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108 Advances in Productive, Safe, and Responsible Coal Mining

Fig. 7.3 3D shell model.

z Point (B, x, y, z)
or (B, r, a, b, g)

Generator

r
g
L
b
a
y

B-field
x

Fig. 7.4 Generator and magnetic-field coordinate system.

is centered at the origin. Eqs. (1a), (1b) are equivalent representations of the shell
functions in the Cartesian and the direction cosine systems, respectively. In Eq.
(7.1), ρ represents the distance from a point on the shell to the origin; α, β, and γ rep-
resent angles from the x-, y-, and z-axes, respectively, to the line on which ρ is mea-
sured. A shell can be generated from Eq. (7.1) with a given B reading, and each shell is
described by a function in the form of either (1a) or (1b) that is uniquely and
completely defined by two parameters, a and b, as defined in terms of the B reading
by (1c) and (1d). The shell shape parameter, a, determines the variation of the shell
from its basic shape of a sphere with radius, b, the shell size parameter.