• Ferguson, B. G., , and Lo K. W. , 2000: Turbo-prop and rotary-wing aircraft flight parameter estimation using both narrow-band and broadband passive acoustic signal processing methods. J. Acoust. Soc. Amer.,108, 1763–1771.

  • Finn, A., , and Franklin S. , 2011a: Acoustic sense and avoid for UAVs. Proc. Seventh Int. Conf. on Intelligent Sensor Signal Network and Information Processing, Adelaide, SA, Australia, IEEE, Paper 1569493569.

  • Finn, A., , and Franklin S. , 2011b: UAV-based atmospheric tomography. Proc. 2011 Australian Acoustical Society Conf., Gold Coast, QLD, Australia, Australian Acoustical Society, Paper 14. [Available online at http://www.acoustics.asn.au/conference_proceedings/AAS2011/papers/p14.pdf.]

  • Haacke, E. M., , Brown R. W. , , Thompson M. R. , , and Venkatesan R. , 1999: Magnetic Resonance Imaging: Physical Principles and Sequence Design. Wiley-Liss, 914 pp.

  • Jovanović, I., 2008: Inverse problem in acoustic tomography: Theory and applications. Ph.D. thesis, Ecole Polytechnique Federale de Lausanne (EPFL), 139 pp.

  • Jovanović, I., , Sbaiz L. , , and Vetterli M. , 2009: Acoustic tomography for scalar and vector fields: Theory and application to temperature and wind estimation. J. Atmos. Oceanic Technol., 26, 14751492.

    • Search Google Scholar
    • Export Citation
  • Kelley, N. D., , Jonkman B. J. , , and Scott G. N. , 2007: Comparing pulsed Doppler LIDAR and SODAR and direct measurements for wind assessment. Proc. WindPower 2007 Conf., Los Angeles, CA, Amer. Wind Energy Assoc., NREL/CP-500-41792.

  • Ostashev, V. E., , Vecherin S. N. , , Wilson D. K. , , Ziemann A. , , and Goedecke G. H. , 2008: Recent progress in acoustic tomography of the atmosphere. IOP Conf. Ser.: Earth Environ. Sci.,1, 012008, doi:10.1088/1755-1315/1/1/012008.

  • Quan, Y., , and Huang L. , 2007: Sound-speed tomography using first arrival transmission ultrasound for a ring ray. Proc. SPIE,6513, 651306, doi:10.1117/12.709647.

  • Spiesberger, J. L., , and Fristrup K. M. , 1990: Passive localization of calling animals and sensing of their acoustic environment using acoustic tomography. Amer. Nat., 135, 107153.

    • Search Google Scholar
    • Export Citation
  • Stewart, R. R., 1991: Exploration Seismic Tomography: Fundamentals. Course Notes Series, Vol. 4, Society of Exploration Geophysicists, 140 pp.

  • Stull, R., 1988: An Introduction to Boundary Layer Meteorology. Atmospheric Sciences Library, Kluwer Academic, 666 pp.

  • Wiens, T., , and Behrens P. , 2009: Turbulent flow sensing using acoustic tomography. Proc. Inter-Noise 2009: Innovations in Practical Noise Control, Ottawa, ON, Canada, International Institute of Noise Control Engineering.

  • Wilson, D. K., , and Thomson D. W. , 1994: Acoustic tomographic monitoring of the atmospheric surface layer. J. Atmos. Oceanic Technol., 11, 751769.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 29 29 10
PDF Downloads 22 22 9

Three-Dimensional UAV-Based Atmospheric Tomography

View More View Less
  • 1 Defence and Systems Institute, University of South Australia, Mawson Lakes, South Australia, Australia
© Get Permissions
Full access

Abstract

This paper presents a method for tomographically reconstructing spatially varying three-dimensional atmospheric temperature profiles and wind velocity fields based on passive acoustic travel time measurements between a small unmanned aerial vehicle (UAV) and ground-based microphones. A series of simulations are presented to provide an indication of the performance of the technique. The parametric fields are modeled as the weighted sum of radial basis functions (RBFs) or Fourier series, which also allow local meteorological measurements made at the UAV and ground receivers to supplement any time delay observations. The technique has potential for practical applications such as boundary layer meteorology and theories of atmospheric turbulence and wave propagation through a turbulent atmosphere.

