Low Grazing Angles Research Articles

Low-grazing angle scattering from rough surfaces in a duct formed by a linear-square refractive index profile

The problem of rough surface scattering and propagation over rough terrain in a ducting environment has been receiving considerable attention in the literature. One popular method of modeling this problem is the parabolic wave equation (PWE) method. An alternative method is the boundary integral equation (BIE) method. The implementation of the BIE in inhomogeneous media (ducting environments) is not straightforward, however, since the Green's function for such a medium is not usually known. In this paper, a closed-form approximation of the Green's function for a two-dimensional (2-D) ducting environment formed by a linear-square refractive index profile is derived using asymptotic techniques. This Green's function greatly facilitates the use of the BIE approach to study low-grazing angle (LGA) rough surface scattering and propagation over rough surfaces in the aforementioned ducting environment. This paper demonstrates how the BIE method can model the combined effects of surface roughness and medium inhomogeneity in a very rigorous fashion. Furthermore, it illustrates its capability of accurately predicting scattering in all directions including backscattering. The boundary integral equation of interest is solved via the method of ordered multiple interactions (MOMI), which eliminates the requirements of matrix storage and inversion and, hence, allows the application of the BIE method to very long rough surfaces.

Bistatic scattering characterization of complex objects

Discusses the bistatic scattering nature of complex metal objects and assesses the accuracy of several common bistatic scattering prediction techniques: a common physical optics/physical theory of diffraction (PO/PTD) based simulation package, Kell's (1965) scattering center-derived monostatic-to-bistatic equivalence theorem (MBET), and Crispin's (Crispin and Siegel 1968) PO-based MBET. Monostatic and bistatic measured and simulated data are gathered and compared for three test objects of increasing complexity. Delineation between specular and nonspecular effects is highlighted to help explain when prediction techniques fail. The PO code proves erroneous at low grazing angle receive antenna positions and does not predict nonspecular type scattering well. Interestingly, however, it does accurately compute specular reflections from electrically small surface features. Kell's and Crispin's MBETs are also studied. For simple objects (e.g., flat plate) both MBETs predict scattering fairly well for bistatic angles of 30-40/spl deg/, with Kell's having a slight edge at larger angles. As the complexity of the object increases, MBET accuracy decreases. Neither MBET is particularly capable at bistatic angles greater than 15/spl deg/ for objects whose scattered field is primarily comprised of specular interactions (minimally complex). Both tend to predict lower returns at larger bistatic angles. MBET accuracy holds for smaller bistatic angles with increasing geometrical complexity. The object whose geometry contains large shadowing features and a cavity supports multi-bounce, diffraction, and surface wave phenomena. The accuracy of both MBETs is limited to bistatic angles of only 5-10/spl deg/ in this case. Each tends to predict higher than measured scattering at larger bistatic angles.

Translation to the normal distribution for radar clutter

The single point statistics of some high-resolution low-grazing angle radar sea clutter are examined. Three different distributions are used to model the cumulative density of the data. The Weibull and the K-distribution both require the addition of a Rayleigh distributed component to give a good fit to the data. This Rayleigh distributed component has a mean level significantly higher than the thermal noise level. A third model, the 'sinusoidal bound system' (sin S/sub B/) is also developed. It performs very well in fitting the extremes of the cumulative distribution, particularly the upper limit, which is not well fitted by the other models.

Low grazing angle bistatic sea floor scattering on the Florida Atlantic coastal shelf

Observations of bistatic scattering at moderate frequencies 3750 Hz, 7500 Hz, and 15 000 Hz and low grazing angles (2°–20°) are presented with a geoacoustical description of the site. Given a source–receiver separation of 80.7 m, bistatic scattering strengths in the sandy sediments at the measurement site range from −70 to −15 dB. The observed bistatic scattering at low grazing angles depends primarily on the incident bearing angle. Bistatic scattering values are highest along the transect between the source and receiver. Maximum scattering strengths (−20 to −15 dB) appear 30 m from the receiver. Regions of high scattering (>−30 dB) strength are centered along the direct path between the source and receiver. The contribution of volume scattering to the observed scattering pattern is not very clear. However, given the sandy sediments found at the site, roughness scattering is expected to be a major contributor to the observed bistatic scattering patterns.

