Geoscience Reference
In-Depth Information
Fig. 6. Volcanic particle contributions to Doppler spectra in different sounding conditions.
(a) When the antenna points upward (e.g. at summit craters from the flanks), ascending
volcanic particles in red induce echoes with an along-beam velocity component away from
the radar (positive radial velocity range, right part of spectrum), whereas falling particles in
blue induce radial velocities toward the radar (negative radial velocity range, left part of
spectrum). (b) The contributions are reversed when the antenna beam points downward
(e.g. down towards a crater from the rim).
For a given range gate and for each component of the complex raw signals,
N
c
successive
digitized samples (coherent integrations) are added together and then averaged in the time
domain. This integration process acts as a low-pass filter reducing the high frequency noise
and improving the signal-to-noise ratio. In order to avoid aliasing, the value of
N
c
must be
adapted to expected maximum eruption velocities, in such a way that the Nyquist frequency
f
N
is higher that any Doppler frequency:
1
f
(7)
N
2
NT
cr
where
T
r
is the pulse repetition period of the radar. From (6) and (7) it results that the
maximum radial velocity which can be measured without ambiguity is given by:
V
(8)
max
4
NT
cr
After
N
c
pulses have been integrated, the coherent integration stage is repeated until a
sequence of 64 integrated complex data is obtained. For each range gate, the 64 coherently
integrated complex data are used as a time series input to a FFT (Fast Fourier Transform)
algorithm in order to obtain the power spectrum of the radar echo. The frequency resolution
(frequency interval between two consecutive spectral lines) is given by:
1
f
NT
(9)
64
cr
Therefore, the corresponding velocity resolution is:
V
(10)
128
NT
cr
