Coseismic Deformation Obtained by Various Technical Methods and Its Constraint Ability to Slip Models of Maduo Earthquake

Abstract

The coseismic deformation field on both sides of the fault, especially the distribution and change characteristics of near-field deformation, not only provides important constraints for the fine inversion of the slip distribution model but also serves as an important basis for the anti-disruption defense of the cross-fault linear engineering facilities. In this paper, we used Sentinel-1 satellite data to obtain the coseismic deformation field of the Maduo earthquake by using InSAR and offset techniques. We quantitatively compared the coseismic displacement of the three types of data: InSAR, offset, and optical images. The results show that optical images and offset provided more robust near-fault (<2 km) deformation insights than InSAR, which exhibited irregular deformation patterns due to incoherence near the fault. The maximum relative displacements for InSAR and offset observations are ~2.8 m and 4 m, respectively. Then we tested various fault slip models with different data constraints, revealing that a combined inversion of GPS, InSAR, and offset data offers superior constraints on slip distribution. This integrative approach effectively captured both shallow and deep fault slip, particularly near the fault zone. The eastern branch fault model, jointly constrained by GPS, InSAR, and offset data, is the optimal coseismic slip distribution model for the Maduo earthquake, and the maximum slip is 5.55 m.

1. Introduction

The Bayanhar block is a large tectonic unit in the central part of the Tibetan Plateau on the Western Chinese mainland, and is a secondary active block of the Tibetan Plateau active massif. The block spans the entire Tibet Plateau from west to east, approximately 2000 km long, its movement is mainly controlled by the large sinistral strike slip faults on its north and south sides (Figure 1a) [1,2]. Along the boundary fault zones of the Bayanhar block, seismicity is relatively frequent, and within the Bayanhar block, a small number of seismic events still occur despite weaker seismicity; the 2021 Mw 7.4 Maduo earthquake occurred on a secondary fault within the Bayanhar block [3]. The Maduo earthquake occurred on 22 May 2021 Beijing time in Maduo County, Qinghai Province (98.34°E, 34.59°N), with a magnitude of Mw 7.4 and a focal depth of about 17 km (China Earthquake Networks Center, 2021). After the Maduo earthquake, many researchers studied the coseismic surface deformation characteristics through various methods such as field investigations, UAV photography, high-resolution optical images, InSAR, and GPS geodesy. They also studied the coseismic fault slip distribution of the Maduo earthquake and its stress impact on peripheral faults [3,4,5,6,7,8,9]. Based on the results of relocated aftershocks and field investigations, the earthquake was found to have occurred in the Jiangcuo fault zone, which is a branch fault located approximately 70 km south of the northern boundary fault of the eastern part of the Bayanhar block. The rupture extended from the epicenter to both ends, and the surface rupture zone caused by the earthquake reached 160 km, showing that the surface rupture has typical left-lateral strike-slip movement characteristics and segmental differences [10,11,12].

Many researchers have obtained the coseismic displacement field of the Maduo earthquake using different methods. According to field investigations and UAV image interpretation results, the horizontal displacements within the rupture segment are mostly distributed between 0.2 and 2.6 m [13]. The maximum displacement is located at the western end of the fault (Eling Lake segment). The surface rupture zone produced by this earthquake shows obvious segmentation, forming two large fracture gaps within the surface rupture zone (Figure 1c), and they are the two largest discontinuous surface ruptures in recorded strike-slip earthquakes [12]. The InSAR method reveals a broadly distributed coseismic deformation, peaking at 1–2 m at the fault’s eastern part, contrasting with field observations of maximum displacement at the western end [14,15,16]. This is because the displacement observed in the field is obtained by directly measuring landmark features such as disconnected roads and gullies, while the InSAR deformation field includes disconnected landmarks and secondary cracks. The GPS-measured coseismic horizontal displacement, ranging from 0.2 to 1 m, is notably less than that observed by InSAR and field investigations. This discrepancy is largely due to the sparse distribution of GPS stations in the Maduo earthquake area, especially in the near-fault zone [8,17].

