A ship moving through the water generates a broad spectrum of surface 
waves, which propagate away from their point of origin on the ship track. 
Waves satisfying the Bragg criterion will be concentrated along a pair of 
lines separated by a half-angle of approximately 
C 
a = tan”! y* cos $1, (1) 
S 
where cq is the group velocity of the Bragg waves, Vs is the ship 
speed, and ¢ is the radar look direction with respect to the ship track. A 
diagram illustrating these waves is shown in Figure 1, for a more complete 
discussion of this model refer to Lyden, et al. (1985a) 
L-band (23.5 cm wavelength) SAR images collected under very calm sur- 
face (low wind) conditions often show bright lines forming narrow angles 
which agree with the angles predicted by the model discussed above. 
Examples include the wakes produced by the USNS Quapaw in Dabob Bay, 
Washington, during the 1983 Georgia Strait Experiment (Kasischke, et al., 
1983), as well as several other wakes observed under similar conditions 
behind various ships during the same experiment. One such example is shown 
in Figure 2. This image of the Quapaw was collected on 28 July 1983 during 
pass 3 of the DREP 8 mission. This image was remapped from a slant-range 
to a ground-range representation and the wake angle was measured using two 
procedures. The first was based on a regression analysis of the brightest 
points along each arm while the other procedure examined the autocorrela- 
tion functions of angularly integrated slices across the wake arms. The 
autocorrelation procedure was performed with the center of integration at 
the ship's location, and with the center at the intersection of the wake 
arms based on the regression method. These wake angle measurements are 
presented in Figure 3 along with those predicted by Eq. (1) for first- and 
second-order Bragg waves. The predicted wake angles include the effects 
of: scanning distortion or relativity effects, Doppler displacement due to 
surface motion, and the variation of Bragg wavelength with incidence angle. 
Several points can be made regarding the wake angles presented in 
Figure 3. The regression analysis placed the intersection of the two wake 
arms 320 m forward of the observed ship location. This may indicate that 
the waves producing the V-wake arms in the SAR image are not generated at 
the ship's centerline but at the edges of the hull. An alternative expla- 
nation given by Swanson (1986) is that the wake arms are initially dis- 
placed outward due to their interaction with surface currents associated 
with ship-generated vortices. In his study, Swanson showed close agreement 
between the autocorrelation measurements centered at the ship and predic- 
tions by a model which incorporated vortex surface currents. The results 
presented in Figure 3 indicate close agreement between the angle predic- 
tions for first-order Bragg scattering, the regression measurements, and 
the autocorrelation measurements when the center of integration was located 
forward of the ship. It is interesting to note that the predicted angles 
and those measured by the autocorrelation method with the center forward of 
the ship increase with distance behind the ship due to the change of Bragg 
wavelength with incidence angle. Several other passes from the Georgia 
Strait Experiment were examined with similar results. 
An interesting subset of these cases are those for which the SAR look 
direction is more nearly parallel to the ship track (i.e., ¢ = 0) as shown 
for Ship 2 in Figure 4. In this case, the wake lines are observed to be 
nearly parallel but displaced in the SAR along-track direction by an 
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