Dynamic Modeling of Infrasound Generation from Vulcanian Explosions

Volcano infrasound provides a complementary view of volcanic processes to seismic waves, as the atmosphere exhibits contrasting wave propagation characteristics to the crust. Potential benefits include a more uniform velocity structure, shorter wavelengths enabling better spatial resolution, and lower attenuation improving remote monitoring capabilities. Recent work on volcano infrasound has employed kinematic source descriptions, in terms of such quantities as mass flux for a monopole point source. Such descriptions are quite useful for the inverse problem of inferring mass flux from infrasound data. In this study, we introduce a dynamic source model incorporating the physical processes that determine how the cloud of eruptive gas and ash expands outward to generate the infrasound signal. Our dynamic source model could ultimately be coupled to an unsteady conduit flow model, providing a means to infer more details of the eruption process from recorded infrasound signals. Our model describes a vulcanian eruption where mass is ejected into the atmosphere forming a cloud of gas and ash. Infrasonic acoustic waves are generated by the expansion of the cloud. The model goes beyond linear acoustics by accounting for nonlinear terms in the compressible Euler equations for the surrounding atmosphere. The model presently consists of a system of nonlinear ordinary differential equations, expressing the balance of mass, momentum, and energy, that can be solved for the evolution of the radius of the cloud and pressure and temperature within it. Entrainment and heat exchange with the surrounding atmospheric air can be accounted for. Our analysis is inspired by similar models of underwater explosions (Gilmore, 1952) and seismic air-guns (Ziolkowski, 1970). We aim to use the model to investigate how acoustic signals change when volcano properties, such as vent geometry, are varied. Our longer-term goal is to couple the atmospheric infrasound model presented here to an unsteady conduit flow model by mass, momentum, and energy conservation at the vent. The combined system will enable simulation of the complete suite of seismic-acoustic signals allowing the timing and development of eruptive source processes to be investigated in detail.