Due to differences in data and models, there are discrepancies in the maximum slip and slip distribution patterns of previous studies (Figure 2a). The coseismic maximum slip inverted from InSAR data is about 5~6 m, with a relatively shallow rupture depth and a more continuous slip distribution [4,14,15,18]. The coseismic maximum slip inverted from GPS data is about 4 m, presenting multiple concentrated asperities. The rupture depth is slightly deeper than the result inverted from InSAR data, and the rupture reaches the surface [19,20]. The coseismic maximum slip inverted from combined InSAR and GPS data is about 3~5 m. Only the maximum slip inverted by Guo, et al. (2021) is 9.3 m, which is much higher than the maximum slip inverted by previous studies [21,22,23,24,25]. There is also controversy over whether there is a shallow slip deficit [14,17,26].

This paper focuses on a detailed comparison and analysis of various coseismic deformation observations, exploring their correlations, differences, and causes. We study how different methods reflect fault zone displacement and deformation distribution, and how observation data types and fault geometry impact slip distribution inversion results. Our research uses Sentinel-1 data to capture the complete InSAR coseismic deformation field of the Maduo earthquake and surface rupture trace. We also collect observation results from other methods, such as UAVs and optical remote sensing, for a comprehensive comparison. Additionally, we create four fault geometry models and evaluate the quality and constraint ability of the slip models through multiple data inversions.

2. Data and Methods

2.1. Different Types of Coseismic Deformation Data

We collected field investagation/UAV data, optical image data, and GPS data [3,5,8]. We obtained two tracks of Sentinel-1 SAR observations of the Maduo earthquake (ascending is track T99, descending is track T106). GAMMA (2015 version) software is used to perform D-InSAR processing on these images to derive the coseismic deformation field. The DEM data is used to remove the topographic phase and the flat phase to obtain the interference map. To enhance the signal-to-noise ratio, we conduct multilook processing with factors of ten and two in the range and azimuth directions, respectively. The interferograms are then subjected to adaptive filtering. To improve unwrapping accuracy, we masked the incoherent region caused by the water body and the near-field unwrapping error. Finally, we unwrapped the interferogram using the minimum cost flow (MCF) method to obtain the coseismic deformation field results. We used the offset-tracking method to obtain distance offset results. These results were used for subsequent comparative analyses and the inversion of the slip distribution.

2.2. Normalisation and Comparison of Different Types of Coseismic Displacement Data

The coseismic deformation data obtained using different methods show inconsistent displacement directions. InSAR and offset methods measure displacement along the line-of-sight (LOS) direction of SAR satellites. Optical imagery captures horizontal displacement along the east-west and north-south directions. Field investigations and UAV image measurements yield the relative displacement of the two plates along the fault dislocation direction. To conduct a quantitative comparative study of the coseismic deformation field observed by these different methods, we uniformly convert the displacements obtained by InSAR, offset, and optical images to the direction along the fault. The process of converting and comparing these different types of data is shown in Figure 3. For the LOS deformation obtained by InSAR and offset-tracking, we combine the ascending and descending coseismic deformation fields, and solve the 2.5-dimensional (2.5-D) displacement field containing east-west (D_ew) and vertical (D_ud) displacements using the following formula:

$$D_{los}={-D}_{ew}\sin \theta \cos \alpha +D_{ns}\sin \theta \sin \alpha +D_{ud}\cos \theta$$

(1)

in which θ is the incident angle and α is the heading angle, the north-south deformation is set to 0 (D_ns = 0). In the subsequent relative displacement comparison, we only use the east-west horizontal displacement for comparison. For optical images, with a fault strike of 282°, the east-west (D_ew) and north-south (D_ns) displacements can be projected to the parallel fault direction using the following formula:

$${\mathrm{D}=D}_{ew}\sin \phi +D_{ns}\cos \phi$$

(2)

in which φ is the fault strike.

