choclo.prism.kernel_ee#
- choclo.prism.kernel_ee(easting, northing, upward, radius)[source]#
Kernel for easting-easting component of the tensor due to a prism
Evaluates the integration kernel for the easting-easting 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 arctangent 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,northingandupwardshifted coordinates.
- easting
- Returns:
- kernel
float Value of the kernel function for the easting-easting component of the tensor due to a rectangular prism evaluated on a single vertex.
- kernel
Notes
Computes the following numerical kernel on the passed shifted coordinates:
\[k_{xx}(x, y, z) = - \operatorname{safe-arctan} \left( yz, xr \right)\]where
\[\begin{split}\operatorname{safe-arctan} \left( y, x \right) = \begin{cases} \text{arctan}\left( \frac{y}{x} \right) & x \ne 0 \\ \frac{\pi}{2} & x = 0 \quad \text{and} \quad y > 0 \\ -\frac{\pi}{2} & x = 0 \quad \text{and} \quad y < 0 \\ 0 & x = 0 \quad \text{and} \quad y = 0 \\ \end{cases}\end{split}\]References