November, 2008 Bermuda ITW Numerical Simulation of Infrasound Propagation, including Wind, Attenuation, Gravity and Non-linearity Catherine de Groot-Hedlin Scripps Institution of Oceanography University of California, San Diego

November, 2008 Bermuda ITW Overview Linear propagation –Finite difference, time-domain method (FDTD) vs. rays –Examples: Advected (windy) propagation into a shadow zone Comparison of advected propagation with and without attenuation Comparison of low frequency advected propagation with and without gravity Nonlinear propagation (future work) –Use of mesh-free methods –Example: solution of Berger’s equation

November, 2008 Bermuda ITW Infrasound Propagation in a shadow zone: Rays

November, 2008 Bermuda ITW Pressure wavefields in a shadow zone FDTD pressure solutions shows infrasound energy entering “shadow” zones

November, 2008 Bermuda ITW FDTD waveform results vs. rays Shadow zone as indicated by rays Low frequency infrasound is diffracted into the shadow zone

November, 2008 Bermuda ITW Finite-Difference, Time-Domain method Equations are discretized, i.e. Useful for modeling SMOOTH pressure fields, i.e. linear propagation Field variables are defined only at nodes, e.g. in a staggered grid V x are leftward-pointing arrows V z are upward-pointing arrows P nodes are at the center of cells

November, 2008 Bermuda ITW Attenuation Equations for propagation in a windy, absorptive medium Equation for acoustic pressure Equation for particle velocity The viscosity  is approximately constant (but attenuation is not)

November, 2008 Bermuda ITW Attenuation and Dispersion Combine equations (set wind=0) to get a 2nd order equation for pressure: and derive a solution of the type where gives the dispersion c p (  ) and the attenuation 

November, 2008 Bermuda ITW Dispersion Predicted dispersion for a constant viscosity coefficient  =1.7x10 -5 kg m -1 s -1 Dispersion is negligible below 120 km altitude

November, 2008 Bermuda ITW Atmospheric attenuation predicted attenuation solution for  =1.7x10 -5 kg m -1 s -1

November, 2008 Bermuda ITW Environmental model Source at 50 km Source has peaks at f=0.01, 0.04, and 0.07 Hz

November, 2008 Bermuda ITW Ray results Source at 50 km altitude Receivers along ground at 50 km intervals from -300 km to 300 km Arrivals on ground are direct arrivals (DA) and thermospheric refractions (TR) TR DA TR

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) attenuation T = 192 s

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) attenuation T = 384 s

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) attenuation T = 576 s

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) attenuation T = 768 s

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) attenuation T = 960 s shows attenuation of thermospheric refractions

November, 2008 Bermuda ITW Comparison of waveforms and spectra in attenuating vs. non-attenuating media attenuating media non-attenuating media Direct arrivals are minimally attenuated Thermospheric refractions are attenuated at 0.07 Hz, not at 0.01 Hz, for refractions at altitudes > 110 km.

November, 2008 Bermuda ITW Effect of Gravity on Infrasound Infrasound propagtion equations, including gravity:

November, 2008 Bermuda ITW Low frequency source for infrasound propagation example, including gravity Source consists of the superposition of 3 wavelets Low frequency wavelet has energy at f<buoyancy frequency Higher frequency wavelets should be minimally affected by inclusion of gravity terms

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) gravity T=256 s

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) gravity By T=640 s, low frequencies are strongly reflected from the sound speed gradient at 100km

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) gravity T=1024 s

November, 2008 Bermuda ITW Propagation with (top) and without (bottom) gravity T=1408 s

November, 2008 Bermuda ITW Comparison of waveforms and spectra for low frequencies, with (left) and without (right) gravity terms Large differences in pressure, particularly at low frequencies Including gravity terms Not including gravity terms

November, 2008 Bermuda ITW Non-linear propagation Steep gradients in the acoustic wave solution Finite difference methods, or spectral methods would require a VERY high level of discretization Instead, use a RADIAL BASIS FUNCTION method

November, 2008 Bermuda ITW Radial Basis Function method The RBF method is meshfree The grid is refined or coarsened depending on the level of accuracy needed Solution is defined at all points, not just at nodes Nonlinear propagation equations pressure Incompressible Navier-Stokes for particle velocity The latter is related to Burgers equation

November, 2008 Bermuda ITW Conclusions Have developed a working code to compute linear infrasound propagation through a windy atmosphere –Plan to run it to model propagation of WSMR shots to regional distances (where shock waves aren’t observed) Am working on non-linear propagation code –Plan to run it to model propagation of WSMR shots to the near-field (where shock waves are observed) Work on gravity waves in a windy environment is still a work in progress