George H. Goedecke

Scattering by irregular inhomogeneous particles via the digitized Green's function algorithm.

The digitized Greens function (DGF) algorithm and the underlying theory are described. This finite element algorithm models dielectric particles of arbitrary shape and arbitrary optical structure. DGF predictions of differential and total cross sections are compared with predictions of Mie and EBCM algorithms for several homogeneous spheres and spheroids. Results of tests of convergence of the DGF calculation as the number of elements are increased are presented. Computer time and storage requirements as functions of wavelength and particle size, shape, and optical structure are discussed.

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...

Scattering of millimeter waves by snow crystals and equivalent homogeneous symmetric particles

The digitized Greens function code was used to compute differential and total cross sections of several model snow crystals and of several homogeneous highly symmetric equivalent particles of the same general shape and size as the snow crystals at a wavelength of 10 mm. Optical constants of equivalent particles were derived using the Biot-Arago, Lorentz-Lorenz, and Bruggemann mixing rules. Reasonable agreement was found for equivalent particles whose mass distributions were most similar to those of the snow crystals. Overall, the Bruggemann mixing rule produced the best match.

Spectral broadening of sound scattered by advecting atmospheric turbulence

Scattering and spectral broadening of a monochromatic sound wave by atmospheric turbulence that is flowing with a uniform constant horizontal wind is considered. The acoustic source and a detector are at rest and at different positions in a ground-fixed frame. Analytic expressions are derived for the sound pressure scattered to the detector by a single eddy. Since distances and the scattering angle change with time as the eddy flows through the scattering volume, the detector signal has time-dependent amplitude and frequency, for which general formulas are derived. A computer code is developed that calculates the scattered signal and its Fourier transform from a single eddy, or from a steady-state collection of eddies of many different scale lengths that represents isotropic homogeneous turbulence flowing with the wind. The code utilizes a time-shift algorithm that reduces the calculation time substantially. Several numerical results from this code are presented, including simulations of a recent experiment. The predicted spectral shape, including peak width and jaggedness, are in good agreement with experiment.

Recent progress in acoustic tomography of the atmosphere

Acoustic tomography of the atmospheric surface layer is based on measurements of travel times of sound propagation among different pairs of sources and receivers usually located several meters above the ground on a horizontal scale of about 100 m. The measured travel times are used as input data in an inverse algorithm for reconstruction of temperature and wind velocity fields. Improved knowledge of these fields is important in boundary layer meteorology, theories of turbulence, and studies of electromagnetic and acoustic wave propagation in the atmosphere. In this paper, a short overview and current status of acoustic travel-time tomography of the atmosphere are presented. A brief description of a 3D array for acoustic tomography of the atmosphere which is being built at the Boulder Atmospheric Observatory is given. Furthermore, different inverse algorithms for reconstruction of temperature and velocity fields are discussed, including stochastic inversion and a recently developed time-dependent stochastic inversion. The latter inverse algorithm was used to reconstruct temperature and wind velocity fields in acoustic tomography experiments. Examples of the reconstructed fields are presented and discussed.

Acoustic scattering by atmospheric turbules

Atmospheric turbulence is modeled as a collection of self-similar localized eddies, called turbules. Turbulent temperature variation and solenoidal velocity structure function spectra and the corresponding average acoustic scattering cross sections are calculated for several isotropic homogeneous turbule ensembles. Different scaling laws for turbule strengths, number densities, and sizes produce different power-law spectra independent of turbule morphology in an “inertial range” of the spectral variable K. For fractal size scaling and Kolmogorov power law ∝K−11/3 in the inertial range, not only do turbule strengths scale like the one-third power of the size, but also the turbule packing fractions are scale invariant, as are the expressions derived for the structure parameters (CT2,Cv2). The inertial range boundaries of the spectral variable and scattering angles are easily estimated from the inner and outer scales of the turbulence. They depend weakly on turbule morphology, while the spectra and cross sec...

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

Refractive indices of powdered materials using attenuated total reflectance spectroscopy

The attenuated total reflectance spectroscopy method of determining the complex refractive indices of materials which occur only as small particles was applied at a 10.6-microm wavelength to numerous pressed powder samples. Fresnel relations were used to obtain best fit values for the complex refractive indices of the samples. Good fits were obtained only when the particles were small compared to the wavelength. For such samples, several effective medium theories were used to predict values of bulk material refractive indices from those of samples with different volume packing fractions. Only the Bruggeman theory produced consistent results.

Sound-wave coherence in atmospheric turbulence with intrinsic and global intermittency.

The coherence function of sound waves propagating through an intermittently turbulent atmosphere is calculated theoretically. Intermittency mechanisms due to both the turbulent energy cascade (intrinsic intermittency) and spatially uneven production (global intermittency) are modeled using ensembles of quasiwavelets (QWs), which are analogous to turbulent eddies. The intrinsic intermittency is associated with decreasing spatial density (packing fraction) of the QWs with decreasing size. Global intermittency is introduced by allowing the local strength of the turbulence, as manifested by the amplitudes of the QWs, to vary in space according to superimposed Markov processes. The resulting turbulence spectrum is then used to evaluate the coherence function of a plane sound wave undergoing line-of-sight propagation. Predictions are made by a general simulation method and by an analytical derivation valid in the limit of Gaussian fluctuations in signal phase. It is shown that the average coherence function increases as a result of both intrinsic and global intermittency. When global intermittency is very strong, signal phase fluctuations become highly non-Gaussian and the average coherence is dominated by episodes with weak turbulence.

Spherical wave propagation through inhomogeneous, anisotropic turbulence: log-amplitude and phase correlations.

Inhomogeneity and anisotropy are intrinsic characteristics of daytime and nighttime turbulence in the atmospheric boundary layer. In the present paper, line-of-sight sound propagation through inhomogeneous, anisotropic turbulence with temperature and velocity fluctuations is considered. Starting from a parabolic equation and using the Markov approximation, formulas are derived for the correlation functions and variances of log-amplitude and phase fluctuations of a spherical sound wave. These statistical moments of a sound field are important for many practical applications in atmospheric acoustics. The derived formulas for the correlation functions and variances generalize those already known in the literature for two limiting cases: (a) homogeneous, isotropic turbulence, and (b) inhomogeneous, anisotropic turbulence with temperature fluctuations only. Furthermore, the formulas differ from those for the case of plane wave propagation. Using the derived formulas and Manns spectral tensor of velocity fluctuations for shear-driven turbulence, the correlation functions and variances of log-amplitude and phase fluctuations are studied numerically. The results obtained clearly show that turbulence inhomogeneity and anisotropy significantly affect sound propagation in the atmosphere.