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.

Behaviour of scattering from a rough surface at small grazing angles

The particular problem of wave scattering at low grazing angles is of great interest because of its importance for the long-distance propagation of radio waves along the Earth's surface, radar observation of near surface objects, as well as solving many other fundamental and applied problems of remote sensing. One of the main questions is: how do the scattering amplitude and specific cross section behave for extremely small grazing angles? We consider the process of wave scattering by a statistically rough surface with the Neumann boundary condition. This model corresponds to sound scattering from a perfectly ‘hard’ surface (for example, the interface between air and the sea surface) or ‘vertically’ polarized electromagnetic waves scattered by a perfectly conducting one-dimensional (i.e. cylindrical) surface when the magnetic field vector is directed along the generating line of this cylindrical surface. We assume that the surface roughness is sufficiently small (in the sense of the Rayleigh parameter) and the surface is rigorously statistically homogeneous and therefore, infinite. We confine ourselves only to the first-order approximation of small perturbation theory and therefore consider every act of wave scattering in the Born approximation when the Bragg scattering process takes place. Only one resonant Fourier component of surface roughness is responsible for the scattering in a given direction. However, we take into account the attenuation of incident and scattered waves due to the multiple scattering processes on the path ‘before’ and ‘after’ a scattering event in a given direction. Also we consider every one of these multiple scattering events only in the Born approximation. The main result we have obtained is that for small grazing angles the scattering cross section of the diffuse component decreases as the second power of the grazing angles with respect to the incident and scattered directions, and as the fourth power of the grazing angle for the backscattering (radar) situation. Generalizing our results from plane-wave scattering to finite beams allows us to obtain the criterion on the beamwidth. For sufficiently narrow beams the multiple scattering processes do not play any role because of a short ‘interaction path’, and only single Bragg scattering determines the scattering amplitude (which does not tend to zero for small grazing angles). However, for sufficiently wide beams the result obtained for infinite plane waves becomes valid: due to the above-mentioned multiple scattering processes, the scattering amplitude tends to zero for small grazing angles. Consequently, the behaviour of the scattering cross section for small grazing angles depends on the radiation pattern width of the transmitting and receiving antennae: for sufficiently wide beams the scattering cross section decreases to zero at small grazing angles, but for narrow beams it tends to the finite non-zero value.

The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces

In Holliday et al. (1995, 1996), the iterative forward-backward (FB) method has been proposed to solve the magnetic field integral equation (MFIE) for smooth one-dimensional (1-D) rough surfaces. This method has proved to be very efficient, converging in a very small number of iterations. Nevertheless, this solution becomes unstable when some obstacle, like a ship or a large breaking wave, is included in the original problem. In this paper, we propose a new method: the generalized forward-backward (GFB) method to solve such kinds of complex problems. The approach is formulated for the electric field integral equation (EFIE), which is solved using a hybrid combination of the conventional FB method and the method of moments (MoM), the latter of which is only applied over a small region around the obstacle. The GFB method is shown to provide accurate results while maintaining the efficiency and fast convergence of the conventional FB method. Some numerical results demonstrate the efficiency and accuracy of the new method even for low-grazing angle scattering problems.

Continuous monitoring of fish in a shallow channel using a fixed horizontal sonar

An acoustic monitoring program of herring migration in Drogden channel, near Copenhagen, Denmark was conducted from June 1996 until the end of May 1997. Fixed 100-kHz side-looking sonars provided nearly continuous surveillance in a 1-km-wide by 12-m-deep navigation channel. Water temperature, salinity, and current profiles were simultaneously monitored at this site. The sonars were positioned to insonify regions near the seabed at ranges up to 800 m, such that the typical reverberation was due to low-grazing angle seabed backscatter. It was found that under normal, weakly stratified flow conditions, fish schools attributable to herring (Clupea harengus) were observed from the 50- to 500-m range. This could be done despite interference from the dense vessel traffic, specifically direct echoes from hulls, propeller cavitation noise, and bubbly wakes. At close ranges (<150 m) hyperbolic trajectories attributable to individual herring were observed, with horizontal advection speeds in close agreement with measured current magnitudes. It was further observed that occasional intrusions of saline bottom waters created strong upward-refracting conditions that significantly limited the range for fish school detection. Ray-tracing analysis is used to define the insonified areas and describe the backscattered reverberation under normal and stratified flow conditions. It is shown using simulations of fish-school echoes that seabed-reflected multipaths can create an upward bias in fish-school densities calculated using echo-integration techniques.

