Global morphology of infrasound propagation



[1] Atmospheric sound waves in the 0.02–10 Hz region, also known as infrasound, exhibit long-range global propagation characteristics. Measurable infrasound is produced around the globe on a daily basis by a variety of natural and man-made sources. As a result of weak classical attenuation (∼0.01 dB km−1 at 0.1 hz), these acoustic signals can propagate thousands of kilometers in tropospheric, stratospheric, and lower thermospheric ducts. To model this propagation accurately, detailed knowledge of the background atmospheric state variables, the global winds and temperature fields from the ground to ∼170 km, is required. For infrasound propagation calculations, we have developed a unique atmospheric specification system (G2S) that is capable of providing this information. Using acoustic ray tracing methods and detailed G2S atmospheric specifications, we investigate the major aspects of the spatiotemporal variability of infrasound propagation characteristics.

1. Introduction

[2] Atmospheric sound in the 0.02–10 Hz frequency band is known as infrasound. Classical molecular attenuation of infrasound is approximately proportional to the square of frequency (∼0.01 dB km−1 at 0.1 hz), so unlike audible frequencies, infrasound can propagate thousands of kilometers through ducts formed in the troposphere, stratosphere, and lower thermosphere. Natural sources of infrasound are earthquakes [Blanc, 1985], ocean wave surface resonances (microbaroms) [Posmentier, 1967; Arendt and Fritts, 2000], avalanches and rockfall [Bedard and Georges, 2000], auroral sources [Procunier, 1971; Wilson, 1972], volcanic activity [Garcés et al., 1999], severe storms and tornados [Georges, 1973], and meteors (bolides) [ReVelle and Whitaker, 1999; Evers and Haak, 2001]. Man-made sources of infrasound are chemical explosions, mining blasts [Hagerty et al., 2002], the bow shocks of supersonic aircraft [Le Pichon et al., 2002] and space shuttle [Sorrells et al., 2002], and nuclear detonations [Stevens et al., 2002].

[3] Since the early cold war days of monitoring nuclear explosions, there have been significant advances in infrasound detectors (microbarographs), autonomous site operations, and signal processing. For detecting clandestine nuclear tests, sixty new infrasound arrays will be deployed at various sites around the globe, along with new and existing seismometers and hydrophones, to form the International Monitoring System (IMS) network. Several of the IMS infrasound arrays are now operational [Brown et al., 2002]. The measurement and characterization of both natural and man-made sources provides excellent diagnostics for the IMS network. As a result, observations from these arrays are being made available to the atmospheric and acoustic research communities. The availability of these data provides an opportunity to carry out advanced infrasonic research, as well as atmospheric science.

[4] Infrasound is also known to play a role in lithosphere-atmosphere-ionosphere interactions. Ionospheric perturbations due to infrasound generated by earthquakes and other sources have been well documented and studied [e.g., Davies and Archambeau, 1998]. Additionally, it is thought that infrasound may be an important source of heating in the lower thermosphere [Rind, 1977; Hickey et al., 2001]. Infrasound could also be a non-negligible source of momentum in the lower thermosphere.

[5] The general characteristics of infrasound propagation are a function of the magnitude and direction of the vertical gradients in the background wind and temperature fields. Accurate propagation calculations thus require detailed knowledge of the atmospheric state variables as the result of this functional dependence. This dependence has even lead several researchers to suggest that infrasound can be used as an atmospheric remote sensing tool in the way acoustic tomography is used in oceanography and seismology [e.g., Groves, 1955b; Rind and Donn, 1975; Donn and Rind, 1979]. In fact, the existence of the stratopause was first hypothesized in the early 1920s based on the audibility of explosions at large distances [Groves, 1955a; Brown and Hall, 1978].

[6] For these reasons it is useful to investigate how the natural variability of the atmosphere influences the global morphology of infrasound propagation. This paper is a follow-up to a recent paper by Garcés et al. [2002], which documents a theoretical study of the effects of the solar migrating tides, solar EUV flux, and geomagnetic activity on the propagation of infrasound. In the present paper we investigate the global nature of the partitioning of infrasonic energy into various atmospheric ducts in the troposphere, stratosphere, and lower thermosphere.

