Acoustic scattering from a rough sea surface: the mean field by the integral equation method

In this paper, the electromagnetic (EM) scattering characteristics from the ship-induced Kelvin wake on the rough sea surface is investigated, which plays an important role in the ship detection and identification as well as the parameter inversions. The profile of ship-induced Kelvin wake is constructed according to the corresponding Kelvin model. And the rough sea surface is obtained through the double superposition method. The Integral Equation Model (IEM) is utilized to calculate the EM scattering from the ship-induced Kelvin wake on the rough sea surface. The bistatic scattering RCS from the ship-induced Kelvin wake on the rough sea surface is compared with that of simple sea surface. In addition, the effects of the ship speed on the scattering features are also discussed. In the end, the general mechanism of the ship-induced Kelvin wake on the rough sea surface is summarized.

The problem of very high frequency (VHF) radiowave propagation over the sea surface at low grazing angles is of a great interest for a lot of applications including radar backscattering at different polarizations. Existing theoretical approaches predict much bigger backscattering cross section for vertical polarized (TM) waves as compared to horizontal polarized (TE) waves, and are unable to give satisfactory explanation of experimental results showing that these two values occasionally can be of the same order. In this paper two main features are taken into account in a theoretical investigation of the processes of VHF radiowave backscattering by the rough sea surface at low grazing angles: a) distortion of the incident plane wave by diffraction effects at the sea wave crests prior to scattering by smallscale roughness; b) the concave form of the most part of the visible undulating sea surface. The incident wave diffraction caused by sea wave crests is considered using the simplest model of the crest shape, i.e. a perfectly conducting wedge. It is shown that the diffraction in forward direction at low grazing angles increases the strength of the horizontal polarized field as compared to the vertical polarized one just near the boundary between shadowed and illuminated parts of the surface. Back scattering of electromagnetic waves from cylindrical impedance concave statistically rough surface is studied analytically by the small perturbation method.

The actual rough sea surface is described by Pierson-Moscowitz (PM) spectrum and Monte Carlo method; the composite electromagnetic scattering from the double rectangular crosssection conductor columns above the rough sea surface is investigated using the hybrid methodthe Method of Moment with the Kirchhoff approximation. Angular distribution curves of composite scattering coefficient are obtained; and this coefficient that varies with the parameter of sea surface, rectangular cross-section conductor columns and incident waves is calculated in detail. The characteristics of the composite scattering coefficient from the double rectangular cross-section conductor columns above the rough sea surface are also obtained. Results show that the hybrid methodthe Method of Moment with the Kirchhoff approximation, compared to the traditional Method of Moment, can obtain higher accuracy. Moreover, the hybrid method can effectively reduce the computation time and memory footprint, and the performance becomes more favorable with the increase of the sizes of rough surface.

Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem (RT) and the method of equivalent edge currents (MEC) are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation (KA) method and physical optics (PO) method, respectively. The effects of the backscattering radar cross section (RCS) and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.

Summarizes the scattering properties of a rough surface as a function of observation parameters, physic and geometric characteristics of the surface. This study is applied to the oceanic surface. Results are presented in the form of polarimetric signature as a function of the transmitter location and receiver location for a bistatic radio-link over the rough sea surface. The like- and cross-polarized received power are directly calculated using the scattering coefficients, without calculating the Mueller matrix. The Kirchhoff model and the small perturbation method are applied to determine the scattering coefficients. The polarization states, obtained for the minima and maxima received power in order to increase the performance of a bistatic radio-link, or to improve the discrimination power of a radar target are investigated. It is observed that for a fixed transmitter location and receiver location it is possible to choose a polarization state minimizing the scattered power from a rough sea surface, independently of the sea state. An electromagnetic wave scattered from a target is a vectorial quantity containing polarimetric information. This information is a function of the target, and also depends on the observation parameters. The purpose of this paper is to present, the polarimetric signature of the rough sea surface in order to increase the performance of a bistatic radio link (decreasing fading effect, for example), or to improve the discrimination power of a radar target or to identify a target.

