I'll make a leap of faith, and assume that you are referring to a spherical spatial correlation structure.
A spherical spatial correlation structure has two parameters: $n$, the "nugget" effect, which acts to reduce all the correlations between two observations more than 0 distance apart, and $d$, the range (distance) over which the correlations will be nonzero. Slightly rephrasing the documentation from R's nlme package:
The correlation between two observations a distance $r < d$ apart is,
if the nugget effect is zero, $1 - 1.5(r/d) + 0.5(r/d)^3$. If $r\ge d$
the correlation is zero. If there is a nugget effect $n$, the
correlation is just $(1-n)(1 - 1.5(r/d) + 0.5(r/d)^3)$ for all
observations for which $r > 0$.
The "spherical" refers to its symmetry with respect to direction, like a sphere with respect to the origin, rather than to the shape of the surface from which the data was collected, although, confusingly, it is also the name of the structure. However, it does seem to me that, if there is correlation between your observations that is related to distance between them regardless of direction, a spherical spatial correlation structure would be a reasonable first try. There are other spatial correlation structures, though, e.g., Gaussian or exponential (which also are symmetric with respect to direction.)
A reference is "Statistics for Spatial Data", by N. A. C. Cressie, 1993.