2. Infrasound Propagation

[7] There are a number of techniques used for modeling the propagation of infrasound in the atmosphere: normal modes [Pierce, 1967], classical ray tracing [Georges, 1971], Green's functions [Gilbert and Di, 1993], Tau-P ray tracing variants [Garcés et al., 1998], and parabolic equations [Lingevitch et al., 2002]. Ray tracing formulations provide a straightforward way to calculate infrasound propagation paths, including reflection heights, travel times, and wave front arrival angles. To investigate the global morphology of infrasound propagation, we will examine the relationship of ray turning heights to the global characteristics of the atmosphere.

[8] Classical ray tracing methods assume the propagation of a plane parallel acoustic wave front in a locally linear medium. The equations of propagation [e.g., Groves, 1955a] are

equation image
equation image

where the r is the position of the wave front and k is the wave front normal unit vector. Here c is the sound speed and u is the wind vector, both of which are implicit functions of r. In the ray approximation, acoustic waves above 0.01 Hz are independent of buoyancy effects.

[9] The above ray equations can be simplified for local propagation calculations by assuming a horizontally stratified, range-independent, plane parallel atmosphere [Groves, 1955b; Thompson, 1972]. The sound speed (c) and horizontal wind components (u, v) are thus functions of altitude z only. It is further assumed that the vertical wind component is negligible. Finally, ray curvatures dkx/dz, dky/dz, and dkz/dz are assumed negligible over the space of a wavelength [Lighthill, 1978; Garcés et al., 1998]. Under these assumptions, equation (1a) reduces to

equation image

Equation (1b) reduces to

equation image

where the index of refraction (n) is

equation image

Equations (2a)(2c) make up a system of six ordinary differential equations that can be integrated numerically given c(z), u(z), v(z), and the initial ray conditions r0 and k0.

[10] To demonstrate the general behaviors of infrasound propagation for an arbitrary set of atmospheric conditions, a set of equally spaced rays from an isotropically radiating point source is integrated. The 1-km gridded profiles shown in Figure 1 are used as the background atmosphere. The data and methodology used to generate these atmospheric profiles are discussed in section 3. Static sound speed is calculated from atmospheric temperature T using the relationship c2 = γRdT/M, where γ = 1.4 is the approximate ratio of specific heats, R is the molar gas constant for dry air (Rd = 287.05 J kg −1 K−1), and M is an altitude-dependent mean molecular weight (kg mol−1).

Figure 1.

The atmospheric zonal wind velocity (dashed line), meridional wind velocity (dash-dotted line) and sound speed (solid line) profiles at 45°S, 260°E on 17 June 2001 at 0600 UTC.

[11] Two 1000-s integrations are performed, one oriented in the east-west direction, and one oriented in the north-south direction. The initial acoustic wave fronts are composed of 760 individual ray elements separated by 0.25° in a two-dimensional (2-D) semicircular configuration. Integration is performed using a fourth-order Runge-Kutta method with a fixed 2-s time step. Gridded values for dc(zi)/dz, du(zi)/dz, and dv(zi)/dz are calculated from c(zi), u(zi), and v(zi) by second-order centered finite differencing. Linear interpolation is used to determine continuous values of c(z), dc(z)/dz, u(z)…etc. along the integration path. Perfect planar reflection is assumed at the surface.

[12] The results are shown in Figure 2. The time-dependent locations of the composite wave fronts are shown at 5-min intervals. The full propagation paths are shown at 5° intervals. A rough indication of the signal strength is given by the separation of adjacent rays. Three main ducts form; a tropospheric duct to the south (Figure 2, bottom), a stratospheric duct to the east (Figure 2, top), and a thermospheric duct in all directions. A significant fraction of the infrasound also radiates or escapes into the upper thermosphere where it does not return to the ground at measurable levels. The multidimensional nature of energy or signal partitioning into each of these four channels will be explored in detail later.

Figure 2.

A 1000-s infrasound ray-tracing simulation performed in the east/west (top) and north/south (bottom) planes. The initial acoustic wave front is composed of a semicircular fan of a 720 infrasonic ray elements. The location and evolution of the composite wave front(s) are shown at 5-min intervals.

3. Atmospheric Specifications

3.1. Atmospheric Data Sources

[13] Numerous governments and agencies build and maintain networks of ground-based weather stations and meteorology satellites. Using the combination of rigorous statistics and geophysical fluid models, several Numerical Weather Prediction (NWP) centers (e.g., National Centers for Environmental Prediction; European Center for Medium Range Weather Forecasting) continuously assimilate global observations to produce lower atmospheric specifications and forecasts. These NWP products, updated several times daily, typically range from the surface to ∼35 km (10 mbar) and have a spatial resolution up to 1° × 1°.

