Correction of Ionosphere for InSAR by the Combination of Differential TEC Estimators

Low frequency spaceborne SAR configurations are favoured for global forest mapping applications and D-InSAR applications over natural terrain. Several missions have been scheduled to be launched / or proposed to be implemented in the next years: JAXA’s ALOS-II (L-band), NASA’s Destyni (L-band), DLR’s Tandem-L (L-band) and ESA’s BIOMASS (P-band) are some of them. A common challenge for all these missions is to control / compensate the disturbances induced by the ionosphere. At these lower frequencies the ionosphere effects several components of the SAR measurements performed: It delays the group velocity of the transmitting / receiving pulses, advances their phase(s) and rotates their polarisation state. Accordingly, it distorts not only intensity but also polarimetric, interferometric and polarimetric interferometric observation spaces. The total electron content (TEC) is the most decisive parameter in the characterisation of the ionosphere. It is defined as the integrated electron number density per unit volume along the direction of propagation. Most of the free electrons are distributed within a relatively narrow altitude range allowing modelling the ionosphere as a thin layer at a fixed altitude. In this case the ionosphere can be characterised by a 2-D scalar field of TEC [1], [2]. Depending now on the SAR configuration and its observation space different correction approaches are possible leading to a wide range of calibration algorithms. In this paper we propose a concept towards the generalisation of ionospheric calibration methodology by integrating a number of individual approaches / algorithms. In this sense, a novel generic correction schema based on a combined (and improved) estimation of the 2-D TEC field (or the associated differential TEC field in the interferometric case) from a set of individual data based TEC and/or TEC gradient estimates is introduced and discussed. As a special case a combined 2-D (differential) TEC field estimator based on (differential) TEC estimated from Faraday rotation measurements and (differential) TEC gradients obtained from the estimation of azimuth/range (differential) shifts is presented. Both observations are independent, allowing establishing an inverse problem for the (differential) TEC estimation. Geophysical knowledge as the anisotropic nature of the TEC distribution can be incorporated as a priori information in the “combined” (differential) TEC estimator. The performance of the proposed approach is tested using ALOS quad-pol interferometric data sets over several test sites in Alaska. The achieved estimates are characterised by a significantly improved performance: While the FR based estimator suffers from the random granular deviation pattern of TEC after conversion, the proposed combined estimator effectively is free of such artefacts. Emphasis is given in the role of polarisation in the TEC estimation procedure [3] and on the calibration of Pol-InSAR data. References [1] Franz J. Meyer and Jeremy Nicoll, “Prediction, detection, and correction of Faraday rotation in full-polarimetric L-band SAR data”, IEEE Trans. Geosci. And Remote Sensing, 46(10), Oct., 3076-3086, 2008 [2] Xiaoqing Pi, Anthony Freeman, Bruce Champman, Paul Rosen, and Zhenhong Li, “Imaging ionospheric inhomogeneities using spaceborne synthetic aperture radar”, Jour. of Geophysical Research, 116, A04303, 2011 [3] Jun Su Kim, Konstantinos Papathanassiou, Shaun Quegan and Neil Rogers, “Estimation and correction of scintillation effects on spaceborne P-band SAR images”, in Proceedings of IGARSS2012, 23-27. Jul., 201

SAR Observation of Ionosphere Using Range/Azimuth Sub-Bands

In SAR applications, the ionosphere is normally considered as a disturbance that has to be removed or compensated for. In this paper the ionosphere is the objective of observation. This is motivated by the fact that nowadays polarimetric SAR systems can provide high resolution ionospheric maps that are not possible using conventional ionospheric mapping tools. This paper investigates a set of new ionospheric parameters that can be observed and mapped by SAR by exploring range and azimuth sub-bands. The range sub-bands are used to estimate the ionosphere independently of polarimetry. The azimuth sub-bands are related to the three-dimensional geometry of the ionosphere, as well as, to its dynamic component. The potential to estimate these parameters from SAR sub-bands is discussed and first results using ALOS PALSAR data are presented

Percolation properties of growing networks under an Achlioptas process

We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with the probability $\delta$, a link is formed between two nodes chosen by an AP. We find that there occurs the percolation transition with varying $\delta$ and the critical point $\delta_c=0.5149(1)$ is determined from the power-law behavior of order parameter and the crossing of the fourth-order cumulant at the critical point, also confirmed by the movement of the peak positions of the second largest cluster size to the $\delta_c$. Using the finite-size scaling analysis, we get $\beta/\bar{\nu}=0.20(1)$ and $1/\bar{\nu}=0.40(1)$, which implies $\beta \approx 1/2$ and $\bar{\nu} \approx 5/2$. The Fisher exponent $\tau = 2.24(1)$ for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.Comment: 4 pages, 5 figures, 1 table, journal submitte