zar ruk') The name given by Maillet to resistivity parameters or curves that deal with layered anisotropic materials. The '''dar Zarrouk variable''' is the '''transversal unit resistance''' (<math>\rho_{T}</math>), the depth integral of the transverse resistivity perpendicular to the strata; the '''dar Zarrouk function''' is the [[Dictionary:longitudinal unit conductance|longitudinal unit conductance]] (<math>\frac{1}{\rho_{L}}</math>), the depth integral of the conductivity parallel to the strata; and the '''dar Zarrouk curve''' is a plot of the mean resistivity (<math>\rho_{T}</math>) of the formation down to the depth ''z'', plotted versus the anisotropy coefficient times <math>z (\rho_{T}\rho_{L})^{1/2}</math>:  
  
 
<center>&#x03C1;<sub>''T''</sub>=&#x03A3;&#x03C1;<sub>''i''</sub>''z''<sub>''i''</sub>&#x0020;and&#x0020;1/&#x03C1;<sub>''L''</sub>=&#x03A3;''z''<sub>''i''</sub>/&#x03C1;<sub>''i''</sub>,</center>
 
<center>&#x03C1;<sub>''T''</sub>=&#x03A3;&#x03C1;<sub>''i''</sub>''z''<sub>''i''</sub>&#x0020;and&#x0020;1/&#x03C1;<sub>''L''</sub>=&#x03A3;''z''<sub>''i''</sub>/&#x03C1;<sub>''i''</sub>,</center>
  
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where <math>z_{i}</math> are layer thicknesses.<ref>Maillet, R., 1947, The fundamental equations of electrical prospecting: Geophysics, 12, 529–556.</ref>
  
 
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== References ==
where ''z''<sub>''i''</sub> are layer thicknesses. See Maillet (1947).
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{{reflist}}
  
 
[[Category:Pages with unformatted equations]]
 
[[Category:Pages with unformatted equations]]

Revision as of 14:34, 20 January 2015

(dar zar ruk') The name given by Maillet to resistivity parameters or curves that deal with layered anisotropic materials. The dar Zarrouk variable is the transversal unit resistance (), the depth integral of the transverse resistivity perpendicular to the strata; the dar Zarrouk function is the longitudinal unit conductance (), the depth integral of the conductivity parallel to the strata; and the dar Zarrouk curve is a plot of the mean resistivity () of the formation down to the depth z, plotted versus the anisotropy coefficient times :

ρT=Σρizi and 1/ρLzii,

where are layer thicknesses.[1]

References

  1. Maillet, R., 1947, The fundamental equations of electrical prospecting: Geophysics, 12, 529–556.