15 dB

62

62

22

10

5

ε = 10.5

10.4 found at JPG. The solid curve is the beam pattern within the plane of the transect

and is perpendicular to the direction of antenna polarization. The dotted curve is the

beam pattern in the plane of the antenna polarization, which is perpendicular to the

transect direction. Individual pattern 3-dB beamwidths are indicated at the point of

the arrows. A typical form of the radiated wavelet is also shown. The curves assume

that the transmitter and receiver antennas are coincident. They are actually spaced

about 15 cm apart in the 300-MHz unit and slightly less in the 600-MHz unit.

cal factor equal to the solid angle subtended by the sur-

face of a perfect electric conductor (PEC), where the

face required to exclude the singularity when **r **equals

tangential electric field E is negligible. In terms of

locally flat surface, α is one-half. The surface currents

integrals over the metal surface S,

^

^

α(**r**)**E**(**r**) = ∫∫ *dS *′ *i*ω *g*(r, **r **′)J(r ′) +

points outward from the surface, while the tangential

electric field, proportional to n **E, **has been consid-

^

ered negligible (perfect conductor). The scalar Green

( ) ()

()

+

∇∇g r, **r **′ ⋅ **J r **′ **E r**

(7)

function g is

() ()

( ) ( ) ()

,

(8)

α **r H r **= ∫∫ *dS *′ ∇*g *r, **r **′ **J r **′ **H r**

4π*R*

^

Taking the vector cross product of n with equation

where **r **and **r**′ are observation and integration field

(7) for **H **leads to

points, respectively; is the magnetic permeability of

{

α (r) J (r) ∫∫ *dS*′ (n (r) ⋅ **J**(r′))∇*g*(r, **r**′)

the soil, taken here to be that of free space (4π 107

^

H/m); *k *is the electromagnetic wavenumber (m1); and

}

netic fields, respectively. The quantity α is a geometri-

^

^

21