[14] Unlike the troposphere and lower stratosphere, where reliable atmospheric specifications are routine, none of these centers regularly specify and produce forecasts above the stratosphere. This is no surprise given the lack of operational measurements of the middle and upper atmosphere. However, sparse and sporadic scientific data have often been available.

[15] In addition to the global-scale circulation patterns the predominant dynamical fluctuations of the upper atmosphere are the migrating diurnal and semidiurnal tides driven by solar heating [e.g., Hedin, 1991; Forbes, 1995]. On average, the global circulation patterns and migrating tides are repeatable from day to day and year to year and can be parameterized well with empirical models. Like the meteorology of the lower atmosphere, these oscillations also change throughout the seasons. The Mass Spectrometer and Incoherent Scatter Radar empirical model (MSISE-90) and the Horizontal Wind Model (HWM-93) were developed to specify the meteorology of the upper atmosphere [Hedin, 1991; Hedin et al., 1996]. These empirical models represent a statistical view of a multidecadal historical archive of scientific measurements. The HWM and MSIS class models currently provide the best available means of obtaining high-resolution empirical estimates of global neutral winds, temperatures, pressures, and major species concentrations for the middle and upper atmosphere. These models are available as FORTRAN subroutines and include embedded empirical spherical harmonic (SH), vector spherical harmonic (VSH), and Fourier coefficient sets. Model outputs are produced given the input parameters: day-of-year, universal time, latitude, longitude, altitude, solar local time, and geophysical indices for solar flux and geomagnetic activity. The model's internal empirical coefficients have been derived from a multidecade database (40 years) of satellite- and ground-based measurements using a unique set of model generation routines. Recently a new version of the MSIS model (NRLMSIS-00) has been completed [Picone et al., 2002].

3.2. A Global Ground-to-Space Specification

[16] There is an increasing need to have accurate and timely specifications of the entire atmosphere for scientific research and engineering applications. As indicated, current time data and detailed forecasts are now only routinely available in limited altitude regions (e.g., below 35 km). Many researchers are not aware of sources or quality of atmospheric parameter sets for higher regions, nor are they prepared to combine parameter sets for different altitude regions into a coherent specification that applies to an arbitrary location and altitude. To meet this challenge, an atmospheric specification system that fuses state of the art empirical models with operational NWP specifications has been developed. The Naval Research Laboratory Ground to Space (NRL-G2S) semiempirical spectral model produces global specifications and forecasts that are seamless and self-consistent from the ground to 750 km.

[17] Figure 3 illustrates the current situation and the NRL-G2S model. The figure shows, as a function of altitude and latitude, three different specifications of the zonal (eastward velocity component) of the wind at 120°E on 31 January 1999 at 1200 UTC, which are currently available. Figure 3a shows the HWM-93 empirical model, and Figure 3b shows a corresponding NWP product. The detail of Figure 3b is desirable but is arbitrarily terminated at the product's upper boundary, whereas many of these details are unresolved by the more extensive HWM model. Figure 3c shows how the G2S system preserves and extrapolates NWP details to higher altitudes using context provided by HWM-93 while at the same time combining the two parameter sets into a coherent seamless global field. As a result, the salient features of both specifications are discernable in the G2S specifications.

Figure 3.

Three typical atmospheric specifications of the eastward wind velocity component (zonal) at 120°E on 31 January 31 1999 at 1200 UTC. (a) Horizontal Wind Model (HWM-93) empirical wind model, b) Numerical Weather Predication analysis products (e.g., National Oceanic and Atmospheric Administration-National Centers for Environmental Prediction (NOAA-NCEP)), and c) The Naval Research Laboratory (NRL) Ground-to-Space (G2S) semiiempirical spectral model.

[18] The G2S methodology represents an extension of the NWP specifications into space, or alternatively an assimilation of NWP data into the empirical model. The smoothness of the composite field is a desirable quality that is not generally achievable using straightforward spatial interpolation. The G2S model has overcome this problem through spectral decomposition of the parametric fields in the two atmospheric regions.

