Infrasound Monitoring for Atmospheric Studies pp 541-573 | Cite as

# Numerical Methods to Model Infrasonic Propagation Through Realistic Specifications of the Atmosphere

## Abstract

To model infrasonic propagation, two areas must be adequately addressed. First, the environment must encompass a domain spanning from the ground to the lower reaches of the thermosphere, and its properties must be resolved at a scale comparable to the acoustic wavelengths of interest. Second, the relevant fundamental physics that influence the wave propagation must be captured in the numerical models that are applied.

To address these challenges, a large amount of work has been completed by researchers in fields spanning from traditional acoustics to upper atmospheric physics. In this chapter, this body of work is reviewed with an emphasis on its applicability to the modeling and interpretation of infrasonic observations.

Global climatological models have largely been replaced in current infrasound modeling practice by atmospheric specifications that combine output from numerical weather prediction models for the lower atmosphere with empirical models for the upper atmosphere. Recently developed specifications incorporate higher-resolution, regional or mesoscale weather analysis products in order to improve fidelity below altitudes of 50 km. Specifications that utilize a terrain-following coordinate system, including high-resolution topography, enable the incorporation of additional physical effects.

These specifications are unable to resolve all fine-scale stochastic phenomena, e.g., atmospheric irregularities smaller than the model resolution, fine-scale structures at altitudes above 50 km, and gravity wave fluctuations. In particular, gravity waves are of interest because their spatial scales are of the same order as infrasonic wavelengths. Because atmospheric fine-scale structure is inherently turbulent, spectral formulations are used to capture the energy distribution across space-time scales relevant to infrasound and to generate representative realizations of variable fields.

The fundamental physical processes that affect infrasound, much like those of higher frequency acoustics, include refraction, diffraction, scattering, absorption, dispersion, and terrain. In addition, nonlinear effects can become significant near the source and at high altitudes. Several numerical approaches have been used for modeling infrasonic propagation often based on analogous models for underwater and outdoor sound propagation. They can be loosely classified under the headings of geometric (ray tracing, Gaussian beam, tau-p), continuous wave (parabolic equation or PE), full-wave (normal mode, finite-difference time domain, time-domain PE), and nonlinear (e.g., NPE). A good introductory source to the underlying computational aspects is (Jensen F, Kuperman W, Porter M, Schmidt H (1994) Computational ocean acoustics. AIP Press, New York). (Although this reference is primarily intended for ocean acoustics, many of the models carry over to the atmosphere and the presentation is superb.) A general overview of the propagation models is presented here with their corresponding strengths and weaknesses highlighted in the context of infrasonic studies. Also included are examples of modeling studies using high-resolution atmospheric specifications.

## Keywords

Propagation modeling Atmospheric specification Numerical methods Nonlinear propagation Spectral methods## References