This paper presents the characteristics of radio wave scattering from rough sea surfaces in Ka-band. The physical optics method, which is one of the high frequency approximation algorithm, is employed to calculate radar cross section of electromagnetic simulation models of rough sea surfaces with Ship-EDF software. Rough sea surfaces are divided into six levels according to the wind speed over them. The simulation results show the effection that wind speed, the grazinng angle and frequency of radio wave have on the monostatic radar cross section of rough sea surfaces under the conditions of both horizontal and vertical polarization. With the increase of the roughness of sea surfaces and grazing angle of radio wave, the radar cross section value of rough sea surfaces increase. The frequencies of Ka-band have little contribution to the radar cross section value.

The Numerical Solution of Integral Equations on the Half-Line

Recent and ongoing efforts to characterize sea bed parameters from measured acoustic pulse decay have neglected the effects of sea surface roughness. In this paper, these effects are investigated using a rough surface version of RAMPE, RAMSURF, and random rough surface realizations, calculated from a 2D JONSWAP sea surface spectrum with directional spreading. Azimuthal dependence is investigated for sandy bottoms and found that the rate of pulse decay increases when the surface wave fronts are perpendicular to the path of acoustic propagation and higher significant wave height results in higher decay rates. Additionally, the effects from sea surface roughness are found to vary with different waveguide parameters including but not limited to sound speed profile, water depth, and seabed properties. Of particular interest are the combined effects of sea bed properties and rough sea surfaces. It is shown that when clay like sediments are present, higher-order modes are strongly attenuated and effects due to interaction with the rough sea surface are less pronounced. Finally, possible influences of sea-state and 3D out-of-plane propagation effects on the seabed characterization efforts will be discussed. [Work supported by ONR.]

We present a new formulation of the integral equation (IE) method for models with variable background conductivity. This method overcomes the standard limitation of the conventional IE method related to the use of a horizontally layered background only. The new IE method still employs the Green's functions for a horizontally layered 1‐D model. However, the new method allows us to use an inhomogeneous background with the IE method. The method was carefully tested for modeling the electromagnetic (EM) field for complex structures with known variable background conductivity. It can find wide application in modeling EM data for multiple geological models with some common geoelectrical features. As an example, we consider marine controlled source EM (MCSEM) application for simulating EM response of a petroleum reservoir in the presence of a salt dome structure.

At wind speeds higher than a few meters per second, when breaking waves are present, the sea surface roughness is accompanied by an assemblage of microbubbles forming different structures or clouds, varying in range and in time. For simplicity, in terms of an average bubble population, the time and space varying assemblage of microbubbles is often assumed to be uniform and referred to as the subsurface bubble layer. Of fundamental importance is the role that this subsurface bubble layer may play in connection with scattering from a rough air/sea interface. The purpose of this paper is to determine the effect that the rough surface in the presence of this subsurface bubble layer has on the total field at low frequencies. Numerical calculations indicate that at low frequencies the bubble layer shifts the incident angle on the surface to steeper angles. In addition it was found that the enhancement of the total field is a consequence of scattering at the rough surface in the presence of the upper refracting bubble layer. An enhancement of approximately 40 dB with respect to the bubble-free medium was obtained very near the surface for a frequency of 400 Hz, with a nominal grazing angle of 20 deg, and a void fraction at the surface of 3.2×10−5. The enhancement decreases to about 10–15 dB at 10 m below the surface, but is still significant at depth exceeding the bubbly region. For a void fraction at the surface of 3.1×10−6 the enhancement is approximately 5 dB.

An improved shooting and bouncing rays and two-scale method (SBR-TSM) based on message passing interface (MPI) is developed to analyze the composite electromagnetic scattering from multiple targets above a rough sea surface in this letter. The TSM is used to calculate the scattering of the rough sea surface, and the improved SBR method is used to calculate the target, target-target, and target-sea coupling scattering. Moreover, different from the traditional SBR algorithm, the roughness coefficient is introduced to correct the complex reflection coefficient for the target-sea coupling scattering in this letter. MPI is used to accelerate the improved SBR-TSM, and the results demonstrate the accuracy and efficiency of this method.

