Stokes’s Kernel and Integral (pygeoid.integrals.stokes)
Stokes integral and kernel.
- class pygeoid.integrals.stokes.StokesKernel[source]
Stokes kernel class.
- kernel(spherical_distance)[source]
Evaluate Stokes spherical kernel.
This method will calculate the original Stokes’s function.
- Parameters:
spherical_distance (Quantity) – Spherical distance, in radians.
Notes
In closed form, Stokes’s kernel depends on the spherical distance \(\psi\) by [1]_:
\[S\left(\psi\right) = \dfrac{1}{\sin{(\psi / 2)}} - 6\sin{(\psi/2)} + 1 - 5\cos{\psi} - 3\cos{\psi} \ln{\left[\sin{(\psi/2)} + \sin^2{(\psi/2)}\right]}.\]References
- derivative_spherical_distance(spherical_distance)[source]
Evaluate Stokes’s spherical kernel derivative.
The derivative of the Stokes function is the Vening-Meinesz function.
- Parameters:
spherical_distance (Quantity) – Spherical distance.
Notes
The derivative of Stokes’s kernel is the Vening-Meinesz and it depends on the spherical distance \(\psi\) by [1]_:
\[\dfrac{d S\left(\psi\right)}{d\psi} = - \dfrac{\cos{(\psi / 2)}}{2\sin^2{(\psi / 2)}} + 8\sin{\psi} - 6\cos{(\psi / 2)} - 3\dfrac{1 - \sin{(\psi / 2)}}{\sin{\psi}} + 3\sin{\psi}\ln{\left[\sin{(\psi/2)} + \sin^2{(\psi/2)}\right]}.\]References
- property name
Return kernel name.