Application of atmospheric correction in the measurement of land displacements using the PSInSAR technique, on the example of the Tahmoor mining region, Australia

. InSAR ( Interferometric Synthetic Aperture Radar ) techniques are a very good tool for identification and observation of surface area displacements. Achieved accuracy of several centimeters, still do not allow for the quantitative analysis of the observed movements. Due to the high dynamics of phenomena in the Earth's atmosphere, one of the biggest limitations of InSAR are disturbances caused by changes in the atmosphere, between two measurements, on the basis of which an interferogram is created. In order to reduce the impact of the atmosphere on the SAR signal course, an atmospheric correction is applied.This study presents the results of calculations using the PSInSAR technique for the Tahmoor mining area located in south-eastern Australia, from 2006-2010. The atmospheric correction was determined: in an empirical way - on the basis of a linear relation between the signal phase and the topography of the area, based on data from the ERA - Interim weather model and data from the MERIS spectrometer.


Introduction
The underground mining exploitation has a significant impact on the surface area, which can cause, among others, the formation of low-maintenance pits. The range and size of vertical displacements of the area depends on many factors: geological and tectonic conditions, methods and operation time, as well as the geometrical location of the deposit. The shifting of the earth's surface can cause damage to buildings and technical infrastructure [1,2]. Classic geodetic measurement techniques are characterized by very high accuracy, however, the result obtained is discrete and the measurement is time-consuming. The InSAR techniques are a modern and innovative tool for identifying and observing pseudo-vertical displacements of the terrain surface.
Their advantage is a quasi-continuous representation, both in time and space. Achieved accuracy of several centimeters, still do not allow for the quantitative analysis of the observed movements. One of the biggest limitations of InSAR are disturbances caused by changes in the atmosphere, between two measurements, on the basis of which an interferogram is created [1,3]. In order to reduce the impact of the atmosphere on the SAR signal course, an atmospheric correction is applied. It is important that the determined atmospheric refraction values were best suited to the SAR data, both spatially and temporally. The atmospheric correction can be determined by several methods: empiric [4,5], using weather models [1,4], spectrometric data [6] and GNSS measurements [7].

Basic theory
The interferometric phase can be described as the sum of the following components [8,9]: where: ϕ -interferometric phase (phase difference between two images), W{•} -the operator of the wrapped phase, фref -the component of the reference system in which heights are determined, фtopo -phase shift associated with terrain, фdefo -phase shift associated with land displacement, фorb -phase shift associated with the inaccuracy of determining the orbit, фatm -atmospheric delay, фscat -phase shift resulting from the scattering properties of a given pixel, фnoise -phase noise.
An additional limitation are the temporal, spatial and geometrical decorrelations that reduce the coherence of signals. The first two result from the variable scattering characteristics, which may be caused by the change in the vegetative cycle phase between successive image acquisitions or the occurrence of the snow cover. The lack of a geometric correlation is dependent on the length of the orbital base, which affects the differences in the angle of incidence of the radar beam [8]. The decorrelations can be effectively eliminated using computational techniques based on the processing of many images made at different times, for example the PSInSAR (Permament Scatter InSAR) technique described below [10] or the SBAS (Small Baseline Subset) technique [11].

PSInSAR technique
The PSInSAR technique was developed by Ferretti et al. [10]. It is based on the creation of differential interferograms between the master image and other images (slaves), and then taking into account only those pixels for which the reflection's intensity is strong and stable over time, and independent of the angle of incidence [9]. These pixels are called stable diffusers (PS), the decisive factor for qualifying a pixel as a PS is the level of decorrelation. The accuracy of the PSInSAR method depends on many factors: the SAR sensor used, the number of images, the time differences between individual acquisitions, the distance from the reference point and the mutual coherence of the diffusers [12].
In the case of measurements with InSAR techniques, the difference in atmospheric delay between the two acquisition of imaging is significant [13,14]. Atmospheric delay, depending on the layer in which it occurs we can divide into: ionospheric and tropospheric. The ionospheric delay is only relevant for longer waves, in the P and L range, which are rarely used for InSAR measurements [14]. Most often, the atmospheric delay is considered as the impact of the troposphere on the SAR signal between the surface area and the upper limit of the troposphere (2): where: θ -determines the angle of the wave, λ -wavelength, −4 -the ratio of transformation of pseudorange growth to phase delay.

The influence of the atmosphere
With reference to the wet and dry constituent, tropospheric delay can be divided into two components resulting from the vertical, layered temperature distribution and dry air pressure as well as turbulent disturbances, which are the carriers of water vapour. The first one is relatively easy to model and usually correlates with the topography of the site. The second one due to the heterogeneous character is very difficult to determine [8], and its value is definitely more important in determining the correction for measurements using InSAR techniques.

