## 2 Overview of InSAR Methodology
### InSAR Technique for the Estimation of Surface Displacements
Hence, we can rewrite Equation (34) as:  
\[\Delta\varphi=\frac{4\pi}{\Lambda}d_{LOS}+\Delta\varphi_{artifacts} \tag{35}\]  
Accordingly, by assuming the (actual) signal and the additive phase artefacts are uncorrelated, the variance of the DInSAR phase signal \(\sigma_{\Delta\varphi}^{2}\) can be modelled as:  
\[\sigma_{\Delta\varphi}^{2}=\left(\frac{4\pi}{\Lambda}\right)^{2}\sigma_{d_{ LOS}}^{2}+\sigma_{\Delta\varphi_{artifacts}}^{2} \tag{36}\]  
As a consequence, long-wavelength RADAR systems (e.g., operating at L-band) are characterized by less accurate measurements of the LOS deformation through SAR interferometry. At the same time, as earlier said, temporal decorrelation is less severe at L-band, thus leading to a reduced standard deviation of the noise. Hence, there is a balance between these two distinctive effects. In particular, the authors of [70] have demonstrated that LOS range precision of ALOS is globally 1.5 times worse than the corresponding measurements obtained using the C-band ERS RADAR system. As far as residual topographic artefacts are concerned, they are due to inaccurate knowledge of height topography by the used DEM of the area used for interferogram flattening. The residual topographic phase \(\Delta\varphi_{topo}\) depends on RADAR parameters as well as on the perpendicular baseline of the considered interferogram. Note that multi-pass interferometry techniques (which are addressed in the following Section 2.3) permit to recover and compensate for such artefacts. The exploited strategy consists in correlating the residual topographic phase terms of a long-lasting sequence of InSAR interferograms with their relevant perpendicular baselines (for instance, see [71]). As far as orbit errors are concerned, the critical information is the separation between the two acquisition tracks. The estimation and correction of satellite orbit errors that corrupt the computed differential SAR interferograms have already been the matter of previous studies [72; 73; 74; 75; 76]. In many cases, the phase artefacts induced by orbit errors are merely approximated with their linear (or quasi-linear) components, often referred to as \"orbital ramps,\" and then compensated. Moreover, other techniques exploit the pixel offsets between the interferometric image pairs to estimate the baseline components [77; 78]. The main drawback of this class of algorithms is their limited estimation accuracy that confines their use to preliminary coarse orbit estimation. Accordingly, an additional baseline refinement step is necessary, typically performed by solving for the baseline components that minimize the phase difference between the unwrapped interferometric phase and the corresponding synthetic interferogram. A multi-orbit correction method has recently been proposed in [79] to align the achieved precision of the corrected RADARSAT-1 orbits to that of the precise orbits of the other first-generation C-band spaceborne SAR sensors (e.g., the ERS, ENVISAT sensors of ESA). In particular, the algorithm in [79] investigates the differential phase gradient directly computed from the wrapped interferograms and is focused on the estimation of the perpendicular baseline and of the parallel baseline azimuth rate components, separately performed along the range and azimuth directions, respectively. Starting from the estimates carried out on the interferograms, the orbit correction associated with each SAR acquisition is retrieved by solving a system of linear equations via the Singular Value Decomposition (SVD) method [80]. Finally, for what attains the Atmospheric Phase Screen (APS), the phase artefact is due to the heterogeneity of the medium crossed by the transmitted electromagnetic signal. Studies have shown that APS is correlated over space but uncorrelated in time [81]. In fact, the dominant contribution to the path delay component of phase error is from the spatial heterogeneity of the wet component of the atmospheric refractivity [81; 82; 83; 84; 85], which primarily depends on local temperature, pressure and humidity.