Study of the Characteristics of a Co-Seismic Displacement Field Based on High-Resolution Stereo Imagery: A Case Study of the 2024 MS7.1 Wushi Earthquake, Xinjiang

Abstract

The precise characterization of surface rupture zones and associated co-seismic displacement fields from large earthquakes provides critical insights into seismic rupture mechanisms, earthquake dynamics, and hazard assessments. Stereo-photogrammetric digital elevation models (DEMs), produced from high-resolution satellite stereo imagery, offer reliable global datasets that are suitable for the detailed extraction and quantification of vertical co-seismic displacements. In this study, we utilized pre- and post-event WorldView-2 stereo images of the 2024 Ms7.1 Wushi earthquake in Xinjiang to generate DEMs with a spatial resolution of 0.5 m and corresponding terrain point clouds with an average density of approximately 4 points/m². Subsequently, we applied the Iterative Closest Point (ICP) algorithm to perform differencing analysis on these datasets. Special care was taken to reduce influences from terrain changes such as vegetation growth and anthropogenic structures. Ultimately, by maintaining sufficient spatial detail, we obtained a three-dimensional co-seismic displacement field with a resolution of 15 m within grid cells measuring 30 m near the fault trace. The results indicate a clear vertical displacement distribution pattern along the causative sinistral–thrust fault, exhibiting alternating uplift and subsidence zones that follow a characteristic “high-in-center and low-at-ends” profile, along with localized peak displacement clusters. Vertical displacements range from approximately 0.2 to 1.4 m, with a maximum displacement of ~1.46 m located in the piedmont region north of the Qialemati River, near the transition between alluvial fan deposits and bedrock. Horizontal displacement components in the east-west and north-south directions are negligible, consistent with focal mechanism solutions and surface rupture observations from field investigations. The successful extraction of this high-resolution vertical displacement field validates the efficacy of satellite-based high-resolution stereo-imaging methods for overcoming the limitations of GNSS and InSAR techniques in characterizing near-field surface displacements associated with earthquake ruptures. Moreover, this dataset provides robust constraints for investigating fault-slip mechanisms within near-surface geological contexts.

1. Introduction

Surface deformation induced by strong earthquakes has consistently been a pivotal focus in seismology and structural geology research. Such seismic events commonly result in pronounced surface ruptures, accompanied by distinctive co-seismic displacement fields [1,2,3]. As direct manifestations of seismic activity, the geometry and spatial patterns of these surface ruptures, together with their corresponding co-seismic displacement fields, explicitly reveal the rupture propagation pathways and intricate dynamic mechanisms underlying earthquakes. Furthermore, these surface expressions encapsulate crucial insights into the variations in stress fields preceding and succeeding seismic events [4,5,6,7]. High-precision observations of surface ruptures, coupled with quantitative analyses of co-seismic displacement fields, provide robust evidence that is critical for elucidating rupture dynamics, characterizing fault activity, and identifying the spatial and geometric properties of faults. Such rigorous analysis significantly advances our comprehension of regional stress-field evolution, both temporally and spatially [8,9,10,11,12]. Additionally, these detailed deformation data constitute an indispensable scientific basis for seismic hazard assessments, emergency response planning following earthquakes, and strategic decision making for disaster mitigation [13,14].

Field surveys conducted after earthquakes represent traditional methods for documenting co-seismic displacement fields near faults, providing direct and intuitive evidence of surface rupture features. However, these measurements typically rely on assessing displacement from specific geomorphic markers; they are thus inherently constrained by the precision of the available measurement techniques and accessibility limitations in challenging terrains. In contrast, UAV platforms equipped with high-resolution visible-light and multispectral cameras can, in the immediate aftermath of an earthquake, acquire wide-area, high-definition surface imagery of the affected region and—through aerial survey data—produce orthophotos and digital elevation models (DEMs), thereby effectively supplementing the spatial information gaps of traditional field measurements. However, in practice, this approach is constrained by weather, environmental factors, and airspace regulations, and its limited endurance and flight coverage make it less cost-effective and more difficult to deploy over extensive surface rupture zones [15]. Consequently, it remains difficult to achieve comprehensive and precise measurements of co-seismic displacement across extensive regions, with local displacement assessments potentially subject to inaccuracies.