Area of research and displacements characteristics
This article focuses on the mining area of Tahmoor, located on the south-east coast of Australia (New South Wales; Fig. 1). Coal mining was started in 1979, initially the operation was carried out with a room and pillar system. Since 1987, the operation has been carried out with a continuous longwall system, at a depth of 200 to 400 m. In 2006-2010, the operation was carried out on longwalls from 23A to 25, extraction dates for walls relevant for these measurements are given in Tab. 1 [15]. The area of exploitation (Fig. 2) runs under the builtup areas (Tahmoor city), and such infrastructure facilities as railway lines (embankments and tracks), tunnels and culverts are the most endangered [16].
In the area of walls 24A and 25, twice higher settlement values were observed, compared to the forecasted values (Tab. 2). This is probably due to the flow of groundwater towards the Bargo River [15].

Measurement data
The actual measurements of displacements were carried out using the PSInSAR technique. 39 SAR images from the Envisat satellite (ASAR), made from June 2006 to September 2010, were used to perform the calculations (Tab. 3). As the reference image (master), the imaging was identified on May 2, 2008 (Fig. 3). Temporarily, the data includes operation on walls from 23B to 25. However, the effect of field excavation may be visible even many months after its completion.
To determine the atmospheric correction by the linear method, only the interferograms were used directly. The amendment was determined on the basis of a linear relationship between the phase and the topography of the area, based on formula (3): where: KΔφ -the estimated relationship phase -topography, h -ground level, Δφ0 -constant deviation coefficient relative to the entire inferferogram.
Determining of the delay is not differentiated into wetand dry refraction component, this is the total relative delay between master and the slave image [5]. In this method, the topography of the area is the most important. If the area on which the measurement is carried out is not varied (terrain denominations are small), this technique will not be effective [12,17,18]. The atmospheric correction was also determined on the basis of data from the ERA-Interim weather model, the spatial resolution of which is about 80 km and the temporal distance is 6 hours. The model provides information on pressure and dry air temperature as well as air humidity [19].
In addition, a wet component of the atmospheric correction was determined based on spectrometric measurements. The calculations came from the MERIS spectrometer, which operated on the Envisat platform. For this reason, the data do not require time-space interpolation. The spectrometer is a passive device, therefore it can perform measurements only during the day and with relatively low cloud cover, therefore, the data are available not for every interferogram (Tab. 3). The spectrometric measurement consists in the acquisition of radiation on channels sensitive and insensitive to water vapour, which allows to determine the water vapour content in the atmosphere column (PWV). The results obtained from the MERIS spectrometer are supplemented by a dry delay component, based on data from the ERA-I weather model. The graphs (Fig. 4) present the results for individual interferograms, taking into account the corrections applied for the A-A' cross-section (Fig. 5). It should be noted that the lack of continuity of the cross-section results from the point-based representation of the resultsin the form of PS points. The land displacements are visible on the cross-section in the range from 26,500m every 34,000 m (on a stretch of 7.5 km length). In this case, subsidence is continuous, therefore for the imaging done before the master display (2 May 2008), the values (in radians) will be lower in comparison to the area that is not decreasing. For images taken after master imaging, they will reach higher values. This is due to the reference of results to one master display. It should also be noted that after transforming the values into metric units, their sign changes. This is due to formula (4):  Analyzing the results for the unwrapped phase, reduced by DEM and orbit errors and taking into account the atmospheric correction -determined by different methods (Fig.6), it should be noted that it achieves the value of even a dozen or so radians (15 August 2006 and17 April 2009), which indicates significant influence of the atmosphere. The smallest (absolute) correction values were observed using the empirical (linear) correction method. In addition, the results for this method significantly deviate from the values determined by means of spectrometric data and the weather model. This is due to small height difference, up to a maximum of several hundred meters. On the cross-section, there is a large correlation between the correction value, determined on the basis of spectrometric data and the ERA-I weather model. The results, based on spectrometric measurements, were supplemented with a dry component from the weather model, however its value is low compared to the wet component of the delay (Fig.  6).
The largest delay values are visible for the wet component determined on the basis of spectrometric data (Fig. 6). Their distribution is heterogeneous and very dynamic.
It can be seen that the highest (absolute) values occur in the coastal region and in the highly urbanized area of Sydney. In the area of the Tahmoor mine, there are not observed any specific disturbances, the impact of moist air masses from the ocean is no longer reflected in a visible way in the atmospheric correction.