A Goaf-Locating Method Based on the D-InSAR Technique and Stratified Okada Dislocation Model
"> Figure 1
<p>Geographic location of the study area.</p> "> Figure 2
<p>Scheme of the proposed S-ODM. The boxes outlined with dotted lines represent parameters estimated by the proposed algorithm, which form the goaf parameters.</p> "> Figure 3
<p>Spatial geometrical relationships of three coordinate systems. (<b>a</b>) Spatial relationships among the three coordinate systems. (<b>b</b>) Top view of the two ground-based coordinate systems.</p> "> Figure 4
<p>The layered structure of the coal overburden. The deformation is transmitted to the ground surface through multiple strata.</p> "> Figure 5
<p>Scheme of RM-DBC. (<b>a</b>) Simulation deformation example; the red rectangle is the stable area without subsidence. (<b>b</b>) The deformation binary conversion result.</p> "> Figure 6
<p>The optimization process of GA-PSO. <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mn>0</mn> <mi>n</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>∈</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>s</mi> <mi>i</mi> <mi>z</mi> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> represents the initial particle swarm and is constructed using seven parameters (i.e., <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, <span class="html-italic">L</span>, <span class="html-italic">W</span>, <span class="html-italic">H</span>, <span class="html-italic">m</span>, <math display="inline"><semantics> <mi>φ</mi> </semantics></math>, and <math display="inline"><semantics> <mi>α</mi> </semantics></math>). <math display="inline"><semantics> <msubsup> <mi>Q</mi> <mi>i</mi> <mi>n</mi> </msubsup> </semantics></math> (<span class="html-italic">i</span> is the iteration number, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> </mrow> </semantics></math>) represents the <math display="inline"><semantics> <msubsup> <mi>P</mi> <mn>0</mn> <mi>n</mi> </msubsup> </semantics></math> particles sorted by fitness value, and <math display="inline"><semantics> <msubsup> <mi>P</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </semantics></math> is the particle swarm optimized by PSO and the GA for the next iteration.</p> "> Figure 7
<p>Ground deformation of simulated mining. (<b>a</b>) Ground subsidence. (<b>b</b>,<b>c</b>) Horizontal deformation in the north–south and east–west directions, respectively. (<b>d</b>) Simulated LOS deformation. The blue and pink rectangles represent the simulated and estimated work faces.</p> "> Figure 8
<p>Time-series cumulative subsidence map of the study area. The black line is the 15325 working face.</p> "> Figure 9
<p>(<b>a</b>) Comparison between the InSAR measurements from 13 October 2015 to 5 March 2016 and the leveling measurements from 10 October 2015 to 4 March 2016. (<b>b</b>) The InSAR-derived deformation for the same period.</p> "> Figure 10
<p>(<b>a</b>–<b>e</b>) Five time-series results filtered using a binary filter with a threshold of 2.6 mm, encompassing the coal mining period.</p> "> Figure 11
<p>The RM-DBC results for the study area. (<b>a</b>) The subsidence profile along the 234° direction. (<b>b</b>) The performance for all directions, where the length of the polar axis represents the sum of the pixel values in each direction and the angle represents the angle between the ray and the north direction.</p> "> Figure 12
<p>The goaf-locating results using the S-ODM. The upper and bottom layers are the LOS deformation based on the S-ODM-inversed and InSAR-derived information, respectively. The pink and blue cuboids represent the in situ measured goaf and the S-ODM-estimated goaf, respectively.</p> "> Figure 13
<p>Comparison of the deformation results generated by the S-ODM, PIM, ODM, and D-InSAR for the strike and dip directions, respectively.</p> "> Figure 14
<p>Influence of monitoring errors on the estimated geometric parameters of underground goaves.</p> ">
Abstract
:1. Introduction
2. Study Area and Datasets
3. Methods
- Acquire times-series line-of-sight (LOS) deformation utilizing the D-InSAR technique;
- Determine the S-ODM parameters based on basic geological investigations;
- Apply the ray method to estimate the goaf azimuth with the textures and trends of the InSAR-derived deformation;
- Use GA-PSO to estimate the goaf parameters. The process will stop when either the best fitness value is less than the threshold or the iteration number reaches a preset maximum value.