Currently, advanced geodetic and remote sensing techniques, including global navigation satellite systems (GNSS), interferometric synthetic aperture radar (InSAR), and optical imagery subpixel correlation, are effective and complementary methods for studying co-seismic displacement fields [16,17]. GNSS enables precise measurements of co-seismic displacements at sub-centimeter accuracy across extensive spatial scales [18]. Nonetheless, the inherently sparse spatial distribution of GNSS observation points, particularly in localized areas, restricts its ability to accurately resolve detailed vertical displacement patterns in proximity to fault zones [2,19,20,21]. InSAR techniques frequently face significant challenges in near-fault zones (typically within ~1–2 km of fault traces), where pronounced surface ruptures and complex topographic disturbances produce steep deformation gradients. Such gradients severely degrade interferometric phase coherence, causing densely packed or overlapping interferometric fringes that commonly result in phase unwrapping errors and compromised measurement accuracy [22,23]. Although optical remote sensing imagery combined with subpixel correlation techniques effectively resolves detailed horizontal co-seismic displacement fields from high-resolution pre- and post-earthquake images, its sensitivity to vertical displacements remains comparatively limited. Despite the partial improvements achieved through multi-angle or stereo imagery approaches, accurately characterizing vertical co-seismic displacements within near-fault zones continues to pose substantial challenges [24,25]. Therefore, accurately retrieving fine-scale vertical co-seismic displacement fields near fault traces continues to be a prominent challenge and research direction in seismic studies.

In recent years, the increasing availability of high-resolution three-dimensional topographic datasets, including digital elevation models (DEMs) and light detection and ranging (LiDAR) point clouds, has provided valuable datasets for differential geomorphological analyses, enabling the precise quantification of vertical co-seismic displacement fields across earthquake rupture zones [26]. Methods involving co-registration and differential analysis of pre- and post-earthquake DEMs, derived from high-resolution stereo imagery, have demonstrated substantial potential for accurately extracting vertical co-seismic displacement fields. In particular, by generating comprehensive displacement maps spanning the entire surface rupture zone and calculating vertical displacement vectors from pre- and post-event point cloud datasets, these approaches effectively produce high-resolution and precise measurements of vertical co-seismic deformation.

In this study, we selected the 2024 MS7.1 Wushi earthquake in Xinjiang as a representative case to investigate vertical co-seismic deformation. Using the Iterative Closest Point (ICP) algorithm, we accurately co-registered and performed differential analysis of pre- and post-earthquake DEMs derived from high-resolution stereo imagery acquired by the WorldView-2 satellite, subsequently deriving the vertical component of the three-dimensional co-seismic displacement field. A classical and widely employed method in three-dimensional data registration, the ICP algorithm iteratively establishes nearest-neighbor correspondences between source and target point clouds, systematically minimizing the Euclidean distances between these point pairs. Through this iterative process, the ICP algorithm determines an optimal rigid-body transformation—comprising rotation and translation—to achieve the precise global alignment of the point clouds [27,28]. This technique has been effectively adapted in recent earthquake deformation studies, demonstrating its ability to robustly retrieve high-resolution, detailed co-seismic displacement fields [29,30].

In advanced investigations within seismology and structural geology, ICP-based surface deformation extraction has proven highly effective and has been successfully applied in several notable seismic events. For example, following the 2011 Mw7.1 Fukushima earthquake in Japan [12], the 2013 Mw7.7 Balochistan earthquake in Pakistan [31], and the 2016 Mw7.0 Kumamoto earthquake along the Futagawa–Hinagu fault zone in Japan [32], researchers employed the ICP algorithm to align high-resolution pre- and post-event three-dimensional point clouds. These efforts enabled the precise reconstruction of co-seismic displacement fields, demonstrating the method’s robustness and accuracy in capturing complex surface deformation patterns associated with major fault ruptures. Practical experience indicates that the effectiveness and final accuracy of the ICP algorithm not only depend on its implementation and parameter settings but are also heavily reliant on the quality and spatial resolution of the input point cloud data. In situations with severe surface ruptures, major changes in surface cover, or large differences in viewing angles between pre- and post-event acquisitions, basic ICP methods may fail to achieve reliable alignment. To address these challenges, additional preprocessing steps or improved ICP variants—such as feature-constrained alignment, multi-resolution (pyramid) approaches, or local filtering techniques—are often required to ensure stable and accurate registration results.

This study first outlines the complete technical workflow for generating digital elevation models (DEMs) from WorldView-2 satellite stereo imagery. It then presents a detailed introduction to the Iterative Closest Point (ICP) algorithm, including its theoretical foundations, implementation steps, and an analysis of its strengths and suitable application scenarios for three-dimensional point cloud registration and differential measurement. By applying this method to pre- and post-earthquake point cloud datasets covering the surface rupture zone and surrounding buffer areas of the 2024 MS7.1 Wushi earthquake in Xinjiang, we successfully extracted the vertical co-seismic displacement field.

