known value at i occurs. This approximation method is an interpolation method
associated with the given data values and is known as a weighted prediction method.
A modification of the above method is obtained as follows. The Kriging weights
can be generalized by requiring the coefficients in equation (9.6) to have the form
Coefficienti=1
dβi
∑nj=11
dβjβ > 0 a constant (9 .7)
and then adjusting the parameter βto achieve some kind of desired result.
Spherical Trigonometry
The figure 9-1 illustrates three points A, B, C on the surface of a unit sphere with
a great circle passing through any two of the selected points. This forms a spherical
triangle. Let α, β, γ denote the angles^2 at the points A, B, C and let a, b, c denote the
length of the sides opposite these angles. On a circle of radius rthe arc length s
swept out by an angle θis given by s=rθ. The sphere being a unit sphere dictates
that the arc lengths a=∠B 0 C, b =∠A 0 C, c =∠A 0 B. One of the basic problems in
spherical trigonometry is to find a relation between the angles α, β, γ and the sides of
arc lengths a, b, c of a spherical triangle. The following illustrates how vectors can be
employed to find such relationships.
Figure 9-1. Spherical triangle with unit vectors ˆeA, ˆeB, eˆC
(^2) The angles are the same as the angles between the tangent lines to the great circles.