[19] The mathematical basis of the G2S model is as follows. Depending on the region and nature of available data, the horizontal variations of the atmospheric state variables are decomposed into spherical and vector spherical harmonics (SH/VSH) [e.g., Swarztrauber, 1993]. These data are typically the NWP specifications and correspondingly gridded empirical model output fields. For globally gridded input data, Fourier transform methods are used to determine the SH/VSH coefficients. For unevenly sampled ground and/or satellite observations, linear least squares methods are used to estimate the spectral coefficients. These calculations can be carried out in near real time or on a case-by-case basis to provide global atmospheric specifications.

[20] Once the SH/VSH harmonics coefficients are determined at all levels throughout the atmosphere, each harmonic order is fit in the vertical direction with rational B splines [DeBoor, 1978] using an error-weighted least squares minimization procedure. This formulation allows for the use of statistical weighting and sidesteps the need to interpolate different types of observations having different granularity. We perform these operations in a vertical pressure coordinate system, using geopotential height to specify the altitude at which a given pressure level occurs over a given location.

[21] Figure 4 shows sample results from the vertical SH/VSH fitting stage for mode numbers (n, m) = (3,1). In Figure 4, Br and Cr are the real parts of the rotational and solenoidal VSH coefficients of the vector wind fields, and Tr and Zr are the real parts of the SH coefficients for the temperature and geopotential height fields. In the full model both the real and imaginary parts are used. For this study the G2S specifications are derived from the NOAA NCEP reanalysis products from 1000 to 10 mbar (0–35 km) (squares in Figure 4), the NASA Data Assimilation Office NWP analysis products from 400 to 0.4 mbar (10–55 km) (circles in Figure 4), and the HWM-93 and MSISE-90 models above 10 mbar (35 km) (triangles in Figure 4).

Figure 4.

Examples of NRL-G2S vertical spherical harmonic (SH)/vector spherical harmonic (VSH) fitting stage for (n = 3, m = 1) using transformed 1 January 2003, 1200 UT data. The raw data sources are NOAA/NCEP reanalysis products from 1000 to 10 mbar (0–35 km) (squares), NASA-Data Assimilation Office (DAO) analysis from 400 to 1 mbar (10–50 km) (circles), and the HWM-93 and Mass Spectrometer and Incoherent Scatter Radar empirical model(MSISE-90) empirical models >10 mbar (triangles). Br and Cr are the real parts of the rotational and solenoidal VSH coefficients of the wind field. Tr and Zr are the real parts for the temperature and geopotential height fields SH coefficients.

[22] Once the rational B spline coefficients have been estimated for all the SH/VSH harmonics out to some spectral order (T), usually T-64 but up to T-120, the coefficients are archived. From these splined harmonic coefficients, inverse transforms are then used to construct vertical profiles at specific locations (see Figure 1). Continuously varying 2-D and 3-D wind and temperature fields with arbitrary orientations and grid densities can be generated. Horizontal gradients, divergence, and stream functions can be calculated directly from the splined VSH coefficients sets. This formulation compresses the information and provides an intelligent way to store, transmit, and reconstruct global volumes of environmental data as needed.

4. Infrasound Propagation Characteristics

[23] Now given the global atmospheric conditions, it is possible to perform a detailed investigation of the global partitioning of infrasonic signals (or energy) between the different atmospheric ducts. Using idealized isotropically radiating surface sources, the fraction of infrasonic energy that radiates into the various atmospheric ducts is calculated at event locations over the entire globe for several representative dates. This information is used to develop a scientific picture of the coupling of atmospheric regions as it relates to infrasonic signal propagation and energy deposition. In operational event detection and location, such calculations can also be used to assess possible propagation paths quickly.

[24] First, consider the 3-D propagation of infrasound from a single isotropically radiating, hemispherical point source at an arbitrary location on the surface of the earth. A uniformly distributed set of initial wave vectors derived from a geodesic tessellation can be used to model this idealized source. The geodesic tessellation is created by subdividing each of the 20 triangular faces of a regular icosahedron into 4 respective subtriangles [e.g., Heikes and Randall, 1995]. After subdividing, the vertices of each new triangle are projected onto the unit sphere to form a new polygon. This subdivision and projection procedure then continues iteratively until a desired resolution is achieved. After four iterations, there are 2592 triangular facets in the upper half of the geodesic tessellation (see Figure 5). The vector averages of the three vertices of each triangular facet of the resulting polygon are used to make the final set of initial wave vectors {k0}.