Following the generation of the vertical displacement field, we further investigated how different window sizes and step lengths used during the ICP processing affect measurement accuracy. In addition, we conducted a comparative analysis to evaluate the validity of various vertical displacement measurement methods. Special attention was given to the complex conditions near the rupture zone, such as steep deformation gradients and significant surface disruptions, where differences in accuracy among these methods became more pronounced. By comprehensively assessing factors including parameter selection, field observations, and data quality, we ultimately identified a vertical co-seismic displacement result that closely aligned with field-measured trends and accurately captured the characteristics of surface deformation.

Strong seismic events are frequently associated with a phenomenon known as the “shallow slip deficit,” where co-seismic displacement values observed at the surface—typically derived from field measurements—are significantly lower than the deeper fault slip inferred from interferometric synthetic aperture radar (InSAR) or other geodetic and seismological inversion techniques [33]. Such discrepancies are commonly attributed to multiple factors. First, fault maturity and subsurface heterogeneity can lead to an uneven distribution of slip [34], with greater displacement occurring at depth than near the surface [35,36]. Second, traditional field-based measurement techniques, which rely on discrete geomorphic markers, often underestimate total displacement by failing to capture the deformation distributed across broader zones. Therefore, disentangling the relative contributions of subsurface slip heterogeneity and the inherent limitations of surface measurements is essential for accurate fault displacement assessment. However, in practical applications, SAR interferograms frequently suffer from coherence loss within 1–2 km of fault traces due to steep phase gradients, resulting in data gaps that hinder researchers’ ability to fully resolve near-surface deformation and total fault slip.

In this study, high-resolution DEMs derived from stereo satellite imagery and processed using the ICP algorithm enabled the extraction of detailed vertical co-seismic displacement fields. These results effectively bridge observational gaps that are often overlooked during field surveys or when using conventional remote sensing techniques, offering valuable insights into near-field deformation in shallow fault zones that are typically inaccessible to traditional InSAR methods.

2. Seismotectonic Setting

On 23 January 2024, an Ms7.1 earthquake struck the Wushi region in Xinjiang. According to observations recorded by the China Earthquake Networks Center (CENC), the focal depth of this seismic event was approximately 22 km. The mainshock was followed by a total of 6282 aftershocks, including eight notable events with magnitudes between Ms 5.0 and 5.7. This earthquake represents the most significant seismic activity recorded within the Tianshan seismic belt since the Ms 7.3 Suusamyr earthquake in Kyrgyzstan in 1992 [37].

The Tianshan seismic belt, a prominent intracontinental tectonic deformation zone within Eurasia, is bordered by the Junggar Basin and Kazakh platform to the north and the Tarim Basin to the south (Figure 1). Since the Cenozoic, the ongoing northward convergence of the Indian plate against the Eurasian plate at a rate of approximately 46 mm/a has resulted in substantial secondary block deformation and fault activity within the Tibetan Plateau. Approximately 6–9 mm/a of this convergence is accommodated by the northwestern Tianshan region, making this area a primary zone for releasing the northwestern component of motion associated with the India–Eurasia collision [38,39,40].

Focal mechanism solutions and aftershock distribution patterns indicate that the 2024 Wushi earthquake was characterized by predominantly thrust-type motion combined with a component of left-lateral strike–slip displacement. The epicenter was located approximately 6 km from the Maidan–Shahylam fault zone—a west-dipping Holocene-active fault zone [38]. Historically, seismic activity along this fault zone has been relatively weak [41], resulting in sparse geodetic data and limited systematic research, especially on the western segment. The most recent paleo-earthquake event documented in this fault segment occurred around 40–480 AD, with an estimated magnitude of Mw7.5 [42]. According to studies conducted by Wu et al. [43], the geological shortening rate along the Maidan fault during the Late Quaternary was estimated at approximately 1.19 ± 0.25 mm/a. GPS-derived geodetic measurements further indicate a shortening rate ranging between 1.15 and 2.10 mm/a, accompanied by a left-lateral strike–slip rate of approximately 1.56 ± 0.64 mm/a [38,44].

