Differentiation of depth-gravity anomaly function.

Apr 3, 2021
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Assume we measure bouguer anomaly (g) and depth (H) of the certain horizon through a profile at each point. Based on data we get a correlation between H and g and express it with a polynomial equation like H(g)=a1g^n+a2g^(n−1)+...+a .What the first and second derivative of the equation will give us?
 
Jan 27, 2020
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Replying to orxan662:

The Bouguer anomaly is a gravity anomaly, corrected for the height at which it is measured and the attraction of terrain.

Assume we measure bouguer anomaly (g) and depth (H) of the certain horizon through a profile at each point. Based on data we get a correlation between H and g and express it with a polynomial equation like 𝐻(𝑔)=𝑎1𝑔𝑛+𝑎2𝑔𝑛−1+...+𝑎𝑛H(g)=a1gn+a2gn−1+...+an.

𝐻′(𝑔)=𝑛𝑎1𝑔𝑛−1+(𝑛−1)𝑎2𝑔𝑛−2+…+𝑎𝑛−1H′(g)=na1gn−1+(n−1)a2gn−2+…+an−1 and 𝐻″(𝑔)=𝑛(𝑛−1)𝑎1𝑔𝑛−2+(𝑛−1)(𝑛−2)𝑔𝑛−3+…+2𝑎𝑛−2H″(g)=n(n−1)a1gn−2+(n−1)(n−2)gn−3+…+2an−2.

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Hartmann352
 
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