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\section{Calculating induced dynamic pressure changes in the magma chamber}  \subsection{Method}  %We numerically estimate pressure changes induced in the magma chamber by a nuclear explosion.  We use PyLith, ``a finite-element code for dynamic and quasistatic simulations of crustal deformation, primarily earthquakes and volcanoes'' \cite{Aagaard_2013} \cite{Aagard2013a,Aagaard2013b}  to compute pressure changes induced in the magma chamber by a nuclear explosion. The region around Baekdu and the nuclear test site is represented by a 400 $\times$ 400 $\times$ 100 km domain (Fig. XXa). We adopt a velocity structure inferred for the region by \citet{DUAN_2005}. For simplicity, we assume that the entire domain is a single layer of crust with Vs = 3.25 km/s and Vp = 5.62 km/s. A magma chamber has been detected beneath Baekdu from low shear wave velocity in the depth range of 10-16 km \cite{ZHANG_2002}. Based on this observation, we assume that the magma chamber is a sphere of 3 km radius, of which center is at 13 km depth and 142 km away to the northeast of the center of the domain, where we put the explosion source. The S and P wave speeds of 3.0 km/s and 5.19 km/s are assigned to the chamber based on \cite{ZHANG_2002}.   %To represent anelastic attenuation in the crustal materials and in the magma chamber, the isotropic linear Maxwell viscoelastic rheology is assumed. The constant viscosities of the crust and the magma chamber are 10$^{19}$ and 10$^{18}$ Pa$\cdot$s, respectively. 
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