To better compare the deformation trends and differences between different datasets, we create a series of cross-fault profiles of different lengths for the three displacement fields along the fault direction. This allows us to quantitatively compare the distributional changes in differences in deformation data observed along the same profile. According to the segmentation of fault rupture and the distribution characteristics of surface rupture in field investigation, we obtained a total of seven cross-fault deformation profiles. The cross-fault profile changes of four different lengths are compared, 80 km long profiles are aimed at comparing the deformation trend on the large scale of the InSAR, 40 km long profiles are aimed at comparing the deformation differences of different data within the coverage area of the optical image, and the near-field 20 km long profiles are designed to compare the characteristics of the distributional changes in large deformations near faults revealed by different data. We compare the relative displacements of the three types of data at different locations (Figure 4). Based on the displacement fields of InSAR, offset, and optical data along the fault direction, we also calculate the gradient of displacement change of the three deformation data in the vertical fault direction in order to further determine the width of the high-gradient large deformation zone along the fault zone, which is very important for the anti-fracture defense of cross-fault linear engineering.

2.3. Inversion and Comparison of Coseismic Slip Models with Different Data and Different Fault Geometric Constraints

2.3.1. Determination of the Geometric Model of the Maduo Earthquake Seismogenic Fault

We determine the location and strike of the seismogenic fault based on the surface rupture trace of the earthquake fault, obtained by offset-tracking. This information, combined with field investigation results and previous research, divides the fault into five segments. Four of these segments are the main rupture fault, while the fifth segment is a branch fault at the eastern extremity of the rupture zone [27]. Each subfault plane is discretized into several 2 km × 2 km grids, with the fault model’s depth extending to 20 km below the ground surface. We restrict the dip angle of the north-south tilted segments to be varied from 60° to 90°, and determine the optimal dip angle by the grid search method [30]. To reduce data computation and improve computational efficiency during the inversion, we downsample the coseismic deformation field using a triangular mesh. Subsequently, we invert the coseismic slip distribution using the steepest descent method (SDM) with a Poisson’s ratio of 0.25, based on the homogeneous elastic half-space dislocation model [31]. After repeated trial calculations to find the optimal solution, it is finally determined that in the five-segment fault model, segments F1–F4 are all north-dipping with dip angles of 90°, 75°, 80°, and 80°, respectively. The fifth segment, which is a branch fault at the eastern extremity of the main rupture, is south-dipping with a dip angle of 80°.

2.3.2. Inversion of Slip Distribution Models with Different Datasets and Different Fault Geometry Constraints

There are various models of slip distribution inversion for the existing research results of the Maduo earthquake. We categorize the existing model results into two main types: different fault models and different constraint datasets used in inversion. There are four types of fault models: the eastern branch of the fault, the western branch of the fault, branches at both ends of the fault, and a straight fault without branches. The different constraint datasets mainly include three types: inversion with InSAR data, inversion with GPS data, and joint inversion with InSAR and GPS data. In order to test the constraint ability of different data on different models, we set up four fault models: the eastern branch model, the western branch model, the model with branches at both ends, and the model without branches. We then use InSAR data, GPS data, joint inversion with InSAR and GPS, joint inversion with InSAR, and GPS, and offset to invert the coseismic slip distribution, and compare and analyze the differences in the inversion results of different datasets. Considering the high spatial resolution of the InSAR data and the large observation range covering the whole deformation field, we first use the InSAR ascending and descending data to invert the four fault models separately to test the influence of different fault geometries on the inversion results of fault slip distribution.

3. Results

3.1. InSAR Coseismic Deformation Field

The unwrapped interferograms and coseismic deformation field reveal that the Maduo earthquake caused a wide range of surface deformation. The maximum Line-of-Sight (LOS) relative displacement is about 2 m (Figure 5c,d), and the maximum range offset is about 2.4 m (Figure 5e,f). In the ascending deformation field, the north side of the fault line shows movement towards the satellite, while the south side shows movement away from the satellite. The deformation on both sides of the descending is exactly opposite that of the ascending, indicating a left-lateral strike-slip feature of the fault. We can judge the segmentation of the surface rupture from the changes in near-field deformation values from west to east in the coseismic deformation field. The entire deformation field appears to have two large deformation zones on both sides of the epicenter, with the deformation east of the epicenter being larger than that to the west. The deformation gradient in the near-field area on both sides of the fault is large and gradually flattens towards the far-field. Additionally, Figure 5 clearly shows that InSAR interferometric measurements can obtain a wide range of deformation, but there are many missing values near the fault trace due to incoherence (Figure 5a–d). In contrast, the offset-tracking technique can obtain continuous distribution change images of large deformation values near the fault (Figure 5e,f).

