PROGRAMAS Y METAS EN EL SECTOR INFANCIA Y ADOLESCENCIA

Atmospheric noise in interferograms is caused by variation of water vapour, temperature and pressure in different SAR acquisitions. A brief description of atmospheric noise is presented in Chapter 3 before postseismic interferograms for the Damxung earthquake are presented. Here, I introduce mitigation techniques that are used in this thesis, with a focus on using MEdium Resolution Imaging Spectrometer (MERIS) data and the ERA-interim weather model together to mitigate the atmospheric noise.

At present, multiple techniques exist in mitigating the influence from atmospheric delay. A thorough review is given by Ding et al. (2008). The techniques fall into two general categories: those that use external data, and those that do not. In this thesis, I implement a phase-based linear correction for postseismic interferograms following the Damxung and Yutian earthquakes, and minimise atmospheric delay in the

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Tarapaca earthquake postseismic study with the aid of external satellite data and weather models.

Figure 2. 1. Comparison of (a) elevation and (b) LOS phase for a postseismic interferogram of the Damxung earthquake. The example interferogram is constructed from SAR acquisitions on 2009 September 6 and 2010 January 24. (c) and (d) show the correlation of elevation and LOS phase along two profiles A-A’ and B-B’ as marked in (a), respectively. Black boxes in (b) marked with n

and s are the regions over which the correlation coefficients are calculated and shown in Fig. 2.2.

Linear correction is based on the empirical linear relationship between interferometric phase and topography (Cavalié et al., 2007, 2008). Fig. 2.1, for

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example, shows the correlation of one postseismic interferogram of the Damxung earthquake with elevation. Usually, the linear correlation factor is determined at an interferogram scale (Cavalié et al., 2007). However, the linear relationship may change across the interferogram. The variation of correlation factor is demonstrated in Fig. 2.2, where in the southern area, a larger conversion factor is required. Use of the linear correction method may also mistakenly remove deformation signal, which may correlate with topography, for example in volcanic deformation. The linear method to jointly correct topography-correlated atmospheric noise and orbital error is described in Chapter 3. Fig. 2.3 shows an example of the method being applied to a postseismic interferogram of the Damxung earthquake. After the joint correction, the remaining atmospheric noise is most profound in the southern part, at a level of ~ 1 cm, while in the area surrounding the earthquake zone (central area of the interferogram), the phase is close to zero, demonstrating the effectiveness of the joint linear correction method.

Figure 2. 2. Phase plotted against elevation for pixels boxed in two sub-regions in the south and north of the interferogram, as shown in Fig. 2.1b. The correlation coefficient for the southern sub- region (ks) is larger than that for the northern region (kn), demonstrating the inhomogeneity of the phase-elevation correlation across the interferogram.

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Figure 2. 3. An example demonstrating joint estimation of topography-correlated atmospheric noise and orbital error. Panels from left to right show (a) an original interferogram from the postseismic study of the Damxung earthquake (090906-100124), (b) joint estimation of topography-correlated atmospheric noise and orbital error, and (c) corrected interferogram.

MERIS was another sensor on board the Envisat satellite and measured the solar radiation reflected by Earth’s surface and clouds. It was originally designed for studies of ocean biology and marine water quality by observation of ocean color. With a field of view of 68.5° around nadir, MERIS covers a swath of 1150 km and global coverage is usually within three days. Out of the 15 spectral bands, two are in the near-infrared, allowing a measurement of Precipitable Water Vapour (PWV). Two levels of water vapour products are provided with different spatial resolutions. One is known as the full resolution product (~ 300 m) and the other is with reduced resolution of ~ 1.2 km. I use the latter to simulate the atmospheric delay due to spatiotemporal variations of both water vapour and temperature, which is accordingly named as wet delay.

Weather models, such as the ERA-interim, also provide an estimation of water content. However, in comparison to MERIS data, models have shortcomings in several respects. First, MERIS data are simultaneously obtained with SAR images; thus, they share almost identical propagation paths. The ERA-interim model only

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provides estimates of water vapour every six hours, which means an interpolation of two estimates encompassing the SAR acquisition is necessary. Alternatively, one can use only the closest estimation in time as an approximation. Secondly, the ERA- interim model samples every ~ 75 km. For a typical ASAR image with ~ 100 km range width, only several sample points are available to be interpolated for a simulated atmospheric delay due to water vapour. Obviously, the ERA-interim resolution is much lower than that of the MERIS data. Third, the theoretical accuracy of MERIS PWV retrieval could reach 1.7 mm (Bennartz & Fischer, 2001), corresponding to a 10.8 mm uncertainty in LOS direction (assuming a 23° incidence angle). Li et al. (2006) compared the PWV values between MERIS and GPS/Radiosonde measurements and found an agreement with root-mean-square (RMS) of ~ 1.1 mm, which corresponds to a LOS atmospheric delay of ~ 7.4 mm. The use of ERA-interim, however, has different levels of success in mitigating atmospheric noise, given the above-mentioned shortcomings (Jolivet et al., 2014).

MERIS receives radiation reflected by both Earth’s surface and clouds. When clouds are present, the PWV estimated is thus applicable in the region above the clouds with highest altitude. To obtain the PWV between the land and the satellite, it is necessary for us to select MERIS data with low cloud cover. This requirement potentially limits the number of interferograms that can be corrected using the MERIS data. In Chapter 5, the PWV is converted to LOS wet delay using the equation:

(2.1)

where θinc is the radar incidence angle, and Π is a conversion factor relating PWV to LOS wet delay. Π is dimensionless, with its value depending on the mean atmospheric temperature, but typically within a range of 6.0 – 6.5 (Bevis et al., 1992, 1994). I use a value of 6.2 in converting PWV to wet delay for the Tarapaca

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earthquake, as Walters et al. (2013) used in the study of interseismic strain accumulation across the Ashkabad fault.

In addition to the wet component, tropospheric stratified delay also includes a hydrostatic delay that is caused by tropospheric pressure difference. An estimate of hydrostatic delay can be made as a function of ground pressure, which can be assumed as an exponential decrease with height above sea level:

(2.2)

where k is the conversion factor between ground pressure and LOS hydrostatic delay, assumed to be 0.23 cm/hPa by Davis et al. (1985), P0 is the sea level pressure and h is the altitude, which can be derived from the DEM. I use the sea level pressure provided by the ERA-Interim instead of the MERIS direct measurement, which has large error according to Ramon et al. (2003). An example of using MERIS data and ERA-interim model to correct Tarapaca postseismic interferogram is shown in Fig. 2.4.

Orbital error is modelled and removed as a linear ramp in all three studies. The linear approximation would not affect the deformation signals, because the latter are either cropped out before estimation of orbital error, or not linear in trend. In Chapter 3, I propose a joint inversion strategy for reducing atmospheric noise and orbital error, and this approach is also applied in Chapter 4.

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Figure 2. 4. An example demonstrating mitigation of atmospheric noise using MERIS data and the ERA-Interim weather model. Panels from left to right show an original interferogram from the postseismic study of the Tarapaca earthquake (050926-0811124), wet delay computed from MERIS data, dry delay from ERA-Interim weather model, estimated orbital error, and corrected interferogram.