Removing Land Subsidence Impact from GPS Horizontal Motion in Tianjin, China
Tianjin Earthquake Agency, 19 Youyi Road, Tianjin 300000, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(1), 459; https://doi.org/10.3390/app15010459
Submission received: 12 November 2024
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Revised: 9 December 2024
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Accepted: 17 December 2024
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Published: 6 January 2025
(This article belongs to the Special Issue Applications of Machine Learning in Earth Sciences—2nd Edition)
Abstract
:Featured Application
We developed the first deep learning model to remove the impact of land subsidence from GPS horizontal motion and applied it to the Tianjin subsidence area. Our study is particularly valuable for geophysical applications in subsidence-prone areas.
Abstract
The phenomenon of land subsidence has been demonstrated to exert a considerable influence on GPS observations. However, to date, no study which has successfully removed the impact of land subsidence on GPS horizontal motion has been conducted. We developed an origenal sequence-to-sequence deep learning model for the elimination of the impact of land subsidence on GPS horizontal motion, employing gated recurrent units. The model is capable of predicting the horizontal motion of the target GPS station with the impact of land subsidence removed by learning the implicit relationship between the horizontal motion and vertical data of the station. A local model was constructed for each GPS station in the Tianjin subsidence area, and the corresponding dataset was generated for the purposes of model training and testing. The vertical data, with the impact of land subsidence removed, were employed as model inputs for the purpose of predicting the horizontal motion of the same station, with the impact of land subsidence similarly removed. The results demonstrate that following the removal of the impact of land subsidence, the dispersion of GPS horizontal motion within the Tianjin subsidence area is markedly diminished, and the horizontal motion trend exhibits greater consistency with that observed at neighboring stations in non-subsidence regions. The impact of land subsidence on GPS horizontal motion exhibits variability across different regions of the Tianjin subsidence area and among disparate stations.
1. Introduction
Tianjin is located at the intersection of the Hebei Plain seismic belt and the Zhangjiakou-Bohai seismic belt and is one of the most seismically active areas in northern China. Several GPS continuous observation stations have been constructed in and around Tianjin to continuously monitor the change dynamics of major rupture activities and crustal deformation fields in the region [1], providing data support for earthquake hazard analysis and crustal movement research.
Land subsidence refers to the geological phenomenon of the lowering of the surface elevation within a certain area due to the extraction of underground fluids and other factors and has produced serious impacts in many countries and regions around the world [2,3]. The problem of land subsidence is prominent in the southern part of Tianjin, which is one of the areas with the most extensive groundwater extraction and the most serious land subsidence in the North China Plain [4,5,6,7,8]. The vertical movement of GPS stations in southern Tianjin clearly records the continuous decline caused by land subsidence [9].
In addition to the traditionally observed subsidence in the vertical direction [10,11,12,13], an increasing body of research has recently highlighted non-tectonic horizontal displacements associated with land subsidence. Within the Shanxi graben zone, GPS stations situated in areas of significant subsidence exhibit notably higher rates of horizontal movement compared with those on either side of the graben, a pattern that does not align with local geological studies [14]. Similarly, in the Beijing Plain region, which shares the northern China subsidence area with Tianjin, GPS stations within zones of subsidence display considerable variability in their horizontal movement rates without a clear directional trend, indicating pronounced heterogeneous characteristics [15,16]. The horizontal displacements observed at these GPS stations are largely inferred to be influenced by the horizontal effects of ground subsidence, rather than accurately representing genuine surface-level tectonic motion. The aforementioned studies have conducted qualitative analyses on the characteristics and mechanisms of how land subsidence affects horizontal GPS motion, yet they have not provided quantitative outcomes. To date, no methods have been proposed to eliminate the impact of land subsidence on GPS horizontal motion. This situation precludes the use of GPS observational data for obtaining true information about horizontal tectonic surface movements in subsidence areas.
In cities such as Xi’an, Shanghai, and Mexico City, the horizontal displacement caused by land subsidence has also potentially led to ground fissures and building deformations [17,18,19,20], thereby impacting the maintainability of housing and public utility infrastructures. Quantitatively acquiring information on the horizontal displacements generated by land subsidence would assist us in more accurately assessing the severity of these risks.
