Two-Scale Kirchhoff Theory: Comparison of Experimental Observations With Theoretical Prediction

We introduce a non-perturbative two scale Kirchhoff theory, in the context of light scattering by a rough surface. This is a two scale theory which considers the roughness both in the wavelength scale (small scale) and in the scales much larger than the wavelength of the incident light (large scale). The theory can precisely explain the small peaks which appear at certain scattering angles. These peaks can not be explained by one scale theories. The theory was assessed by calculating the light scattering profiles using the Atomic Force Microscope (AFM) images, as well as surface profilometer scans of a rough surface, and comparing the results with experiments. The theory is in good agreement with the experimental results.Comment: 6 pages, 8 figure

Application of a maximum likelihood processor to acoustic backscatter for the estimation of seafloor roughness parameters

Maximum likelihood (ML) estimation is used to extract seafloor roughness parameters from records of acoustic backscatter. The method relies on the Helmholtz–Kirchhoff approximation under the assumption of a power‐law roughness spectrum and on the statistical modeling of bottom reverberation. The result is a globally optimum, highly automated technique that is a useful tool in the context of seafloor classification via remote acoustic sensing. The general geometry of the Sea Beam bathymetric system is incorporated into the design of the ML processor in order to make it applicable to real acoustic data collected by this system. The processor is initially tested on simulated backscatter data and is shown to be very effective in estimating the seafloor parameters of interest. The simulated data are also used to study the effect of data averaging and normalization in the absence of system calibration information. The same estimation procedure is applied to real data collected over two central North Pacific seamounts, Horizon Guyot and Magellan Rise. The Horizon Guyot results are very close to estimates obtained through a curve‐fitting procedure presented by de Moustier and Alexandrou [J. Acoust. Soc. Am. 90, 522–531 (1991)]. In the case of Magellan Rise, discrepancies are observed between the results of ML estimation and curve fitting

Time dependent seafloor acoustic backscatter (10-100kHz)

A time-dependent model of the acoustic intensity backscattered by the seafloor is described and compared with data from a calibrated, vertically oriented, echo-sounder operating at 33 and 93 kHz. The model incorporates the characteristics of the echo-sounder and transmitted pulse, and the water column spreading and absorption losses. Scattering from the water–sediment interface is predicted using Helmholtz–Kirchhoff theory, parametrized by the mean grain size, the coherent reflection coefficient, and the strength and exponent of a power-law roughness spectrum. The composite roughness approach of Jackson et al. [J. Acoust. Soc. Am. 79, 1410–1422 (1986)], modified for the finite duration of the transmitted signal, is used to predict backscatter from subbottom inhomogeneities. It depends on the sediment’s volume scattering and attenuation coefficients, as well as the interface characteristics governing sound transmission into the sediment. Estimation of model parameters (mean grain size, roughness spectrum strength and exponent, volume scattering coefficient) reveals ambiguous ranges for the two spectral components. Analyses of model outputs and of physical measurements reported in the literature yield practical constraints on roughness spectrum parameter settings appropriate for echo-envelope-based sediment classification procedures

Remote sensing of sediment characteristics by optimized echo-envelope matching

A sediment geoacoustic parameter estimation technique is described which compares bottom returns, measured by a calibrated monostatic sonar oriented within 15° of vertical and having a 10°–21° beamwidth, with an echo envelope model based on high-frequency (10–100 kHz) incoherent backscattertheory and sediment properties such as: mean grain size, strength, and exponent of the power law characterizing the interface roughness energy density spectrum, and volume scattering coefficient. An average echo envelope matching procedure iterates on the reflection coefficient to match the peak echo amplitude and separate coarse from fine-grain sediments, followed by a global optimization using a combination of simulated annealing and downhill simplex searches over mean grain size, interface roughness spectral strength, and sediment volume scattering coefficient. Error analyses using Monte Carlo simulations validate this optimization procedure. Moderate frequencies (33 kHz) and orientations normal with the interface are best suited for this application. Distinction between sands and fine-grain sediments is demonstrated based on acoustic estimation of mean grain size alone. The creation of feature vectors from estimates of mean grain size and interface roughness spectral strength shows promise for intraclass separation of silt and clay. The correlation between estimated parameters is consistent with what is observed in situ

Doppler spectra of airborne sound backscattered by the free surface of a shallow turbulent water flow

Measurements of the Doppler spectra of airborne ultrasound backscattered by the rough dynamic surface of a shallow turbulent flow are presented in this paper. The interpretation of the observed acoustic signal behavior is provided by means of a Monte Carlo simulation based on the Kirchhoff approximation and on a linear random-phase model of the water surface elevation. Results suggest that the main scattering mechanism is from capillary waves with small amplitude. Waves that travel at the same velocity of the flow, as well as dispersive waves that travel at a range of velocities, are detected, studied and used in the acoustic Doppler analysis. The dispersive surface waves are not observed when the flow velocity is slow compared to their characteristic velocity. Relatively wide peaks in the experimental spectra also suggest the existence of nonlinear modulations of the short capillary waves, or their propagation in a wide range of directions. The variability of the Doppler spectra with the conditions of the flow can affect the accuracy of the flow velocity estimations based on backscattering Doppler. A set of different methods to estimate this velocity accurately and remotely at different ranges of flow conditions is suggested