Corresponding author address: Kevin Rogers, Defence and Systems Institute, Mawson Lakes, SA 5095, Australia. E-mail: kevin.rogers@unisa.edu.au

Abstract

This paper presents a method for tomographically reconstructing spatially varying three-dimensional atmospheric temperature profiles and wind velocity fields based on passive acoustic travel time measurements between a small unmanned aerial vehicle (UAV) and ground-based microphones. A series of simulations are presented to provide an indication of the performance of the technique. The parametric fields are modeled as the weighted sum of radial basis functions (RBFs) or Fourier series, which also allow local meteorological measurements made at the UAV and ground receivers to supplement any time delay observations. The technique has potential for practical applications such as boundary layer meteorology and theories of atmospheric turbulence and wave propagation through a turbulent atmosphere.

Corresponding author address: Kevin Rogers, Defence and Systems Institute, Mawson Lakes, SA 5095, Australia. E-mail: kevin.rogers@unisa.edu.au

1. Introduction

Tomography is widely used in physics, medicine, and the remote sensing of different media (Haacke et al. 1999; Stewart 1991). There are a number of advantages for tomographic observations compared with conventional atmospheric soundings, as they enable reconstruction of cross-sectional “slices” of atmospheric temperature and wind velocity profiles, and enable monitoring of their evolution in time and space (Spiesberger and Fristrup 1990). It is then possible to provide information on the representativeness of point measurements and the homogeneity of other point observations (Wilson and Thomson 1994). Surveys of recent progress in the field of acoustic tomography of the atmosphere are contained in Jovanović (2008) and Ostashev et al. (2008).

The measurement technique employed here compares the acoustic spectra emitted by an unmanned aerial vehicle (UAV) with the Doppler-shifted spectra received at several ground-based microphones (Finn and Franklin 2011b), which may be up to 3 km away (Ferguson and Lo 2000; Finn and Franklin 2011a). The data are then converted into effective propagation delay values (Ferguson and Lo 2000; Jovanović et al. 2009). However, the technique is generally applicable to any observation technique that delivers atmospheric or oceanic time delay observations, including those made by unmanned underwater vehicles (UUVs). This technique also offers a number of additional advantages when compared with existing observational techniques.

The first is hardware cost since conventional meteorological devices used to measure atmospheric wind velocities [e.g., mast-mounted anemometers, sonic detection and ranging (sodar), or lidar] require expensive hardware (Kelley et al. 2007). In particular, the erection and maintenance costs of masts become very high as observation altitudes increase. This is not an issue for the proposed technique, which (aside from the capital cost of the UAV, which may be hired relatively inexpensively) relies upon hardware costing only a few thousand dollars.

Second, the presence of masts can obstruct or distort local wind flow patterns (Wilson and Thomson 1994). The proposed technique does not introduce any obstructions within the measurement space that can distort the measurements.

Third, one of the main issues for existing outdoor acoustic tomography methods is the formulation of robust and accurate reconstructions of the temperature and wind-velocity fields from a spatially limited set of observations (Jovanović et al. 2009; Ostashev et al. 2008). This is overcome as the resolution of the reconstruction of the atmospheric profiles is governed predominantly by the number and spacing of receivers and the duration of the observed spectra relative to the sampling frequency. The trajectories described by the UAV are also under user direction so the observation paths of the rays are controllable. This means that the size, shape, and location of the measurement space can be easily modified on site. Moreover, as the receivers need only determine their location (rather than be placed) to an accuracy of about ±1 m and inexpensive commercially available code and carrier-phase real-time kinematic differential GPS (DGPS) techniques exist at these levels, the prospect of rapid—even aerial—deployment is a viable option. The entire system may also be made mobile.

Fourth, as the aircraft has no pilot, it can be made small, can travel slowly, and therefore has low kinetic energy, which reduces the consequences of a crash. Thus, the UAV may be flown with relative safety at any altitude from a few meters to several kilometers, in dangerous environments (such as near hurricanes, cyclones, volcanoes, or bush-fire fronts), over complex terrains (such as close to factories or near chimney plumes), or over rough terrain (such as gullies for examining nocturnal drainage flows or katabatic winds). Echoes and multipath reflections from complex structures may be handled in accordance with Ferguson and Lo (2000) and Finn and Franklin (2011a).

