Christophe Millet

A low-order reduced model for the long range propagation of infrasounds in the atmosphere

This paper considers a class of low-order, range-dependent propagation models obtained from the normal mode decomposition of infrasounds in complex atmospheres. The classical normal mode method requires calculating eigenvalues for large matrices making the computation expensive even though some modes have little influence on the numerically obtained results. By decomposing atmospheric perturbations into a wavelet basis, it is shown that the most sensitive eigenvalues provide the best reduced model for infrasound propagation. These eigenvalues lie on specific curves in the complex plane that can be directly deduced from atmospheric data through a WKB approach. The computation cost can be reduced by computing the invariant subspace associated with the most sensitive eigenvalues. The reduction method is illustrated in the case of the Fukushima explosion (12 March 2011). The implicitly restarted Arnoldi algorithm is used to compute the three most sensitive modes, and the correct tropospheric arrival is found with a cost of 2% of the total run time. The cost can be further reduced by using a stationary phase technique. Finally, it is shown that adding uncertainties triggers a stratospheric arrival even though the classical criteria, based on the ratio of stratospheric sound speed to that at ground level, is not satisfied.

The Representation of Gravity Waves in Atmospheric General Circulation Models (GCMs)

A potential long-term application of infrasound detection is related to the fact that nonlinear mountain flow dynamics and breaking gravity waves (GWs) in the high atmosphere produce infrasounds and/or affect the propagation of the infrasounds. In the future, we can imagine that the compressible models developed in meteorology will permit to link these mesoscale meteorological events to the infrasounds they produce.

Acoustic near field of a transonic instability wave packet

We consider the problem of acoustic radiation generated by a spatial instability wave on a weakly developing shear flow. Assuming a local WKBJ approximation for the instability wave near its maximum, we compute the acoustic pressure field by using a Fourier transform along the streamwise direction. When the instability wave is close to transonic near its maximum amplitude, approximations for this pressure field are obtained by a steepest descent method. A branch cut and several saddle points are shown possibly to contribute to the approximation. A detailed analysis of these contributions is provided. The modifications of the acoustic field when we pass from subsonic to supersonic are examined. In particular, the superdirective character of the acoustic field of subsonic instability waves and the directivity pattern of supersonic waves are shown to be both compatible with our mathematical description and associated with a single saddle-point contribution. The acoustic near field is also shown to possess a caustic around which a specific approximation is derived. In a large region of the physical space, the near field is composed of two saddle-point contributions. Close to the shear flow, one of these contributions degenerates into a branch-point contribution which always becomes dominant over the instability wave downstream of a location that is computed. An interesting phenomenon is observed in certain regions downstream of the maximum: the transverse behaviour of the instability wave has to be exponentially growing far from the shear layer to match the acoustic field. We demonstrate that this phenomenon neither requires a branch-point contribution nor a supersonic instability wave.

Infrasound propagation and model reduction in randomly layered media

A consensus has emerged within the infrasound research community that gravity waves are filtered out in the available atmospheric models. Apart from occasionally strong lower-atmospheric effects, the major wave influences occur in the middle atmosphere, between 10 and 110 km altitudes. In the present approach, the unresolved gravity waves are represented as a random field that is superimposed on the average background state, and the wave equation is solved using a reduced-order model, starting from the classical normal mode technique. The reduced model is obtained by retaining a few propagating modes, with the aim of simplifying the acoustic model to the point that the predicted statistics of waveforms are correct, even though some small irrelevant details is lost. We focus on the asymptotic behavior of the transmitted waves in the weakly heterogeneous regime, for which the coupling between the wave and the medium is weak. The statistics of a transmitted broadband pulse are computed by decomposing the ori...

Non-orographic Gravity Waves: Representation in Climate Models and Effects on Infrasound

Long-range infrasound propagation is controlled by atmospheric waveguides that extend up to the mesosphere and lower thermosphere and whose efficiency is affected by gravity waves (GWs). These GWs are not explicitly represented in the global models often used to calculate infrasound propagation because their spatial scales are well below the models’ resolution. These unresolved GWs also transport momentum and control in good part the large-scale circulation in the middle atmosphere. These two issues make that the GWs need to be parameterized to improve the datasets used to calculate infrasound propagation as well as in the atmospheric general circulation model (AGCMs) that are used to make weather forecasts and climate predictions. These two issues gain in being treated in conjunction. From this, improved infrasound calculations could be made by using a realistic amount of GWs. In return, using infrasound records could help specifying important characteristics of the GWs that are parameterized in the climate models. The paper presents a research framework developed to address these issues. It first presents a non-orographic GWs parameterization used and tested in a well-established AGCM, emphasizing the most recent developments, like the introduction of stochastic techniques and a better specification of the GWs sources. The significance of GWs on the global climate is then illustrated by making sensitivity tests where the frontal and convective GWs parameters are moderately changed. These changes impact the structure of the jets in the midlatitude stratosphere and the intensity of the sudden stratospheric warmings. The paper also presents a method to calculate long-range infrasound propagation, and to incorporate the contribution of the GWs that are parameterized in the AGCM. We then show that the changes in GW parameters tested in the model also impact infrasound propagation. This makes infrasound detection a potential tool to tune GWs parameterization in large-scale models.

