Sergey N. Vecherin

Time-dependent stochastic inversion in acoustic travel-time tomography of the atmosphere

Stochastic inversion is a well known technique for the solution of inverse problems in tomography. It employs the idea that the propagation medium may be represented as random with a known spatial covariance function. In this paper, a generalization of the stochastic inverse for acoustic travel-time tomography of the atmosphere is developed. The atmospheric inhomogeneities are considered to be random, not only in space but also in time. This allows one to incorporate tomographic data (travel times) obtained at different times to estimate the state of the propagation medium at any given time, by using spatial-temporal covariance functions of atmospheric turbulence. This increases the amount of data without increasing the number of sources and∕or receivers. A numerical simulation for two-dimensional travel-time acoustic tomography of the atmosphere is performed in which travel times between sources to receivers are calculated, given the temperature and wind velocity fields. These travel times are used as da...

Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion.

Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDSI accounts for the correlation of temperature and wind velocity fluctuations both in space and time and therefore yields more accurate reconstruction of these fields in comparison with algebraic techniques and regular stochastic inversion. To use TDSI, one needs to estimate spatial-temporal covariance functions of temperature and wind velocity fluctuations. In this paper, these spatial-temporal covariance functions are derived for locally frozen turbulence which is a more general concept than a widely used hypothesis of frozen turbulence. The developed theory is applied to reconstruction of temperature and wind velocity fields in the acoustic tomography experiment carried out by University of Leipzig, Germany. The reconstructed temperature and velocity fields are presented and errors in reconstruction of these fields are studied.

Optimal sensor placement with signal propagation effects and inhomogeneous coverage preferences

The optimal sensor placement problem consists of determining the number, types, and locations of sensors satisfying inhomogeneous coverage requirements while minimising a specified cost function. The cost function can reflect various factors such as the actual cost of the sensors, their total number, and energy consumption. A strict and general formulation of the problem is described here for sensors characterised by probability of detection at some specified probability of false alarm. The formulation includes non-uniform coverage preferences and realistic, non-line-of-sight detection accounting on signal propagation effects. The optimisation is expressed as a solution to a binary linear programming problem. While exact solution of this problem is typically prohibitive, a fast greedy algorithm is presented that yields a near-optimal solution. It can also be successfully applied to improve coverage of an existing sensor network. This approach compares very favourably to an alternative heuristic strategy based on placing sensors one-by-one in the previously worst-covered location.

Three-Dimensional Acoustic Travel-Time Tomography of the Atmosphere

Acoustic travel-time tomography is a remote technique that can be used for reconstruction of temperature and wind velocity fields in the atmosphere. In the literature, results of two-dimensional tomography of the atmosphere have been reported so far. This paper presents an algorithm for reconstruction of temperature and wind velocity fields in three-dimensional tomography. In the algorithm, stratification of the atmosphere is taken into account explicitly. This allows high accurate reconstruction of stratified mean temperature and wind velocity fields. The fields of fluctuations are reconstructed with the use of three-dimensional time-dependent stochastic inversion. Estimation of the errors of reconstruction is also presented. A numerical experiment with large-eddy simulation is used to confirm the efficiency of the developed theory.

Recent progress in acoustic travel-time tomography of the atmospheric surface layer

Acoustic tomography of the atmospheric surface layer (ASL) is based on measurements of the travel times of sound propagation between sources and receivers which constitute a tomography array. Then, the temperature and wind velocity fields inside the tomographic volume or area are reconstructed using different inverse algorithms. Improved knowledge of these fields is important in many practical applications. Tomography has certain advantages in comparison with currently used instrumentation for measurement of the temperature and wind velocity. In this paper, a short historical overview of acoustic tomography of the atmosphere is presented. The main emphasis is on recent progress in acoustic tomography of the ASL. The tomography arrays that have been used so far are discussed. Inverse algorithms for reconstruction of the temperature and wind velocity fields from the travel times are reviewed. Some results in numerical simulations of acoustic tomography of the ASL and reconstruction of the turbulence fields in tomography experiments are presented and discussed. Zusammenfassung

Source localization from an elevated acoustic sensor array in a refractive atmosphere