3.2. Comparative Analysis of Coseismic Displacement Field Obtained from InSAR, Offset and Optical Images

To compare and analyze the coseismic deformation fields obtained by different methods, we convert the LOS deformation fields from InSAR and offset, as well as the east-west and north-south deformations measured by optical imagery, into strike-slip deformations along the fault strike (Figure 6 and Figure 7). This conversion follows the method introduced in Section 2.2. A comparison of Figure 5 and Figure 6 reveals that the spatial distribution of the coseismic deformation field, extracted by offset-tracking and optical images, is more continuous. Even near the fault rupture trace, dense deformation data is present, clearly indicating the fault surface rupture trace locations and the geometry of the eastern branch. The coseismic deformation field extracted by the offset-tracking method appears smoother and more continuous (Figure 7b). In contrast, the deformation field measured by the optical image is noisier, with a few areas of missing values (Figure 7c). This noise is primarily attributed to the use of 10 m resolution images captured by Sentinel 2 in this study, which, due to their lower spatial resolution, result in larger noise in the extracted results. InSAR data can capture the entire deformation field (Figure 6a and Figure 7a), but the missing value phenomenon is relatively serious. This is because the Maduo earthquake area is located at the source of the Yellow River, and the lake water body is developed. InSAR can’t obtain information from the water surface. Additionally, the deformation gradient along the fault line is too large for InSAR to measure, causing data incoherence. This is also the bottleneck and challenge of InSAR using phase to observe seismic deformation.

To further quantitatively reveal the variations in coseismic deformation of the Maduo earthquake extracted by different methods, we plot seven cross-fault profiles from west to east along the fault, with the locations shown in Figure 6a. Along these seven profile locations, we plotted four sets of profiles with different lengths of 80 km, 40 km, 20 km, and 10 km across the fault, aiming to analyze the differences in three types of observation data at various magnification scales in detail (Figure 8). Comparative analysis of these profiles shows that the overall morphology of the cross-fault deformation profiles revealed by different types of data is consistent, all exhibiting an increasing deformation trend from approximately 40 km in the far field to the fault trace. InSAR and offset data reflect the overall deformation distribution from the far field to the near field, while optical imagery provides deformation within 20 km on each side of the fault. In terms of deformation magnitude, the five profiles (Profiles AA′–EE′) located in the central-western part of the fault all exhibit similar characteristics of cross-fault displacement changes. The deformation observed by optical imagery is significantly greater than that observed by InSAR and offset on the northern side of the fault, while on the southern side, the deformation observed by optical imagery is significantly less than that observed by InSAR and offset, but the results of InSAR and offset are essentially consistent.

This may be mainly related to the different deformation components observed by different technical methods. InSAR/offset observations mainly capture east-west deformation, with little contribution from north-south deformation, while optical image observations capture contributions from both east-west and north-south directions, so there are some differences in the observation results. The two profiles (FF’, GG’) located in the eastern part of the fault have good agreement with the three observations, which may be related to the fault bifurcation, and the fault strike is close to the EW direction without the NS deformation component. From the perspective of near-fault deformation, both offset and optical images can basically extract the large deformation close to the fault rupture trace. While InSAR has missing values near the fault, but the missing values vary in different sections, such as profiles DD′ and EE′ in the middle of the fault, there is a missing value only in the area of about 1 km on both sides of the fault. While in the other profiles, the width of missing values reaches 2 km or more. In general, the combination of the three types of observation data can provide a more comprehensive observation of near-field fault deformation.

In order to further reflect the width of large deformation along the fault as revealed by different observation data, we calculated the displacement gradient of the coseismic deformation field of the Maduo earthquake obtained by three different observational means (Figure 9). Figure 8 shows that the gradients of the three types of data are relatively consistent, showing that the deformation gradient along the fault trace is much larger than that on both sides of the fault. The deformation gradient on the eastern side of the fault is larger than that on the western side of the fault, and the deformation gradient is largest in the eastern branch of the fault (Figure 9). The difference is that the displacement gradient along the fault direction of the offset results reflects the gradient change of the entire deformation field more completely. The value of the offset gradient is also significantly larger than that of the other two types, especially at the location of the eastern fault bifurcation. The deformation gradient reflected by the offset reaches 350–400 mm/km, while the deformation gradient reflected by the InSAR and the optical image is 200–300 mm/km. It can be seen that the offset technique is an indispensable method to obtain large gradient deformation in near-fault.

