Stokes’s Kernel and Integral (pygeoid.integrals.stokes)

Stokes integral and kernel.

class pygeoid.integrals.stokes.StokesKernel

Stokes kernel class.

kernel(spherical_distance: Unit("deg"))

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

[1]	Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman, San Francisco

derivative_spherical_distance(spherical_distance)

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

[1]	Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman, San Francisco

name

Return kernel name.

class pygeoid.integrals.stokes.StokesExtendedKernel

name

Return kernel name.