The Morávka meteorite fall: 2. Interpretation of infrasonic and seismic data

Abstract— The sound production from the Morávka fireball has been examined in detail making use of infrasound and seismic data. A detailed analysis of the production and propagation of sonic waves during the atmospheric entry of the Morávka meteoroid demonstrates that the acoustic energy was produced both by the hypersonic flight of the meteoroid (producing a cylindrical blast wave) and by individual fragmentation events of the meteoroid, which acted as small explosions (producing quasispherical shock waves). The deviation of the ray normals for the fragmentation events was found to be as much as 30° beyond that expected from a purely cylindrical line source blast. The main fragmentation of the bolide was confined to heights above 30 km with a possible maximum in acoustic energy production near 38 km. Seismic stations recorded both the direct arrival of the airwaves (the strongest signal) as well as air‐coupled P‐waves and Rayleigh waves (earlier signals). In addition, deep underground stations detected the seismic signature of the fireball. The seismic data alone permit reconstruction of the fireball trajectory to a precision on the order of a few degrees. The velocity of the meteoroid is much less well‐determined by these seismic data. The more distant infrasonic station detected 3 distinct signals from the fireball, identified as a thermospheric return, a stratospheric return, and an unusual mode propagating through the stratosphere horizontally and then leaking to the receiver.     

Numerical Simulation of Ionospheric Disturbances Generated by the Chelyabinsk and Tunguska Space Body Impacts

Numerical simulation of atmospheric disturbances during the first hours after the Chelyabinsk and Tunguska space body impacts has been carried out. The results of detailed calculations, including the stages of destruction, evaporation and deceleration of the cosmic body, the generation of atmospheric disturbances and their propagation over distances of thousands of kilometers, have been compared with the results of spherical explosions with energy equal to the kinetic energy of meteoroids. It has been shown that in the case of the Chelyabinsk meteorite, an explosive analogy provides acceptable dimensions of the perturbed region and the perturbation amplitude. With a more powerful Tunguska fall, the resulting atmospheric flow is very different from the explosive one; an atmospheric plume emerges that releases matter from the meteoric trace to an altitude of the order of a thousand kilometers.     

Propagation of auroral infrasonic waves studied by ray-tracings

On the basis of a ray tracing method the propagation and the attenuation of an auroral infrasonic wave are studied. Relations between the direct and reflected waves recorded at the Syowa Station, Antarctica, are clarified with regard to; (1) the delay time, (2) the intensity ratio, and (3) trace velocities. The time required for a wave to travel from the source to the ground is calculated as a function of a source altitude. The retardation time of the wave arrival behind the zenith crossing of the source current is deduced. A method is proposed for estimating the altitude of a source current from the retardation and a trace velocity of the wave. It is concluded that the existence of a supersonic equatorward motion of an electrojet which continues for a certain distance is necessary for the observation of auroral infrasonic waves. This distance must exceed at least 60 km equatorwards from the zenith to enable the direct wave to be observed and with total length of 930 km to enable the reflected wave to be observed. From these conditions it is also concluded that the infrasonic wave is not seen in mid latitudes and the reflected wave is a rare phenomenon.     

Parameters of infrasonic waves generated by the Chelyabinsk meteoroid on February 15, 2013

Data from infrasound stations are used to determine the basic parameters of infrasonic waves generated during the passage and airburst of the Chelyabinsk space body: time lag, duration, spectral structure, dispersion dependence, and celerity. A simulation is performed for the parameters of the infrasonic waves. A comparison between the simulation and observation results shows a good agreement.     

The Seismic Efficiency of Space Body Impacts

The numerical analysis of the propagation of shock waves initiated by either a space body striking the Earth’s surface, or underground explosions, allows us to compare the energies required to attain the same amplitudes of shock waves at impacts and explosions. Proceeding from this and based on the data of seismic efficiency of underground explosions, the authors have estimated the fraction of the kinetic energy of a space body transformed into the energy of seismic disturbances when the body strikes the Earth. This fraction is about 10^–3, which is an order of magnitude more than the most common estimates. Space bodies decelerating and collapsing in the atmosphere also generate seismic waves in the ground due to the impact of the air-shock wave on the Earth’s surface. In this case, the seismic efficiency is considerably lower, according to the calculations, it is about 10^–5.     