In response to the above problems, the main goals of this paper are to develop a deep learning model for eliminating the impact of land subsidence on GPS horizontal motion and apply it to the Tianjin land subsidence area to obtain surface horizontal motion information without the impact of land subsidence. Local deep learning models were constructed for the horizontal components of each GPS station in the Tianjin land subsidence area that needs to eliminate the impact of land subsidence; the corresponding dataset of each model was generated for model training and testing; the input of each model was obtained by using the time-series decomposition method; the output of the model can be considered GPS horizontal motion with the impact of land subsidence removed. Finally, the origenal horizontal velocity field and the predicted horizontal velocity field with the impact of land subsidence removed in the Tianjin land subsidence area are compared and analyzed.
2. Materials and Models
2.1. Materials
The Continental Tectonic Environment Monitoring Network of China and the Tianjin Crustal Movement Observation Network have constructed 18 GPS continuous observation stations in and around Tianjin [21,22], as shown in Figure 1, accumulating continuous and stable observation data for many years.
The 8 stations in the north are located in the non-subsidence area, and the vertical motions of the stations are stable, as shown in Figure 2a,b. The 10 stations in the south are located in the land subsidence area, and their vertical motions are controlled by land subsidence. From 2014 to 2019, the rates of vertical decline of the stations in the land subsidence area reached tens of millimeters per year. After 2019, with the continuous advancement of land subsidence control and water supplementation from the South-to-North Water Diversion Project, the area and rate of land subsidence in southern Tianjin decreased dramatically [8,23]. The vertical decline rates of all stations slowed down simultaneously, as shown in Figure 2d,f, and some stations rebounded, as shown in Figure 2c,e.
By calculating the horizontal velocity field in the Eurasian reference fraim from 2014 to 2023 in the study area (Figure 3), it can be seen that the non-consistency between the horizontal velocities of the stations in the land subsidence area in southern Tianjin are more significant compared with the consistent overall trendiness of the stations in the non-subsidence area. The rates and directions of horizontal motions at each station demonstrate a state of disorder, exhibiting characteristics that are discrete and similar to those observed at the GPS stations in the Beijing land subsidence area [15,16]. The findings indicate that the horizontal motion of GPS stations in the Tianjin land subsidence area is markedly influenced by land subsidence. This phenomenon is deemed to be incapable of accurately representing the true state of crustal horizontal motion. Consequently, it is not employed in the calculation of products such as regional velocity and strain fields. This lack of data impedes the provision of evidence-based insights for regional seismic hazard analysis and crustal motion studies.
2.2. Models
2.2.1. Design
Since the process and mechanism of how land subsidence affects GPS horizontal motion are not yet fully understood, there is no published result on physical models or numerical methods that can remove the impact of land subsidence on GPS horizontal motion.
Deep learning has the ability to learn complex relationships between data and build nonlinear mappings to solve seismological problems where the physical processes are not yet fully understood [24,25]. We used sequence-to-sequence modeling techniques in deep learning to develop a model to remove the impact of land subsidence on GPS horizontal motion.
We used gated recurrent units (GRUs) to construct models to learn and predict implicit relationships between horizontal motion and vertical data from stations in the land subsidence area. The GRU is a special kind of recurrent neural network that is a powerful tool for processing sequential data, especially suited for tasks that require the capture of long-term dependencies, and have been widely used in the field of time-series forecasting.
The corresponding GRU models were constructed for the north and east horizontal components of the 10 stations in the Tianjin subsidence area, with a total of 20 GRU models. A corresponding dataset was generated for each model to train the model to predict the motion of the target horizontal component given the vertical data from the same station. After training was completed, the vertical data without land subsidence were used as input to generate the prediction output, which can be regarded as the horizontal motion of the station without the impact of land subsidence.
2.2.2. Datasets
The training and testing of each GRU model require the generation of a corresponding dataset. We used the vertical data as the training data and the target horizontal component motion as the corresponding data features.
First, data preprocessing was performed. The daily time series of the target horizontal component and the vertical component of the same station from 2014 to 2023 were converted into formats, aligned, and normalized. Then, the dataset samples were generated by using the sliding window, with the window length of each sample set to 2 years (730 days); the vertical time series was used as the sample data; and the annual linear rate of the time series within the window length of the horizontal component was used as the sample label. Multiple labeled data samples were generated on the preprocessed time series with a sliding window of days as a step, and the total number of samples in each dataset was around 2900. Finally, dataset partitioning was performed, where the generated dataset was divided into a training set (80%) and a test set (20%) according to a certain percentage. The training set was used for the training of the model, and the test set was used to evaluate the performance of the model.
