IEEE Geoscience and Remote Sensing Magazine - March 2013 - 26
(a)
(b)
(c)
(d)
(e)
FIGURE 16. L-band amplitude image (HV polarization) of the Remingstorp test site (a). Four coherence images (scaled from 0 (black)
to one (white)) corresponding to interferograms acquired at different spatial baselines with k z = 0.01, 0.05, 0.1 and 0.15 rad/m,
respectively (b)-(e).
where h V indicates the height (or depth) of the volume. k z is
given by (see (33))
kz =
2mrTi
2r
= h (38)
m sin (i i)
amb
and corresponds to the effective vertical (interferometric)
wavenumber that depends on the imaging geometry (Ti is
the incidence angle difference between the two interferometric images induced by the baseline and i i the local incidence angle) and the radar wavelength m. z 0 is a reference
height and { 0 = k z z 0 the associated interferometric phase.
Figure 16 illustrates the dependency of c Vol on the vertical structure dependency F (z): On the left-hand side is the
L-band amplitude image (HV polarization) of the Remingstorp test site located in Sweden. It is a forested site and
includes a number of bare fields and lakes. The four coherence images shown on the right (scaled from 0 (black) to one
(white)) correspond to interferograms acquired at different
spatial baselines with k z = 0.01, 0.05, 0.1 and 0.15 rad/m,
respectively. The temporal baseline for each interferogram
is about 5 minutes so that temporal decorrelation can
be - at least in first order - neglected. As expected from (37),
bare fields, characterized by a Dirac-like vertical scattering
contribution have, after range and azimuth common-band
filtering, a coherence
c = c SNR c Vol = c SNR exp (ik z z 0), (39)
whose magnitude c = c SNR is independent of the spatial baseline (i.e., k z). The loss of coherence is due to SNR
decorrelation. In contrast to them, forested stands are characterized by an extended vertical scattering contribution
that leads to a monotonically declining c Vol (k z) behavior.
26
Indeed, c = c SNR c Vol is decreasing over all forested areas in
the image. Note that the lakes decorrelate at each baseline
primarily due to SNR decorrelation.
Accordingly, c Vol contains the information about the
vertical structure of the scatterer and is the key observable
for the quantitative estimation of volume parameters from
Pol-InSAR measurements.
B. Information extraction
from InSAR Coherence inversion
The estimation of F (z) (and/or associated structure paramv ) measurements at different polarizaeters) from c Vol (k z, w
tions and (spatial) baselines according to (37) is a unique
opportunity provided by Pol-InSAR observations. Indeed,
for the estimation of F (z) (and/or associated structure
v ) measurements at different
parameters) from c Vol (k z, w
v indicates the
polarizations (where the unitary vector w
polarization dependency [18], [107] and (spatial) baselines
by means of (37) two approaches have been explored in
the literature:
1) The first one is to model F (z) by parameterizing its
shape in terms of geometrical and scattering properties and
v ) measurements to estimate the indito use then c Vol (k z, w
vidual model parameters. In this case, the scattering model
is essential for the accuracy of the estimated parameters.
On the one hand, the model must contain enough physical structure to interpret the Pol-InSAR coherences, while,
on the other hand, it must be simple enough in terms of
parameters in order to be determinable with a limited number of observations.
For natural volume scatterers multilayer statistical models that account for the different scattering and propagation properties at the different heights (depths) within
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