Influence of galactic nuclear explosions on the efficiency of the process of star formation

Periodic explosions in the nucleus of a galaxy generate strong shock waves. The shock waves, in moving outwards, produce highly compressed thin layers of gas at distances much larger than the thickness of the layer. When the gas in this layer undergoes fragmentation, the Jeans mass is found to be much less than that if the fragmentation proceeded under normal gravitational pull. It is, therefore, concluded that the explosive events in the galactic centres make the process of star formation highly efficient in the central region of galaxies.     

The Košice meteorite fall: Atmospheric trajectory,fragmentation, and orbit

The Ko?ice meteorite fall occurred in eastern Slovakia on February 28, 2010, 22:25 UT. The very bright bolide was imaged by three security video cameras from Hungary. Detailed bolide light curves were obtained through clouds by radiometers on seven cameras of the European Fireball Network. Records of sonic waves were found on six seismic and four infrasonic stations. An atmospheric dust cloud was observed the next morning before sunrise. After careful calibration, the video records were used to compute the bolide trajectory and velocity. The meteoroid, of estimated mass of 3500 kg, entered the atmosphere with a velocity of 15 km s^?1 on a trajectory with a slope of 60° to the horizontal. The largest fragment ceased to be visible at a height of 17 km, where it was decelerated to 4.5 km s^?1. A maximum brightness of absolute stellar magnitude about ?18 was reached at a height of 36 km. We developed a detailed model of meteoroid atmospheric fragmentation to fit the observed light curve and deceleration. We found that Ko?ice was a weak meteoroid, which started to fragment under the dynamic pressure of only 0.1 MPa and fragmented heavily under 1 MPa. In total, 78 meteorites were recovered in the predicted fall area during official searches. Other meteorites were found by private collectors. Known meteorite masses ranged from 0.56 g to 2.37 kg. The meteorites were classified as ordinary chondrites of type H5 and shock stage S3. The heliocentric orbit had a relatively large semimajor axis of 2.7 AU and aphelion distance of 4.5 ± 0.5 AU. Backward numerical integration of the preimpact orbit indicates possible large variations of the orbital elements in the past due to resonances with Jupiter.     

Genesis—An artificial,low velocity “meteor” fall and recovery: September 8, 2004

Abstract— On September 8, 2004, Genesis, a manmade space capsule, plummeted to Earth after almost three years in space. A ground‐based infrasound array was deployed to Wendover, Nevada, to measure the “hypersonic boom” from the reentry, since the expected initial reentry speed of the body was about 11 km/sec. Due to the complete failure of its dual parachute system, we had a unique opportunity to assess the degree of reliability of our previously developed relations for natural meteors and bolides to analyze this well‐characterized manmade body. At ?20–50 km from the nominal trajectory, we succeeded in recording over two minutes of infrasonic signals from Genesis. Here we report on subsequent analyses of these infrasonic data, including an assessment of the expected entry characteristics on the basis of a bolide/meteor/fireball entry model specifically adapted to modeling reentering manmade objects. From these simulations, we were able to evaluate the line source blast wave relaxation radius, the differential acoustic efficiency, etc., to compute an approximate total power balance during entry. Next, we analyzed the detailed signals arriving from Genesis using a numerical, signal detection and wave processing software package (Matseis/Infra_Tool). We established the initial and subsequent arrivals and evaluated its plane wave back azimuths and elevation arrival angles and the degree of maximum, pair‐wise cross‐correlation, its power spectrum, spectrogram analysis, standard seismic f‐k analysis, etc. From the associated entry parameters, we computed the kinetic energy density conservation properties for the propagating line source blast waves and compared these predictions against observed ground‐based infrasound amplitude and wave period data as a function of range. We discovered that previously computed differential acoustic efficiencies were unreliable at Mach numbers below about 10. This is because we had assumed that a line source explosion was applicable, whereas at very low Mach numbers, typical of recovered meteorites, the detailed source characteristics are closer to those of supersonic objects. When corrections for these unphysical, very high efficiencies were made, agreement between theory and observations improved. We also made an assessment for the energy of the blast wave source from the ground‐based infrasound data using several other techniques that were also adapted from previous bolide studies. Finally, we made a top‐down‐bottom‐up assessment of the line source wave normals propagating via refraction downward into the complex middle atmospheric environment. This assessment proved to be generally consistent with the digital signal processing analysis and with the observed time delay between the known Genesis reentry and the infrasonic observations.     