Depending upon the number and density of the ground receivers, the tomographic profiles can then be reconstructed for different regions of the atmosphere: the surface layer, which extends a few meters above the ground (although a propeller-driven aircraft flying so close to the ground may well disturb the atmosphere under observation); the boundary layer, which extends up to heights of a few hundred meters; or—subject to the performance envelope of the UAV—even up to heights of several kilometers.

This technique does have some disadvantages compared with sodar and lidar: the technique loses accuracy at greater heights. However, as most atmospheric variation occurs close to the ground, it is possible to trade off spatial resolution against measurement accuracy at greater altitudes. Also, although the capital cost of the sensing equipment is low, the running costs over extended periods would be higher. Individual UAVs may be deployed for up to 40 h and would require less than half an hour between missions for refueling. If even longer periods are required, multiple UAVs can be deployed, which would enable continuous monitoring for an indefinite period. However, the technique would mainly be useful for relatively short-term, intensive monitoring (i.e., hours to days) rather than long-term in situ measurement sequences (i.e., weeks to months).

2. Acoustic observation and tomographic inversion

The atmospheric profile is derived using a two-stage process. First, the sound wave travel times are derived from the Doppler shift for sound waves from the UAV to the ground receivers. The estimated sound travel times are then used to derive the atmospheric temperature and wind profile using tomographic inversion.

a. Atmospheric observation

Here, we briefly describe the technique for determining the acoustic propagation delay. This is described in more detail in Finn and Franklin (2011b).

The travel time for the acoustic wave to propagate from the UAV to the ground sensors is derived from the formula for the Doppler shift:
e1
where is the normalized frequency of the narrowband tones of the UAV’s signature [which are generated by a combination of its engine firing sequence, its propeller blade rate, and their harmonics; Finn and Franklin (2011b)] at time t, is the approach velocity of the UAV toward the ground microphone at time t, is the average speed of sound from the UAV to the ground microphone at time t, is the travel time from the UAV to the ground microphone, and is the frequency received at the ground microphone at time . An iterative estimate of the acoustic propagation delay, , may then be obtained using
e2
where is the distance from the UAV to the ground microphone at time t. Equation (2) is only effective when the Doppler shift (i.e., the approach velocity) is not close to zero. Consequently, UAV profiles must be designed to induce significant Doppler shifts at the ground microphones and/or data should be statistically filtered where the Doppler shift is small.

b. Tomographic inversion

Here, we describe the technique for determining the tomographic inversion process that enables derivation of the 3D atmospheric temperature and wind field profiles.

The speed of sound through the atmosphere is , where is Laplace’s speed of sound, is the specific heat ratio, is the gas constant for air, T is the virtual acoustic temperature (in K), V is the wind vector, and is the unit vector in the direction of the sound wave. If the fields are linearized about mean values , , and , the travel time () for sound ray i from location Xi,1 to Xi,2 is (Jovanović 2008; Ostashev et al. 2008; Wiens and Behrens 2009)
e3
where is the path distance, is the mean sound speed, is the mean wind speed vector over the volume, is the unit vector in the direction of sound ray i, is the temperature deviation at location X, is the wind speed deviation at location X, and is an integration length along the ray’s path.
Both and may be independently approximated by a network of weighted radial basis functions (RBFs) (Wiens and Behrens 2009), which are three-dimensional Gaussian functions of the form where r is the distance from the RBF spatial center and k is a scaling factor, which is the same for all RBFs and all networks. For this simulation, the RBF centers were distributed evenly inside the volume at the vertices of a three-dimensional lattice. Thus, the temperature and wind fields are approximated by
e4
e5
e6
e7
where Nr is the number of RBF centers for each component.

The above equations can be expressed in matrix notation as , where F(X) is a (4 × 1) column vector of temperature and wind speed component deviations, W is a (4 × Nr × 1) column vector of parameter weights, and is a (4 × Nr − 4) matrix of RBFs.

