 A logarithmic transformation (of order "m" with center "p") of an elliptic surface or fibration turns a fiber of multiplicity 1 over a point "p" of the base space into a fiber of multiplicity "m".It can be reversed, so fibers of high multiplicity can all be turned into fibers of multiplicity 1, and this can be used to eliminate all multiple fibers.Logarithmic transformations can be quite violent