[S-VC50_2AM1] Dynamics of volcanic eruptions and igneous activities

[SVC50-01] The mathematical link between stratigraphic grain size variation of fall deposits and its time variation at the source

*Yu IRIYAMA¹, Atsushi TORAMARU², Tetsuo YAMAMOTO³ (1.Department of Earth and Planetary Sciences, Graduate School of Sciences, Kyushu University, 2.Department of Earth and Planetary Sciences, Faculty of Sciences, Kyushu University, 3.Center for Planetary Science, Kobe University)

Keywords:pyroclastic fall deposits, grain size distribution, stratigraphic variation, development of eruption

Pyroclastic fall deposits which are produced by explosive volcanic eruption have various information on the eruption events. The areal distributions of pyroclastic fall deposits such as maximum grain size, median grain size, thickness, mass per unit area, etc. reflect the intensity in a single eruption and the wind conditions. Stratigraphic grain size variations of pyroclastic fall deposits also reflect the temporal behavior of the eruption intensity. For example, normal or reverse grading structures in the pyroclastic fall deposits have been attributed to temporal variation in the volcanic intensity (column height) and/or in the initial grain size distribution at the vent. However, no quantitative methodology has been developed to relate the temporal variation of source characteristics (column height and initial grain size distribution) to stratigraphic variation of grain size distribution at the deposits. In this study, we consider the mathematical description in 1D fall-sedimentation process, which relates the temporal variation of source grain size distribution to stratigraphic variation of grain size distribution.The number of grains in a size bin must be conserved during sedimentation process and results in the same value at the arrival time on the deposits. The number of a specific-size grains between at the fallout time and at given times is linked by Lagrangian description. The key point is that the grain size and the departure time at the source are mutually related to the grain size and the arrival time at the deposits. As the arrival time corresponds to the stratigraphic location at the deposit, the stratigraphic variation of grain size in the deposit can be connected to the grain size characteristics and departure time at the source using the condition of grain number conservation. As a result, when the time variations of source grain size distribution and of fallout height are given, we obtain the temporal variation of grain size distribution at the sedimentation surface. It means that different sizes of grains which settle at the same arrival time are traced back to the different source time and height. The arrival time on the deposit can be related to the stratigraphic height in the deposit by the differential equation of increasing rate of the thickness, which equals to the volume flux through the sedimentation surface. By using these mathematical descriptions, we develop the mathematical method to link the temporal variation of eruption intensity to the stratigraphic variation of grain size distribution in the fall deposits.