Short answer
Double-bounce backscatter or far shore brightening are radar industry phrases referring to the physical effect of multipath propagation: A target is illuminated by a direct ray and also by reflected/indirect rays. All rays are scattered back to the antenna. Indirect illumination can happen after reflection on the ground or on water, particularly salted water which is more reflective than fresh water. A typical case is the double bounce on wetland ground and vertical tree trunks.
Radar double-bounce backscatter
Calm water and flat ground make good mirrors for microwaves, and when not orthogonal to incident rays they reflect them away from the radar antenna. the related areas appear black on the screen. This contrasts with bright double-bounces.
The same effect happens in urban areas with bounces on ground and buildings:
Double-bounce backscatter in urban area, source
On the picture above, the radar beam comes from the right/east side (as indicated by the green arrow). There is a street crossing NW to SE which appears in black because this is a smooth surface at the wavelength scale, with mostly specular reflection. However reflected rays are at the optimal angle to reach the buildings on the west side of the street and return to the sensor. The buildings are illuminated both by the direct rays and by the rays bounced by the street material, some of these rays are scattered back to the antenna, the radar cross-section (RCS) of these buildings is overrepresented. None of the buildings on the east side appear as bright, because the double-bounce is not possible.
In multipath propagation, the resulting power depends on the phase difference between the received rays. The general case where a lot of rays are involved (diffuse reflection) leads to phase differences randomly distributed and no higher reflected power, but the case when there are only two rays involved (two-ray ground-reflection model) can lead to over brightening. This happens when the phase is the same, that is when all reflections occur on surfaces tangent to the first Fresnel volume boundary, for reasons explained in the additional sections.
Two-ray reflection is frequent in satellite imaging (dihedral or trihedral return). There are a few techniques to mitigate it, e.g. based on transmitter and receiver antenna with different polarizations. But these anomalies are actually used to extract more information from the radar image, this is the ground for radar polarimetry which exploits the fact that each time a bounce occurs, the signal phase is reversed. Polarimetry uses extensively DSP to split echos according to their type, and create synthetic representations that transform initial over-brightness into something else, thus eliminating over-brightness (more).
Sum of two waves
When a reflection occurs, the sign of the signal amplitude is changed, this corresponds to a phase shift of 180°. The target is illuminated by two waves with opposed amplitudes, but one has traveled a longer distance, hence it has been also phase-shifted by an additional amount (180° + x°). Interferences can be constructive when amplitudes have the same sign, or destructive when amplitudes have not the same sign. Let's imagine 20% of the wave is reflected (orange below) and let's compute the sum for various delay (phase) values:
Direct and indirect waves interference
When the additional phase shift is between -90° (+270°) and +90 the interference is constructive: The sum is larger than the direct signal (the actual range varies depending on the ratio between direct and indirect waves amplitude).
Volume of constructive interferences
This range corresponds to a range of additional travel time for the indirect wave, and to a range of distances from the centerline (line of sight) for the location of the reflection.
These points of reflection are within a volume bounded by an ellipse having the radar and the target as focuses. It's named the first Fresnel ellipsoid, after the great engineer and physicist.
Multipath propagation within first Fresnel ellipsoid
For 2GHz and a distance of 30 km between radar and target, this volume is very thin. The largest diameter of the ellipsoid, found at equal distance from focuses, is only 68m (calculator). For an airborne radar, it means the reflection we are interested in can only occur close to the shore. There are other larger Fresnel ellipsoids confocal to the first one, and half of them allow constructive interferences, but as they are more off-center, the energy drops rapidly, in practical only the first ellipsoid is taken into account.
Mitigation
Multipath effect is often mitigated by diversity, which means using multiple frequencies, or multiple antennas.
An example is GNSS (GPS, Galileo, ...) where frequencies are diffracted by ionosphere, introducing a pseudorange error. Different frequencies are diffracted differently. For authorized users, the diffraction error can be quantified, and corrected by measuring at different frequencies. Similarly because reflection depends on Fresnel ellipsoids, which size is different for different frequencies, multipath can be quantified in radar.
The antenna diversity can be based on sophisticated technologies, the phased array antenna is a most simple one. The array is composed of tens or hundreds of small antennas. The signal they transmit or receive can be delayed individually. This allows to sense multiple wavefront planes at the same time, and identify reflected wavefronts.
MIMO approach (multiple inputs, multiple outputs) is based on both diversities. MIMO is also used for 5G cellular networks to take advantage of multipath propagation (if your WiFi access point has several external antennas, you're likely using MIMO too).
As said earlier when a wave is reflected its phase is changed, but its polarization is also affected (polarization is the plane the electric field of the EM wave lies in). Echos can be identified as resulting from an odd or even number of bounces, thus double-bounced rays can be removed.
Another technique consists in preventing waves from leaving the reflecting material. Reflection must be transformed into a refraction. Waves can be polarized in a direction parallel to the plane (p-waves) or perpendicularly to the plane (s-waves). At some angles, close to Brewster's angle, only p-waves can leave the reflecting surface, s-waves are refracted and absorbed by the material. Reflection can be eliminated this way too, but this requires a specific location for the radar and the capability to create s-waves.