Figure 1. (a) Tectonic setting of the Tianshan region and surrounding areas, showing the location of the detailed study area (figure (b)). (b) Tectonic setting of the 2024 Wushi earthquake. The thin and thick black lines are faults [45]. The black dashed line denotes the trace of the blind fault [45]; the red star indicates the epicenter of the Wushi earthquake (from the GCMT); the large red circles represent historical earthquakes with magnitudes of Ms ≥ 7.0, while the small red circles indicate historical earthquakes with magnitudes between Ms 6.0 and 7.0. MDF: Maidan Fault, KTF: Kalpin Tagh Fault, TSF: Toshgan Fault, DSXF: Dashixia Fault, KKSF: Kukesale Fault. The focal mechanism solution indicates that the mainshock was mainly a reverse faulting event with a subordinate strike-slip component.

Figure 1. (a) Tectonic setting of the Tianshan region and surrounding areas, showing the location of the detailed study area (figure (b)). (b) Tectonic setting of the 2024 Wushi earthquake. The thin and thick black lines are faults [45]. The black dashed line denotes the trace of the blind fault [45]; the red star indicates the epicenter of the Wushi earthquake (from the GCMT); the large red circles represent historical earthquakes with magnitudes of Ms ≥ 7.0, while the small red circles indicate historical earthquakes with magnitudes between Ms 6.0 and 7.0. MDF: Maidan Fault, KTF: Kalpin Tagh Fault, TSF: Toshgan Fault, DSXF: Dashixia Fault, KKSF: Kukesale Fault. The focal mechanism solution indicates that the mainshock was mainly a reverse faulting event with a subordinate strike-slip component.

The 2024 Wushi earthquake constitutes the first Mw ≥ 7.0 event recorded on this fault, interrupting a long-standing period of low-level seismicity within the region. The fault zone, approximately 15–17 km wide, comprises multiple sub-parallel secondary faults, which are predominantly characterized by thrust movements accompanied by left-lateral strike–slip deformation, collectively exhibiting a northwestward dip [46].

The results of UAV photogrammetry and field surveys conducted by Zhang et al. [47] reveal that, within the Qialemati River valley segment, the central portion of the rupture zone predominantly features thrust fault scarps, compressional bulges, and associated secondary fissures, extending approximately 1 km along the strike. Both ends of the rupture zone extend into bedrock regions, resulting in a total rupture length of approximately 4.6 km. Geomorphic units such as unpaved roads, active riverbeds, floodplains, terraces, and gully floors situated along the rupture zone were conspicuously offset by fault activity, forming fresh scarps trending predominantly northwest or southeast. According to field measurements conducted on exposed fault surfaces, the vertical offsets ranged between approximately 30 cm and 100 cm. Although localized evidence of relative uplift on the footwall was occasionally observed, the overall displacement predominantly showed uplift of the hanging wall. No prominent evidence of significant strike–slip displacement was documented, consistent with a predominantly reverse faulting mechanism within this region.

The distribution of co-seismic fault scarps along the rupture zone exhibited a gradual decrease in scale from the central segment toward both western and eastern extremities. Surface ruptures primarily intersected Quaternary conglomerate layers or elevated geomorphic surfaces, resulting in multiple sets of tensile fractures, ranging from a few to several tens in number, either parallel or orthogonally intersecting each other. These tensile fissures likely developed through the combined influences of thrust faulting and gravitational loading from local topography, thus reflecting both the dominant role of tectonic compression in surface deformation and the modifying effects of topographic loading on the local rupture patterns.

3. Data and Methods

3.1. DEM Extraction Based on WorldView-2 Stereo Pairs

Three-dimensional datasets such as digital elevation models (DEMs) and LiDAR (light detection and ranging) point clouds provide high-precision topographic information that is crucial for the quantitative study of active tectonics. These datasets have significant applications in analyzing and comparing pre- and post-earthquake topographic changes and assessing seismic impacts, serving as fundamental sources for investigating fault displacement, slip rates, and fault geometry. In this study, we utilize point cloud data and DEMs derived from WorldView-2 satellite stereo imagery. WorldView-2, launched in 2009 by Maxar Technologies, is the second satellite in the WorldView series and is equipped with a high-resolution multispectral sensor offering spatial resolutions of up to 0.46 m. This high resolution enables the precise characterization of the Earth’s surface at detailed scales. The sensor aboard WorldView-2 captures imagery across eight spectral bands, including visible and near-infrared spectra, and it has a wide swath width of approximately 16.4 km, allowing for multiple imaging passes over the same area within short intervals [48]. As a high-resolution optical remote sensing platform, WorldView-2 provides a robust data foundation for extracting terrain information. Compared to traditional LiDAR point cloud data—which typically offers higher precision but relies heavily on costly field-based acquisitions that are subject to weather conditions and geographic complexities—WorldView-2 satellite imagery is more accessible, has broader coverage, and possesses stronger repeat observation capabilities. These advantages effectively overcome LiDAR’s temporal and spatial limitations, significantly enhancing research efficiency while simultaneously meeting the precision requirements necessary for active tectonics research. Such strengths underscore the unique technical advantages and research value of WorldView-2 satellite data, which are particularly thoroughly demonstrated in this study’s high-precision spatiotemporal deformation analysis of the three-dimensional co-seismic displacement field associated with the 2024 Wushi earthquake.

