The theory of electromagnetic Remote Sensing to random sea waves
The volume scattering equations
Model
The scattering medium is inhomogeneous medium layer of containing bubbles, and its top surface is random rough surface with two-dimension slope Z
x and Z
y
If measurement is at the incident angle
qi direction (i.e. backscattering case), the, the probability distribution of slopes can be written (2.1)
P
q(Z
x, Z
y) = (1+Z
xtg
q)P(Z
x, Z
y)
from Fig.1 we can know, the slope can be written as
| Zx = cosjntgqn |
 |
| Zy = cosjntgqn |
so expression (2.2) can be re-written as
--------------------(2.2)
The dielectric coefficient
e(z) of sea water of containing bubbles can composite from average eielectric
ea and fluctuating dielectric coefficient
ef(z)(Zeng.Q.A.1983) i.e
---------------------(2.3)
and let a = <
ea (z) > , <
ef ³ 0 . The dielectric coefficient of pure sea water is
--------------------(2.4)
In above expression, the dielectric coefficient of high frequency is
e¥
The static state dielectric coefficient
es, the delay time
t and conductivity of sea water
si can be found from Zeng Q. A. (1983)
In some extent of wind speed, the content of bubbles volume in sea waves is expressed by R so the average dielectric coefficient of sea water with the bubbles can be written as
------------------------(25)
The correlation coefficient of fluctuating dielectric coefficient is
-------------------------(26)
Where Iz is horizental correlation length, and Iv is vertical correlation length,
s is fluctuating variance of dielectric coefficient (L,Tsang 1985)
--------------------------(27)
where
The equation of volume scattering field
If correlation length of fluctuating medium is bigger than the incident wave length and neigligical affect of depolarization,the wave equation of inhomogeneous medium can be written as
---------------------------(2.8)
where
is total electric field in air
----------------------------(2.9)
where
is scattering field
is transmitted field from the inhomogeneous medium into air. Under average
Field approximation the transmitted field satisfies equation
---------------------------(3.10)
Let us substitue (2.10) in (2.9), and take note of (2,11), then we can obtain
---------------------------(2.11)
Let
Can be written equation (2.12) to standard form of random differential equation
-----------------------------(2.12)
Where static state operator