The emissivity model for rough sea surface [Remote Sensing Environ. 24, 313-329 (1988)] is inspected in light of the measured surface emissivity. In the presence of moderate wind (5 m/s or less), the emissivity model is found to be adequate for small to moderate view angles. For large view angles, the discrepancy between the computed and the measured emissivity is large, but one can reduce this considerably by incorporating the reflected sea surface emission into the emissivity model. In addition, examination of the spectral variation of the observed and computed emissivity suggests the need for refined measurements of the complex refractive index. An improved model is constructed to calculate the rough sea surface emissivity that can be used to provide accurate estimates of sea surface skin temperatures from remotely sensed radiometric measurements. An important feature of the improved model is that the computed sea surface emissivity is only weakly dependent on wind speed for most view angles used in practice.

This paper compares the accuracy of the integral equation method and the multiple scales method in solving the amplitude equation of multi degree of freedom nonlinear vibration systems. We consider three examples: a two-degree-of-freedom stainless-steel beam system controlled by a saturation controller, a three-degree-of-freedom rotating compressor blade model and a four-degree-of-freedom horizontally supported Jeffcott-rotor system controlled by a PPF controller. The amplitude equations are obtained by applying the integral equation method and the method of multiple scales. The stability analysis is achieved based on the Floquet theory together with Routh–Hurwitz criterion. Furthermore, we modified the iterative procedure of the integral equation method to make the analytic approximate solution more accurate. Finally, the analyses show that in most cases, the analytical solutions obtained by the integral equation method are more excellent agreement with the numerical solutions than the most commonly used method of multiple scales. Therefore, the integral equation method is worth popularizing to obtain the approximate analytical solutions of the multi-degree-of-freedom nonlinear vibration system.

The integral equation method has been proven to be an efficient tool to model three‐dimensional electromagnetic problems. Owing to the full linear system to be solved, the method has been considered effective only in the case of models consisting of a strongly limited number of cells. However, recent advances in matrix storage and multiplication issues facilitate the modeling of horizontally large structures. Iterative methods are the most feasible techniques for obtaining accurate solutions for such problems. In this paper we demonstrate that the convergence of iterative methods can be improved significantly, if the original integral equation is replaced by an equation based on the modified Green's operator with the norm less or equal to one. That is why we call this technique the Contraction Integral Equation (CIE) method. We demonstrate that application of the modified Green's operator can be treated as a preconditioning of the original problem. We have performed a comparative study of the convergence of different iterative solvers applied to the original and contraction integral equations. The results show that the most effective solvers are the BIGGSTAB, QMRCGSTAB, and CGMRES algorithms, equipped with preconditioning based on the CIE method.

The rigorous evaluation of the NRCS (Normalized Radar Cross Section) of an object above a one-dimensional sea surface (2D case) needs to numerically solve a set of discretized integral equations involving a large number of unknowns. Thus, the direct solution of the impedance matrix equation via LU decomposition becomes the most expensive step in the MoM (Method of Moments) procedure. So, in order to minimize the computation cost, the iterative domain decomposition method called EPILE (Extended Propagation-Inside-Layer Expansion) was used and then was combined with the FBSA (Forward-Backward with Spectral Acceleration) to calculate the local interactions on the rough sea surface. The resulting fast method is called EPILE+FBSA. In this paper, we take advantage of the rank-deflcient nature of the coupling matrices, corresponding to the object-surface interactions, to further reduce the complexity of the method by using the ACA (Adaptive Cross Approximation). Thus, the coupling matrices are strongly compressed without a loss of accuracy and the memory requirement is then strongly reduced. For a cylinder above a rough sea surface, the results show the e-ciency of the accelerated EPILE+FBSA+ACA method.