3.3. Comparison of Near-Field Cross-Fault Strike-Slip Deformations Obtained from Different Data Sources

Comparative analysis of the InSAR, offset, and optical image results projected onto the fault strike reveals that the displacement extracted from the optical image along the entire fault zone is larger than that extracted by InSAR and offset (Figure 7 and Figure 8). However, InSAR has more missing values near the fault. In order to further quantitatively reveal the differences in near-fault coseismic deformation extracted by InSAR, offset, optical imagery, and field investigation/UAV mapping, we plot the relative displacement curves across the fault at different distances from the fault for three types of continuous-field observations (Figure 10). The specific method is as follows: based on the surface rupture trace, take 2 km as the width of the profiles along the fault strike, and calculate the relative displacement over a 1 km length range on each side of the fault at different distances. We design three comparison schemes, 1 km on each side of the fault (the yellow area in Figure 4), 1~2 km (the green area in Figure 4), and 4~5 km (the purple area in Figure 4).

The results show that within a 1 km range on either side of the fault, the relative displacements revealed by offset data and optical imagery data are quite consistent in terms of distribution morphology and deformation magnitude along the fault (Figure 10a). Both of them have two displacement peaks appearing at both the eastern and western ends, which are consistent with the field investigation results. However, the relative displacement of InSAR data fluctuates greatly and even fails to show a deformation trend. This is due to the large area of missing data caused by incoherence in the near-field area within 1 km on each side of the fault, indicating that InSAR has difficulty reflecting large deformation near the fault. Within a 1~2 km range on either side of the fault, the relative deformation trend of InSAR has good consistency with that of offset and optical images and is also close to the displacement results of field investigation (Figure 10b). However, there is still significant fluctuation at the eastern end of the fault, which may be due to the existence of the eastern branch fault, leading to a larger area of incoherence in the InSAR results, more data loss, and consequently smaller and less stable observation results. Within a 4~5 km range on either side of the fault, the results from InSAR, offset, and optical imagery are basically consistent, except that the relative deformation observed by InSAR is slightly lower than that observed by offset and optical imagery at both ends (Figure 10c). We can see that the maximum relative displacements for InSAR and offset observations are ~ 2.8 m and 4 m (Figure 10). Overall, all three are greater than the displacements from field investigations, with the deformation at the eastern end of the fault being significantly greater than at the western end, and the relative deformation shown by all three data types is relatively gentle at the western end of the fault.

3.4. Coseismic Slip Model Inversion Results Constrained by Different Datasets and Different Fault Models

The slip distribution results, derived from separate InSAR data inversions for four distinct fault models, show considerable variation (Figure 11). For the unbranched fault model, the maximum slip is 8.01 m, corresponding to a moment magnitude of Mw 7.40. In contrast, the eastern branch fault model shows a maximum slip of 4.86 m (Mw 7.40), while the western branch fault model registers a higher maximum slip of 8.54 m (Mw 7.40). The model incorporating branch faults at both ends yields a maximum slip of 5.05 m, slightly differing in its moment magnitude of Mw 7.41. Regardless of the fault geometry, the maximum slip of the inversion is located in the eastern part of the fault. The maximum slip of the no-branch and western branch fault models is located at the easternmost part of the main fault. The maximum slip of the eastern branch and both end branch fault models is located east of the epicenter. There are three obvious asperities along the fault, and the rupture reaches the surface. Due to the fact that the western branch is complex and the existence of this branch is controversial, and no evidence of surface rupture has been found either in field investigation or in imagery, we do not consider it too much [3,4,32]. We select two fault models from the above four models, the no branch fault and the eastern branch fault. Then we add GPS data to participate in the inversion to test the constraining ability of different datasets, and use GPS data, joint GPS, and the InSAR dataset to constrain the inversion of the two selected fault models, respectively (Figure 12). After several experimental tests of the model, the weight of the GPS and InSAR inversions was finally determined to be 4:1 based on the minimum matching error of the data and the model.

