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The sedimentary history of an ocean basin is controlled by complicated variations in such factors as the sources of sediments, their solubilities, and the motions of the oceanic crust. However, important large-scale features and basic relationships can be investigated with vastly simplified models such as the one described here. The complexity required of a model is in part determined by the amount of data available; as gaps in our knowledge of the historical record are filled, more detailed models will be useful. The features in the sedimentary record which suggested the development of the model are discussed elsewhere in this volume and in Heezen et al. (1973). Here we are concerned with the mathematics of the model and with several examples which match the available data more or less well. The two major sources of oceanic sediments are windblown continental dust and the remains of organisms living in the ocean. Except near such exceptional sources as volcanoes, the dust contribution is relatively small and uniform over the basin, and leads, in first approximation, to a uniform rate of abyssal clay formation. In contrast, variations in organic productivity and solubility of organic remains lead to important and systematic regional differences in the rate of organic sedimentation. The solution rates of the calcareous and siliceous tests that are the main organic sediment components are controlled by factors such as temperature and pressure. The result of the dependence is that carbonate and silica compensation depths exist below which no sedimentary record of ordinary organic productivity is found, as discussed by Berger (1967) and Peterson (1966). However, anomalously high rates of productivity can deposit so much organic material that the solution mechanism does not operate rapidly enough to dissolve all the remains. For our purposes, the important location of such productivity is the narrow zone of equatorial upwelling between the northern and southern hemisphere current systems (Arrhenius, 1952). The concepts of sea-floor spreading are important in a discussion of sedimentation because they provide a systematic framework for the motions of the oceanic crust below the compensation depth and beneath the equator. Crust is formed at mid-ocean ridges above the compensation depth but rapidly drops below it, effectively eliminating organic sedimentation except on those portions of the plate beneath the equator. Basically the mathematics of a model describing these phenomena is a simple bookkeeping operation. Consider a section perpendicular to the ridge crest. Whatever the relative motion of the equatorial zone, it may be described in the model by its speed and width projected on the section. At each step in time, we.must calculate which sedimentation rates apply to each point on the section and add that then deposited to the thickness already there. Then at suitable time intervals, isochrons can be drawn through the thickness generated to produce a model geologic section. Several parallel sections give a rather complete history of the basin, which may then be compared with the data obtained from boreholes. Our model isochrons give more detail than those of Winterer (1972), who calculated total sediment thickness in the eastern Pacific, and now some data from the older western Pacific are available. The approximations in the model and coarseness of the data permit only qualitative comparisons, but the method still provides valuable information on the history of plate motion. In particular, since the position of the geographical equator relative to the plate is important in the model, it will be useful in studying absolute, as opposed to relative, plate motions.

A Model of Sedimentation on a Moving Plate, with an Application to the History of the North Pacific