The great circle distance is calculated by the function rdist.earth in library fields.
The distance measures implemented in sphet are:
'euclidean': \(\sqrt{\sum{(x_i - y_i)^2}}\)
'chebyshev': \(max(|x_i - y_i|)\)
'braycur': \( \frac{\sum{|x_i - y_i|}}{\sum{|x_i + y_i|}}\)
'canberra': \( \frac{\sum{|x_i - y_i|}}{\sum{|x_i| + |y_i|}} \)
'gcircle': see spDists, which uses an approximation to the WGS84 spheroid.