Ionosphere disturbances accompanying the flight of the Chelyabinsk body

Data received from a network of ionosondes located at distances of 1500–3100 km from the Chelyabinsk meteorite site are used to analyze ionospheric disturbances at a height of approximately 300 km following the flight and explosion of the space body. The fall of the meteoroid is believed to be accompanied by the generation of gravitational waves in the neutral atmosphere and traveling ionospheric disturbances. The velocity and period of the latter are 600–700 m/s and 70–135 min, respectively; the amplitude of relative electron concentration disturbances is 10–20%. There is evidence of the 6–7 h ionospheric presence of wave electron concentration disturbances with relative amplitude of 10–20%, which could have been caused by long-living whirlwinds in the upper atmosphere.     

Determination of the height of the “meteoric explosion”

When cosmic bodies of asteroidal and cometary origin, with a size from 20 to approximately 100 m, enter dense atmospheric layers, they are destroyed with a large probability under the action of aerodynamic forces and decelerated with the transfer of their energy to the air at heights from 20–30 to several kilometers. The forming shock wave reaches the Earth’s surface and can cause considerable damage at great distances from the entry path similar to the action of a high-altitude explosion. We have performed a numerical simulation of the disruption (with allowance for evaporation of fragments) and deceleration of meteoroids having the aforesaid dimensions and entering the Earth’s atmosphere at different angles and determined the height of the equivalent explosion point generating the same shock wave as the fall of a cosmic body with the given parameters. It turns out that this height does not depend on the velocity of the body and is approximately equal to the height at which this velocity is reduced by half. The obtained results were successfully approximated by a simple analytical formula allowing one to easily determine the height of an equivalent explosion depending on the dimensions of the body, its density, and angle of entry into the atmosphere. A comparison of the obtained results with well-known approximate analytical (pancake) models is presented and an application of the obtained formula to specific events, in particular, to the fall of the Chelyabinsk meteorite on February 15, 2013, and Tunguska event of 1908, is discussed.     

Plasma wave propagation in the neighborhood of a magnetic neutral point

A linearized magnetohydrodynamic formalism is used to examine the propagation in two dimensions of transverse waves in a plasma in which is embedded a curl-free magnetic field. Only waves of frequency less than the ion cyclotron frequency are considered. The behavior of a wave packet near the magnetic neutral point is deduced from the general solution to the problem, which is found in terms of Bessel functions whose order is frequency dependent. It is shown that a disturbance propagates through the medium with a group velocity that decreases from the speed of light at large distances from the neutral point to zero at the neutral point, and that the amplitudes of the velocities associated with the disturbance diverge there. It is suggested that the stagnation of waves near the origin and the deformation of the magnetic field resulting from the large plasma-flow velocities may provide a clue to the formation of the magnetic neutral sheet required by several flare theories and a theory of the acceleration of cosmic rays.     