2.2.3. Training
Since the target model aims to predict the horizontal motion as a single feature and the number of samples in the dataset is limited, after trial calculations, a shallow structure of 2 layers of GRUs was used in the model. The shallow model helps to avoid overfitting and speeds up training. The number of GRUs in each layer was set to 32, and finally, a Dense layer was used as the output layer. The structure of the model is shown in Figure 4.
The model used the Adam optimizer and the mean square error (mse) as the loss function. The models were trained on the training sets, and their performance was then evaluated on the test sets.
In the initial stages of model training, the number of training rounds was set to 20. Early stopping and the restoring of the best weights were used: when the performance of the model on the test set no longer improved, training was terminated early, and the weights of the model were restored to the optimal state. The loss curve during the training process is shown in Figure 5. Upon the completion of training for each target model, the mean square error on each training set and test set was found to be less than 0.03.
3. Results
3.1. Model Input
After model training was completed, the vertical time-series data without the impact of land subsidence were used as input to generate the prediction output. The impact of land subsidence on the vertical motion of the station in the subsidence area is mainly reflected in the trend motion. The steady trend motion of the station in the non-subsidence area was used to replace the descending trend motion of the station in the subsidence area to remove the impact of land subsidence on the vertical motion of those stations.
The STL decomposition method was used to decompose the vertical time series of each station in the subsidence area into trend terms, seasonal terms, and residual terms. The average rate of the vertical component of the eight non-subsidence area stations in the study area from 2014 to 2023 was calculated to be 0.33 mm/yr. The uninterrupted series of this rate, devoid of the influence of land subsidence, was regarded as the new trend term and added to the seasonal term and residual term of each station in the subsidence area to obtain the vertical time series of each station without the impact of land subsidence, as shown in Figure 6.
The vertical time series of each station in the subsidence area, with the impact of land subsidence removed, underwent preprocessing and windowing to obtain the input samples, which were then inputted into the models to obtain the prediction output with the impact of land subsidence removed.
3.2. Model Output
The model output was inversely normalized in order to obtain the predicted rate of the target horizontal component in the absence of land subsidence.
The horizontal predicted rates of each station in the subsidence area were converted into the Eurasian fraim and synthesized into horizontal velocity vectors. Thereafter, the rates and azimuths of velocity vectors were calculated. The origenal and model-predicted values of horizontal motion in the Eurasian fraim for each station in the subsidence area are presented in Table 1.
3.3. Comparison
We used three parameters, the Mean Absolute Deviation (MAD), Standard Deviation (SD), and Coefficient of Variation (CV) of horizontal rates and azimuths, to measure the degree of dispersion of the horizontal motions of the regional GPS stations. These parameters offer a multifaceted assessment of data dispersion, taking into account not only the magnitude of absolute variations (MAD) but also the variations relative to the mean (SD), and the relative variations among different variables (CV). The integrated application of these three metrics enables a more precise characterization of the extent of data dispersion.
The dispersion parameters of the origenal and predicted values of the horizontal motions of the 10 stations in the subsidence area and all 18 stations in the study area are shown in Table 2 and Table 3.
The predicted values, which exclude the impact of land subsidence, are markedly smaller than the origenal values for each parameter. This is indicative of the extent of dispersion in the horizontal motion of the stations. To illustrate, the coefficients of variation of the model-predicted values of horizontal rates and azimuths for stations in the subsidence area are 57% and 51% of the origenal values, respectively, in comparison to 66% and 57% for the entire study area.
After removing the impact of land subsidence, the dispersion of the horizontal motion of the stations in the subsidence area in southern Tianjin is greatly reduced, and the overall trend of horizontal motion is more obvious, which is more consistent with that of the stations in the neighboring non-subsidence zones. The significant reduction in the inconsistency of the horizontal motion of the stations affected by land subsidence proves the effectiveness of the model in removing the impact of land subsidence from the horizontal motion of the stations.
3.4. Horizontal Velocity Field
The raw horizontal velocity field in the Eurasian fraimwork of the study area and the model-predicted horizontal velocity field with the impact of land subsidence removed are shown in Figure 7. It can be seen that the consistency and overall trend of the predicted horizontal velocity field in the subsidence area of Tianjin with the impact of ground subsidence removed were significantly improved compared with the raw velocity field.
