(1) is a function of the spherical distance y and the Moho-depth parameter s = 1-[tau], with D'/R and D' is the Moho depth.
where Do is the nominal (mean) value of the Moho depth, I is the Euclidean spatial distance of two points (r, [OMEGA]) and (r' Q'), and y is the respective spherical distance. The formula in Eq.
Let [F.sub.1], [F.sub.2] be the points on the 2-dimensional sphere [S.sup.2], [F.sub.1] [not equal to] [F.sub.2] and the spherical distance [delta]([F.sub.1], [F.sub.2]) := 2c < [pi].
As the shortest spherical distance cannot be larger than n there is additional restriction in spherical geometry: c < a < [pi] - c.
where [r.sub.i]--the spherical distance
to the center of rotation, [[alpha].sub.i], [[delta].sub.i]--equatorial coordinates of chosen point, [[alpha].sub.0], [[delta].sub.0]--equatorial coordinates of the center of rotation.
Then the spherical distance
AB between A and B is equal to [angle]AOB and recall that [[angle].sub.P]AOB is equal to the interior angle P of the spherical triangle [delta]APB.
Spherical distance is the arc length of an arc of a great circle, up to [pi].
that is the set of points of [S.sup.d] whose spherical distance to a is at most [theta].
where the spherical distance
[psi] is defined by the cosine theorem
Integral kernel K in equation (1) was defined for parameters [psi] and s, where [psi] is the spherical distance
between observation and (running) integration points (r, [OMEGA]) and (r', [OMEGA]'), and s a ratio function of the Moho depth T and Earth's mean radius R, i.e.
Various least-squares stochastic solutions are applied to estimate the maximum spherical distance
of the near-zone surface integration area and the maximum degree of the GGM coefficients based on empirical models for the harmonic and terrestrial gravity anomaly degree variances.
Its value is only a function of the spherical distance
between the integration point and the dummy point.