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I bring you a geologically-related problem... I need to solve this equation, found in an article. As I am a geologist, I am learning integrals, but this one is out of my reach right now, so any help/guidelines would be really appreciated while calculating CV (Coefficient of Variation).

Consider a stratigraphic sequence made of stratigraphic surfaces (simplier: A few planes/[segments, in 2D] one above another separated by some distance).

So the equation is:

$$CV = (\int_{L}[\frac{\Delta\eta(x)_A,_B}{\overline\Delta\eta_A,_B}-1]^2dL)^\frac{1}{2}$$

Where

  • $\Delta\eta(x)_A,_B$ is the local deposit thickness (lenght) between stratigraphic surfaces A and B (two planes/segments) (known parameter).
  • $\overline\Delta\eta_A,_B$ is the the mean deposit thickness between stratigraphic surfaces A and B measured over L (planes are irregular and local thickness is not the same everywhere) (known parameter)
  • $L$ is the total horizontal lenght of the cross secction analyzed (We analyze a 2D section) (known parameter too)

Which gives me headache is that I can't integrate anything, because I know all parameters and $L$ is in the limit, because of the $dL$. I can use R, Python and Matlab, so no problem with that kind of responses.

Thank you

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    By $dL$ you mean $dx$? $\Delta\eta(x)_A,_B$ is a function of $x$, which runs over an interval of length $L$? Do you know anything about that function? If you want a formula for the integral, you'll need a formula for that function. If you don't have a functional form but can measure its values at certain points, you can use numerical methods to approximate the integral. – 2017-01-18
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    That's what I thought at first. But, no, $dL$ is $dL$, that's the odd thing here (I've taken the equation from a scientific article, so we suppose it is correct). It is strange they don't give us a function of x. The only thing I need to do is to measure values at certain points. Many thanks for your response. – 2017-01-18

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