Surface chemical characterization and surface diffraction effects of real margarite (001); an angle-resolved XPS investigation

The (001) surface of natural pure margarite was chemically characterized by angle-resolved Xray photoelectron spectroscopy (ARXPS). The extreme surface sensitivity of ARXPS permits concluding that the chemical composition of the near-surface region differs from the bulk because of the strong anisotropy of the margarite structure. Depth profiling was carried out by angle resolved spectroscopy that is a non destructive measuring technique. More grazing polar angles sample increasingly superficial layers of the margarite. The topmost layers are made up of C, due to the mineral/atmosphere interaction. At low grazing angles the concentration of Si increases, and both Al and Ca decreases; therefore we conclude that the tetrahedral sheet is the topmost monolayer. Repulsion between the octahedral and tetrahedral sheets is probably responsible for the cleavage. Photoelectron diffraction effects are also clearly evidenced by Si, Ca, and Al. Single-scattering cluster calculations were performed in simulating scanned angle core emission. The calculated patterns do not show a reasonable agreement with experimental data.

Comparison of seafloor character as measured by calibrated vertical-incidence profiler and sidescan sonar

Sidescan sonar backscatter from a variety of continental shelf bottom types reveals considerable divergence from vertical-incidence reflection coefficients. Acoustic data are from a 300-kHz sidescan sonar and a calibrated, constant beam width, 10–50 kHz vertical incidence profiler, and are supported by extensive physical, geoacoustic, textural, and morphologic measurements. Bottom types include a wide range of quartzose and carbonate sands and silts, seagrass, coral heads, coral reef, and hardbottoms. The two systems show notable divergences over seagrass and carbonate hardbottoms, which produced low normal-incidence reflection coefficients but high backscatter from sidescan sonar, and smooth, packed sands, which gave high normal-incidence reflection coefficients but low sidescan backscatter. The divergences appear to be caused by bottom roughness. Narrow-beam, vertical incidence systems are subject to signal loss from out-of-beam scattering over rough bottoms, whereas roughness increases backscatter at the low grazing angles over which the sidescan system operates. Although both systems will accurately map bottom character, there is no direct correspondence betwen the two vis-à-vis bottom type. Therefore, to extend seafloor classification from vertical incidence profiling into an areal approach with sidescan sonar requires more than simple lateral extrapolation. [Work supported by ONR.]

A new, semiempirical model for predicting bistatic surface backscattering strengths

A Lloyd-mirror model of bubble-cloud scattering, along with perturbation theory for the rough air–sea interface, have been used as a basis for generating a new algorithm for predicting the strength of acoustic backscatter from the ocean surface. Multiparameter curve fits of the model to acoustic data from the Critical Sea Test program (1988–1996) and other at-sea experiments have been used to derive a new, semiempirical description of the dependence of surface backscattering strength on the incident and scattered grazing angles, the acoustic frequency, and environmental descriptors. The model represents an advance on previous algorithms (Chapman–Harris, Ogden–Nicholas–Erskine) in several ways: (1) a much improved, physics-based description of the grazing-angle dependence, applicable to arbitrarily low grazing angles; (2) a much improved description of low-to-moderate sea-state bubble scattering; (3) can handle vertically bistatic geometries; and (4) is applicable to a broader range of frequencies (50 to 5000 Hz). [Work supported by ONR.]

