# choclo.prism.kernel_nu#

Kernel for northing-upward component of the tensor due to a prism

Evaluates the integration kernel for the northing-upward component of the tensor generated by a prism [Nagy2000] on a single vertex of the prism. The coordinates that must be passed are shifted coordinates: the coordinates of the vertex from a Cartesian coordinate system whose origin is located in the observation point.

This function makes use of a safe natural logarithmic function [Fukushima2020] that guarantee a good accuracy on every observation point.

Parameters
• easting (float) – Shifted easting coordinate of the vertex of the prism. Must be in meters.

• northing (float) – Shifted northing coordinate of the vertex of the prism. Must be in meters.

• upward (float) – Shifted upward coordinate of the vertex of the prism. Must be in meters.

• radius (float) – Square root of the sum of the squares of the easting, northing and upward shifted coordinates.

Returns

kernel (float) – Value of the kernel function for the northing-upward component of the tensor due to a rectangular prism evaluated on a single vertex.

Notes

Computes the following numerical kernel on the passed shifted coordinates:

$k_{yz}(x, y, z) = \operatorname{safe-ln} \left( x + r \right)$

where

$\begin{split}\operatorname{safe-ln}(x) = \begin{cases} 0 & |x| < 10^{-10} \\ \ln (x) \end{cases}\end{split}$

References