Figure 5.

The turning height (zmax) of 2592 infrasound ray elements from an idealized isotropically radiating surface source. The ray turning heights are displayed as a function of the initial launch azimuth and elevation (ko). The source origin is located at the center of the tessellated sphere.

[25] Again with the G2S environmental profiles in Figure 1, equations (2a)(2c) are integrated for each wave vector in the set {k0} until one of two situations occurs; kz < 0 for reflection or z > 165 km for escape. Figure 5 shows the turning height (zmax) for each ray emitted by our hypothetical point source as a function of initial launch azimuth and elevation. Four distinct groups form: those rays ducted in the troposphere below ∼16 km (dark blue area in Figure 5), those ducted in the stratosphere around 40–55 km (light blue area in Figure 5), those ducted in the lower thermosphere around 110–160 km (orange area in Figure 5), and those escaping (open area of Figure 5). This figure illustrates the 3-D nature of the partitioning of infrasound energy into the various propagation paths for a single event location and set of atmospheric conditions.

[26] Ducts form when conditions are sufficient to cause a situation where kz eventually becomes negative. On examining equations (2b) and (2c) it can be seen that when n > 0 the vertical component of the wave vector (kz) decreases with time. This usually occurs for downwind propagation or in regions of a positive temperature lapse rate (dT/dz > 0). As in Figure 2, infrasound emanating from the source at low elevation angles in a southerly direction is ducted in the troposphere by the meridional wind jet located near 10 km (see Figure 1). Low angle rays propagating eastward are ducted in the stratosphere by the eastward wind jet centered near 55 km. The remaining infrasound rays either are ducted in the lower thermosphere by the positive thermospheric temperature lapse rate or escape into the upper thermosphere.

[27] A local partitioning fraction for each of the atmospheric ducts can be estimated from the total surface area of each subgroup within the space k0. In the example shown, 7.7% of the radiated infrasound energy is ducted in the troposphere, 13.2% is ducted in the stratosphere, 61.6% is in the thermosphere, and 17.5% escapes into the upper thermosphere. The four channels are defined as zmax < 20 km (tropospheric), 20 km < zmax < 70 km (stratospheric), 70 < zmax < 165 km (thermospheric), and zmax > 165 (escape). These criteria are broader than the regions where ducting usually occurs but are chosen as such for computational convenience. The altitude z is defined as geodetic altitude, relative to mean sea level. The infrasound partitioning fractions are quantitatively determined by summing over the number of elements propagating within a given duct, weighted by the fractional area of the corresponding triangular element.

4.1. Ducting Heights From the Tau-P Method

[28] Following from the derivation in [Garcés et al., 1998] the horizontal range (X) and travel time (T) for a given ray (p) undergoing a single skip can be written as

equation image
equation image

where s = c1 is the slowness and p is a ray parameter. The integral taken is over the total vertical distance traveled by the ray during the up leg (z+) and down leg (z). The parameter p is unique to each set of initial ray conditions (k0). Furthermore, it remains constant along the entire propagation path. It is defined as

equation image

where is equation imagex a transformed horizontal wave vector so that equation imagey = 0. The variable ũ is the projection of the horizontal wind along the original direction of propagation. Although p is constant along the entire ray path, its value is dictated by the ambient conditions at the source altitude (co, uo). From X and T it is possible to determine the Hamiltonian of the system, τp = TpX, where p plays the role of a generalized momentum [Buland and Chapman, 1983; Goldstien, 1980]. From equations (3) and (4), τp can be expressed as

equation image

In all cases the quantity in angle brackets (f) must be >0 because X and T must be real numbers. The integrals are therefore limited to the region below the first real root of the integrand if the lower bound is the surface of the earth. Consequently, the turning point of a given ray (zmax) is easily determined as the first real root of f.

[29] To within the distance of the vertical atmospheric grid spacing, a good estimate of the reflection height of a given ray can be quickly obtained by locating the first grid point above the source where f < 0. It is sufficient to use atmospheric profiles with a vertical spacing of 0.25 km for the purposes of this paper, as any resulting errors are negligible compared to the bounds used to establish the various groupings. The ducting fractions obtained are indistinguishable from those obtained via full ray integration. The key advantage of this method over integration of equations (2a)(2c) is that it requires appreciably less computational effort.

