Stanley M. Flatté

Intensity images and statistics from numerical simulation of wave propagation in 3-D random media

An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.

Simulation of point-source scintillation through three-dimensional random media

We have calculated intensity spectra and variances for waves emanating from a point source and propagating through extended three-dimensional random media by simulation. Spectra of the medium fluctuations considered were power-law, power-law with inner scale, and Gaussian spectra. The simulations covered the regimes of weak fluctuations and strong focusing, including the peak of the intensity variance and beyond. The intensity variances are substantially larger than both the corresponding results for plane-wave incidence and the theoretical calculations for point sources by other authors. Our simulation results agree reasonably closely with the results of laserpropagation experiments over kilometer-length paths in the atmosphere.

Comparisons of measured and predicted acoustic fluctuations for a 3250-km propagation experiment in the eastern North Pacific Ocean

During the Acoustic Engineering Test (AET) of the Acoustic Thermometry of Ocean Climate (ATOC) program, acoustic signals were transmitted from a broadband source with 75-Hz center frequency to a 700-m-long vertical array of 20 hydrophones at a distance of 3252 km; receptions occurred over a period of six days. Each received pulse showed early identifiable timefronts, followed by about 2 s of highly variable energy. For the identifiable timefronts, observations of travel-time variance, average pulse shape, and the probability density function (PDF) of intensity are presented, and calculations of internal-wave contributions to those fluctuations are compared to the observations. Individual timefronts have rms travel time fluctuations of 11 to 19 ms, with time scales of less than 2 h. The pulse time spreads are between 0 and 5.3 ms rms, which suggest that internal-wave-induced travel-time biases are of the same magnitude. The PDFs of intensity for individual ray arrivals are compared to log-normal and expone...

Internal‐wave effects on 1000‐km oceanic acoustic pulse propagation: Simulation and comparison with experiment

A recent 1000‐km acoustic pulse transmission experiment in the Pacific revealed unexpected fluctuations on received wavefronts, including a dominant rapid variation, called the broadband fluctuation, with time scales less than 10 minutes and spatial scales of less than 60 m; a distinct breakdown of the geometrical optics wavefront pattern and broadening of the wavefront near the transmission finale; and a coherent wavefront motion with a timescale near the semi‐diurnal tidal period. Parabolic‐equation numerical simulations have been carried out which utilize environmental data and which take into account internal‐wave‐induced sound‐speed perturbations obeying the Garrett–Munk (GM) spectral model. It is shown that the effects of internal waves can account for the broadband fluctuations, the breakdown of the geometrical optics pattern, and the wavefront broadening. The sensitivity of these fluctuations to internal‐wave energy and modal content is examined. The spectral energy in the GM model at tidal period...

Wavefront folding, chaos, and diffraction for sound propagation through ocean internal waves

This work presents an analysis of the effects of ocean internal waves on long-range acoustic pulse propagation from the geometrical-optics point of view. The chaotic behavior of rays and the microfolding of timefronts are investigated. The extent of the region of the timefront in which strongly chaotic rays appear, and the strength of the rays’ sensitivity to initial conditions, are found to depend on the average (range-independent) sound-speed profile, on the range from the source to the receiver, and on the internal-wave spectral model, but not on the specific realization of the internal waves. For a particular experiment (SLICE89), it is concluded that the observed depth diffusion of energy in the late-arriving portion of the timefront is a result of refraction (of geometrical-optics rays), not diffraction. It is found that internal-wave effects cause an upper turning point of a ray to be spread to the extent of 10 km horizontally and 100 m vertically, which affects the resolution of ocean-acoustic tom...

PROBABILITY-DENSITY FUNCTIONS OF IRRADIANCE FOR WAVES IN ATMOSPHERIC TURBULENCE CALCULATED BY NUMERICAL SIMULATION

We have carried out numerical simulations of waves traversing a three-dimensional random medium with Gaussian statistics and a power-law spectrum with inner-scale cutoff. The distributions of irradiance on the final observation screen provide the probability-density function (PDF) of irradiance. For both initially plane and initially spherical waves the simulation PDF’s in the strong-fluctuation regime lie between a K distribution and a log-normal-convolved-with-exponential distribution. We introduce a plot of the PDF of scaled log-normal irradiance, on which both the exponential and the lognormal PDF’s are universal curves and on which the PDF at both large and small irradiance is shown in detail. We have simulated a spherical-wave experiment, including aperture averaging, and find agreement between the simulated and the observed PDF’s.

Inhomogeneities near the core-mantle boundary evidenced from scattered waves: A review

Statistical properties of small-scale inhomogeneities (wavelengths between 20 and 70 km) near the core-mantle boundary are inferred from scattered core waves. Observations of scattered core waves at large seismic arrays and worldwide networks indicate that the inhomogeneities have a global nature with similar characteristics. However, there may exist a few regions having markedly stronger or weaker strengths. Scattering by volumetric inhomogeneities of about 1% inP-wave velocity in the lower mantle or by about 300 m of topographic relief of the core-mantle boundary can explain the observations. At present it is not possible to rule out either of these two alternatives, or a combination of both.

Measured wave‐front fluctuations in 1000‐km pulse propagation in the Pacific Ocean

A 1000‐km acoustical transmission experiment has been carried out in the North Pacific, with pulses broadcast between a moored broadband source (250‐Hz center frequency) and a moored sparse vertical line of receivers. Two data records are reported: a period of 9 days at a pulse rate of one per hour, and a 21‐h period on the seventh day at six per hour. Many wave‐front segments were observed at each hydrophone depth, and arrival times were tracked and studied as functions of time and depth. Arrivals within the final section of the pulse are not trackable in time or space at the chosen sampling rates, however. Broadband fluctuations, which are uncorrelated over 10‐min sampling and 60‐m vertical spacing, are observed with about 40 (ms)2 variance. The variance of all other fluctuations (denoted as low‐frequency) is comparable or smaller than the broadband value; this low‐frequency variance can be separated into two parts: a wave‐front segment displacement (with vertical correlation length greater than 1 km) t...

Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment

Irradiance variance for optical propagation through atmospheric turbulence is calculated by numerical simulation. Let l0 be the inner scale, Rf be the Fresnel scale, and β02 be the weak-fluctuation irradiance variance at zero inner scale. Then results in the strong-focusing regime just past the peak can be summarized by σI2 = 1.74 − 0.092β0 + 0.60(l0/Rf) for a plane wave and σI2 = 3.02 − 0.35β0 + 5.56(l0/Rf) for a point source. These numerical results are in excellent agreement with experimental results.

Transmission fluctuations across an array and heterogeneities in the crust and upper mantle

Adopting the spectral approach, we derive the formulation of angular coherence and transverse coherence of transmission fluctuations. Our derivation and results provide new insight on transmission fluctuation analysis. A review of research work on fluctuation analysis using observations at large seismic arrays such as LASA and NORSAR-follows. We point out that the model of a single-layer Gaussian medium cannot explain the angular coherence of NORSAR data and a more general model of a non-Gaussian, multi-scale, vertically inhomogeneous random media is needed. The model of a two-layer power-law medium proposed by Flatté and Wu is among the simplest of such models.