Stratigraphic variation in the grain size distribution (GSD) of plinian pyroclastic fall deposits reflects volcanic activity. To extract information on volcanic activity from the analyses of deposits, we propose a one-dimensional theory that provides a formula connecting the sediment GSD to the source GSD. As the simplest case, we develop a constant-source model (CS model), in which the source GSD and the source height are constant during the duration of release of particles. We assume power laws of particle radii for the terminal fall velocity and the source GSD. The CS model can describe an overall (i.e., entire vertically variable) feature of the GSD structure of the sediment. It is shown that the GSD structure is characterized by three parameters, that is, the duration of supply of particles to the source scaled by the fall time of the largest particle, ts/tM, and the power indices of the terminal fall velocity p and of the source GSD q. We apply the CS model to samples of the Worzel D ash layer and compare the sediment GSD structure calculated by using the CS model to the observed structure. The results show that the CS model reproduces the overall structure of the observed GSD. We estimate the duration of the eruption and the q value of the source GSD. Furthermore, a careful comparison of the observed and calculated GSDs reveals new interpretation of the original sediment GSD structure of the Worzel D ash layer.
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