Vening Meinesz Kernel and Integral (pygeoid.integrals.veningmeinesz)¶
Vening Meinesz kernel.
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class
pygeoid.integrals.veningmeinesz.
VeningMeineszKernel
[source]¶ Vening Meinesz kernel class.
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kernel
(spherical_distance: Unit("deg"))[source]¶ 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
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name
¶ Return kernel name.
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