To evaluate the travel time in Eq. (3), it is necessary to integrate and along the linear ray path between Xi,1 and X i,2. Each RBF term in the network projects a Gaussian function along each ray path. The Gaussian function is a maximum at the closest point along the line to the RBF center (Xc,j), and the peak magnitude is dependent on the RBF weight and the shortest distance between the RBF center and the ray path. For ray i, the length of the ray is and the unit vector in the direction of the sound ray is . The length along the line from the start () to the closest point to an RBF center () is and the location of the closest point is . The shortest distance from the RBF center to the sound ray is thus . Thus, for a temperature term,
e8
The integral of a Gaussian function is the error function . Thus,
e9
Similar equations can be derived for each of the wind speed components. Equation (3) can now be rearranged as , where d is an (m × 1) column vector; WT, Wx, Wy, and Wz are (Nr × 1) column vectors; and , , , and are (m × Nr) matrices. Or in matrix form, with elements as follows:
e10
e11
e12
e13
e14

If the travel times are known, we can now solve for using weighted least squares. This allows estimation of the temperature and wind speed at any location within the volume. However, we can improve the estimate of the RBF weights by taking additional measurements of wind speed and temperature at the ground sensors and at the UAV. We can then use the above equations to constrain the least squares adjustment by estimating the RBF weights , , , and , where , i = 1, … , Mr (the number of temperature and wind speed measurements), and j = 1 … Nr. These equations can then be combined into a single matrix relationship, where b is a column vector containing all travel time and direct measurements of temperature and wind speed deviations and is an (m × n) matrix, which is an extension of the and matrices. This latest equation can then once again be solved for the RBF weights () using weighted least squares, which minimizes , where is a diagonal matrix containing the inverse variances of the measurement errors.

In the above technique, the atmospheric temperature and wind speed perturbations were modeled using radial basis functions, as they provide a continuous atmospheric model. However, Fourier series or wavelets may also be used. For example, the atmospheric parameters can be represented using spatial Fourier series; for example,
e15
where are the relative Cartesian coordinates, varying in the range . Equation (15) can be converted into the weighted sum of individual sine and cosine terms, which then allows the integral to be evaluated and substituted into Eq. (3). The Fourier weights can then once again be evaluated using a weighted least squares method.

In some cases, modeling accuracy may be improved by constraining the least squares tomographic adjustment using known atmospheric characteristics (Quan and Huang 2007). This includes both direct measurements of temperature and wind speed at the ground sensors and/or sensors on board the UAV as well as estimates of underlying meteorological traits. The underlying meteorological traits include the adiabatic temperature lapse rate and typical horizontal wind speed versus height characteristics. The temperature of the lower troposphere generally falls linearly as a function of altitude. A typical value for the adiabatic lapse rate is approximately 6°C (km)−1, but the lapse rate is variable and can be one of the parameters that is estimated by the least squares algorithm. Similarly, the underlying or “background” wind speed can be approximated by the wind speed log law (up to 20-m height) or the wind speed power law (up to 2000-m height). Beyond this height, the wind speed tends to be constant for the measurement ranges of interest (Stull 1988).

3. Simulation study

A simulated atmosphere was generated to assess the reconstruction performance of the techniques described above. The target atmosphere was synthesized by assigning random weights to a number of RBFs to simulate complex foreground variations in the temperature and wind velocities. The simulated atmosphere was not representative of a real-world atmosphere, but was used to demonstrate proof of concept. Foreground temperature perturbations with maxima and minima of 10°C and wind velocities of up to 15 m s−1 were superimposed onto a 20°C static background. A UAV was then “flown” through this target atmosphere at 32 m s−1. The tomographic inversion procedures described in the previous section were then used to estimate the relevant temperature profiles and wind velocity fields within a three-dimensional atmospheric volume. Both the Fourier series and RBF techniques have been used to reconstruct atmospheric properties and yield similar results.

Figure 1 shows the arrangement of the UAV trajectory, ground receivers, and RBF centers. The UAV trajectory is shown in green, which follows a rising helical path over the top of the outermost ground sensors up to 1000 m and then spirals in toward the center on a horizontal plane at a height of 1000 m. The acoustic ground sensors (microphones) are shown by crosses. There are 49 ground sensors spaced 125 m apart inside the circumference of the UAV trajectory. The scalar temperature profile and the vector wind profile inside the UAV trajectory are modeled by curve fitting the weighted sum of the RBFs. The red circles are the locations of the RBF centers. There are 65 RBF centers and they are spaced 250 m apart on a 3D grid inside the cylindrical UAV volume. In reality, a dynamic atmosphere would likely change over an observation period of 5 min so the result will be an amortized profile.