Hydrodynamic effects in low-grazing angle backscattering from the ocean

Time series of returned power, Doppler spectra and range versus time intensity (RTI) images collected from low-grazing angle radar backscattering from the ocean present features which cannot be explained solely within the framework of resonant Bragg scattering. We propose that most of the observed characteristics are a consequence of the way in which waves evolve on the surface of the ocean. We have built a model consisting of a hydrodynamic module and a radar response module. The hydrodynamics module includes most of the physics thought to be relevant to the evolution of a wavefield (i.e., nonlinear interactions, wind, and wavebreaking). The radar module computes the backscattering as the accumulation of Bragg response from every tilted facet of the reconstructed surface, except for those locations where hydrodynamic conditions leading to wavebreaking are detected. Facets involved in wavebreaking are assumed to contribute to the backscattering in a quasi-specular polarization independent fashion. The hydrodynamics module is used to simulate the evolution of a nonlinear wave field, starting from essentially monochromatic conditions. The evolution reproduces known characteristics of these systems, including the generation of sideband instabilities and downshifting. The radar response module is then exercised on the resulting surface at various stages of development. Simulated RTIs at very low-grazing angles reproduce the observed polarimetric characteristics, as well as their behavior when the grazing angle is increased. Simulated Doppler spectra reproduce the peak separation phenomenon observed in field measurements at very low-grazing angles and also show a behavior similar to that shown by field data when the grazing angle is increased.

Reflection loss from a "Pierson-Moskowitz" sea surface using the nonlocal small slope approximation

The lowest-order nonlocal small slope approximation (NLSSA) reflection coefficient is derived, and numerical results are presented for one-dimensional (1D) surfaces, satisfying the Dirichlet boundary condition. Reduction to the perturbation expression occurs in the small height limit, and the first term of the reflection coefficient gives the Kirchhoff approximation (KA) result. Numerical results for the reflection loss at low grazing angles using a Pierson-Moskowitz spectrum are compared with those of other approximate methods as well as with exact integral equation (IE) results. For those cases when exact results are available, the NLSSA is found to give accurate results, comparable to those of the small slope approximation (SSA) and superior to those of classical perturbation theory (PT) and the KA.

Radar clutter attractor: implications for physics, signal processing and control

A discussion is presented on the chaotic dynamics of sea clutter in the light of current knowledge about chaos theory. The discussion builds on experimental results reported by Haykin and Puthusserypady (see Chaos, vol.7, p.777-802, 1997, IEE 1997 Radar Conf., Edinburgh, Scotland, p.14-16, 1997, and Chaotic dynamics of sea clutters, Wiley, 1999) on the chaotic dynamics of sea clutter under varying environmental conditions and on the dynamic reconstruction of sea clutter using a regularised radial-basis function network. The experimental results presented are for a marine radar operating at low grazing angles. The implications of the chaotic dynamics of sea clutter are discussed in the context of physical aspects of sea clutter, simulation of sea clutter, the detection of a target signal embedded in sea clutter, and the stability of the predictive model used to perform the dynamic reconstruction of sea clutter.

Simulation of the Orographic Influence on Weather Radar Using a Geometric–Optics Approach

Abstract A computer code for radar site assessment, including ground clutter, beam occultation, and earth curvature–atmospheric refraction factors, has been developed. The code uses topographic information in the form of a raster Digital Elevation Model, air refractive index profile in the boundary layer, surface backscattering cross section per unit area at grazing angles as derived from literature, and ancillary information, if available, derived from a land use–land cover map. This algorithm is independent of a specific radar site and radar system. Several benefits in dealing with open problems of radar meteorology and of radar design could be derived from its use, namely, better estimate of precipitation at ground level through vertical echo profile correction, scanning strategy, land clutter measurements at low grazing angles, and characterization of seasonal and topographic effects. The raster-based approach used in implementing the code makes it compatible with any spatial resolution desired. Simpl...

The surprising relationship between the atomic Lamb shift and acoustics

An analogy with a well-known quantum effect provides insight into the low grazing angle interaction of an acoustic field with a rough surface. The Lamb shift in the hydrogen atom is produced by random fluctuations that ultimately arise from second quantization. These can be introduced phenomenologically into the old quantum theory. Since the Coulomb potential is the Green’s function for 3-D space, a contact potential affecting the first moment of the field survives stochastic averaging, and produces the Lamb shift. [For example, C. Cohn-Tanoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992), p. 317.] For a classical acoustic field in the low grazing angle limit (described by the parabolic equation), a rough surface along an interface or a cusp generates a similar contact potential. This leads to a modified range-independent propagation equation for the first moment of the stochastic acoustic field. New boundary conditions at the interface lead to roughness-induced modifications to Snell’s Law. [Work supported by ONR.]