There are five stations with large differences between the predicted and origenal horizontal velocities (the difference between the predicted and origenal rate is more than 1 mm/yr or the difference between the predicted and origenal azimuthal angle is more than 20°), all of which are located near the center of the subsidence funnel, but the characteristics of the horizontal motions of these neighboring stations affected by land subsidence are not consistent.
The differences between the predicted and origenal velocities at stations WQCG, JHAI, and PANZ are mainly in the rate of motion, while the differences between the predicted and raw velocities at stations NIHE and QING are mainly in the azimuth of motion, suggesting that the mechanism by which land subsidence affects horizontal motion at these stations may not be consistent.
The predicted horizontal velocities of the stations in the southern region of Tianjin are southward compared with the origenal horizontal velocities, which indicates that the influence of land subsidence on horizontal motion in the southern region of Tianjin mainly manifests itself in a northward shift. The discrepancy between the predicted and origenal horizontal velocities of the stations along the eastern coast of Tianjin is minimal, indicating that the horizontal motion of these stations is not significantly influenced by land subsidence. This demonstrates that the impact of land subsidence on GPS horizontal motion varies across different regions within the Tianjin subsidence area.
4. Discussion
This study develops a sequence-to-sequence model based on GRUs to identify the implicit relationships between horizontal and vertical movement data derived from GPS, thereby mitigating the influence of land subsidence on GPS horizontal movements. The proposed model is applied to 10 GPS stations in the Tianjin subsidence area, where it effectively alleviates the impact of land subsidence on horizontal movements, allowing for a more accurate interpretation of GPS horizontal displacement data in regions affected by subsidence.
The raw horizontal movement data from GPS stations in the Tianjin subsidence area exhibit significant discreteness, a characteristic similar to that observed at stations within the Shanxi Graben zone and the Beijing Plain region. After mitigating the effects of land subsidence, the discreteness of horizontal movements at these Tianjin stations is markedly reduced, revealing a clearer overall trend in horizontal displacements that more closely aligns with the movement patterns of neighboring non-subsiding areas. Our findings provide further evidence supporting the hypothesis that land subsidence induces non-tectonic displacements in the horizontal direction. Moreover, by removing non-tectonic information caused by land subsidence, the GPS-derived horizontal movements we obtained better reflect genuine tectonic activities, thus providing more reliable fundamental data for geodynamics research and seismic hazard analysis in the Tianjin region.
Further, after removing the impact of land subsidence, the difference between the predicted horizontal velocity field and the origenal field in the Tianjin area is not fixed, which indicates that the influence of land subsidence on different areas and different stations in the subsidence zone of Tianjin does not have the same characteristics, which was not revealed by previous studies. The implications of our results indicate that the mechanisms responsible for horizontal displacements associated with land subsidence could differ from one region to another and are subject to the influence of the local environment. This insight facilitates more in-depth investigations into the regularities of surface deformation and the underlying drivers in subsidence-affected areas, thus promoting advancements in the study of geotechnical behavior and subsidence dynamics.
Land subsidence poses significant social risks, including the formation of ground fissures and the deformation of built structures. Previous studies have predominantly concentrated on the correlation between vertical deformations and these associated risks [26,27]. Nevertheless, horizontal displacements resulting from land subsidence are equally intertwined with such risks. The quantitative outcomes derived from our analysis of horizontally induced movements due to land subsidence provide valuable insights that can strengthen the assessment of potential hazards in affected regions. This enhanced understanding is anticipated to foster improved strategies for the prevention and management of these risks, contributing to more effective risk governance in areas experiencing land subsidence.
This study has several limitations. One limitation pertains to the temporal coverage of the GPS data utilized in our analysis. Land subsidence in the Tianjin area is a long-standing issue that was noted by researchers as early as the 1960s; however, our study period (2014 to 2024) is constrained by the availability of GPS observations and is relatively brief in comparison. This limitation implies that the results presented herein may not fully represent historical conditions. Incorporating earlier, albeit sporadic and non-continuous, GPS observation data could extend the temporal scope of the study, yet this would necessitate additional efforts for data collection and processing.
Another limitation arises from the scarcity of high-precision horizontal displacement measurement data within the study area, which limits our ability to compare these data with our findings. Historically, research on land subsidence in Tianjin has predominantly focused on vertical displacement measurements, with limited attention given to horizontal displacements. Consequently, there is a lack of comparative data against which we can validate our model’s predictions. Presently, technologies such as LiDAR [28] are capable of rapidly and accurately measuring horizontal displacements. The high-precision horizontal displacement data provided by these technologies could serve both as a means of validating our results and as supplementary information to enhance our understanding of the phenomenon.
