# Introduction

This is an excerpt of the modeling part of the paper, (Hong 2016). The abstract of the paper is included below for interested readers.

Strong ground motions induce large dynamic stress changes that may disturb the magma chamber of a volcano, thus accelerating the volcanic activity. An underground nuclear explosion test near an active volcano constitutes a direct treat to the volcano. This study examined the dynamic stress changes of the magma chamber of Baekdusan (Changbaishan) that can be induced by hypothetical North Korean nuclear explosions. Seismic waveforms for hypothetical underground nuclear explosions at North Korean test site were calculated by using an empirical Green’s function approach based on a source-spectral model of a nuclear explosion; such a technique is efficient for regions containing poorly constrained velocity structures. The peak ground motions around the volcano were estimated from empirical strong-motion attenuation curves. A hypothetical M7.0 North Korean underground nuclear explosion may produce peak ground accelerations of 0.1684 m/s2 in the horizontal direction and 0.0917 m/s2 in the vertical direction around the volcano, inducing peak dynamic stress change of 67 kPa on the volcano surface and  120 kPa in the spherical magma chamber. North Korean underground nuclear explosions with magnitudes of 5.0–7.6 may induce overpressure in the magma chamber of several tens to hundreds of kilopascals

# Verifying dynamic stress changes using a numerical models

## Model Setup

We compute dynamic stress changes induced in the magma chamber by a nuclear explosion using PyLith, “a finite-element code for dynamic and quasistatic simulations of crustal deformation, primarily earthquakes and volcanoes”(Aagaard 2013, Aagaard 2013a).

A magma chamber has been detected beneath Baekdu from low shear wave velocity in the depth range of 10-16 km (ZHANG 2002). Based on this observation, we assume that the magma chamber is a sphere of a 3 km radius and is contained in a 12 $$\times$$ 15 $$\times$$ 15 km rectangular box representing the crust (Fig. \ref{fig:planewave_domain}a) We approximate the waves propagating through the magma chamber as a pulse of plane wave. Our goal to estimate only the peak stress change justifies this simplification. The plane wave is generated by the time-dependent displacement uniformly applied on one boundary, which is given as $u(t) = u_{0}\frac{t}{\tau}\exp\left(-\frac{t}{\tau}\right),$ where $$u$$ is the boundary-norma