ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 17 
as the cutoff frequency of a duct as a function of its 
height in feet and AM, the decrease of M in the in- 
version layer. These values are the result of a some- 
what crude approximation and should not be taken 
to indicate more than the order of magnitude of the 
frequency at which this effect occurs. 
See (ale INN ST 
SSE 
PLATT N TTA TAL I econ 
ha NANT 
aeons 
NE 
AN 
CENT NIN UN 
d IN FEET 
Figure 7. Maximum wavelength trapped in a simple 
surface duct. Duct width d in feet. A M is total decrease 
of M in duct. Amax = 2.5d V A M 10-5. 
REFLECTION FROM ELEVATED LAYERS 
Reflection from elevated layers has so far been 
observed systematically only under the rather spe- 
cial meteorological conditions at San Diego, but it 
probably occurs elsewhere, though with a lesser 
degree of regularity. It appears when there is a 
strong elevated M inversion. Such an M curve is 
very nearly equivalent to a true discontinuity of 
refractive index, and the effect on a wave traversing 
such a region is similar to that of a boundary between 
two media, the more nearly so, the larger the M- 
inversion gradient. If there is a true discontinuity, 
an incident wave is split up into a reflected and a 
transmitted wave. If the discontinuity is replaced 
by an M inversion layer, the reflected wave still 
persists but becomes weaker the less steep the in- 
version. The distinction between this phenomenon 
and the apparent reflection in the duct where the 
rays become horizontal before turning downward is 
usually fairly clear-cut. The true reflection described 
here occurs primarily in waves which are so long as 
to be below the cutoff. 
There exists a case of gradual transition between 
two media with different refractive indices for which 
the wave equation can be integrated.‘** 4% 
This can be applied qualitatively to the case,77 
in so far as earth’s curvature can be neglected. 
Figure 8 shows the calculated ratio in decibels of 
DECIBELS 
89° \s9°14" 
9°18 89°20' 89° 2I' 
89°10 . 
0 100 200. 300. 400° «800 600 700 
D_ STRATUM THICKNESS 
A WAVELENGTH 
Figure 8. Calculated reflection ratio in decibels. 
reflected to incident wave for various angles of in- 
cidence plotted against the ratio of thickness of the 
transition layer to wavelength as abscissa. 
The verification of this theoretical concept in the 
San Diego experiments will be discussed in the next 
chapter. 