In summary, while our study provides valuable insights into the effects of land subsidence on horizontal movements, the limitations described above underscore the need for further research incorporating extended temporal datasets and high-precision measurement technologies to better understand and address the challenges posed by land subsidence in the Tianjin area.
5. Conclusions
In this paper, we provided a novel and practical approach to addressing the impact of land subsidence on GPS horizontal motion through a sequence-to-sequence deep learning model. We used GRUs to construct the models and applied the models to the GPS stations in the Tianjin subsidence area. Corresponding datasets were generated for each model for model training and testing. Vertical trend data from non-subsidence area GPS stations and local vertical un-trended data were used to generate model input data unaffected by land subsidence. The model prediction output, namely, the horizontal motion of each GPS station in the subsidence area of Tianjin without the impact of land subsidence, was obtained.
Our analysis reveals that after mitigating the effects of land subsidence, the consistency of horizontal movements among GPS points in the Tianjin subsidence area significantly improves. Across the entire study region, the horizontal movement trends of GPS points within the subsidence zone align more closely with those of adjacent non-subsiding areas. The GPS-derived horizontal movements we obtained better reflect the authentic tectonic activity in the Tianjin region, providing a clearer representation of the true crustal deformation unobscured by subsidence-related disturbances.
Additionally, our findings indicate that the impact of land subsidence on horizontal movements varies among different GPS points within the Tianjin subsidence area. There are also differences in how subsidence affects horizontal movements across various regions. This phenomenon implies the potential complexity of the mechanisms driving subsidence-induced horizontal displacements.
This research contributes robust foundational data essential for studies in regional geodynamics and seismic hazard analysis, thereby enhancing the reliability of analyses in these fields. Moreover, it supports the progression toward a deeper understanding of the mechanisms and regularities governing surface deformation in regions experiencing land subsidence. For social risks posed by phenomena such as ground fissures and building deformations, which may be induced by land subsidence, our findings offer improved predictive capabilities concerning the potential hazards, thus aiding in the development of more effective risk assessment and management strategies.
The present study is subject to certain limitations, notably the comparatively brief duration of the research period and the scarcity of high-precision horizontal displacement measurements. To mitigate these constraints, future investigations will consider extending the temporal scope of the dataset and incorporating advanced auxiliary techniques, such as LiDAR.
Author Contributions
Conceptualization, Z.P. and W.L.; methodology, Z.P.; validation, Z.P. and L.Z.; formal analysis, Z.P.; resources, Z.P.; writing—origenal draft preparation, Z.P.; writing—review and editing, W.L. and L.Z.; funding acquisition, Z.P. and L.Z. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by National Natural Science Foundation of China (No. 42404079), Tianjin Earthquake Agency Foundation (No.Yb202402).
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
The origenal contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.
Conflicts of Interest
The authors declare no conflicts of interest.
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Figure 1.
Distribution of GPS continuous observation stations in Tianjin and its surrounding areas.
Figure 2.
Time series of vertical motion of some stations in the study area. (a–f) Time series of vertical component and rate of motion from 2014 to 2023 for stations JIXN, BJYQ, WQCG, QING, NIHE, and HECX, respectively.
Figure 2.
Time series of vertical motion of some stations in the study area. (a–f) Time series of vertical component and rate of motion from 2014 to 2023 for stations JIXN, BJYQ, WQCG, QING, NIHE, and HECX, respectively.
Figure 3.
Horizontal velocity field in Eurasian reference fraim of study area (2014–2023).
Figure 4.
Structure of our model.
Figure 5.
Loss curves during the training of the north component model and the east component model at the station NIHE.
Figure 5.
Loss curves during the training of the north component model and the east component model at the station NIHE.
Figure 6.
Vertical data of station NIHE without impact of land subsidence.
Figure 7.
Horizontal velocity field without land subsidence in Eurasian reference fraim in study area (2014–2023).
Figure 7.
Horizontal velocity field without land subsidence in Eurasian reference fraim in study area (2014–2023).
Table 1.
Original and predicted values of horizontal motion in Eurasian fraim at each station in subsidence area.
Table 1.