Experimental results for detection of buried objects at low grazing angles

Extension of buried object detection sonar system concepts to include low grazing angle geometries (i.e., beyond critical angle) would provide useful gains in coverage rate, provided acceptably high detection probabilities can be maintained for sufficiently low probabilities of false alarm. Several experiments have recently been conducted at shallow water sites with sandy seabottoms near Elba Island, Italy, in order to study the acoustic backscattering characteristics of the seabed and buried targets in a range of grazing angles both above and below the nominal critical angle of the seabed. A parametric sonar with significant secondary frequency source levels in the range 2–16 kHz was used (the size of the targets yielded ka values also in the approximate range 2–16). Modeling results for buried objects have shown that subcritical insonification can produce relatively high monostatic echo levels, especially at lower frequencies where the evanescent field is strongest. Some results of the experiments are discussed which show promising SNR improvements for subcritical cases when the lowest parts of the frequency band are emphasized, in empirical agreement with the models.

The Helmholtz–Kirchhoff approach to modeling penetration of acoustic waves into rough seabeds

The Helmholtz–Kirchhoff integral is applied to model the penetration of sound waves into sandy seafloors at grazing angles above and below the critical angle. Although the conditions for the validity of the Kirchhoff approximation can be limiting, this approximation should be valid at high frequency for gently undulating seafloor surfaces even at moderate to low grazing angles, providing that the self-shadowing effect is carefully removed. The analytical development of the method is first presented, followed by numerical examples and comparisons with the experimental data of Maguer et al. [SACLANTCEN report, SR-287, April 1998]. The model predicts, in agreement with the 2- to 15-kHz acoustic data, the frequency where the contributions due to roughness effects begin to dominate those due to the evanescent wave. Secondary effects such as Bragg interference patterns and the loss of signal coherence with grazing angle or depth are correctly predicted. The model simulations strongly suggest that roughness of the sediment interface is most likely the cause of anomalous sound penetration into the seabed.

Space‐time properties of radar sea spikes and their relation to wind and wave conditions

Low‐grazing angle (LGA) radar sea spikes were observed with a high‐resolution, dual‐polarization, X band imaging radar deployed on the floating instrument platform (FLIP) during the Marine Boundary Layer Experiment (MBLEX) held off the California coast during April–May 1995. Spatiotemporal statistics of observed sea spike events are presented, including duration, velocity, and directional distributions. The dependence of these parameters on wind and wave conditions is compared to theoretical predictions and to similar measurements of breaking wave signatures obtained with passive acoustic techniques by Ding and Farmer [1994]. The density of sea spikes (events per unit time per unit area) and the fractional surface coverage are estimated as a function of friction velocity and compared to theoretical predictions. Though we find consistency between the dynamical aspects of sea spike events and of acoustic wave‐breaking signatures, we do not observe a predicted cubic u* dependence of sea spike density. Differences may be a consequence of the specific nature of low‐grazing angle scattering at X band (and higher) frequencies. We observe an approximately quadratic dependence on u* of sea spike fractional surface coverage which is insensitive to the choice of backscattered power threshold over a 9 dB range.

Boundary scattering limitations to fish detection in shallow waters

This work reviews high-frequency, low-grazing angle surface and bottom reverberation effects relevant to fish detection in shallow waters. Simple acoustic reverberation models are presented, which include the effects of Bragg scattering from surface wind waves, sediment backscatter, and scattering and absorption within air bubble layers created by breaking waves and boat wakes. A simple example, with a 200 kHz narrow-beam sonar in water depth of 5 m, is used to demonstrate these reverberative interference effects. When present, air bubble layers cause serious interference with fish detection, such that even large fish (TS=−30 dB) could not be detected beyond 50 m range. Under calm conditions without bubbles, reverberation from gravel or rocky sediments would limit detection of small fish (TS=−50 dB) at ranges greater than 50 m. Air bubbles within boat wakes generate strong backscattering and cause shadowing (transmission loss exceeding 20 dB) of targets behind them.