Fig. 1.
Fig. 1.

UAV profile.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00036.1

Figure 2 is a simplified illustration of the sound ray paths propagating between the UAV and the microphones used to calculate the temperature and wind velocity profile. The simulated signal processing regime used an analog-to-digital conversion (ADC) sampling rate of 50 kHz and an FFT size of 218 with 50% overlapping blocks (i.e., the ray path samples are observed at 1 Hz). With 49 ground sensors, this represents a dense and well-conditioned matrix of around 15 000 observations for the inversion, with rays intersecting most of the cylindrical volume (although less densely nearer the top). Furthermore, each RBF is intersected by an average of about 230 observations at a variety of ranges from its center and different grazing angles. As velocity field errors have a tendency to grow in the direction perpendicular to individual ray paths (Ostashev et al. 2008), this leads to reduced velocity field errors. This also provides a well-conditioned least squares inversion that resolves the contribution of each RBF and assists in the discrimination between the scalar temperature and the directional wind speed effects, which are coupled in accordance with the terms in Eq. (3).

Fig. 2.
Fig. 2.

Sound ray paths.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00036.1

In simulations in which no errors were introduced onto the time delay observations, reconstruction of the target atmosphere was exact. However, typically front-end signal processing errors will lead to Doppler, and hence time delay measurement, errors that will in turn result in estimation errors in the reconstruction of the atmospheric profiles. Consequently, acoustic travel times between the UAV and a two-dimensional array of ground receivers were contaminated with 1σ Gaussian random errors of up to 0.1% of the true pathlength. Random measurement errors of 1°C for temperature and 1 m s−1 (1σ) for wind speed were also introduced into the direct meteorological measurements made at the ground sensors and the UAV. Figures 3 and 4 show a comparison between a horizontal slice of the target and reconstructed atmospheres at an altitude of 500 m. Temperature is color coded and wind fields are represented as arrows. Figure 5 shows a series of horizontal slices of the reconstructed profile at 200-m-height intervals. The estimated temperature profiles and horizontal wind speed directions are shown.

Fig. 3.
Fig. 3.

Target temperature and wind fields.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00036.1

Fig. 4.
Fig. 4.

Reconstructed temperature and wind fields.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00036.1

Fig. 5.
Fig. 5.

Temperature profile with horizontal wind directions superimposed.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00036.1

Figure 6 shows differences between the target and reconstructed profiles for a series of cross sections through the observed atmosphere. Each slice shows color-coded temperature estimation errors and also shows vectors for the actual (black) and estimated (red) wind vectors. The left-hand images show horizontal slices(at 250, 500, and 750 m) and the right-hand images show vertical slices through the X and Y axes, respectively.

Fig. 6.
Fig. 6.

Difference plots of 3D tomographic reconstructions of the atmospheric temperature and wind velocities (represented as horizontal and vertical slices through the atmosphere).

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00036.1

The results are only meaningful inside the cylindrical volume of the UAV trajectory. The root-mean-square errors are less than 0.4°C and 0.4 m s−1, and the maximum error (~1.7°C) occurs at an altitude of ~750 m. This is because the observation matrix is sparse at this altitude and it is a reasonable distance from the direct measurements. An improved UAV trajectory delivers better results. Figure 6 also illustrates that the wind estimates are very close to the target values.

In this simulation the RBF centers are regularly spaced at 125-m intervals. This regularity of spacing is not a requirement as the atmosphere is typically more variable near ground level. Consequently, the spacing between the RBF centers may be set closer together in this region and increased at higher altitudes.

Ultimately, the number of receivers per unit length (or area) and the RBF density combine to limit the spatial resolution of the technique. If the spacing between the RBF centers is less than about 1.5 times the ground sensor separation, the estimation errors in the tomographic inversion increase dramatically. Otherwise, if the ratio between the sensor spacing and the spacing between the RBF centers is kept constant, the estimation errors are approximately inversely proportional to RBF spacing (Fig. 7). This is because the number of RBF weights that need to be estimated increases when the RBF spacing is reduced. In other words, there is an accuracy penalty for aiming for too fine a spatial resolution.

Fig. 7.
Fig. 7.

