  The avalanche properties of models that exhibit 'self-organized criticality'
(SOC) are still mostly awaiting theoretical explanations. A recent mapping
(Europhys. Lett.~53, 569) of many sandpile models to interface depinning is
presented first, to understand how to reach the SOC ensemble and the
differences of this ensemble with the usual depinning scenario. In order to
derive the SOC avalanche exponents from those of the depinning critical point,
a geometric description is discussed, of the quenched landscape in which the
'interface' measuring the integrated activity moves. It turns out that there
are two main alternatives concerning the scaling properties of the SOC
ensemble. These are outlined in one dimension in the light of scaling arguments
and numerical simulations of a sandpile model which is in the quenched
Edwards-Wilkinson universality class.