The study area is situated northwest of Wushi County in the Aksu region, Xinjiang, adjacent to the Maidan–Shahylam fault zone. To analyze surface deformation before and after the Wushi earthquake, we acquired multispectral stereo image data from WorldView-2 for February 2019 and October 2024 (

Table 1. Detailed information about the WorldView-2 stereo imagery used.

NO.	Sensor	Product Level	Product ID	Acquisition Date	Cloud Coverage	Coordinate System
1	Linear array camera	Level-2A	050250350	16 February 2019	10.2%	WGS1984
2	Linear array camera	Level-2A	017345495	15 October 2024	1.5%	WGS1984

). Using remote sensing software platforms such as PCI (v2016), we extracted high-precision DEMs and corresponding point cloud data from these stereo images, establishing baseline datasets representing pre- and post-earthquake conditions in the Wushi region. However, due to factors such as post-seismic land-cover changes, observational noise, satellite attitude deviations, and image distortions, elevation values for certain pixels exhibit systematic biases, subsequently affecting data accuracy and reliability. Thus, establishing a rigorous data preprocessing and registration calibration workflow is essential prior to extracting vertical displacement fields for the Wushi earthquake. This workflow involves strategically placing ground control points (GCPs), employing refined stereo-matching algorithms, and implementing multi-scale filtering and noise suppression strategies to guarantee sufficient precision and stability in differential analyses. The specific procedural steps (Figure 2) are as follows:

(1)

Data input and projection setup: input stereo imagery data, define a consistent universal transverse mercator (UTM) projection coordinate system tailored to the local zone (Northern Hemisphere Zone 44, EPSG: 32644), and set units to meters to facilitate accurate subsequent computations.

(2)

Absolute orientation and control point extraction: utilize automatic control-point extraction methods based on reference DEMs and orthorectified imagery, inputting geographic locations and elevation information of these points to complete absolute orientation. This step ensures spatial consistency among different image datasets, effectively reducing systematic errors induced by satellite attitude and image distortions.

(3)

Ground tie-point collection: collect more than 150 ground tie-points from the oriented imagery, ensuring their root mean square (RMS) errors remain within 1.5 to achieve high positional matching accuracy across datasets.

(4)

DEM parameter configuration and extraction: define suitable DEM resolution, terrain detail levels, and sampling intervals according to research objectives, ultimately generating a DEM with a spatial resolution of up to 0.5 m. This DEM accurately reflects the terrain morphology within the study area and corrects systematic errors resulting from satellite attitude deviations and image distortion effects.

In this study, we initially integrated vector data representing the primary seismogenic fault of the mainshock with a Digital Elevation Model (DEM). The fault zone extends approximately 4.6 km in length and dips toward the northwest (NW). Using this linear fault data as the baseline, we established a buffer zone characterized by a composite geometry consisting of rectangular and semicircular sections, with a buffering radius set to 2 km. This buffer zone was designated as the core area for extracting the co-seismic displacement field, featuring sparse vegetation coverage and minimal anthropogenic structures, while also encompassing representative geomorphic units such as river channels, bedrock regions, and alluvial fans (Figure 3). Subsequently, we utilized Global Mapper software (v23) to generate point cloud data from the integrated DEM within the defined study area. The point cloud was constructed to ensure a consistent point spacing of 0.5 m, with elevation values for each point directly corresponding to the center of the respective pixel cells in the original DEM.