Characterization of Rough Fractal Surfaces from Backscattered Radar Data

In this paper the scattering of electromagnetic (EM) waves, emitted by a monostatic radar, from rough fractal surfaces is examined by using the Kirchhoff approximation. Of particular interest here is the way that the level of roughness of the fractal surface affects the backscattered EM wave captured by a synthetic aperture radar (SAR) and whether the roughness of the surface can be estimated from these SAR radar measurements. More specifically, the scattering coefficient of the backscattered signal is calculated for a number of radar frequencies and for different values of the surface fractal dimension. It is found here that the slopes between the main lobe and the first sidelobes emerging in the backscattering coefficient as a function of the wavenumber of the incident EM waves increase with the surface fractal dimension. Therefore, we conclude in this paper that the magnitude of the above slopes provides a reliable method for the classification of the rough fractal surfaces. Applications of the proposed method can be found, for example, in the characterization of the sea state from measured SAR radar data

Electromagnetic Scattering and Statistic Analysis of Clutter from Oil Contaminated Sea Surface

In order to investigate the electromagnetic (EM) scattering characteristics of the three dimensional sea surface contaminated by oil, a rigorous numerical method multilevel fast multipole algorithm (MLFMA) is developed to preciously calculate the electromagnetic backscatter from the two-layered oil contaminated sea surface. Illumination window and resistive window are combined together to depress the edge current induced by artificial truncation of the sea surface. By using this combination, the numerical method can get a high efficiency at a less computation cost. The differences between backscatters from clean sea and oil contaminated sea are investigated with respect to various incident angles and sea states. Also, the distribution of the sea clutter is examined for the oil-spilled cases in this paper

Beyond bathymetry: Mapping acoustic backscattering from the deep seafloor with Sea Beam

In its standard mode of operation, the multibeam echosounder Sea Beam produces high resolution bathymetric contour charts of the seafloor surveyed. However, additional information about the nature of the seafloor can be extracted from the structure of the echo signals received by the system. Such signals have been recorded digitally over a variety of seafloor environments for which independent observations from bottom photographs or sidescan sonars were available. An attempt is made to relate the statistical properties of the bottom‐backscattered sound field to the independently observed geologicalcharacteristics of the seafloor surveyed. Acoustic boundary mapping over flat areas is achieved by following trend changes in the acoustic data both along and across track. Such changes in the acoustics are found to correlate with changes in bottom type or roughness structure. The overall energy level of a partial angular‐dependence function of backscattering appears to depend strongly on bottom type, whereas the shape of the function does not. Clues to the roughness structure of the bottom are obtained by relating the shape of the probability density function of normal‐incidence echo envelopes to the degree of coherence in the backscattered acoustic field

Elastic wave scattering from randomly rough surfaces

Elastic wave scattering from randomly rough surfaces and a smooth surface are essentially different. For ultrasonic nondestructive evaluation (NDE) the scattering from defects with smooth surfaces has been extensively studied, providing fundamental building blocks for the current inspection techniques. However, all realistic surfaces are rough and the roughness exists in two dimensions. It is thus very important to understand the rough surface scattering mechanism, which would give insight for practical inspections. Knowledge of the stochastics of scattering for different rough surfaces would also allow the detectability of candidate rough defects to be anticipated. Hence the main motivation of this thesis is to model and study the effect of surface roughness on the scattering field, with focus on elastic waves. The main content of this thesis can be divided into three contributions. First of all, an accurate numerical method with high efficiency is developed in the time domain, for computing the scattered waves from obstacles with arbitrary shapes. It offers an exact solution which covers scenarios where approximation-based algorithms fail. The method is based on the hybrid idea to combine the finite element (FE) and boundary integral (BI) methods. The new method efficiently couples the FE equations and the boundary integral formulae for solving the transient scattering problems in both near and far fields, which is implemented completely in the time domain. Several numerical examples are demonstrated and sufficiently high accuracy is achieved with different defects. It enables the possibility for Monte Carlo simulations of the elastic wave scattering from randomly rough surfaces in both 2D and 3D. The second contribution relates to applying the developed numerical method to evaluate the widely used Kirchhoff approximation (KA) for rough surface scattering. KA is a high-frequency approximation which limits the use of the theory for certain ranges of roughness and incidence/scattering angles. The region of validity for elastic KA is carefully examined for both 1D and 2D random surfaces with Gaussian spectra. Monte Carlo simulations are run and the expected scattering intensity is compared with that calculated by the accurate numerical method. An empirical rule regarding surface parameters and angles is summarized to establish the valid region of both 2D and 3D KA. In addition, it is found that for 3D scattering problems, the rule of validity becomes stricter than that in 2D. After knowing the region of validity, KA is applied to investigate how the surface roughness affects the statistical properties of scattered waves. An elastodynamic Kirchhoff theory particularly for the statistics of the diffused field is developed with slope approximations for the first time. It provides an analytical expression to rapidly predict the expected angular distribution of the scattering intensity, or the scattering pattern, for different combinations of the incidence/scattering wave modes. The developed theory is verified by comparison with numerical Monte Carlo simulations, and further validated by the experiment with phased arrays. In particular the derived formulae are utilized to study the effects of the surface roughness on the mode conversion and the 2D roughness caused depolarization, which lead to unique scattering patterns for different wave modes.Open Acces