A new method to model thickness distribution and volume of tephra deposits
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Understanding tephra thickness distribution is important as it helps reconstruct the eruption histories of volcanoes. We present an algorithm that models tephra thickness with less subjectivity than is the case with hand-drawn isopachs, the current methodology. This algorithm separates the thickness of a tephra fall deposit into a trend and local variations, and models them separately using segmented linear regression and ordinary kriging. The distance to the source vent and a new parameter, the (azimuthally) “normalized distance,” are used to characterize the trend model. This algorithm is applied to thickness datasets for the Fogo Member A and North Mono Bed 1 tephras. Simulations on subsets of data and cross-validation are implemented to test the effectiveness of this algorithm in the modeling of the trend models and local variations respectively. The results indicate that volume estimations and isopach maps of resulting models are consistent with previous studies, but point to some inconsistencies in the hand-drawn maps and interpretations. The inconsistencies in mapping consist of a lack of adherence to data in drawing isopachs locally. With respect to interpretation, as the model assumes a stable wind field, divergences from such as reflected in isopach data are readily noticed. In this respect, although the impact of wind was weak on the Fogo A deposit, it was also not unidirectional throughout deposition of the entire deposit. The combination of a new, “plus-one” transformation and the isopach algorithm is furthermore proposed to estimate the extent of a tephra fall deposit. A limitation of the algorithm is that one must manually estimate the wind direction based on the thickness data. The wind direction is critical because it determines the values of the normalized distances.