Dispersive shock waves in the solar wind

Compressional waves in the solar wind propagating over large distances are likely to steepen into shock waves where the increase in the amplitude is balanced by dissipation. Dispersive effects caused by, e.g. Hall currents perpendicular to the ambient magnetic field can influence the generation and propagation of shock waves. In the present study the dispersion is considered weak but in time its importance can grow. When the effect of dispersion is strong enough, it can balance the nonlinear steepening of waves leading to the formation of solitons. The obtained results show that the weak dispersion will alter the amplitude and propagation speed of the shock wave. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recent Advances in Bolide Entry Modeling:A Bolide Potpourri*

In this paper, we will review recent research on numerous aspects of bolide entry into a planetary atmosphere, including such topics as the entry dynamics, energetics, ablation, deceleration, fragmentation, luminosity, mechanical wave generation processes, a total (panchromatic) power budget including differential and integral efficiencies vs. time, etc. Fragmentation, triggered by stagnation pressures exceeding the bolide breaking strength, has been included with subsequent wake behavior in either a collective or non-collective behavior limit. We have also utilized the differential panchromatic luminous efficiency of ReVelle and Ceplecha (2002c, Proceedings of Asteroids, Comets, Meteors ACM 2002, 29 July–2August, 285–288) to compute bolide luminosity. In addition we also introduce the concept of the differential and integral acoustic/infrasonic efficiency and generalized it to the case of mechanical wave efficiency including internal atmospheric gravity waves generated during entry. Unlike the other efficiencies which are assumed to be a constant multiple of the luminous efficiency, the acoustic efficiency is calculated independently using a 'first principles' approach. All of these topics have been pursued using either a homogeneous or a porous meteoroid model with great success. As a direct result, porosity seems to be a rather good possibility for explaining anomalous meteoroid behavior in the atmosphere.     

Recent Advances in Bolide Entry Modeling: A Bolide Potpourri

In this paper, we will review recent research on numerous aspects of bolide entry into a planetary atmosphere, including such topics as the entry dynamics, energetics, ablation, deceleration, fragmentation, luminosity, mechanical wave generation processes, a total (panchromatic) power budget including differential and integral efficiencies versus time, etc. Fragmentation, triggered by stagnation pressures exceeding the bolide breaking strength, has been subsequently included in either a collective or non-collective wake behavior limit. We have also utilized the differential panchromatic luminous efficiency of ReVelle and Ceplecha (2002) to compute bolide luminosity. In addition we also introduce the concept of the differential and integral acoustic/infrasonic efficiency and generalized it to the case of mechanical wave efficiency including internal atmospheric gravity waves generated during entry. Unlike the other efficiencies which are assumed to be a constant multiple of the luminous efficiency, the acoustic efficiency is calculated independently using a “first principles” approach. All of these topics have been pursued using either a homogeneous or a porous meteoroid model with great success. As a direct result, porosity seems to be a rather good possibility for explaining anomalous meteoroid behavior in the atmosphere. Invited Paper Presented at Meteoroids 2004; Presented at University of Western Ontario, London, Ontario, Canada, August 16–20, 2004     

Leading wave as a component of the spiral pattern of the galaxy

The spiral pattern of the Galaxy, identified by analyzing the kinematics of young stars within 3 kpc of the Sun, is Fourier decomposed into spiral harmonics. The spiral pattern of the Galaxy is shown to be representable as a superposition of trailing and leading waves with interarm distances of λ = 1.8 ± 0.4 and 4 ± 2 kpc, respectively. Shock waves are probably present only in the portions of the trailing spiral pattern where it crosses the crest of the leading wave. The small interarm distance of the trailing spiral wave (λ = 1.8 kpc) can be explained by its evolution—by the decrease in the interarmd istance as the wave is displaced toward the inner Lindblad resonance. The Carina arm may be part of this resonance ring.     

