Dictionary:Euler’s homogeneity equation

$(x-x_{0}){\frac {dF}{dx}}+(y-y_{0}){\frac {dF}{dy}}+(z-z_{0}){\frac {dF}{dz}}=N(B-F)$,

where $(x_{0},y_{0},z_{0})$ is the source location whose magnetic field $F$ is measured at $(x,y,z)$; B is the regional value of the total field; and $N$ is Euler’s structural index. $N$ is a measure of the rate of field change with distance. For example, the magnetic field of a sphere falls off as the cube $(N=3)$, of a pipe as the square $(N=2)$, of a thin dike linearly $(N=1)$, for a more or less linear basement fault or dyke $(N=0.5)$, of a semi-infinite body, not at all $(N=0)$. An Euler depth estimate increases with increased $N$. Real bodies are simulated by a superposition of bodies.

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