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