Correction to: A new method to identify the source vent location of tephra fall deposits: development, testing, and application to key Quaternary eruptions of Western North America

A new method to identify the source vent location of tephra fall deposits based on thickness or maximum clast size measurements is presented in this work. It couples a first-order gradient descent method with either one of two commonly used semi-empirical models of tephra thickness distribution. The method is applied to three tephra thickness and one maximum clast size datasets of the North Mono and Fogo A tephra deposits. Randomly selected and localized subsets of these datasets are used as input to evaluate its performance. The results suggest the utility of the method and show that estimating the dispersal axis is a more robust way to constrain the vent location compared with directly estimating the vent coordinates given sparse observations. Local change in dispersal direction can be detected given localized observations. Bootstrap aggregating and visualizing the surface of the cost function are used to analyze epistemic uncertainty for the method. Our discussion focuses on how different features of tephra deposits and technical aspects of the method would affect the performance of the method. Suggestions on how to use the method given limited observations are listed. One subset of the North Mono Bed 1 thickness dataset and thickness datasets of the Trego Hot Springs and Rockland tephras are used as case studies. The method is then applied to the well-correlated tephra sub-units within the Wilson Creek Formation to estimate their vent location and volume. The simplicity and flexibility of the method make it a potentially useful tool for analyzing tephra fall deposits.