- Ambrosiano J, Plante D, McDonald B, Kuperman W (1990) Nonlinear propagation in an ocean acoustic waveguide. J Acoust Soc Am 87:1473–1481CrossRefGoogle Scholar
- Arrowsmith S, Hedlin M, Ceranna L, Edwards W (2005) An analysis of infrasound signals from the June 3rd, 2004 fireball over Washington State. Inframatics 10:14–21Google Scholar
- Arrowsmith S, Drob D, Hedlin M, Edwards W (2007) A joint seismic and acoustic study of the Washington State bolide: observations and modeling. J Geophys Res 112:D09304CrossRefGoogle Scholar
- Bass H, Hetzer C (2006) An overview of absorption and dispersion of infrasound in the upper atmosphere. Inframatics 15:1–5Google Scholar
- Bass H, Sutherland L, Piercy J, Evans L (1984) Absorption of sound by the atmosphere. In: Mason W., Thurston R (eds) Physical acoustics academic, vol. XVII, chap. 3. Orlando, FL: AcademicGoogle Scholar
- Bass H, Bhattacharyya J, Garcés M, Hedlin M, Olson J, Woodward R (2006) Infrasound. Acoust Today 2(1):9–19CrossRefGoogle Scholar
- Blanc-Benon P, Lipkens B, Dallois L, Hamilton M, Blackstock D (2002) Propagation of finite amplitude sound through turbulence: modeling with geometrical acoustics and the parabolic approximation. J Acoust Soc Am 111:487–498CrossRefGoogle Scholar
- Brachet N, Brown D, Le Bras R, Mialle P, Coyne J (2010) Monitoring the earth’s atmosphere with the global IMS infrasound network. This volume, pp. 73–114Google Scholar
- Brown D, Gault A, Geary R, Caron P, Burlacu R (2001) The Pacific infrasound event of April 23, 2001. Proceedings of the 23rd seismic research review, Jackson Hole, WYGoogle Scholar
- Buland R, Chapman C (1983) The computation of seismic travel times. J Acoust Soc Am 73:1271–1302Google Scholar
- Campus P, Christie DR (2010) Worldwide observations of infrasonic waves. This volume, pp. 181–230Google Scholar
- Ceranna L (2003) Simulating the propagation of infrasound in the atmosphere. Infrasound Technology Workshop, La Jolla, CAGoogle Scholar
- Ceranna L, Le Pichon A (2004) Simulating acoustic wave propagation in the atmosphere. Infrasound Technology Workshop, Hobart, TasmaniaGoogle Scholar
- Ceranna L, Le Pichon A (2006) The Buncefield fire: a benchmark for infrasound analysis in Europe. Infrasound Technology Workshop, Fairbanks, AlaskaGoogle Scholar
- Collins M (1993) A split-step Padé solution for the parabolic equation method. J Acoust Soc Am 93:1736–1742CrossRefGoogle Scholar
- Collins M (1998) The time-domain solution of the wide-angle parabolic equation including the effects of sediment dispersion. J Acoust Soc Am 84:2114–2125CrossRefGoogle Scholar
- de Groot-Hedlin C (2005) Modeling infrasound waveforms in a windy environment. Inframatics 11:1–7Google Scholar
- de Groot-Hedlin C (2006) Finite difference methods for acoustic and acousto-gravity wavefields: application to low frequency infrasound propagation. Proceedings of the 28th seismic research review, Orlando, FLGoogle Scholar
- de Groot-Hedlin C (2007) Finite difference modeling of infrasound propagation to local and regional distances. Proceedings of the 29th seismic research review, Denver, COGoogle Scholar
- Dessa J, Virieux J, Lambotte S (2005) Infrasound modeling in a spherical heterogeneous atmosphere. Geophys Res Lett 32:L12808CrossRefGoogle Scholar
- Dighe K, Whitaker R, Armstrong, 1998: Modeling study of infrasonic detection of a 1 kT atmospheric blast. Proceedings of the 20th annual seismic research symposium, Santa Fe, New MexGoogle Scholar
- Donn W, Rind D (1971) Natural infrasound as an atmospheric probe. Geophys J Roy Astron Soc 26:111–133CrossRefGoogle Scholar
- Donohue D, Kuttler J (1997) Modeling radar propagation over terrain. Johns Hopkins APL Tech Dig 18(2):279–287Google Scholar
- Drob D, Picone J, Garcés M (2003) The global morphology of infrasound propagation. J Geophys Res 108(D21):4680Google Scholar
- Evers L, Haak H (2006) Seismo-acoustic analysis of explosions and evidence for infrasonic forerunners. Infrasound Technology Workshop, Fairbanks, AlaskaGoogle Scholar
- Evers L, Haak H (2007) Infrasonic forerunners: exceptionally fast acoustic phases. Geophys Res Lett 34:L10806CrossRefGoogle Scholar
- Fornberg B, Sloan D (1994) A review of pseudospectral methods for solving partial differential equations. Acta Num 3:203–267Google Scholar