4.2. Global Transmission Fractions

[30] Having defined local partitioning fractions, these calculations are now performed over a global ensemble of idealized sources to produce maps of the global morphology of these fractions. The following three representative cases were chosen: 27 February 2000 at 0600 UTC; 23 June 2001 at 0600 UTC; and 21 September 2001 at 1800 UTC. For these dates, moderate resolution G2S atmospheric specifications (T-64) are used. A second spherical geodesic tessellation is used to establish the event locations for each of the isotropically radiating point sources within the global ensemble. The resulting global maps have a geographic resolution of ∼3°. Interpolation is used to map the tessellated results to a rectangular grid for display. These calculations also account for the Earth's topography, which is implicitly included with the G2S specifications.

[31] Before moving onto the main results, it is helpful to illustrate the importance of accounting for topography and including a detailed lower atmosphere. Figure 6 shows the global tropospheric, stratospheric, and thermospheric ducting fractions for the 27 February 2000 case made using the HWM/MSIS models without topography (Figure 6a), the HWM/MSIS models accounting for topography (Figure 6b), and the complete G2S atmospheric specifications including topography (Figure 6b). A separate color scale for each ducting fraction type is given in Figure 6.

Figure 6.

The 27 February 2000, 0600 UTC tropospheric, stratospheric and thermospheric ducting fractions for a global ensemble of idealized isotropically radiating surface sources using various model assumptions. The first row (Figure 6a) shows the ducting fractions calculated using the HWM/MSIS empirical model without topography. The second row (Figure 6b) shows the fractions calculated using the HWM/MSIS empirical model accounting for topography. The last row (Figure 6c) shows the fractions calculated using the NRL-G2S model including for topography.

[32] As a matter of convenience, several operational NWP specifications (e.g., NOAA-NCEP) and the HWM/MSIS and NRL-G2S models provide outputs on pressure surfaces or at altitudes (relative to mean sea level) that may in fact be situated inside the solid Earth. When performing infrasound propagation calculations, it is important to avoid using these portions of the specifications because of the innate sensitivity of the propagation characteristics to the ambient conditions. Relative to the calculations in Figure 6a, the resulting ducting fractions in Figures 6b and 6c show that infrasound originating on the Tibetan Plateau, Antarctica, and Greenland exhibits much more lower atmospheric ducting than in surrounding regions. This is especially true over Antarctica. In the mathematical framework of the Tau-P equations, these differences are a consequence of the sensitivity of the ray parameters to co and uo. For example, over the Tibetan Plateau the initial distribution of ray parameters (p) from an isotropically radiating source is be noticeably different if determined from spurious values of (co, uo) at mean sea level, instead of from the true ambient conditions at the surface source level near 5 km.

[33] While the HWM/MSIS and NRL-G2S calculations are qualitatively similar on a global scale, there are appreciable differences on regional scales, particularly in the tropospheric ducting fractions. For all cases the ducting fractions calculated via the HWM/MSIS models indicate that minimal tropospheric ducting exists (<2%), in contrast to the G2S results. This is no surprise. The meteorological phenomenon responsible for tropospheric ducting tends toward zero when averaged over the spatiotemporal scales of the empirical models. Compare for example the climatological magnitudes of the zonal wind components of the tropospheric jets (Figure 3a) against the instantaneous G2S values (Figure 3c).

[34] The remaining morphology is discussed in the framework of the G2S-derived results. Figure 7 shows the percentages of acoustic energy partitioning on 23 June 2001. The tropospheric, stratospheric, thermospheric, and escaping fractions are shown. Figure 8 shows the corresponding results for 21 September 2001.

Figure 7.

The 23 June 2001, 1800 UTC ducting fractions for a global ensemble of idealized isotropically radiating surface sources. The fractions of tropospheric ducting (zmax < 20 km), stratospheric ducting (20 km < zmax < 70 km), thermospheric ducting (70 km < zmax < 165 km), and escape (zmax > 165) are shown from left to right.

Figure 8.

Global ducting fractions for 21 September 2001 at 0600 UTC.

4.2.1. Tropospheric Ducting

[35] The calculations demonstrate that a small but important fraction of the available infrasonic energy, up to 20%, can be ducted in the troposphere. This ducting mainly occurs in localized regions at middle and high latitudes. This is particularly apparent in Figure 6, where the ducting traces the narrow courses of the tropospheric jet streams. Isolated tropospheric disturbances and topography also play a role.

