Electromagnetic Scattering from Rough Sea Surface
Covered with Oil films
REN Xin-cheng
School of Physics and Electronic Information
Yan’an University
Yan’an, China
xchren@yau.edu.cn
WANG Yu-qing
School of Physics and Electronic Information
Yan’an University
Yan’an, China
ydxxxyrenxch@163.com
Abstract—A composite random rough surface model is
presented for describing rough sea surface covered with oil films,
the electromagnetic wave scattering from this sea surface is
studied based on the Stratton-Chu integral equations mainly. A
general expression for the radar cross section is derived taking
into account a modulation of the rough surface by long surface
waves, and the formulae of scattering coefficient is obtained
further. The curves of the scattering coefficient of HH
polarization with varying of the scattering angle are obtained by
numerical implementation, the influence of the root mean square
and correlation function of small scale roughness, the ratio of the
root mean square and correlation function of large scale
roughness, wave number of space, the amplitude of spatial
fluctuation, the electromagnetic wave irradiation area, the root
mean square and correlation function of large scale roughness
and the frequency of the incident wave on the scattering
coefficient is discussed. The numerical results show that the
influence of these factors on the scattering coefficient is very
complex.
Keywords—electromagnetic scattering; the Stratton-Chu
integral equations; rough sea surface; oil films
I. INTRODUCTION
To detect and monitor oil films at sea is becoming
increasingly important, because of the threats posed by such
pollution to marine and wildlife [1-2]. In recent years, remote-
sensing techniques and corresponding processing techniques
have been developed for this purpose [3-4]. It was shown that
oil films when spread on the surface of rough sea damp the
surface waves. Many studies have been reported on
electromagnetic wave scattering from rough sea surface, David
E. Freund et al. have studied a numerical assessment of the
Miller-Brown Approximation using a horizontally polarized 3-
GHz line source [5], Gabriel Soriano et al. proposed a cutoff
invariant Two-Scale Model in electromagnetic scattering from
sea surfaces[6]. But few studies have been reported on
electromagnetic wave scattering from rough sea surface
covered with oil films, only Nicolas Pinel et al. proposed a
modeling of the bistatic electromagnetic scattering from sea
surfaces covered in oil for microwave applications [7].
In this letter, an approach for a description of the
composite random rough surface is developed in order to have
some progress in the solution of electromagnetic scattering
from rough sea surface covered with oil films.
II. FORMULATION
We consider here the case that the size of the illuminated
surface is sufficiently large what allows us to use analytical
averaging for both the small- and large-scale roughness. Since
the amplitude of the statistically homogeneous small scale
component of the sea surface may be modulated by the large-
scale components of the surface waves, a statistically
inhomogeneous surface may appear. In order to take into
account this effect and to increase the range of the wave
solutions, the large-scale roughness is described in terms of
Physical Optics theory. The developed approach allows us to
investigate the strong reduction of the surface roughness
which appears when oil films are on sea.
Consider electromagnetic wave scattering from a perfectly
conducting random rough surface. Assume that a large surface
wave with some random parameters modulates this surface.
Here we consider only the case when both incident and
scattered waves show horizontal polarization. The electric and
magnetic fields inside a closed surface may be determined by
the Stratton-Chu integral equations [8]. A full-wave technique
following the KA has been developed [9] and examined for
the magnetic induction. A similar approach for the electric
field has been used.
According to the reference [10], the first term of the
solution of the integral equation for the electric field shows the
form
)(
4
xfixi
Rki
z
zx
dxe
R
eik
E
(1)
Here
means distance between a point at the surface and
the observation point,
,
,
where
and
are the incidence and scattering angles, respectively,
is the
wave vector of the incident wave, and
means surface
height at the horizontal position
.
The intensity of the scattered electromagnetic field can
readily write
)](
~
)(
~
[)]()([)(
'
'''
~
xMxMixMxMixxi
zzx
edxdxI
(2)