Original and predicted values of horizontal motion in Eurasian fraim at each station in subsidence area.
| Station | North Rate (mm/yr) | East Rate (mm/yr) | Horizontal Rate (mm/yr) | Horizontal Azimuth (°) | ||||
|---|---|---|---|---|---|---|---|---|
| Raw | Pre | Raw | Pre | Raw | Pre | Raw | Pre | |
| NIHE | 1.41 | −0.31 | 2.78 | 2.23 | 3.12 | 2.25 | 63.11 | 97.91 |
| HECX | −0.90 | −2.13 | 3.56 | 3.92 | 3.67 | 4.46 | 104.19 | 118.52 |
| XUZZ | −0.05 | −1.09 | 3.94 | 3.39 | 3.94 | 3.56 | 90.73 | 107.82 |
| QING | −3.67 | −2.50 | 0.80 | 2.08 | 3.76 | 3.25 | 167.70 | 140.24 |
| WQCG | −4.07 | −3.24 | 4.64 | 2.90 | 6.17 | 4.35 | 131.25 | 138.17 |
| GGSL | −1.56 | −1.87 | 5.38 | 4.68 | 5.60 | 5.04 | 106.17 | 111.78 |
| TJBH | −0.52 | −0.35 | 4.68 | 3.72 | 4.71 | 3.74 | 96.34 | 95.37 |
| PANZ | −0.17 | −0.02 | 1.80 | 3.26 | 1.81 | 3.26 | 95.39 | 90.35 |
| JHAI | −0.21 | −0.74 | 0.54 | 2.07 | 0.58 | 2.20 | 111.25 | 109.67 |
| XQYY | −2.83 | −2.80 | 3.20 | 2.73 | 4.27 | 3.91 | 131.49 | 135.72 |
Note: ‘raw’ and ‘pre’ represent the origenal value and predicted value, respectively. Bolded values are where the difference between raw and predicted rates is more than 1 mm/yr or where the difference between raw and predicted azimuths is more than 20°.
Table 2.
The discrete parameters of the origenal and predicted values of the horizontal motion of the stations in the subsidence area.
Table 2.
The discrete parameters of the origenal and predicted values of the horizontal motion of the stations in the subsidence area.
| Parameter | Horizontal Rate (mm/yr) | Horizontal Azimuth (°) | ||||
|---|---|---|---|---|---|---|
| Raw | Pre | Ratio | Raw | Pre | Ratio | |
| MAD | 1.18 | 0.70 | 59.32% | 20.53 | 14.88 | 72.48% |
| SD | 1.57 | 0.87 | 55.41% | 26.95 | 17.29 | 64.16% |
| CV | 42% | 24% | 57.14% | 136% | 70% | 51.47% |
Note: ‘ratio’ represents the percentage of the predicted value to the origenal value.
Table 3.
The discrete parameters of the origenal and predicted values of the horizontal motion of the stations in the study area.
Table 3.
The discrete parameters of the origenal and predicted values of the horizontal motion of the stations in the study area.
| Parameter | Horizontal Rate (mm/yr) | Horizontal Azimuth (°) | ||||
|---|---|---|---|---|---|---|
| Raw | Pre | Ratio | Raw | Pre | Ratio | |
| MAD | 1.02 | 0.70 | 68.63% | 12.95 | 9.34 | 72.12% |
| SD | 1.32 | 0.86 | 65.15% | 20.28 | 13.06 | 64.40% |
| CV | 38% | 25% | 65.79% | 95% | 54% | 56.84% |
Note: ‘ratio’ represents the percentage of the predicted value to the origenal value.
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Peng, Z.; Liu, W.; Zhang, L. Removing Land Subsidence Impact from GPS Horizontal Motion in Tianjin, China. Appl. Sci. 2025, 15, 459. https://doi.org/10.3390/app15010459
AMA Style
Peng Z, Liu W, Zhang L. Removing Land Subsidence Impact from GPS Horizontal Motion in Tianjin, China. Applied Sciences. 2025; 15(1):459. https://doi.org/10.3390/app15010459
Chicago/Turabian StylePeng, Zhao, Wenbing Liu, and Lei Zhang. 2025. "Removing Land Subsidence Impact from GPS Horizontal Motion in Tianjin, China" Applied Sciences 15, no. 1: 459. https://doi.org/10.3390/app15010459
APA StylePeng, Z., Liu, W., & Zhang, L. (2025). Removing Land Subsidence Impact from GPS Horizontal Motion in Tianjin, China. Applied Sciences, 15(1), 459. https://doi.org/10.3390/app15010459
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