A solution of linearized Einstein field equations in vacuum used for the detection of the stochastic background of gravitational waves

A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the linearized Ricci tensor results equal to zero. Then the effect on test masses of our solution, which is a gravitational wave, is discussed. In our solution test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. In this way it is possible to think that gravitational waves would be longitudinal waves, but, from careful investigation of this solution, it is shown that the tidal forces associated with gravitational waves act along the directions orthogonal to the direction of propagation of waves. The computation is first made in the long wavelengths approximation (wavelength much larger than the linear distances between test masses), then the analysis is generalized to all gravitational waves.

In the last sections of this paper it is shown that the frequency dependent angular pattern of interferometers can be obtained from our solution and the total signal seen from an interferometer for the stochastic background of gravitational waves is computed.     

Forced waves in the martian atmosphere from MGS TES nadir data

We have analyzed the temperature retrievals from Mars Global Surveyor (MGS) Thermal Emission Spectrometer (TES) nadir spectra to yield latitude-height resolved maps of various atmospheric forced wave modes as a function of season for a full Mars year. Among the isolated wave modes is the zonal mean, time mean temperature, which we used to derive zonal mean zonal winds and stationary wave quasi-geostrophic indices of refraction, diagnostic of their propagation. The diurnal Kelvin wave was isolated in the data, with results roughly consistent with models (Wilson and Hamilton, 1996, J. Atmos. Sci. 33, 1290-1326). The s = 1 and s = 2 stationary waves were found to have significant amplitude in ducts extending up the winter polar jets, while the s = 3 stationary wave was found to be confined to near the surface. The s = 1 stationary wave was found to have little phase tilt with height during northern winter, but significant westward phase tilt with height in the southern winter. This indicates that the wave carries heat poleward, slightly more than that found in Barnes et al. (1996; J. Geophys. Res. 101, 12,753-12,776). The s = 1 stationary wave is likely the dominant mechanism for eddy meridional heat transport for the southern winter. We noted that the phase of the s = 2 stationary wave is nearly constant with time, but that the s = 1 stationary wave moved 90° of longitude from fall to winter and back in spring in the North. While interannual variability is not yet addressed, overall, these results provide the first comprehensive benchmark for forced waves in Mars’s atmosphere against which future atmospheric models of Mars can be compared.     

Alfvén waves in a space plasma and its role in the solar wind interaction with comets

The importance of Alfvén wave generation in interacting plasmas is discussed in general and illustrated by the example of solar wind interaction with cometary plasma. The quasi-linear theory of Alfvén wave generation by cometary ions at distances far from the cometary nucleus is reviewed. The incorporation of a diabatic plasma compression effects into this theory modifies the spectrum of Alfvén waves and the integral intensity of magnetic field fluctuations previously published. These results are in quantitative agreement with thein situ observations near the comets Giacobini-Zinner and Halley. However, the polarization of quasi-linearly excited waves needs further detailed comparison with observations.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Numerical simulation of atmospheric bore waves on Mars

The Viking Orbiters imaged early morning, long, linear wave clouds along the flanks of the Tharsis volcanoes during late northern spring and early summer. These clouds are believed to be a product of either an atmospheric bore wave or a hydraulic jump generated by nightly katabatic winds. The Mars Regional Atmospheric Modeling System was used to study the interaction of the katabatic flows with the surrounding atmosphere to determine what mechanism is responsible for the clouds. Simulations at Ls=90°, 100°, 142°, 180°, 270°, and 358° were conducted focusing on the eastern flank of Olympus Mons. Model results compare well with Viking observations and closely approximate theoretical treatments of atmospheric bores. Strong downslope flows are simulated during the night, with a bore wave forming on and behind a well-defined katabatic front. The observed seasonality of the clouds was reproduced in the simulations; the bore was deeper and faster during northern summer and weakest during the winter. When the bore was strong, it was undular in form, and generated vertically propagating gravity waves in the atmosphere above. During the winter, the atmospheric structure was such that any gravity waves generated damped with height. Less atmospheric water vapor abundance during northern winter, as compared to the summer, is also a factor in the seasonality of the wave clouds. This study concludes that bore waves are the most likely mechanism for the generation of the observed linear wave clouds.