Long-range propagation of nonlinear infrasound waves through an absorbing atmosphere.

The Navier-Stokes equations are solved using a finite-difference, time-domain (FDTD) approach for axi-symmetric environmental models, allowing three-dimensional acoustic propagation to be simulated using a two-dimensional Cylindrical coordinate system. A method to stabilize the FDTD algorithm in a viscous medium at atmospheric densities characteristic of the lower thermosphere is described. The stabilization scheme slightly alters the governing equations but results in quantifiable dispersion characteristics. It is shown that this method leaves sound speeds and attenuation unchanged at frequencies that are well resolved by the temporal sampling rate but strongly attenuates higher frequencies. Numerical experiments are performed to assess the effect of source strength on the amplitudes and spectral content of signals recorded at ground level at a range of distances from the source. It is shown that the source amplitudes have a stronger effect on a signal's dominant frequency than on its amplitude. Applying the stabilized code to infrasound propagation through realistic atmospheric profiles shows that nonlinear propagation alters the spectral content of low amplitude thermospheric signals, demonstrating that nonlinear effects are significant for all detectable thermospheric returns.

A 500-kiloton airburst over Chelyabinsk and an enhanced hazard from small impactors.

Most large (over a kilometre in diameter) near-Earth asteroids are now known, but recognition that airbursts (or fireballs resulting from nuclear-weapon-sized detonations of meteoroids in the atmosphere) have the potential to do greater damage than previously thought has shifted an increasing portion of the residual impact risk (the risk of impact from an unknown object) to smaller objects. Above the threshold size of impactor at which the atmosphere absorbs sufficient energy to prevent a ground impact, most of the damage is thought to be caused by the airburst shock wave, but owing to lack of observations this is uncertain. Here we report an analysis of the damage from the airburst of an asteroid about 19 metres (17 to 20 metres) in diameter southeast of Chelyabinsk, Russia, on 15 February 2013, estimated to have an energy equivalent of approximately 500 (±100) kilotons of trinitrotoluene (TNT, where 1 kiloton of TNT = 4.185×10(12) joules). We show that a widely referenced technique of estimating airburst damage does not reproduce the observations, and that the mathematical relations based on the effects of nuclear weapons--almost always used with this technique--overestimate blast damage. This suggests that earlier damage estimates near the threshold impactor size are too high. We performed a global survey of airbursts of a kiloton or more (including Chelyabinsk), and find that the number of impactors with diameters of tens of metres may be an order of magnitude higher than estimates based on other techniques. This suggests a non-equilibrium (if the population were in a long-term collisional steady state the size-frequency distribution would either follow a single power law or there must be a size-dependent bias in other surveys) in the near-Earth asteroid population for objects 10 to 50 metres in diameter, and shifts more of the residual impact risk to these sizes.

Nonlinear synthesis of infrasound propagation through an inhomogeneous, absorbing atmosphere.

An accurate and efficient method to predict infrasound amplitudes from large explosions in the atmosphere is required for diverse source types, including bolides, volcanic eruptions, and nuclear and chemical explosions. A finite-difference, time-domain approach is developed to solve a set of nonlinear fluid dynamic equations for total pressure, temperature, and density fields rather than acoustic perturbations. Three key features for the purpose of synthesizing nonlinear infrasound propagation in realistic media are that it includes gravitational terms, it allows for acoustic absorption, including molecular vibration losses at frequencies well below the molecular vibration frequencies, and the environmental models are constrained to have axial symmetry, allowing a three-dimensional simulation to be reduced to two dimensions. Numerical experiments are performed to assess the algorithm's accuracy and the effect of source amplitudes and atmospheric variability on infrasound waveforms and shock formation. Results show that infrasound waveforms steepen and their associated spectra are shifted to higher frequencies for nonlinear sources, leading to enhanced infrasound attenuation. Results also indicate that nonlinear infrasound amplitudes depend strongly on atmospheric temperature and pressure variations. The solution for total field variables and insertion of gravitational terms also allows for the computation of other disturbances generated by explosions, including gravity waves.

Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere.

Equations applicable to finite-difference time-domain (FDTD) computation of infrasound propagation through an absorbing atmosphere are derived and examined in this paper. It is shown that over altitudes up to 160 km, and at frequencies relevant to global infrasound propagation, i.e., 0.02-5 Hz, the acoustic absorption in dB/m varies approximately as the square of the propagation frequency plus a small constant term. A second-order differential equation is presented for an atmosphere modeled as a compressible Newtonian fluid with low shear viscosity, acted on by a small external damping force. It is shown that the solution to this equation represents pressure fluctuations with the attenuation indicated above. Increased dispersion is predicted at altitudes over 100 km at infrasound frequencies. The governing propagation equation is separated into two partial differential equations that are first order in time for FDTD implementation. A numerical analysis of errors inherent to this FDTD method shows that the attenuation term imposes additional stability constraints on the FDTD algorithm. Comparison of FDTD results for models with and without attenuation shows that the predicted transmission losses for the attenuating media agree with those computed from synthesized waveforms.

Excitation of T-phases by seafloor scattering.

T-phases excited by suboceanic earthquakes are classified into two types: abyssal phases which are excited near the earthquake epicenter at seafloor depths far below the SOFAR velocity channel, and slope T-phases which are excited at continental, or ocean island slopes and ridges at distances up to several hundreds of kilometers from the epicenter. In this article, it is demonstrated that approximate time-frequency characteristics of both classes of T-phase can be synthesized under the assumption that T-phases are excited by scattering from a rough seafloor. Seafloor scattering at shallow depths preferentially excites low order acoustic modes that propagate efficiently within the ocean sound channel minimum. At greater depths, scattering excites higher order modes which interact weakly with the seafloor along much of the propagation path. Using known variations in near-source bathymetry, T-phase envelopes are synthesized at several frequencies for several events south of the Fox Islands that excited both types of T-phase. The synthesized T-phases reproduce the main time vs frequency features of each type of arrival; a higher frequency, nearly symmetric arrival excited near the epicenter and a longer duration, lower frequency arrival excited near the continental shelf, with a peak amplitude at about 5 Hz.

Mantle discontinuity structure beneath the southern east pacific rise from P-to-S converted phases

Receiver functions derived from teleseismic body waves recorded by ocean-bottom seismometers on the southern East Pacific Rise reveal shear waves converted from compressional waves at the mantle discontinuities near 410- and 660-kilometer depth. The thickness of the mantle transition zone between the two discontinuities is normal relative to the global average and indicates that upwelling beneath the southern East Pacific Rise is not associated with an excess temperature in the mantle transition zone.