Vening Meinesz Kernel and Integral (pygeoid.integrals.veningmeinesz)

Vening Meinesz kernel.

class pygeoid.integrals.veningmeinesz.VeningMeineszKernel

Vening Meinesz kernel class.

kernel(spherical_distance)

Evaluate Vening Meinesz kernel.

Parameters:

• spherical_distance (float or array_like of floats) – Spherical distance, in radians.

• degrees (bool, optional) – If True, the spherical distance is given in degrees, otherwise radians.

Notes

The derivative is the Vening-Meinesz and it depends on the spherical distance \(\psi\) by [1]:

\[V\left(\psi\right) = \dfrac{d S\left(\psi\right)}{d\psi} = - \dfrac{\cos{(\psi / 2)}}{2\sin^2{(\psi / 2)}} + 8\sin{\psi} - 6\cos{(\psi / 2)} - 3\dfrac{1 - \sin{(\psi / 2)}}{\sin{\psi}} + 3\sin{\psi}\ln{\left[\sin{(\psi/2)} + \sin^2{(\psi/2)}\right]},\]

which is the derivative of Stokes’s kernel with respect to \(\psi\).

References

[1]

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

property name

Return kernel name.