3.1. Differential InSAR
3.2. Stratified Okada Dislocation Model
3.3. Underground Goaf Locating
3.3.1. Mining Azimuth Estimation
3.3.2. Estimation of Goaf Parameters
4. Results
4.1. Simulation Results
4.2. Real Data Results
4.2.1. Deformation Results
4.2.2. Goaf Azimuth Estimate
4.2.3. Underground Goaf Locating
5. Discussion
5.1. Comparison with Existing Methods
5.2. Errors Introduced by GA-PSO
5.3. Influence of Ground Deformation Monitoring Errors
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Interferogram Pair | Spatial Baseline | Time Baseline |
---|---|---|
20150919–20151013 | 101.8260 m | 24 d |
20151013–20151106 | 47.2675 m | 24 d |
20151106–20151130 | 3.1222 m | 24 d |
20151130–20151224 | −30.4078 m | 24 d |
20151224–20160117 | −43.6049 m | 24 d |
20160117–20160305 | −37.7825 m | 48 d |
Parameter | Simulated Value | Estimated Value | Absolute Error | Relative Error |
---|---|---|---|---|
X(m) | 1000 | 1007.26 | 7.26 | - |
Y(m) | 1000 | 995.38 | 4.62 | - |
L(m) | 600 | 627.72 | 27.72 | 4.62% |
W(m) | 100 | 90.36 | 9.64 | 9.64% |
H(m) | 500 | 519.51 | 19.51 | 3.9% |
30 | 26.87 | 3.13 | - | |
45 | 45.77 | 0.77 | - | |
m(m) | 5 | 4.65 | 0.35 | 7% |
Parameter | Real Value | Estimated Value | Absolute Error | Relative Error |
---|---|---|---|---|
X(m) | 1057 | 1078.66 | 21.66 | - |
Y(m) | 565 | 550.38 | 14.62 | - |
L(m) | 493 | 522.21 | 19.21 | 5.92% |
W(m) | 142 | 161.86 | 19.86 | 13.98% |
H(m) | 740 | 701.6 | 38.4 | 5.19% |
13 | 10.98 | 2.02 | - | |
236 | 234 | 2 | - | |
m(m) | 4.5 | 4.70 | 0.20 | 4.4% |
Parameter | True Value | S-ODM | PIM | ODM | |||
---|---|---|---|---|---|---|---|
Estimated Value | Absolute Error | Estimated Value | Absolute Error | Estimated Value | Absolute Error | ||
X(m) | 1057 | 1078.66 | 21.66 | 1089.31 | 32.31 | 1134.14 | 74.14 |
Y(m) | 565 | 550.38 | 14.62 | 545.15 | 19.85 | 512.64 | 52.36 |
L(m) | 493 | 522.21 | 19.21 | 510.62 | 17.62 | 465.14 | 27.86 |
W(m) | 142 | 161.86 | 19.86 | 167.14 | 25.14 | 183.87 | 41.87 |
H(m) | 740 | 701.6 | 38.4 | 687.83 | 52.17 | 680.15 | 59.85 |
13 | 10.98 | 2.02 | 10.08 | 2.92 | 10.12 | 2.88 | |
236 | 234 | 2.0 | 241 | 5.0 | 221 | 15 | |
m(m) | 4.5 | 4.7 | 0.2 | 4.64 | 0.14 | 4.86 | 0.36 |
Parameter | Simulated Value | Estimated Value | Absolute Error | Relative Error |
---|---|---|---|---|
X(m) | 2000 | 2007.26 | 7.26 | - |
Y(m) | 2000 | 1995.38 | 4.62 | - |
L(m) | 500 | 517.72 | 17.72 | 3.54% |
W(m) | 100 | 91.36 | 8.64 | 8.64% |
H(m) | 500 | 519.51 | 19.51 | 3.9% |
15 | 15.87 | 3.87 | - | |
45 | 45.77 | 0.77 | - | |
m(m) | 5 | 4.65 | 0.35 | 7% |
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Zhang, K.; Wang, Y.; Du, S.; Zhao, F.; Wang, T.; Zhang, N.; Zhou, D.; Diao, X. A Goaf-Locating Method Based on the D-InSAR Technique and Stratified Okada Dislocation Model. Remote Sens. 2024, 16, 2741. https://doi.org/10.3390/rs16152741
Zhang K, Wang Y, Du S, Zhao F, Wang T, Zhang N, Zhou D, Diao X. A Goaf-Locating Method Based on the D-InSAR Technique and Stratified Okada Dislocation Model. Remote Sensing. 2024; 16(15):2741. https://doi.org/10.3390/rs16152741
Chicago/Turabian StyleZhang, Kewei, Yunjia Wang, Sen Du, Feng Zhao, Teng Wang, Nianbin Zhang, Dawei Zhou, and Xinpeng Diao. 2024. "A Goaf-Locating Method Based on the D-InSAR Technique and Stratified Okada Dislocation Model" Remote Sensing 16, no. 15: 2741. https://doi.org/10.3390/rs16152741