1
PSInSAR derived method applied at Piton de La Fournaise
2
3
Conventionally, PSInSARTM uses all the dataset images and selects the pixels that show a
4
trend in time consistent with the applied model for velocity to compute time series and an
5
average displacement rate. In highly active volcanic area, the application of this approach
6
would cause the loss of the majority of the pixels. Indeed eruptions or seismic events lead to
7
significant modification of the ground surface which cause a loss of coherence such that many
8
pixels do not obey the model for the whole period of observation. To improve the reliability
9
of measuring points, we developed a PSInSAR derived method.
10
Here, we present an evolution of the patented algorithm. The new approach still relies on the
11
use of point-wise stable radar target but (1) uses a spatial filtering to estimate time series and
12
(2) does not apply any evaluation and removal of the atmospheric phase screen.
13
(1) The description of the deformation trends is possible thanks to filtering operations and
14
relies on the division of the available SAR dataset into different coherent subsets. The
15
division into more coherent subsets is pixel-dependent. For each pixel we apply a non-linear
16
2D filter involving the pixels belonging to a patch of 35m × 35m around the considered pixel.
17
For each subset the evaluation of the deformation rate and its time series is possible. Each
18
subset is independent from the others, as they were different measurement points. Each pixel
19
can therefore show more than one time series, each with its own master acquisition (time
20
reference). The division in different subsets is necessary as the temporal correlation of the
21
motion is instantaneously interrupted when a significant eruption occurs, which generate
22
strong ground deformation and/or lava flow emplacement. Such phenomenon modifies the
23
ground surface (elevation…) and the satellite cannot recognize any radar target that is stable
24
before and after event.
1
25
(2) The abrupt changes provided by the frequent and strong volcanic activity, but also the
26
modification of the ground surface elevation caused by such eruptions with new lava flow
27
emplacements, does not allow us to correctly separate the motion component of the
28
interferometric signal from the atmospheric disturbance one (Atmospheric Phase Screen). The
29
reliability of the time series relies on the fact that the deformation present in such highly
30
active volcano area is of several centimeters up to meters, whereas the atmospheric error leads
31
to noise that is measurable in some centimeters. We performed thus no atmospheric noise
32
filtering. The single displacement measurement precision rises from millimeters to
33
centimeters, whereas the average deformation rate precision depends on the number of
34
acquisitions composing the temporal cluster during which the pixel is considered as coherent.
35
36
Our derived applied algorithm consists mainly in the following steps [Ferretti et al., 2008]:
37
- Spatial noise reduction is performed applying a Goldstein filter [Gabriel et al.; 1989;
38
Goldstein et al., 1998] to each wrapped interferogram. The filtering aids the following spatial
39
phase unwrapping algorithm, but as the drawback that the information is no longer associated
40
to a point-wise target like it used to be in PSInSARTM method. This is a trade-off that it is
41
worth to accept because we are more interested in the overall characterization of the on-going
42
phenomena.
43
- For each interferogram, we evaluated the spatial coherence and selected the points over the
44
threshold given that each interferogram has its own spatial grid to be used in phase
45
unwrapping.
46
- A two-dimensional phase unwrapping is applied to each interferogram [Ghiglia et al.,
47
1994]. The interferometric phases of each pixel to be unwrapped have been selected on the
2
48
basis of the spatial coherence. It may occur that some pixels present more than one temporal
49
cluster to be independently unwrapped in the time domain.
50
- We computed the time series of displacement and the average rate of deformation.
51
Each pixel is analyzed along the stack of the interferograms to determine a subset of SAR
52
acquisition for which it shows a good phase stability. In general, each pixel may have its own
53
particular dataset that can be different from the one used for its neighbors.
54
Two cases are therefore possible: (a) the pixel shows coherence for the duration of one
55
temporal cluster; (b) more than one temporal cluster is found. In the second case, the pixel
56
will have more than one time series.
57
58
References:
59
Ferretti, A., Bianchi, M., Novali, F., Tamburini, A., Rucci, A., 2008, Volcanic deformation
60
mapping using PSInSARTM : Piton de La Fournaise, Stromboli and Vulcano test sites for the
61
GlobVolcano project. USEReST’08 workshop, Napoli, Italy.
62
63
Gabriel A. K., Goldstein R. M., Zebker H. A., 1989, Mapping small elevation changes over
64
large areas: Differential radar interferometry, J. Geophys. Res., 94, B7, 9183–9191.
65
66
Ghiglia D. C., Romero L. A., 1994, Robust two-dimensional weighted and unweighted Phase
67
Unwrapping that uses Fast Tranform and iterative methods, J. Opt. Soc. Amer. A, 11, N. 1,
68
107-117.
3
69
70
Goldstein R. M., Werner C. L., 1998, Radar interferogram filtering for geophysical
71
applications, Geophys. Res. Lett., 25, 21, 4035–4038.
4