[36] Our research suggests that tropospherically ducted infrasound signals have considerable amplitudes, as the acoustic wave fronts are subject to a reduced amount of geometric spreading and molecular attenuation along the vertically constricted propagation paths. As such, tropospheric ducting is important for the detection and location infrasonic events. However, over long horizontal propagation paths a signal might eventually travel into a region where the atmospheric conditions are no longer favorable for tropospheric ducting. Our results show that this can occur over distances of ∼750 km, the scale size of tropospheric weather disturbances. When this happens, the infrasound would then simply start to propagate in one of the other two ducts. Additionally, we hypothesize that across mountainous regions, an increased number of irregular surface reflections could rapidly degrade the coherency of the signals. To account for these effects, a more elaborate 3-D, range-dependent propagation model [e.g., Georges, 1971] is needed.

4.2.2. Stratospheric Ducting

[37] The amount of stratospheric ducting for any given day at a specified point on the globe varies between 0 and ∼40%, with the greatest fractions occurring at the middle and high latitudes. Unlike the tropospheric jet streams, which causes much of the tropospheric ducting, the stratospheric wind jets are significantly broader and can exceed 100 m s−1 in localized regions throughout the solstice periods. The flow is predominately zonal and reverses directions between the winter and summer hemispheres, moving eastward in the winter hemisphere and westward in the summer hemisphere (see Figure 3). These stratospheric wind jets, or polar stratospheric vortices, often oscillate, particularly during the transition from solstice to equinox. During equinox, the polar vortices can become dynamically unstable before subsiding and reversing directions for the next season [e.g., Holton, 1992]. The stratospheric ducting fractions for the 27 September 2001 case (Figure 8) are greatly diminished relative to the 23 June 2001 case near solstice (Figure 7) because the stratospheric winds are much lighter during equinox.

[38] The least amount of stratospheric ducting occurs at equatorial latitudes. First, while significant wind velocities from global wave phenomena can occur occasionally at the equator, the stratospheric winds there are typically transient and light. Secondly, the equatorial tropopause is higher and colder relative to the ground than at other latitudes. From equations (2b) and (2c) it can be seen that, in the absence of strong winds, the vertical component of the wave vector (kz) increases with time when dc/dz < 0. This results in upward refraction. Thus infrasound is refracted upward at a greater rate and over a longer distance than at other latitudes. The infrasonic wave fronts enter the equatorial stratosphere at steeper angles, where they are less likely to be ducted. In the physical context of the Tau-P interpretation the ray parameters fixed by the initial conditions take on values that are unlikely to be reflected in the colder quiescent equatorial tropopause.

[39] In all cases, there is noticeable spatial variability in the global stratospheric ducting fractions. These variations result the from the episodic blocking of low angle rays in the troposphere below, as well as from local meteorological variations in the stratosphere. As with tropospheric ducting, signals traveling more than ∼1000 km horizontally may eventually migrate into regions where stratospheric ducting no longer occurs. Again, a more detailed range-dependent propagation model is needed to account for these effects.

4.2.3. Thermospheric Ducting

[40] On any given day, the amount of thermospheric ducting in the atmosphere typically varies between 40 and 85%. The largest fractions generally occur in the equatorial regions, where the least amount of tropospheric and stratospheric ducting occurs. Conservation laws dictate that thermospheric ducting fractions must be reduced above regions of strong tropospheric and stratospheric ducting. As a rule, the thermospheric ducting fractions are anticorrelated with the fractions of lower atmospheric ducting. This means that the inherent variability of the lower atmosphere is projected into the upper atmospheric ducting fractions through the differential shielding of rays and initial conditions set by the lower atmosphere.

[41] Theory and observation indicate that thermospherically ducted infrasonic signals tend to be fainter than their tropospheric and stratospheric counterparts. This is due to geometric spreading (see Figure 2) and enhanced molecular attenuation processes. The molecular attenuation processes, which become enhanced in the upper atmosphere due to the extremely low particle densities, are important for thermospheric energy deposition. Detailed theoretical estimates of lower thermospheric acoustic attenuation processes were made by Rind [1977]. When compared with a limited set of observations, reasonable but only partial agreement was obtained. Within the uncertainties, however, it is believed that attenuation and dissipation of infrasound in the lower thermosphere may cause significant heating of the lower thermosphere. Rind [1977] estimates that heating rates from steady state microbarom sources might exceed 30 K per day. At these levels of energy input, it is conceivable that infrasound could also act as a direct momentum source. Better estimates of the energy and momentum transfer efficiencies of infrasound, as well as related research, are needed.

