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\begin{document}

\title{A prediction-oriented hazard assessment procedure based on the empirical
falsification principle, application to the Atenquique debris flow,
1955, M\selectlanguage{ngerman}éxico\selectlanguage{english}}



\author[1]{Abani Patra}%
\author[2]{Andrea Bevilacqua}%
\author[1]{Marcus Bursik}%
\author[1]{E. Bruce Pitman}%
\author[1]{David Hyman}%
\author[3]{Ricardo Saucedo}%
\author[4]{José Luis Macìas}%
\affil[1]{University at Buffalo}%
\affil[2]{Istituto Nazionale di Geofisica e Vulcanologia}%
\affil[3]{Universidad Autònoma San Luis Potosì}%
\affil[4]{Universidad Nacional Autònoma de México}%


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  \date{June 09, 2024}


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\begin{abstract}
In this study, we detail a new prediction-oriented procedure aimed at
volcanic hazard assessment based on geophysical mass flow models with
heterogeneous and poorly constrained output information. Our method is
based on an itemized application of the empirical falsification
principle over an arbitrarily wide envelope of possible input
conditions. In particular, instead of fully calibrating input data on
past observations, we create and explore input values under more general
requirements of consistency, and then we separately use each piece of
empirical data to remove those input values that are not compatible with
it, hence defining partial solutions to the inversion problem. This has
several advantages compared to a traditionally posed inverse problem:
(i) the potentially non-empty intersection of the input spaces of
partial solutions fully contains solutions to the inverse problem; (ii)
the partial solutions can provide hazard estimates under weaker
constraints potentially including extreme cases that are important for
hazard analysis; (iii) if multiple models are applicable, specific
performance scores against each piece of empirical information can be
calculated. We apply our procedure to the case study of the Atenquique
volcaniclastic debris flow, which occurred in the State of Jalisco (MX),
1955. We adopt and compare three depth averaged models currently
implemented in the TITAN2D solver, available from vhub.org. The
associated inverse problem is not well-posed if approached in a
traditional way. However, we show that our procedure can extract
valuable information for hazard assessment, allowing the exploration of
the impact of model flows that are similar to those which occurred in
the past, but differ in plausible ways.%
\end{abstract}%



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