COMSOL Acoustics Module Finite Element Modeling for Infrasound Propagation Remote monitoring of a suite of sources, both manmade and naturally occurring, are of interest to military and other government agencies. One such monitoring technology uses infrasound, or subaudible acoustics, which can propagate tens to thousands of kilometers depending on source strength without losing signal character. The following discussion highlights the feasibility of methods for the modeling of infrasound propagation. Generally classified as sound between 0.05 and 20 Hz, infrasound cannot be heard by human beings, but can be detected on specialized subaudible microphones, which operate on the principle of a vibrating pressure field generating recordable electronic impulses. Classical infrasound monitoring focuses on sourceto- receiver distances greater than 250 km, where more recent infrasound monitoring research has focused on distances closer than 150 km, bridging the distance between long-range acoustics and true infrasound monitoring. Historically, parabolic equation (PE) methods have been developed for the numerical solution of long-range (> 500 km) infrasound propagation in a layered atmosphere. This technique can be powerful for long-range propagation due to its simple numerical implementation and limited use of computational resources. PE techniques are analogous to frequency- wavenumber investigations in observed data, predicting how trapped energy and spherical wave front phenomena interact not only in arrival times but also in the attenuation of the observed amplitude. The PE method approximates the wave equation by modeling energy propagation along a cone oriented in a preferred direction. This approximation provides reasonable accuracy over long propagation distances. However, for short-range propagation (< 50 km), the mathematical formulations used in the PE method break down and do not provide sufficient accuracy needed for precise measurements and predictions.  Figure 1. Idealized atmospheric structure with a linear trend in the troposphere. To produce high-fidelity propagation modeling coupled to complex source functions, the author worked in conjunction with Dr. Kyle Koppenhoefer and Dr. Jeffrey Crompton of AltaSim Technologies to develop finite element method (FEM) based acoustic solutions, such as those implemented in COMSOL Multiphysics, to accurately represent the propagation of acoustic waves without the approximations in the PE method. These solutions can be used to provide accurate solutions for short-range propagation acoustic waves where the PE method is not well suited. However, FEM methods require large computational resources (i.e., memory and cpu time) to solve long-range propagation problems makeing accurate solutions difficult. Thus, FEM and PE methods complement each other for the solution of infrasound propagation in layered atmospheres; FEM-based solution providing accuracy in the short range and PE-based solutions accurately simulating behavior at large distances. To validate the use of COMSOL’s FEM acoustics code, we present two cases where the PE and FEM methods are evaluated.  Figure 2. Space Shuttle Columbia on takeoff . Photo courtesy of NASA. Infrasound Propagation Infrasound propagation depends on the effective sound speed (Ceff) of the atmosphere through which it travels, so it is imperative to properly characterize the atmospheric conditions as close to the time and location of the propagation pathway as possible. The propagation pathways are governed by effective sound speed profiles, calculated by: Ceff = Ct + n·v, where Ct ~ 20.07(T)1/2, T is absolute temperature in Kelvin, and n·v is the component of wind speed in the propagation direction. Temperature is the dominant factor in calculating the effective sound speed; wind speed and direction are only secondary factors. In order for up-going infrasonic energy to be observed at Earth’s surface, it must reach an area of higher sound velocity than at the point of origin. If this occurs, the energy turns and then returns to the surface of the earth. Figure 1 shows the sample effective sound speed profile with the regions of the atmosphere labeled. How the atmosphere is quantified for data analysis and modeling depends on the particular areas of the atmosphere through which the infrasound propagates. For source-toreceiver paths of less than 200 km, local meteorological information is imperative to accurately characterize the propagation medium. Surface measurements are inadequate to properly characterize the whole height of the atmospheric profile through which the infrasound propagates. It is necessary to use radiosonde, weather balloon or equivalent measurements for the temperature and wind profiles to create the Ceff used in modeling. For distances greater than 200 km from the source to the receiver, the signal may travel via highly variable energy pathways that travel primarily through the upper atmosphere, the thermosphere, and