3.2. Iterative Closest Point (ICP) Algorithm

The Iterative Closest Point (ICP) algorithm is a high-precision 3D registration technique based on point cloud data and is widely applied in geomorphic-structural evolution analysis, hazard monitoring, and geophysical investigations [28]. Its core objective is to perform a rigid-body transformation (including rotation and translation) between two (or more) point cloud datasets acquired at different times, from different perspectives, or using different sensors, thereby achieving optimal alignment in three-dimensional space and minimizing registration errors (Figure 4) [29]. By iteratively searching for and matching corresponding point pairs, ICP enables the unification of point clouds that initially contain positional discrepancies or observational deviations into a common spatial reference frame. This process provides a high-resolution and finely aligned observational foundation for in-depth studies of terrain relief, tectonic deformation, and geological hazards. When investigating co-seismic deformation using pre- and post-earthquake point cloud datasets, the ICP algorithm plays a pivotal role. Typically, the two point clouds—acquired before and after an earthquake via LiDAR, UAV photogrammetry, or high-resolution satellite stereo imagery—differ in terms of the data source, viewing geometry, and sampling resolution. Through successive iterations, ICP identifies and matches corresponding geomorphic features (e.g., ridgelines, river valleys, fault traces, or other prominent landform textures) and solves for the rigid-body transformation matrix that best aligns the datasets. The algorithm minimizes the Euclidean distance—or other customized distance metrics—between matched point pairs, ultimately yielding optimized registration parameters consisting of both a translation vector and a rotation matrix [30].

The standard workflow of ICP registration includes the following steps. Initialization of correspondences: the two-point clouds are designated as M and N. For each point mᵢ in cloud M, the closest point nᵢ in cloud N is found such that the Euclidean distance between mᵢ and nᵢ is minimized. Computation of rigid transformation: based on the established correspondences, the transformation matrices A (rotation) and B (translation) are computed so as to minimize the root mean square error (RMSE) of Euclidean distances between m_i and n_i. Iterative optimization: the correspondence and transformation estimation process is repeated until either the number of iterations reaches a predefined threshold or the RMSE of all point pairs falls below a specified tolerance. At this point, the alignment is considered complete, and the final transformation matrix φ is obtained.

The point cloud datasets M and N satisfy the following equivalence relationship:

$$\mathrm{M}=\left[\begin{array}{ccc}1& -\gamma & \beta \\ \gamma & 1& \alpha \\ -\beta & \alpha & 1\end{array}\right]\mathrm{N}+\left[\begin{array}{c}tx\\ ty\\ tz\end{array}\right]$$

(1)

where α, β, and γ represent the rotation angles around the x, y, and z axes, respectively, following the counterclockwise convention for positive rotation. The parameters tx, ty, and tz denote the translational displacements along the x, y, and z directions, respectively. During the iterative optimization process, in order to facilitate the calculation of the root mean square error (RMSE), the translation matrix A and the rotation matrix B can be combined into a single 3D rigid-body transformation matrix, denoted as φ:

$$\mathrm{\phi }=\left[\begin{array}{cccc}1& -\gamma & \beta & tx\\ \gamma & 1& \alpha & ty\\ -\beta & \alpha & 1& tz\\ 0& 0& 0& 0\end{array}\right]$$

(2)

Under the ICP algorithm framework, the point cloud registration error E—defined as the root mean square error (RMSE) between two point clouds—can be expressed as the sum of the Euclidean distance differences between the source point cloud M and the target point cloud N, where N_i denotes the i-th closest corresponding point in N to the i-th point in M:

$$\mathrm{E} (\mathrm{A}, \mathrm{B})=\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left|(\mathrm{\phi }\mathrm{N}-\mathrm{M})·\mathrm{n}\mathrm{i}\right|2}$$

(3)

3.3. Calculation of the 3D Co-Seismic Displacement Field of the Wushi Earthquake

To extract co-seismic deformation using the Iterative Closest Point (ICP) algorithm, it is essential to ensure the data quality and accuracy of both pre- and post-earthquake point clouds, as well as the existence of valid overlapping regions between them. On the one hand, a higher degree of overlap and consistency in viewing geometry can effectively reduce uncertainties during the matching process. On the other hand, large discrepancies in point cloud resolution or uneven sampling density may lead to mismatches or convergence issues during ICP iterations. In this study, the ICP algorithm was implemented and optimized within the MATLAB (v2022a) programming environment. Through this approach, the accurate registration of 3D point cloud data was achieved, and the corresponding spatial transformation parameters—namely, the rotation matrix and the translation matrix—were computed. The translation matrix contains a three-dimensional displacement vector that characterizes the spatial distribution of the co-seismic displacement field. Specifically, it captures the strike–slip component along the fault strike, the extensional component perpendicular to the fault, and the vertical displacement component normal to the Earth’s surface.