Localization of sound sources on the ground from an acoustic sensor array elevated on a tethered aerostat is considered. To improve estimation of the source coordinates, one should take into account refraction of sound rays due to atmospheric stratification. Using a geometrical acoustics approximation for a stratified moving medium, formulas for the source coordinates are derived that account for sound refraction. The source coordinates are expressed in terms of the direction of sound propagation as measured by the sensor array, its coordinates, and the vertical profiles of temperature and wind velocity. Employing these formulas and typical temperature and wind velocity profiles in the atmosphere, it is shown numerically that sound refraction is important for accurate predictions of the source coordinates. Furthermore, it is shown that the effective sound speed approximation, which is widely used in atmospheric acoustics, fails to correctly predict the source coordinates if the grazing angle of sound propagation is relatively large.

Incorporating source directionality into outdoor sound propagation calculations

Many outdoor sound sources, such as aircraft or ground vehicles, exhibit directional radiation patterns. However, long-range sound propagation algorithms are usually formulated for omnidirectional point sources. This paper describes two methods for incorporating directional sources into long-range sound propagation algorithms. The first is the equivalent source method (ESM), which determines a compact distribution of omnidirectional point sources reproducing a given directivity pattern in the far field. This method can be used with any propagation algorithm because it explicitly reconstructs a source function as a set of point sources with certain amplitudes and positions. The second is a directional starter method (DSM), which is developed specifically for the parabolic equation (PE) algorithms. This method derives narrow- or wide-angle directional starter fields, corresponding to a given source directivity pattern, without reconstructing the equivalent source distribution. Although the ESM can also be used for the PE, the DSM is simpler and can be more convenient, especially if the sound propagation is calculated only for one or a few azimuthal directions. While these two methods are found to produce generally distinct starter fields, they nonetheless yield identical directivity patterns.

Spatial-temporal coherence of acoustic signals propagating in a refractive, turbulent atmosphere.

Propagation of acoustic signals above an impedance ground in a refractive, turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity is considered. Starting from a parabolic equation, and using the Markov approximation and a locally frozen turbulence hypothesis, closed-form equations for the spatial-temporal statistical moments of arbitrary order of the sound-pressure field are derived. The general theory provides a basis for analysis of many statistical characteristics of broadband and narrowband acoustic signals for different geometries of propagation: line-of-sight propagation, multipath propagation in a refractive atmosphere above an impedance ground, and sound scattering into a refractive shadow zone. As an example of application of this theory, the spatial-temporal coherence of narrowband acoustic signals for line-of-sight propagation is calculated and analyzed. The coherence time of acoustic signals is studied numerically for meteorological conditions ranging from cloudy to sunny conditions, and with light, moderate, and strong wind. The results obtained are compared with available experimental data.

Effect of randomly varying impedance on the interference of the direct and ground-reflected waves.

A randomly varying ground impedance is introduced into the solution for the sound field produced by a point source in a homogeneous atmosphere above a flat ground. The results show that in general the ground with a random impedance cannot be represented by an effective, non-random impedance. The behavior of the solution is studied with a relaxation model for the impedance in which porosity and the static flow resistivity are random variables. Mean values and standard deviations are adopted from measurements of two types of ground surfaces. For both surfaces, the mean intensity of the sound field above a random-impedance ground deviates only slightly from the intensity above a non-random impedance. The normalized standard deviation of intensity fluctuations can, however, be greater than one, thus indicating that for a particular realization of the random impedance, the sound intensity might significantly deviate from the intensity for a non-random impedance.

Acoustic tomography of the atmosphere at the Boulder Atmospheric Observatory.

An array for acoustic tomography of the atmosphere has been built at the NOAA Boulder Atmospheric Observatory. In this paper, a short description of the array and some acoustic tomography results are presented. The array consists of three speaker and five microphone towers located along the perimeter of a square with a side length of 80 m. The towers are 9.1 m high. The speakers and microphones can be located at different (multiple) levels on the towers to do three‐dimensional tomography. The transducers are connected via cables with the central command and data acquisition computer. The array enables measurements of travel times of sound propagation between different pairs of speakers and microphones. The measurements are done repeatedly within a short time interval so that the information about the temporal change in the travel times can be employed in tomographic reconstruction. Then, these travel times are used as input data in a time‐dependent stochastic inversion for reconstruction of temperature an...