A new interpolation method to model thickness, isopachs, extent, and volume of tephra fall deposits
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Tephra thickness distribution is the primary piece of information used to reconstruct the histories of past explosive volcanic eruptions. We present a method for modeling tephra thickness with less subjectivity than is the case with hand-drawn isopachs, the current, most frequently used method. The 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 downwind distance are used to characterize the trend model. The 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 the algorithm in the construction of the trend model and the model of local variations. The results indicate that model isopach maps and volume estimations are consistent with previous studies and point to some inconsistencies in hand-drawn maps and their interpretation. The most striking feature noticed in hand-drawn mapping is a lack of adherence to the data in drawing isopachs locally. Since the model assumes a stable wind field, divergences from the predicted decrease in thickness with distance are readily noticed. Hence, wind direction, although weak in the case of Fogo A, was not unidirectional during deposition. A combination of the isopach algorithm with a new, data transformation can be used to estimate the extent of fall deposits. A limitation of the algorithm is that one must estimate “by hand” the wind direction based on the thickness data.
KeywordsTephra thickness Isopach maps Volume estimation Kriging Interpolation
This research was supported in part by NSF-IDR CMMI grant number 1131074 to E. B. Pitman, AFOSR grant number FA9550-11-1-0336 to A. K. Patra, an NSF-HSEES type 1 grant to B. Houghton, and NSF-HSEES grant number 1521855 to G. A. Valentine. All results and opinions expressed in the foregoing are those of the authors and do not reflect opinions of NSF or AFOSR. We are grateful for the data and insightful comments from Samantha Engwell. We thank AE Costanza Bonadonna and the anonymous reviewers for their suggestions that greatly improved the presentation of the science. Thank you, Solène.
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