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\begin{document}

\title{On the non uniqueness of the source, propagation and site effects
decomposition}



\author[1]{Dino Bindi}%
\author[2]{Kevin Mayeda}%
\author[3]{Daniele Spallarossa}%
\author[4]{Matteo Picozzi}%
\author[5]{Paola Morasca}%
\author[6]{Adrien Oth}%
\author[7]{William R Walter}%
\affil[1]{Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences}%
\affil[2]{Air Force Techical Application Center}%
\affil[3]{University of Genoa}%
\affil[4]{University of Naples Federico II}%
\affil[5]{Istituto Nazionale di Geofisica e Vulcanologia INGV}%
\affil[6]{European Center for Geodynamics and Seismology}%
\affil[7]{Lawrence Livermore National Laboratory (DOE)}%


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  \date{May 23, 2024}


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\begin{abstract}
Although the non-uniqueness of the solution is commonly mentioned in the
context of studies that perform spectral decompositions to separate
source and propagation effects, its impact on the interpretation of the
results is often overlooked. The purpose of this study is to raise
awareness on this important subject for modelers and users of the models
and to evaluate the impact of strategies commonly applied to constrain
the solution. In the first part, we study the connection between the
source-station geometry of an actual data set and the properties of the
design matrix that defines the spectral decomposition. We exemplify the
analyses by considering a geometry extracted from the data set prepared
for the benchmark Community Stress Drop Validation Study (Baltay et al.,
2021). In the second part, we analyze two different strategies followed
to constrain the solutions. The first strategy assumes a reference site
condition where the average site amplification for a set of stations is
constrained to values fixed a-priori. The second strategy consists in
correcting the decomposed source spectra for unresolved global
propagation effects. Using numerical analysis, we evaluate the impact on
source scaling relationships of constraining the corner frequency of
magnitude 2 events to 30 Hz when the true scaling deviates from this
assumption. We show that the assumption can not only shift the overall
seismic moment versus corner frequency scaling but can also affect the
source parameters of larger events and modify their spectral shape.%
\end{abstract}%



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