  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 successfully 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 in cases of sparse observations. The results suggest that
estimating the dispersal axis is a more robust way to constrain the source vent
location with sparse observations. Bootstrap aggregating and examining the
surface of the cost function are proposed to characterize the uncertainty of
the method. Distinctions between the two adopted semi-empirical models of
tephra thickness distribution are discussed. Results from applying the method
to thickness datasets of the Trego Hot Springs and Rockland tephras are
consistent with previous studies, which also provide new estimates on their
total volume. The method is then applied to a series of well-correlated tephra
sub-units preserved within the Wilson Creek Formation to estimate their vent
location and total volume. The simplicity and flexibility of the method make it
a potentially useful and powerful tool for the study of tephra fall deposits of
different characteristics.