- Fritts D, Alexander J (2003) Gravity wave dynamics and effects in the middle atmosphere. R Geophys 22:275–308CrossRefGoogle Scholar
- Gainville O, Piserchia P, Depres B, Have P, Blanc-Benon P, Aballea F (2006) Numerical modeling of infrasound propagation in a realistic atmosphere. Infrasound Technology Workshop, Fairbanks, AlaskaGoogle Scholar
- Gainville O, Blanc-Benon Ph, Blanc E, Roche R, Millet C, Le Piver F, Despres B, Piserchia PF (2010) Misty picture: a unique experiment for the interpretation of the infrasound propagation from large explosive sources. This voslume, pp. 569–592Google Scholar
- Garcés M, Hansen R, Lindquist K (1998) Travel times for infrasonic waves propagating in a stratified atmosphere. Geophys J Int 135:255–263CrossRefGoogle Scholar
- Garcés M, Willis M, Le Pichon A (2010) Infrasonic observations of open ocean swells in the Pacific: deciphering the song of the sea. This volume, pp. 231–244Google Scholar
- Gardner C (1993) Gravity wave models for the horizontal wave number spectra of atmospheric velocity and density fluctuations. J Geophys Res 98:1035–1049CrossRefGoogle Scholar
- Gardner C (1995) Scale-independent diffusive filtering theory of gravity wave spectra in the atmosphere, the upper mesosphere and lower thermosphere: a review of experiment and theory. Geophysical Monograph Series, 87, AGU, Washington, DCGoogle Scholar
- Georges T, Beasley W (1977) Refraction of infrasound by upper-atmospheric winds. J Acoust Soc Am 61:28–34CrossRefGoogle Scholar
- Gibson R, Drob D, Norris D (2006) Advancement of infrasound propagation calculation techniques using synoptic and mesoscale atmospheric specifications. Proceedings of the 28th seismic research review, Orlando, FLGoogle Scholar
- Gibson R, Norris D, Drob D (2008) Investigation of the effects of fine-scale atmospheric inhomogeneities on infrasound propagation. Proceedings of the 30th monitoring research review, Portsmouth, VAGoogle Scholar
- Gottlieb D, Hesthaven J (2001) Spectral methods for hyperbolic problems. J Comput Appl Math 128:83–131CrossRefGoogle Scholar
- Hamilton M, Blackstock D (1998) Nonlinear acoustics. Academic Press, San DiegoGoogle Scholar
- Hedin A, Fleming E, Manson A, Scmidlin F, Avery S, Clark R, Franke S, Fraser G, Tsunda T, Vial F, Vincent R (1996) Empirical wind model for the upper, middle, and lower atmosphere. J Atmos Terr Phys 58:1421–1447CrossRefGoogle Scholar
- Herrin E, Kim T, Stump B (2006) Evidence for an infrasound waveguide. Geophys Res Lett 33:L07815CrossRefGoogle Scholar
- Hesthaven J, Gottlieb S, Gottlieb D (2007) Spectral methods for time-dependent problems. Cambridge University Press, Cambridge, MACrossRefGoogle Scholar
- Hetzer CH, Gilbert KE, Waxler R, Talmadge CL (2010) Generation of microbaroms by deep-ocean hurricanes. This volume, pp. 245–258Google Scholar
- Jensen F, Kuperman W, Porter M, Schmidt H (1994) Computational ocean acoustics. AIP Press, New YorkGoogle Scholar
- Jones M, Riley J, Georges T (1986) A versatile three-dimensional Hamiltonian ray-tracing program for acoustic waves in the atmosphere above irregular terrain. NOAA Special Report, Wave Propagation Laboratory, Boulder, COGoogle Scholar
- Kallistratova M (2002) Acoustic waves in the turbulent atmosphere: a review. J Atmos Ocean Technol 19:1139–1150CrossRefGoogle Scholar
- Kinney G, Graham K (1985) Explosive shocks in air. Springer, New YorkGoogle Scholar
- Kinsler L, Frey A, Coppens A, Sanders J (1984) Fundamentals of acoustics. Wiley, New YorkGoogle Scholar
- Krasnov V, Drobzheva Y, Lastovicka J (2007) Acoustic energy transfer to the upper atmosphere from sinusoidal sources and a role of nonlinear processes. J Atmos Solar-Terr Phys 69:1357–1365CrossRefGoogle Scholar
- Kulichkov S (2004) Long-range propagation and scattering of low-frequency sound pulses in the middle atmosphere. Meteorol Atmos Phys 85:47–60CrossRefGoogle Scholar
- Kulichkov S, Bush G, ReVelle D, Whitaker R, Raspopov O (2000) On so called “tropospheric” arrivals at long distances from surface explosions. Infrasound Technology Workshop, Passau, GermanyGoogle Scholar
- Kulichkov S, Avilov K, Popov O, Baryshnikov A (2003) Experience in using the pseudodifferential parabolic equation method to study the problems of long-rang infrasound propagation in the atmosphere. Inframatics 3:1–5Google Scholar