The inversion results of the GPS data, joint InSAR, and GPS dataset for the two models (no-branch and eastern branch fault models), respectively, show that the slips of the no-branch fault model in the inversion of both datasets are larger than those of the eastern branch fault model (Figure 12). The slip of the eastern branch fault model in the joint inversion of the InSAR and GPS dataset is larger than that in the inversion of the GPS data. The maximum slips of the no-branch and eastern branch fault models in the separate inversion of GPS data are 6.74 m and 4.48 m, respectively. While the maximum slips of the no-branch and eastern branch fault models in the joint inversion of the InSAR and GPS datasets are 6.73 m and 5.49 m, respectively. The results show that the maximum slip occurs near the eastern triple point of the fault, and the slip rupture depth of the eastern part of the fault is larger than the rupture depth of the western part of the fault. Which is consistent with the model results of predecessors, regardless of GPS inversion, InSAR data inversion, or InSAR and GPS dataset inversion jointly. However, the addition of the eastern branch fault significantly reduces the slip in the eastern part of the main rupture zone.

Due to the problem of near-field incoherence in the InSAR data, masking the coseismic deformation field makes the InSAR near-field data missing. This limitation significantly restricts the ability of InSAR data to constrain near-field slips. However, offset results effectively capture the deformation in the fault’s near-field. To leverage this advantage, we have incorporated the offset results into our inversion tests to examine their impact on constraining the inversion process. Considering that the deformation accuracy of the InSAR observation is higher than the offset, only the offset region corresponding to the InSAR incoherent region is selected to make up for the missing data in the InSAR near-field. We use two datasets, InSAR and offset, and GPS and InSAR and offset, respectively, to invert the slip distribution of the no-branch fault model and the eastern branch fault model (Figure 13). For the weights of the data in the joint inversion, we conducted multiple inversion tests with different data weights. We finally set the weights of GPS, InSAR, and offset as 8:2:1, which makes the data and the inverted model fit well. The maximum slip of the no-branch and eastern branch fault models based on InSAR and offset data inversion is 8.64 m and 6.05 m, respectively. The maximum slips obtained from the no-branch and eastern branch fault models based on the joint inversion of GPS, InSAR, and offset data are 7.26 m and 5.55 m, respectively. The area with the maximum slip is still located at the eastern triple point of the fault, and our slip distribution results are also consistent with the results that the eastern deformation of the coseismic deformation field is larger than the western deformation. We find that the maximum slip of the model without a branch on the east side of the fault is much larger than that of the model with a branch, which indicates that the influence of the fault geometry model on the inversion results of the slip distribution is significant. Figure 14 and Figure 15 show the residuals of the eastern branch fault model inverted by GPS, InSAR, and offset.

4. Discussion

4.1. The Ability of Different Observation Methods to Identify Near-Fault Deformation

The distribution change characteristics of the near-field deformation not only provide important constraints for the fine inversion of the slip distribution model in the deep part of the fault but also serve as an important basis for the anti-disruption defense of the linear engineering facilities across the fault. In this paper, we use the coseismic displacement data obtained by three technical methods: InSAR, offset/optical imagery, and field investigation/UAV mapping, to comprehensively compare the deformation characteristics of the Maduo earthquake. In particular, we quantitatively compare and analyze the differences in cross-fault deformation revealed by different data in the area of several kilometers near the fault. The results show that the closer to the fault, the greater the difference in deformation obtained by InSAR, offset, and optical image data. For example, within 1 km on each side of the fault, the InSAR result fluctuates greatly, while the other two results have a similar trend (Figure 10a). The difference in deformation obtained by InSAR, offset, and optical imagery decreases in regions farther away from the fault. In the range of 4~5 km on each side of the fault, the relative deformation revealed by all three types of data tends to be consistent along the fault (Figure 10c). This difference in change is actually related to the deformation characteristics of the fault zone and the observation ability of different technical methods. The fault zone is not a simple flat surface but a complex fracture zone, including the core of the strain concentration and the wing of the crack development [33]. When the earthquake struck, explicit dislocations occurred in the core of the fault rupture zone, which directly broke the gullies, roads, ruts, and other ground features, and field investigations and UAV measurements could effectively extract this dislocation deformation [3,12,13]. However, fault coseismic deformation is much more than this, and a large number of microfractures are generated in the peripheral region of the fault core to absorb slips occurring on the deeper fault plane. The distributed deformation generated by these micro-ruptures cannot be visually identified and can only be extracted by InSAR and optical imagery [5,34]. Theoretically, InSAR can obtain the entire coseismic deformation field, but actually, InSAR is difficult to obtain large gradient deformation near the fault due to the limitation of coherence. In the case of the Maduo earthquake, reliable observations can only be obtained by InSAR in areas more than 2 km away from the fault. Both offset and optical images extract deformation through the cross-correlation of pixel scattering intensities before and after the earthquake, and are not constrained by phase incoherence. So this method is suitable for extracting large deformation on scales ranging from several meters to several kilometers near the fault, and the accuracy of the extracted deformation depends on the resolution of the images used. In summary, different methods have their own advantages, and the combination of multiple methods and complementary advantages can give a complete and fine expression of the seismic deformation field.