In the data processing workflow (Figure 5), the pre-earthquake point cloud (denoted as Wpre) and the post-earthquake point cloud (Mpost) were first subjected to grid-based preprocessing to enhance processing efficiency and accuracy. Subsequently, co-seismic displacement was calculated over the study area using a spatial sliding window approach with variable step sizes and multiple window dimensions. This multi-scale analysis method not only improves the robustness of the displacement field estimation but also mitigates the influence of local outliers on the overall results. The final transformation matrix φ obtained through the ICP procedure can be decomposed into two fundamental components: the translation matrix A and the rotation matrix B, which together describe the complete spatial transformation between the pre- and post-seismic point clouds. This quantitative representation enables a more accurate analysis and interpretation of the spatial distribution characteristics of the co-seismic deformation field and the underlying kinematic mechanisms.

3.4. Measurement of Near-Fault Co-Seismic Displacements

Following the acquisition of the three-dimensional co-seismic displacement field for the study area, this research adopts a comparative multi-method analytical approach to systematically extract near-fault co-seismic displacement along the fault strike. Three different techniques were employed: the line fitting equation method, the mean value difference method, and the buffer zone statistics method. The displacement results derived from each approach were compared against field-measured displacement values to assess their accuracy. The objective is to evaluate the applicability, reliability, and precision differences among these quantification methods under varying geomorphic contexts of the Wushi earthquake, such as bedrock regions and piedmont alluvial fans, as well as across different displacement magnitude ranges (e.g., 0–1 m, >1 m). Through this comparative analysis, the study aims to identify the most accurate and geologically consistent method for quantifying near-fault co-seismic displacement in the Wushi earthquake rupture zone.

3.4.1. Line-Fitting-Based Displacement Estimation Method

The line-fitting-based displacement estimation method is based on the linear characteristics of point cloud data on both sides of the fault; it aims to extract co-seismic displacement by constructing a linear model that describes displacement variation across the fault (Figure 6a). The core principle involves the following steps: first, based on the predefined fault zone width, displacement field point clouds within a certain distance from both sides of the fault are extracted from pre- and post-earthquake datasets. Linear regression is then applied separately to the point clouds on each side, resulting in two fitted straight lines that characterize the displacement gradient. Each fitted line is extended toward the boundary of the fault zone. The vertical coordinate difference (Y-value) between corresponding points on the extended lines at the same fault-normal distance is computed, which represents the co-seismic displacement at that location.

To systematically extract fault displacement information from the co-seismic displacement field image, transects perpendicular to the fault strike were constructed at regular intervals of 30 m along the fault. In total, 157 profile lines were generated, each 400 m in length (200 m extending into the hanging wall and 200 m into the footwall). For each transect, a rectangular buffer zone with a width of 160 m (±80 m from the centerline) was created to extract the local displacement point cloud. Within each buffer zone, the horizontal axis (X) represents the point’s perpendicular distance to the transect centerline, while the vertical axis (Y) denotes the corresponding displacement value. A two-dimensional scatter plot is generated to visualize the local displacement gradient. The effective fault width is determined by analyzing the spatial distribution of central point values, after which linear regression is applied separately to the datasets on each side of the fault to obtain the respective first-order equations. Once the fitted lines are extrapolated across the full fault zone width, the Y-value differences at corresponding positions are calculated, yielding a series of displacement values distributed along the fault strike.

Finally, these displacement values are projected back onto the fault trace and visualized in a two-dimensional map to construct the spatial distribution of near-fault vertical co-seismic displacement.

3.4.2. Mean Value Difference-Based Displacement Estimation Method

The mean value difference method is a widely used approach for quantifying co-seismic displacement, fault scarp height, and other geological parameters, particularly in studies utilizing three-dimensional datasets such as InSAR, LiDAR, or DEM. Its core concept lies in leveraging the statistical characteristics of point cloud data on either side of a fault to quantify co-seismic deformation through the computation of mean displacement values (Figure 6b). Nissen et al. (2014) [12] applied this method in their analysis of the 2011 Fukushima–Hamadori earthquake in Japan, demonstrating its effectiveness and a high degree of automation in earthquake deformation studies.

The fundamental principle of this method is as follows: after defining the width and influence zone of the fault, displacement point cloud data are extracted from both the hanging wall and footwall within a specified range. Statistical analysis is then performed to calculate the mean displacement value on each side. The co-seismic displacement at that location is defined as the difference between the two means. This method offers several advantages, including ease of implementation, high automation potential, and an intuitive representation of the overall distribution pattern of point cloud data.

