During the postglacial sea-level rise, wave action has played an important role in the formation of continental shelves that have an erosional origin. On this basis, a mathematical model of shelf development was completed; the modeling was done by incorporating (1) coastal cliff erosion and (2) the Flandrian transgression. The result was given by the following two equations: (see PDF for equation) and (see PDF for equation) where X* and Z* = the coordinates showing a continental shelf profile; c = cliff recession rate; t = time; ha = ultimate abrasion depth expressed by (see PDF for equation) where Ho and Lo = deep-water wave height and length, respectively, and H and L = wave height and length, at a water depth of ha, respectively; Wo = the initial width of wave-cut terrace given by W0=Wp - (2 X 104)c, where Wp = the present terrace width, defined as the horizontal distance from the present coastline to the location providing a water depth of ha; A = 125 m; and a = 1.98 × 10−4 yr−1.
The validity of this model was investigated in the Byobugaura area of Japan, facing the Pacific Ocean. The result showed that the present model could explain in full the first essentials of continental shelf development.