A new method to identify the source vent location of tephra fall deposits: development and 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 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.

💡 Research Summary

The paper introduces a novel inverse‐modeling framework for locating the source vent of tephra fall deposits using only thickness or maximum clast‑size measurements. The core idea is to couple a first‑order gradient‑descent optimizer with one of two widely used semi‑empirical thickness distribution models: the power‑law‑plus‑exponential model of Gonzalez‑Mellado & Cruz‑Reyna (2010) and the purely exponential model of Yang & Bursik (2016). By taking logarithms of the models, the three shape parameters (maximum thickness, decay rates, etc.) become linear coefficients that can be solved analytically for any assumed vent location (x₀, y₀) and wind direction θ. The remaining unknowns—vent coordinates and wind azimuth—are then found by minimizing a cost function defined as the sum of squared differences between observed log‑thicknesses and model predictions.

The optimization proceeds in two stages. First, for a provisional vent position, a one‑dimensional gradient descent searches for the wind direction that yields the lowest cost. Second, with that optimal wind direction fixed, a two‑dimensional gradient descent updates the vent coordinates until the global minimum of the cost surface is reached. Initial guesses are derived from the centroid of the sample points and the principal axis of the data, but multiple starting points can be employed to avoid local minima.

The authors test the algorithm on four well‑documented datasets: North Mono Beds 1 and 2 (≈100 thickness points each) and the Fogo A deposit (184 points). In these data‑rich cases the method recovers vent locations within 1–2 km of the geologically established vents and reproduces known wind directions. To evaluate performance under sparse sampling, they create random subsets (10–30 % of the full data) and geographically constrained subsets (samples clustered on one side of the vent). Results show that, when observations are limited, estimating the dispersal axis (wind direction) first is more robust than trying to pinpoint the vent directly from thickness centroids. The algorithm still converges to reasonable vent positions, albeit with larger uncertainties.

Uncertainty quantification is achieved through two complementary approaches. Bootstrap aggregating (1,000 resamplings of the data) provides empirical confidence intervals for vent coordinates and wind direction. Visualizing the cost‑function surface (isocontours) reveals the presence of multiple minima and the sensitivity of the solution to initial guesses. Both techniques are demonstrated on the sparse datasets of the Trego Hot Springs (THS) and Rockland tephras, each containing only eight thickness measurements. The derived vent locations and total volumes agree with previous estimates, and the bootstrap intervals quantify the added uncertainty due to sparse data.

Finally, the method is applied to several tephra sub‑units within the Wilson Creek Formation (WCF) of Mono Lake, California. These sub‑units (e.g., Ash A4‑d, B7‑a, A3‑f, A2) have only 4–6 measured thicknesses each. By treating each sub‑unit independently, the authors obtain distinct vent positions and volume estimates, demonstrating that the approach can resolve multiple eruptive sources within a single stratigraphic sequence. The summed volumes of the sub‑units differ by 10–15 % from earlier bulk estimates, highlighting the method’s potential to refine eruption magnitude assessments.

Key advantages of the proposed framework are its simplicity (only thickness or clast‑size data required), computational efficiency (gradient descent converges in a few iterations), and openness (R code publicly released). Limitations include the underlying assumption of a constant wind direction and homogeneous atmospheric diffusion, which may not hold for highly complex or multi‑phase eruptions. The authors suggest integrating global search strategies or coupling with more sophisticated transport models for such cases.

In summary, the study delivers a practical, flexible, and statistically transparent tool for vent‑location inference and volume estimation of tephra deposits, especially valuable when field data are sparse. Its successful validation on both dense and sparse datasets, together with robust uncertainty analysis, positions it as a promising addition to the quantitative volcanology toolbox.