IEEE Geoscience and Remote Sensing Magazine - March 2020 - 79

in the northern direction [94]. However, the InSAR+model
method still has some limitations, the first of which is that
it is model dependent. This implies that it can be used only
in those areas where the deformation patterns follow the
used deformation model (e.g., the surface horizontal motions are linearly proportional to the gradients of the vertical subsidence or the PIM). Because the models used to date
are mainly derived for describing the mining deformation
caused by underground extraction of horizontal or slightly
inclined mineral seams [107], the InSAR+model method
cannot be applied in open-pit mining areas or mining areas
that extract deeply inclined mineral seams [107]. Moreover,
due to the model-dependent nature of the InSAR+model
method, large errors would arise when significant model
errors occur (e.g., in those mining areas with large ground
fissures) [99].
InSAR-BASED MECHANICAL MODEL PARAMETER
INVERSION OF MINING DEFORMATION
The mechanical parameter inversion of a mining deformation model is a routine but essential task for understanding
mining deformation mechanisms, deformation prediction, and mining-related geohazard assessments [3], [8].
The traditional strategy for model parameter inversion is
based on in situ 3D deformation observations measured
by conventional geodetic surveying techniques, a strategy
that has proven to be a costly and low-efficiency approach.
InSAR offers great potential to significantly reduce the
cost and improve the efficiency of mechanical parameter
inversion compared with the traditional strategy. Consequently, some studies have been conducted for the InSARbased mechanical parameter inversion of mining deformation models.
The InSAR-based mechanical parameter inversion mainly consists of three steps: 1) selecting a suitable deformation model that describes mining deformation patterns; 2)
forward construction of a function model that relates the
model parameters of the selected model to InSAR LOS displacement measurements; and 3) inverting model parameters from InSAR LOS displacements measurements. Further details of these three main steps are presented in the
following sections.
MODEL SELECTION
SPATIAL DEFORMATION PREDICTION MODEL
To date, a large number of deformation models have been
developed for describing mining deformation patterns [8].
Therefore, selecting the deformation model is crucial for
mechanical parameter inversion and its related applications. The PIM, which is derived from random medium theory [108], is one of the most popular mining deformation
models used in mining engineering [107], [109]. The PIM
can be applied to predict the surface deformation caused by
underground mining activities in the vertical W and in an
arbitrary horizontal direction U({) using
MARCH 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

	

(

W(x, y) = f1(x, y, P, G)
, (10)
U(x, y, {) = f2(x, y, {, P, G)

where f1 and f2 are two mapping functions whose specific formations are demonstrated in [110] and [111];
(x, y) denotes the coordinates of a surface point; { is the
angle from the advancing direction to the given direction;
G is a parameter vector relating to the mined-out areas;
P = 6q, b, tan b, i 0, s 3, s 1, s 2@ are the full mechanical model
parameters of the PIM, with q being the subsidence factor, b being the horizontal motion constant, tan b being
the tangent of major influence angle, i 0 being the mining propagation angle, and s 3, s 1, s 2 being the offsets of
the injection points in the strike, down-dip, and up-dip
directions of the working panel, respectively. The physical meanings of these model parameters can be found in
[8] and [111]. Note that the model parameter of horizontal motion constant b is related to horizontal movements
only and is independent of vertical subsidence.
Because of the accessibility and acceptable accuracy under
critical extraction (i.e., the size of the mined-out area is equal
to a threshold), researchers have generally preferred the PIM
for subsequent mechanical parameter inversion (e.g., [111]-
[114]). However, due to the assumption of critical extraction,
the PIM shows a poor performance in describing the ground
surface deformation patterns caused by subcritical extraction
[115] and the entire deformation evolution process [116]. In
other words, the PIM is typically used as a spatial model to
predict the final (or static) deformation caused by critical or
supercritical (i.e., the mined-out size is larger than the threshold), instead of a spatiotemporal deformation model prediction caused by the entire mining process.
SPATIOTEMPORAL DEFORMATION PREDICTION MODEL
Integrating a time function in the range of zero to one
with the PIM is a feasible way to develop spatiotemporal
deformation prediction models. Typically, Cui et al. [116]
integrated the Knothe time function, which is a generalized differential equation whose solution is Mitscherlich's
growth law, with the PIM. In doing so, they developed a
model (referred to as a temporal PIM) for TS deformation
prediction caused by the entire underground mining process. Currently, the temporal PIM is a widely used spatiotemporal deformation prediction model [109], [117].
However, the Knothe time function cannot accurately
describe the real temporal evolution of mining subsidence rates and accelerations in theory [118], which results in poor accuracy of the predicted subsidence rates
and accelerations. To overcome this issue, a generalized
PIM [119], where a simplified Boltzmann function is
used to modify the subsidence factor, was proposed as
a new spatiotemporal model for describing the mining
deformation patterns caused by the entire underground
mining process. Theoretically, the generalized PIM could
improve the accuracy of the predicted subsidence rates
and accelerations.
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IEEE Geoscience and Remote Sensing Magazine - March 2020

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