4.2. Differences in Slip Models Constrained by Different Datasets

Based on the testing of four fault models using InSAR, we found that the existence of the eastern branch has a significant impact on the fault slip distribution. Considering that the aftershock distribution and InSAR deformation field both show the eastern branch trace. Therefore, we select no-branch and eastern branch fault models and invert them with different datasets to test the constraint capabilities of different data on the slip distribution models. Comparing different slip models, we found that in the slip distributions inverted by InSAR and GPS data, the slip rupture reaches the surface, while the slip distribution inverted with offset data does not reach the surface with the maximum slip. There is a small amount of slip deficit in the shallow surface region. This may be because the near-field GPS stations are sparse and unevenly distributed, and the missing data caused by the InSAR near-field incoherence cannot constrain the slip situation of the near field. The inclusion of the selected offset data in the inversion makes up for the vacancy in the InSAR data constraints and provides some constraints on the near-field slip distribution. Based on the data and model fitting, as well as the minimum error, we ultimately select the eastern branch fault model based on the joint inversion of GPS, InSAR, and offset as the optimal model for the Maduo coseismic slip distribution, with a maximum slip of 5.55 m. There is a small amount of slip deficit in the shallow crust, and the maximum slip is distributed at the eastern triple junction of the fault. Compared with existing slip models, the slip distribution features in the models based on GNSS data inversion are independent and concentrated [8,17,19], while our final model shows a more continuous slip distribution. In terms of the magnitude of the slip, the maximum slip of our model is much smaller than the slip of 9.3 m [25]. Most of the existing models are based on InSAR or GPS inversion, or based on the joint inversion of the InSAR and GPS datasets. However, our model has been improved by adding offset data to make up for the lack of large deformation near faults.

5. Conclusions

We compared the characteristics of three types of distributed deformation fields of the Maduo earthquake through cross-fault sections, and quantitatively compared the relative displacement values observed by InSAR, offset, and field surveys. We inverted the coseismic slip distribution based on different observation data and fault models. From the results, our key findings include: (1) From west to east, the cross-fault displacement of the Maduo coseismic deformation field gradually increases, and the InSAR data incoherent region also increases from small to large. (2) The displacement gradient shows that the deformation on both sides of the epicenter shows a different pattern. The deformation gradients of InSAR, offset, and optical images all show that the deformation gradient is <200 mm/km west of the epicenter, while the deformation gradient is >200 mm/km east of the epicenter. (3) The maximum relative displacements for InSAR and offset observations are ~2.8 m and 4 m, respectively. A quantitative comparison study of cross-fault profiles shows that within 2 km, InSAR data cannot effectively reflect the deformation trend, while offset and optical imagery can. Beyond 2 km, InSAR, offset, and optical imagery show relatively consistent deformation trends. (4) The branch at the eastern end of the fault has a great influence on the slip distribution, and the slip on the main fault increases significantly when there is no branch at the eastern end. The inverted results show that the eastern branch fault model with GPS, InSAR, and offset data is the optimal coseismic slip distribution model for the Maduo earthquake, and the maximum slip is 5.55 m.