Wind velocity and temperature estimation errors vs RBF spacing.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00036.1

In general, the estimation errors for temperature and wind speed, derived from the inversion, are linearly proportional to the time delay, direct wind speed, and temperature measurement errors. Other sources of error include temporal changes in the atmosphere during the UAV flight and the movement of the UAV during each sampling observation period, as the UAV typically takes several minutes to complete a profile and the sampling interval is typically 1 s. So far, these effects have not been quantified in detail.

4. Concluding remarks

A technique for tomographically estimating 3D atmospheric temperature and wind velocity patterns is presented. The technique exploits the acoustic properties of a small UAV flying over sensors located at ground level, which provides a very cost effective method for measuring atmospheric properties in otherwise hazardous and inaccessible locations. Simulation results indicate that the approach permits estimation of atmospheric conditions with accuracies commensurate with existing techniques and hence at acceptable levels, although this will need to be verified by field trials.

REFERENCES

  • Ferguson, B. G., , and Lo K. W. , 2000: Turbo-prop and rotary-wing aircraft flight parameter estimation using both narrow-band and broadband passive acoustic signal processing methods. J. Acoust. Soc. Amer.,108, 1763–1771.

  • Finn, A., , and Franklin S. , 2011a: Acoustic sense and avoid for UAVs. Proc. Seventh Int. Conf. on Intelligent Sensor Signal Network and Information Processing, Adelaide, SA, Australia, IEEE, Paper 1569493569.

  • Finn, A., , and Franklin S. , 2011b: UAV-based atmospheric tomography. Proc. 2011 Australian Acoustical Society Conf., Gold Coast, QLD, Australia, Australian Acoustical Society, Paper 14. [Available online at http://www.acoustics.asn.au/conference_proceedings/AAS2011/papers/p14.pdf.]

  • Haacke, E. M., , Brown R. W. , , Thompson M. R. , , and Venkatesan R. , 1999: Magnetic Resonance Imaging: Physical Principles and Sequence Design. Wiley-Liss, 914 pp.

  • Jovanović, I., 2008: Inverse problem in acoustic tomography: Theory and applications. Ph.D. thesis, Ecole Polytechnique Federale de Lausanne (EPFL), 139 pp.

  • Jovanović, I., , Sbaiz L. , , and Vetterli M. , 2009: Acoustic tomography for scalar and vector fields: Theory and application to temperature and wind estimation. J. Atmos. Oceanic Technol., 26, 14751492.

    • Search Google Scholar
    • Export Citation
  • Kelley, N. D., , Jonkman B. J. , , and Scott G. N. , 2007: Comparing pulsed Doppler LIDAR and SODAR and direct measurements for wind assessment. Proc. WindPower 2007 Conf., Los Angeles, CA, Amer. Wind Energy Assoc., NREL/CP-500-41792.

  • Ostashev, V. E., , Vecherin S. N. , , Wilson D. K. , , Ziemann A. , , and Goedecke G. H. , 2008: Recent progress in acoustic tomography of the atmosphere. IOP Conf. Ser.: Earth Environ. Sci.,1, 012008, doi:10.1088/1755-1315/1/1/012008.

  • Quan, Y., , and Huang L. , 2007: Sound-speed tomography using first arrival transmission ultrasound for a ring ray. Proc. SPIE,6513, 651306, doi:10.1117/12.709647.

  • Spiesberger, J. L., , and Fristrup K. M. , 1990: Passive localization of calling animals and sensing of their acoustic environment using acoustic tomography. Amer. Nat., 135, 107153.

    • Search Google Scholar
    • Export Citation
  • Stewart, R. R., 1991: Exploration Seismic Tomography: Fundamentals. Course Notes Series, Vol. 4, Society of Exploration Geophysicists, 140 pp.

  • Stull, R., 1988: An Introduction to Boundary Layer Meteorology. Atmospheric Sciences Library, Kluwer Academic, 666 pp.

  • Wiens, T., , and Behrens P. , 2009: Turbulent flow sensing using acoustic tomography. Proc. Inter-Noise 2009: Innovations in Practical Noise Control, Ottawa, ON, Canada, International Institute of Noise Control Engineering.

  • Wilson, D. K., , and Thomson D. W. , 1994: Acoustic tomographic monitoring of the atmospheric surface layer. J. Atmos. Oceanic Technol., 11, 751769.

    • Search Google Scholar
    • Export Citation
Save