propagate vast distances though a medium that changes little over the time span of months. Most of these sources are either large (such as energy from the Krakatoa volcano eruption in 1883, which reverberated around the world eight times before dying out), from substantial vertical seismic displacements from earthquakes, or occur in the upper atmosphere, such as meteorites. Despite the linear depiction of the tropospheric effective sound speed profile from Figure 1, the tropospheric structure is sometimes governed by fast moving weather systems and is considerably more variable than the atmosphere above the tropopause. Short-lived temperature inversions can create ephemeral ducts with higher sound speed velocities than are found at the ground. Being able to accurately quantify these ducts in time and space is imperative for remote monitoring using infrasound by developing computational methods to effectively manage discontinuities and rapid changes in temperature and wind with altitude. [img=Figure 3. The PE solution for the Columbia, above. 1 Hz was taken to be the dominantfrequency for modeling, determined from the observed data. COMSOL FEMAcoustics Module solution, below, for the effective sound speed profile seen in figure2, 0.25 Hz dominant frequency.]http://www.comsol.com/shared/images/stories/finite_element_modeling_infrasound_propagation/html/figure3.jpg[/img] Figure 3. The PE solution for the Columbia, above. 1 Hz was taken to be the dominant frequency for modeling, determined from the observed data. COMSOL FEM Acoustics Module solution, below, for the effective sound speed profile seen in figure 2, 0.25 Hz dominant frequency. Long-Range Infrasound Propagation Worldwide infrasound arrays observe a variety of sources at variable distances. Earthquakes, volcanoes, mining explosions, and man-made atmospheric explosions are some of the most common signals observed on infrasound arrays, but bolides (meteors) and shuttle reentries are also recorded at very long propagation distances, hundreds to thousands of kilometers. “ COMSOL provides highly accurate solutions by solving the partial differential equation for acoustic wave propagation without the approximations used in the PE method.” Observations from supersonic atmospheric sources, such as space shuttle re-entries, have been recorded on the infrasound arrays from initial installation and have been subject to intense study over the years. As early as 1971, infrasound signals were observed from the Apollo spacecraft flights and recordings continue through today. The events of the February 1, 2003 Columbia space shuttle re-entry failure provide the first case where an explosion at altitude has a known location in fourdimensional space and time, as well as a well-characterized atmospheric profile in addition to being recorded on an infrasound array approximately 600 km away in Lajitas, Texas. The three-dimensional shuttle path was recorded by NASA and the timing of the events that led to the disintegration was known; the trajectory and timing can then be combined with a well-characterized atmospheric profile to produce a graphical representation of the paths the acoustic energy takes through the atmosphere. Originally adapted from underwater acoustic studies, PE (Parabolic Equation) modeling provides a field solution for a complete vertical plane at one frequency. An infrasound monitoring community standard PE code was compared in this effort, and it steps forward from a source and calculates an attenuation field for predicting amplitudes along the vertical slice. In using the PE codes, it is imperative that the computational atmosphere be deep enough to include all viable energy pathways. This depth of field required for PE modeling is where the high-accuracy advantage of finite element modeling breaks down. The PE run in Figure 3 took minutes to execute on a laptop system and utilized the effective sound speed profile provided by the Naval Research Laboratory using data from the time of the Columbia disintegration from the NOAA Global Forecast System (GFS), NASA Goddard Space Flight Center (GFSC), and Goddard Earth Observing System (GEOS) system for the 0 to 55 km region, with the explosion located at 62.2 km elevation.  Figure 4. Variable signal character between near-regional and long-range (tele-infrasonic) propagation pathways. In contrast, the FEM solution seen in Figure 3 for the same atmospheric profile took five days to run on a 16 GB quadcore Mac Pro, for 0.25 Hz, and only propagated out to 200 km, rather than the full distance of 600 km (not pictured). The two results correlate well over the distances executed in the FEM model, bearing in mind the change in frequency content from 1 Hz to 0.25 Hz and associated change in wavelength. While accurate, the computational resources required to produce equivalent solutions to the PE codes at these distances indicate that the PE solutions would be more efficient.  