[42] Our results show that local infrasonic energy deposition will be a complex function of the winds and temperatures in the lower and middle atmosphere. Moreover, climatological heating rates from infrasound would be biased toward the equatorial regions and toward sources near mean sea level. Additionally, it is known that the details of the thermospheric ducting also depend on solar local time because of the changing phases and amplitudes of the solar migrating tides [e.g., Rind and Donn, 1975; Garcés et al., 2002]. While this dependence is not apparent in the thermospheric ducting fractions, it is seen in the escape fractions.

4.2.4. Escape Fractions

[43] Infrasound not ducted in the lower thermosphere will propagate into the upper thermosphere where it dissipates and interacts with the ionosphere. The ionospheric response to infrasound has been observed and discussed by several authors [e.g., Blanc and Rickel, 1989; Calais and Minster, 1998; Artru et al., 2001]. The escape fractions for the two examples presented here vary between ∼12 and 17% globally. Compared to the other ducting fractions, the escape fractions are reasonably homogenous around the globe. The longitudinal or local time dependence linked to the phase of the solar migrating tidal winds is visible. The regions of maximum escape flux are shifted by ∼180° as the result of the 12-hour universal time difference between the two examples. This loosely translates into an 180° phase shift of the solar migrating tides. This fact was also confirmed by examining the escape fractions of several consecutive 6-hour periods.

[44] Our calculations further indicate that escape fractions, as well as those for thermospheric ducting, are coupled to changes in the EUV solar flux and geomagnetic activity. These external thermospheric drivers can significantly increase the lower thermospheric temperature gradient and cause enhanced thermospheric ducting. The 81-day average F10.7 solar EUV index for September and June cases are 203 and 151, respectively. Of these the June case shows greatest global fractions of escape. Lower values of solar EUV flux correspond to colder thermospheric temperatures and thus a weaker thermospheric temperature gradient. This results in less thermospheric ducting and a greater escape fraction. This was verified by examination of other periods with higher and lower F10.7 flux values.

5. Conclusions

[45] In this paper, we have investigated the global morphology of infrasound path partitioning in order to develop a scientific picture of the coupling of atmospheric regions as it relates to infrasonic signal propagation and energy deposition. Because each layer of the atmosphere can prevent infrasound from entering the layer above it, infrasound partitioning fractions, as well as infrasound propagation characteristics in general, carry the compound memory of the intervening layers of the atmosphere that they have encountered. The resulting ducting fractions are highly variable and reflect the detailed characteristics of the entire atmosphere.

[46] This work further indicates the importance of accurate atmospheric specification, starting at the source level. If the initial conditions or the intervening atmospheric background conditions are inaccurate, errors in the modeled propagation will naturally accumulate over space and time, leading to inaccurate estimates of ducting heights, as well as travel times, and possibly source location estimates. Therefore in order to relate infrasound propagation calculations to microbarograph observations accurately, the use of detailed atmospheric specifications is highly recommended.

[47] This paper demonstrates the availability of a new semiempirical specification (NRL-G2S), as well as new methodologies, which can be used for scientific research and the monitoring of natural and artificial infrasound events. These new models include important latitudinal, longitudinal, and daily variability as specified by historical and near-real-time operational data. In shifting away from climatologically based atmospheric profiles, however, a great deal of complexity is introduced into the problem of infrasound propagation modeling. This complexity arises from the natural variability of the atmosphere across all levels. It has timescales from several hours to several months and horizontal scales of ∼750 km. We have demonstrated with a simple model that it is now possible to account for this complexity. While the NWP specifications and empirical atmospheric models used in the study have been validated in numerous ways, the ultimate substantiation of our conclusions, and future work, should involve the analysis of infrasonic ground truth events observed by infrasound monitoring networks.


[48] This work was cosponsored by the Defense Threat Reduction Agency and the Department of Energy. Auxiliary support is also provided to NRL by the Office of Naval Research. We would also like to thank the NASA Goddard Space Flight Center, Data Assimilation Office (GSFC-DAO), and the NOAA National Centers for Environmental Predication (NCEP) for making their NWP products available for this scientific research.