A long-standing theory for the genesis of continental crust is that it is formed in subduction zones(1). However, the observed seismic properties of lower crust and upper mantle in oceanic island arcs(2,3) differ significantly from those in the continental crust(4). Accordingly, significant modifications of lower arc crust must occur, if continental crust is indeed formed from island arcs. Here we investigate how the seismic characteristics of arc crust are transformed into those of the continental crust by calculating the density and seismic structure of two exposed sections of island arc (Kohistan and Talkeetna). The Kohistan crustal section is negatively buoyant with respect to the underlying depleted upper mantle at depths exceeding 40 kilometres and is characterized by a steady increase in seismic velocity similar to that observed in active arcs. In contrast, the lower Talkeetna crust is density sorted, preserving only relicts (about ten to a hundred metres thick) of rock with density exceeding that of the underlying mantle. Specifically, the foundering of the lower Talkeetna crust resulted in the replacement of dense mafic and ultramafic cumulates by residual upper mantle, producing a sharp seismic discontinuity at depths of around 38 to 42 kilometres, characteristic of the continental Mohorovicic discontinuity (the Moho). Dynamic calculations indicate that foundering is an episodic process that occurs in most arcs with a periodicity of half a million to five million years. Moreover, because foundering will continue after arc magmatism ceases, this process ultimately results in the formation of the continental Moho.