IEEE Geoscience and Remote Sensing Magazine - March 2020 - 76

caused by underground mining activities. As can be seen,
the ground surface points of the mining area move toward
the center of the deformation basin, and only a few points
possibly deform along the radar LOS or azimuth directions. This means that 1D/2D displacement measurements
cannot reveal the real deformation patterns at most points
of a mining area. To circumvent this, it is essential to reconstruct 3D displacements from SAR-/InSAR-derived 1D/2D
displacement measurements.
SAR/InSAR-BASED 3D MINING DISPLACEMENT
RECONSTRUCTION
Several methods have been developed to reconstruct 3D
mining displacements from InSAR-derived 1D/2D displacement measurements in recent years; these can be
classified into two groups according to the different data
sources used: 1) the combination of multitrack/multisensor InSAR measurements (hereafter referred to as the multitrack/multisensor method) and 2) the integration of InSAR
measurements with a deformation model (hereafter referred to as the InSAR+model method).
COMBINATION OF MULTITRACK/MULTISENSOR
InSAR MEASUREMENTS
It is an ill-posed (or ill-conditioned) problem to fully
estimate 3D displacements from 1D/2D InSAR measurements. Therefore, the multitrack/multisensor method
does the ill-condition regularization of 3D displacement
construction by integrating extra deformation measurements (e.g., generated by DInSAR, MAI, and/or OT) from
multitrack and/or multisensor SAR data sets. This is a
common way to reconstruct the 3D displacements associated with geophysical events such as earthquakes [15],
[87], [88], ice sheet flow [89], [90], and volcanic eruptions
[91] from InSAR measurements. In 2011, Ng et al. [92]
proposed two schemes for fully estimating 3D mining
displacements from multitrack InSAR LOS deformation
measurements. The first involved simultaneously estimating 3D displacements utilizing InSAR LOS measurements from at least three independent geometries using
a weighted least-squares solver based on the following
observation system:

	

R 1 V R
1
1V
1
1
1
Sd LOSW Scos i sin i sin a h - sin i cos a hW W
2
2
2
2
2
Sd LOSW Scos i sin i sin a h - sin i cos a h2W
S
W=S
W > N H, (7)
h
h
SS kh WW SS h
W
k
kW E
k
k
k
d
cos i sin i sin a h - sin i cos a h
T LOSX T
X

where k denotes the number of InSAR LOS measurements.
The other scheme involves a two-step estimation, where
the deformation components in the vertical and eastern
directions are first solved from multitrack InSAR measurements by neglecting the deformation component in the
northern direction. The deformation in the northern direction is then estimated from the residuals of the InSAR measurements after subtracting the projection of the displacement estimates in the vertical and eastern directions from
76

that in the LOS direction. The test over the Appin Mine area
of Australia suggested that the second scheme shows a better
performance in improving the accuracy of 3D mining displacement estimates than does the first scheme and that the
estimation accuracy can be further improved if more InSAR
pairs with different look and heading angles are used.
In 2013, Samsonov et al. [93] extended 3D mining
displacement to TS estimation from multitrack/multisensor InSAR measurements using a TS method termed multidimensional SBAS. This idea was tested over the Greater
Region of Luxembourg using ascending and descending
ERS and ENVISAT SAR data sets. Unfortunately, due to
its limited independent geometries (i.e., two), only 2D TS
mining deformation in the vertical and eastern directions
was retrieved.
INTEGRATION OF InSAR MEASUREMENTS USING
A DEFORMATION MODEL
Unlike the multitrack/multisensor method, the InSAR+model
method regularizes the ill-posed problem of 3D mining
displacement reconstruction by integrating InSAR measurements with model-based constraints. In 2015, Li et al.
[94] proposed a method to completely estimate 3D mining
displacements from a single InSAR LOS displacement measurement, with the assistance of a prior mining deformation model (i.e., that the ground surface horizontal motion
caused by horizontal or nearly horizontal coal seam extraction is linearly proportional to the gradient of the vertical
subsidence in the corresponding direction). This method
first reconstructs two theoretical constraints that relate to the
3D mining displacements according to the following model:
	

'

E = B E $ TW E
, (8)
N = B N $ TW N

where B E and B N denote the proportional coefficients,
which can be readily determined from geomining conditions and deformation maps; and TW E and TW N
represent the gradients of the vertical subsidence in the
eastern and northern directions, respectively. These two
theoretical constraints are then incorporated with the
InSAR-derived 1D LOS deformation to regularize the
ill-condition problem and solve the 3D mining displacements. Finally, a test over the Huaibei coal mining area
of China was conducted to validate the feasibility of this
method. Following this, other cases of fully estimated
3D mining displacements using the same idea on the
basis of DInSAR [95], [96] or OT LOS deformation measurements [97], [98] were reported. Figure 2 displays
the full 3D mining displacements in the Daliuta coal
mining area of China between 21 November 2011 and
2 April 2013, generated by integrating OT-derived LOS
displacement observations using the prior model of (8).
In 2018, Yang et al. [99] proposed an improved method
for retrieving 3D mining displacements, where OT-derived
2D LOS and azimuth displacement measurements, rather
than LOS displacement only, are integrated with these two
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

MARCH 2020
IEEE Geoscience and Remote Sensing Magazine - March 2020

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