diff --git a/Readme.md b/Readme.md index f584705a1bca66eafebd43a1e35ac6faa48b64ed..0214411d7a9d3c52f945b804597a4d0bb28cd273 100644 --- a/Readme.md +++ b/Readme.md @@ -16,7 +16,7 @@ in the field work of *Synthèse géologique* (3rd year) to invert the magnetic anomalies associated with dykes near the shore of the *Lac du Salagou* (SE France). -The anomaly is modelled using the equation (1) and the philosophy presented in +The anomaly is modelled using the equation (1, see below) and the philosophy presented in Beiki \& Pedersen (2012, doi: [10.1111/j.1365-2478.2011.01010.x](https://doi.org/10.1111/j.1365-2478.2011.01010.x)). @@ -26,6 +26,19 @@ The model is designed for a dyke with the following characteristics: <img src='img/cartoon.png' width='500' height='500'> </p> +The anomaly $F$ expected along a profile $x$ is given by +$$ +F(x) = C \Biggl\{\cos\alpha \biggl[\tan^{-1}\Bigl(\frac{x + w}{z}\Bigr) - +\tan^{-1}\Bigl(\frac{x - w}{z}\Bigr)\biggr] + \frac{1}{2} \sin\alpha +\ln\biggl[\frac{(x + w)^2 + z^2}{(x - b)^2 + z^2}\biggr]\Biggr\}, +$$ +with $C = 2kT\sin\beta$, $\alpha = 2I - \beta - 90^\circ$, $k$ the magnetic +susceptibility, $I = \tan^{-1}\bigl(\tan i / \cos\gamma\bigr)$, where $T$ and +$i$ are the intensity and inclination of the magnetic field, respectively, and +$\gamma$ the azimuth of the profile measured clockwise from magnetic north. +For the other symbols please refer to the figure above. + + ## Installation + Unpack the archive at the desired location. @@ -37,12 +50,13 @@ The model is designed for a dyke with the following characteristics: > It ensures that nothing will interfere with the Python libraries > that are part of the OS. + ## To run the program In a terminal run `ml-invert latitude strike filename`. There are several optional parameters to change, for instance, the bounds of -the inverted parameters or the plot the best model. +the inverted parameters or the plot of the best model. The list of the options can be access with `ml-invert -h` or `ml-invert --help`.