- Kulichkov S, Avilov K, Bush G, Popov O, Raspopov O, Baryshnikov A, ReVelle D, Whitaker R (2004) On anomalously fast infrasonic arrivals at long distances from surface explosions. Izv, Atmos Ocean Phys 40:1–9Google Scholar
- Le Pichon A, Blanc E, Drob D, Lambotte S, Dessa J, Lardy M, Bani P, Vergniolle S (2005) Infrasound monitoring of volcanoes to probe high-altitude winds. J Geophys Res 110:D13106CrossRefGoogle Scholar
- Le Pichon A, Antier K, Drob D (2006) Multi-year validation of the NRL-G2S wind fields using infrasound from Yasur. Inframatics 16:1–9Google Scholar
- Lingevitch J, Collins M, Siegmann W (1999) Parabolic equations for gravity and acousto-gravity waves. J Acoust Soc Am 105:3049–3056CrossRefGoogle Scholar
- Lingevitch J, Collins M, Dacol D, Drob D, Rogers J, Siegmann W (2002) A wide angle and high Mach number parabolic equation. J Acoust Soc Am 111:729–734CrossRefGoogle Scholar
- Lott F, Millet C (2010) The representation of gravity waves in atmospheric general circulation models (GCMs). This volume, pp. 679–694Google Scholar
- McDonald B, Kuperman W (1985) Time domain solution of the parabolic equation including nonlinearity. J Comput Math Appl 11:843–851CrossRefGoogle Scholar
- McDonald B, Kuperman W (1987) Time domain formulation for pulse propagation including nonlinear behavior at a caustic. J Acoust Soc Am 81:1406–1417CrossRefGoogle Scholar
- McKenna S (2005) Infrasound wave propagation over near-regional and tele-infrasonic distances. PhD Dissertation, Southern Methodist University, Dallas, TXGoogle Scholar
- McKenna M, Stump B, Hayek S, McKenna J, Stanton T (2007) Tele-infrasonic studies of hard-rock mining explosions. J Acoust Soc Am 122:97–106CrossRefGoogle Scholar
- Norris D (2007) Waveform modeling and comparisons with ground truth events. Infrasound Technology Workshop, TokyoGoogle Scholar
- Norris D, Gibson R (2002) InfraMAP enhancements: Environmental/propagation variability and localization accuracy of infrasonic networks. Proceedings of the 24th seismic research review, Ponte Vedra Beach, FLGoogle Scholar
- Norris D, Gibson R (2004a) Advanced tools for infrasonic modeling. Inframatics 5:13–19Google Scholar
- Norris D, Gibson R (2004b) Validation studies using a TDPE propagation model and near real-time atmospheric specifications. Infrasound Technology Workshop, Hobart, TasmaniaGoogle Scholar
- Norris D, Bongiovanni K, Masi J (2008) Nonlinear propagation modeling of infrasound. J Acoust Soc Am 123:3829CrossRefGoogle Scholar
- O’Brien M, Shields G (2004) Infrasound source location using time-varying atmospheric models. Proceedings of the 26th seismic research review, Orlando, FLGoogle Scholar
- Ostashev V (1997) Acoustics in moving inhomogeneous media. E & FN Spon, LondonGoogle Scholar
- Ostashev V, Wilson D, Liu L, Aldridge D, Symons N, Marlin D (2005) Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation. J Acoust Soc Am 117:503–517CrossRefGoogle Scholar
- Picone J, Hedin A, Drob D, Aiken A (2002) NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues. J Geophys Res 107:1468CrossRefGoogle Scholar
- Pierce A, Kinney W (1976) Computational techniques for the study of infrasound propagation in the atmosphere. Air Force Geophysics Laboratories Technical Report AFGL-TR-76-56, Hanscom AFB, MAGoogle Scholar
- Pierce A, Moo C, Posey J (1973) Generation and propagation of infrasonic waves. Air Force Cambridge Research Laboratories Technical Report AFCRL-TR-73-0135, Bedford, MAGoogle Scholar
- Sutherland L, Bass H (2004) Atmospheric absorption in the atmosphere up to 160 km. J Acoust Soc Am 115:1012–1032CrossRefGoogle Scholar
- Tappert F, Spiesberger J, Boden L (1995) New full-wave approximation for ocean acoustic travel time predictions. J Acoust Soc Am 97:2771–2782CrossRefGoogle Scholar
- Trefethen L (2000) Spectral Methods in MATLAB. SIAM, PhiladelphiaGoogle Scholar
- van der Eerden F, Védy E, Salomons E (2004) Prediction of shock waves over a large distance: a hybrid method. Proceedings of the 11th symposium on long range sound propagation, Fairlee, VTGoogle Scholar
- West M, Gilbert K, Sack R (1992) A tutorial on the Parabolic equation (PE) model used for long range sound propagation in the atmosphere. Appl Acoust 37:31–49CrossRefGoogle Scholar