Mathematical relationship of grain-size distribution between ash cloud and pyroclastic fall deposits in the differential sedimentation process

Abstract:

Grain-size distributions (GSDs) in a pyroclastic fall deposit which is produced by an explosive volcanic eruption has a significant information on the eruption event. The areal distributions of GSDs indicate the eruption intensity and the wind conditions in the isopach and isopleth maps. On the other hand, stratigraphic variations of GSDs such as normal or reverse grading at given localities reflect the temporal behavior of the eruption intensity and/or in the source GSD, along with the influence of differential sedimentation. However, no quantitative modeling has been developed to relate the temporal variation of source characteristics (column height and source GSDs) to stratigraphic variation of GSDs in the deposits. In this study, we develop the mathematical model in 1D differential sedimentation process, which relates a source GSDs as functions of time to GSDs in a deposit, as functions of stratigraphic position. The number of a specific-size grains at the source position on the departure time must equal that at any position and time during settling. The Lagrangian description allows us to relate a GSD at any height and time to the source GSD through settling velocity. Using this, we can calculate the temporal change of deposit thickness and GSD in the deposit. As the first step, we understand what parameters control the thickness of fine-grained layer where the coarsest grains are depleted. Assuming a power-law GSD, we derive the thickness fraction of fine-grained layer to the whole thickness in terms of controlling parameters; a ratio of falling time to eruption duration and value of power on GSD function. By using this mathematical relationship, we estimate the value of power on source GSDs in the 2011 Shinmoedake subplinian eruption, as approximately 4, which is in the reasonable range for GSDs.