Bayesian association of multiple infrasound events using long-range propagation models

The International Monitoring System (IMS) is a worldwide network of monitoring stations that helps to verify compliance with the Comprehensive Nuclear Test-Ban Treaty by detecting events that might indicate violations of the treaty. The IMS uses a combination of four technologies: seismological, radionuclide, hydroacoustic, and infrasound. An important limitation of these technologies is related to the fact that the structure of the propagation medium is partially unknown. This is especially true for the infrasound technology, and indeed, a current trend is to undertake the impact of atmospheric variability on waveforms using computational models. Simulation-based predictions, however, are inherently limited by large uncertainties. Further, many thousands of detections are recorded per week and thus, the problem of calculating plausible waveforms for subsets of detections often leads to computational demands that exceed available resources. In this paper, we present a new powerful statistical model for analyzing and interpreting large-scale IMS data. The method is based on a parallel Markov chain Monte Carlo algorithm and full-wave modeling. The method can detect association when multiple, interacting events are present in the data. The posterior probability of no association can be estimated, thereby providing a way to reduce the false alarm rate in operational-like environments.The International Monitoring System (IMS) is a worldwide network of monitoring stations that helps to verify compliance with the Comprehensive Nuclear Test-Ban Treaty by detecting events that might indicate violations of the treaty. The IMS uses a combination of four technologies: seismological, radionuclide, hydroacoustic, and infrasound. An important limitation of these technologies is related to the fact that the structure of the propagation medium is partially unknown. This is especially true for the infrasound technology, and indeed, a current trend is to undertake the impact of atmospheric variability on waveforms using computational models. Simulation-based predictions, however, are inherently limited by large uncertainties. Further, many thousands of detections are recorded per week and thus, the problem of calculating plausible waveforms for subsets of detections often leads to computational demands that exceed available resources. In this paper, we present a new powerful statistical model for an...

An investigation of infrasound propagation over mountain ranges

Linear theory is used to analyze trapping of infrasound within the lower tropospheric waveguide during propagation above a mountain range. Atmospheric flow produced by the mountains is predicted by a nonlinear mountain gravity wave model. For the infrasound component, this paper solves the wave equation under the effective sound speed approximation using both a finite difference method and a Wentzel-Kramers-Brillouin approach. It is shown that in realistic configurations, the mountain waves can deeply perturb the low-level waveguide, which leads to significant acoustic dispersion. To interpret these results, each acoustic mode is tracked separately as the horizontal distance increases. It is shown that during statically stable situations, situations that are common during night over land in winter, the mountain waves induce a strong Foehn effect downstream, which shrinks the waveguide significantly. This yields a new form of infrasound absorption that can largely outweigh the direct effect the mountain induces on the low-level waveguide. For the opposite case, when the low-level flow is less statically stable (situations that are more common during day in summer), mountain wave dynamics do not produce dramatic responses downstream. It may even favor the passage of infrasound and mitigate the direct effect of the obstacle.

Infrasound scattering from stochastic gravity wave packets

Long-range infrasound propagation problems are characterized by a large number of length scales and a large number of propagating modes. In the atmosphere, these modes are confined within waveguides causing the sound to propagate through multiple paths to the receiver. In most infrasound modeling studies, the small scale fluctuations are represented as a “frozen” gravity wave field that is superimposed on a given average background state, and the normal modes are obtained using a single calculation. Direct observations in the lower stratosphere show, however, that the gravity wave field is very intermittent, and is often dominated by rather well defined large-amplitude wave packets. In the present work, we use a few proper modes to describe both the gravity wave field and the acoustic field. Owing to the disparity of the gravity and acoustic length scales, the acoustic field can be constructed in terms of asymptotic expansions using the method of multiple scales. The amplitude evolution equation involves ...

Spectral broadening of infrasound tones in mountain wave fields

Linear theory of acoustic propagation is used to analyze how infrasounds trapped within the lower tropospheric waveguide propagate across mountain waves. The atmospheric disturbances produced by the mountains are predicted by a semi-theoretical mountain gravity wave model. For the infrasounds, we solve the wave equation under the effective sound speed approximation both using a spectral collocation method and a WKB approach. It is shown that in realistic configurations, the mountain waves can deeply perturb the low level waveguide, which leads to significant acoustic dispersion. To interpret these results, we follow each acoustic mode separately and show which mode is impacted and how. We show that during statically stable situations, roughly representative of winter or night situations, the mountain waves induce a strong Foehn effect downstream which shrinks significantly the waveguide. This yield a new form of infrasound absorption, a form that can largely outweigh the direct effect of the mask the moun...

Interactions between intermittent gravity waves and infrasounds

Infrasound propagation modeling requires accurate wind speed and temperature gradients. Even though the accuracy of atmospheric specifications is constantly improving, it is well-known that the main part of gravity waves is not resolved in the available data. In most infrasound modeling studies, the unresolved gravity wave field is often represented as a deterministic field that is superimposed on a given average background state. Direct observations in the lower stratosphere show, however, that the gravity wave field is very intermittent, and is often dominated by rather well-defined wave packets. These observations suggest that the vertical spectra are likely to result from ensemble averages of quite narrow-banded periodograms. In this study we sample the spectrum by launching few monochromatic waves and choose the gravity-wave properties stochastically to mimic the intermittency. The statistics of acoustic signals are computed by decomposing the original signal into a sum of modal pulses. Owing to the ...