Figure 5. Above ground detonation of 100 lbs of ANFO from calibration experimentation. Short-Range Infrasound Propagation At shorter ranges, the advantage of COMSOL’s FE method is readily apparent. Recently, infrasound propagation over short range, less than 100 km, has become of greater interest. At long distances, such as the Columbia propagation pathways, the fine-scale source structure found in the propagating energy is smeared in the observed signal. At the shorter distances of 30-100 km presented below, retaining source character becomes more important, as there is less smearing in the observed signal. The difference in signal character from small, near-regional impulsive sources, and energy that has traveled much greater distances can be seen in Figure 4. Note the difference in time scale between the recordings, where the near-regional signals last on the order of a few seconds, and the diffuse teleinfrasonic recording lasts on the order of tens to hundreds of seconds. COMSOL provides highly accurate solutions by solving the partial differential equation for acoustic wave propagation without the approximations used in the PE method. Thus, the full characteristics of the source will be included in the solution. Modeling sources as diverse as point explosions, as shown in Figure 4, or structural emanations, COMSOL supports integrating the source and propagation functions in the same model. This flexibility enables infrasound modeling of many conditions that were previously difficult to solve. Thus, COMSOL offers advantages beyond the additional accuracy found in the FEM solutions. It opens up the study of infrasound to a much broader range of sources while permitting the study of infrasound in the near field. COMSOL also provides the capability to develop transient and time-harmonic solutions. The transient solution most accurately represents short duration sources, such as point source explosions shown in Figure 5.  Figure 6. Energy propagation pathways through the lower atmosphere for regional propagation at 2 Hz. Figure 6 shows the propagation of a 2 Hz signal over 30 km produced using COMSOL’s Acoustics Module. The variation of sound speed through the layers of the atmosphere strongly influences the propagation of this signal. When the atmospheric conditions are favorable the acoustic energy refracts to the Earth’s surface. The duct at approximately 2 km traps the acoustic energy necessary to produce favorable likelihood for observing infrasound energy from source to receiver. While future research to optimize boundary conditions and mesh sizes to minimize run time and computational resources is ongoing, COMSOL’s Acoustic Module offers the long-range acoustics and near-regional infrasound monitoring community a very effective tool to produce highly accurate, high-resolution propagation modeling for situations where integrating complex sources is important. ACKNOWLEDGEMENTS The author would like to acknowledge the input of Dr. Eugene Herrin of Southern Methodist University, Dr. Sergei Yushanov of AltaSim Technologies, and Dr. Jason Mc- Kenna of US Army ERDC. The atmospheric database used to model the Columbia was NRL-G2S. Thanks to Doug Drob at the Naval Research Laboratory for providing this data set. For more information on the infrasound signal generated by the Columbia disaster, see McKenna, M., and E. Herrin (2006), Validation of infrasonic waveform modeling using observations of the STS107 failure upon reentry. Geophys. Res. Lett., 33, LXXXXX, doi:10.1029/2005GL024801. Permission to publish was granted by Director, Geotechnical & Structures Laboratory. Approved for public release; distribution is unlimited. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.  Mihan H. McKenna, Ph.D. About the Author Since July of 2005, Dr. McKenna has been a Research Geophysicist in the Structural Engineering Branch of the Geotechnical and Structures Laboratory at the U.S. Army Engineer Research and Development Center (ERDC), a group of 7 R&D laboratories for the US Corps of Engineers (USACE) and the US Army. Dr. McKenna’s area of expertise is acquiring, interpreting, and numerically modeling seismic, acoustic, and infrasound source and propagation phenomenology to support tactical decision makding for forward deployed expeditionary forces. She directs the Denied Area Monitoring and Exploitation Systems working group at ERDC, which has ongoing integrated highperformance computing modeling and experimental research with the Department of Defense, Department of Energy, Defense Intelligence Agency, Los Alamos National Laboratory and academic institutions. She supports several ongoing DARPA and DTRA programs concerned with hard target defeat and strategic imaging and monitoring of trans-national threats. In addition, Dr. McKenna is a federally certified bridge inspector and conducts structural monitoring of transportation infrastructure from remote stand-off. |
分享到
豆瓣网
开心网
人人网
QQ书签
Google
1979个朋友已经阅读过这篇文章
用户评论
没有找到数据. , |
微信
新浪微博