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amplitude factor. The backscattering increases with the increase of the incidence
angle while the forward scattering decreases[10].
A linear fractal Gaussian sea surface model was first presented by Berizzi and
Mess in 1999. Then Longuest-Higgins and Stewart set up a nonlinear one by
applying the nonlinear interaction relationship between long waves and short
ones. Based on these studies, Xie Tao et al developed a new one-dimensional
nonlinear fractal sea surface model and the scattering coecient was attained,
considering the nonlinearities of sea surface and the effect of wind speed. The
numberical results of averaged NRCS(Normalized Radar Cross Section) of elec-
tromagnetic scattering from linear and nonlinear fractal models were compared.
It suggested that the new nonlinear fractal EM backscattering model can po-
tentially be more reliably used to numberically study, involving high sea states
or rough sea[11]. Strictly considering both geometrical fractal characteristic and
permittivity characteristic of sea water, improved integrated model of electro-
magnetic scattering for two dimensional fractal sea surface was built, especially
that the effects of salinity and temperature on the electromagnetic field scat-
tered by sea water were added. In this model, the permittivity of sea water is no
longer a constant but a variable parameter. They incorporated a sea spectrum
that accords with the experimental into the fractal model and the permittivity
of saline water was calculated from Debye equation. This model descripts the
whole electromagnetic scattering characteristics of sea surface, with the error of
backscattering coecient no more than 2 dB[12].
Haykin and Leung presented that sea clutter had a fractal dimensional at-
tractor based on correlation dimension analysis dating back to 1992[13]. The
results of a following research showed that the first Lyapunov exponent of sea
clutters was indeed positive and around 0.015. The chaos inherent of sea clutter
of X-band radar was proved and conclusion was that the movement of sea clut-
ter was controlled by a low-order dynamical attractor[14]. Studies of application
of sea clutter of S-band radar showed that on one hand, sequence signal can
be extracted from mess radar echoes using method of chaos dynamic in ocean
remote sensing . On the other hand, a more accurate model for sea clutters of
S-band radar could be built based on the analysis of the reciprocity mechanism
between S-band radar waves and sea waves in the field of ocean target detection,
utilizing chaos dynamic and FBM. Adopting the model of FBM, Jiang Bin et al
deduced the Hurst exponent based on the observed data. The fractal dimension
of the S-band sea clutter was obtained primaly and it was about 1.5771.The
largest Lyapunov exponent was 0.025, calculated by Rosenstein method. So the
sea clutter of S-band radar was proved to be chaotic and fractal for the first time.
Their research provided a new approach for target detection with the S-band sea
radar[15].
3.3 The Application of Chaos and Fractal in Scatters Synthesis
Fractal theory was previously applied in many analysis problems or in graphics.
In the year 1986, Y. Kim and D. L. Jaggard introduced the concept of fractal
geometry into the problem of random array synthesis in a novel way. They built
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