DIMENSIONAL ANALYSIS IN SEQUENCE STRATIGRAPHY--APPLICATION OF BUCKINGHAM'S P THEOREM TO SHORELINES, COALS, AND LAKES

Even if one cannot specify quantitative dynamical relations or even adequately constrain all variables still it is fruitful to approach the stratigraphic record and its interpretation following the dimensional analysis approach proposed by Lord Rayleigh, formalized by Buckingham, and extended to interpretations of bedform and depositional environments by Southard. Indeed, this approach was initially motivated by a similar quandary of seeking quantitative relations in underconstrained systems. Two avenues are particularly useful in analyses of depositional systems and stratigraphic records: seeking inherent length scales (geometric aspects) and parsing system behavior in terms of competing/interacting rates (kinematic and dynamical aspects).

For shoreline systems, the interaction of rates of clastic sediment supply with accommodation change determines parasequence stacking patterns and shoreline trajectories. For coal-bearing systems, dimensional analysis provides a tie of peat/coal accumulation to both the evolving position of the groundwater table and to coeval shoreline trajectory. It enables quantitative calculations of coal character with respect to rates of peat production and local accommodation and allows prediction of most likely times and areas of coal accumulation through paleolatitude, climatic humidity, and subsidence history. For lakes, this approach sorts through the many competing variables, clarifying key factors for stratal character and preservation. It helps point out that water depth, water chemistry, and climatic humidity are secondary factors convolved into two main state variables: potential accommodation rate and sediment+water supply rate.

Placing system variables in their proper scaling relations is useful not only for quantifying processes and responses, but also commonly leads to deeper qualitative insights into system behavior and its resultant stratal record. The approach of dimensional analysis helps focus investigations on key variables, responses, and feedback links.