In this study, we applied the method to 157 previously defined buffer zones. For each buffer zone, all available point cloud data were extracted and visualized using a uniform statistical plotting method to intuitively represent the local displacement distribution. Subsequently, the mean values of the displacement data in the hanging wall and footwall were computed, and their difference was taken as the co-seismic displacement. To assess the uncertainty in this measurement, a Monte-Carlo-based error analysis was conducted by performing 1000 random simulations within each buffer zone. Specifically, the difference between the mean values of the hanging wall and footwall point clouds within each buffer zone was used to represent the local co-seismic displacement, and the corresponding error range was recorded to reflect the influence of data dispersion on the measurement. Finally, the calculated displacement values, along with their associated errors and projection positions along the fault, were mapped to construct the spatial distribution of near-fault co-seismic displacements.

3.4.3. Fault-Parallel Buffer-Zone-Based Displacement Estimation Method

The fault-parallel buffer zone method is based on the identified fault trace and its spatial extent within the three-dimensional co-seismic displacement field. A fixed offset distance is defined on both sides of the fault, and the original fault line is parallel-shifted to generate two new fault-parallel centerlines. Buffer zones are then constructed around each shifted line, forming two polygonal regions representing the hanging wall and footwall, respectively. The point cloud data within each buffer zone is extracted, with the displacement values used as the Y-axis, and their corresponding projected positions along the original fault trace used as the X-axis. This produces a two-dimensional plot that reveals the spatial variation in displacement across the fault at equivalent positions along the strike. To quantify this variation, a moving window of specified length is defined over each point cloud subset (hanging wall and footwall), and a pairwise traversal is performed along the fault. For each window, the mean displacement value is computed within both zones, and the difference between the means is taken as the co-seismic displacement within that segment. To evaluate the uncertainty in these measurements, a Monte-Carlo-based error analysis is applied by conducting 1000 random simulations within each window to estimate the variability in the mean difference. Using a defined step size, the window is systematically moved along the fault strike direction, and the mean difference and associated uncertainty are computed at each step. The final output is a spatial distribution profile of co-seismic displacement along the fault, where each value corresponds to the mean displacement difference between the two buffer zones at a given fault-parallel position.

In the implementation of this method for co-seismic displacement extraction, the fault was shifted laterally by 125 m on both sides to define the centerlines of the buffer zones. The width of each buffer zone was set to 200 m, and the separation between the two zones corresponds to the defined fault width. After obtaining the point cloud distributions for the hanging wall and footwall, a moving window with a width of 80 m and a step size of 30 m was applied along the fault strike direction. At each step, the window pair traverses the fault-parallel buffer zones, and the mean displacement difference is calculated between the two regions. The resulting co-seismic displacement values, their corresponding projection positions along the fault, and the associated uncertainty estimates were used to generate a spatial distribution map of near-fault co-seismic displacement (Figure 6c).

4. Results

4.1. Spatial Characteristics of the Co-Seismic Displacement Field of the Wushi Earthquake

Figure 7 illustrates the co-seismic displacement field derived from the ICP registration of pre- and post-earthquake point cloud data, processed under varying window sizes (ranging from 10 to 150 m) and step lengths (intervals from 10 to 75 m) during grid-based interpolation. The results show that smaller window sizes capture finer-scale surface details but are more susceptible to noise, often leading to displacement distortion. In contrast, larger window sizes effectively smooth out high-frequency noise but result in overly sparse data distributions, thereby failing to capture the near-fault displacement gradients. In the vertical component, significant displacement differences and a clear boundary are observed between the hanging wall and footwall, with the displacement discontinuity closely aligning with the mapped fault trace. The magnitude of vertical displacement is highest in the near-fault region and gradually decreases with increasing distance from the fault, exhibiting a typical pattern of near-field strain concentration and far-field attenuation associated with co-seismic deformation. In the horizontal components (i.e., E–W and N–S directions), the displacement field shows a general dominance of positive values, particularly in the positive Y-direction (northward displacement). However, when the east–west and north–south components are combined into vector magnitudes, the resulting composite field does not exhibit a distinct boundary across the fault. Consequently, this limits the ability to effectively isolate and quantify the strike–slip and compressional components of the Wushi earthquake’s co-seismic deformation in subsequent analysis.

Based on a grid window size of 100 × 100 m and a 50-m moving step, the co-seismic vertical displacement field in the Z-direction was vectorized. As shown in the displacement vector map (Figure 8), red and blue arrows represent the positive and negative directions of vertical displacement, respectively, with the arrow length proportional to the displacement magnitude. The overall displacement pattern reveals a subsidence of the northwestern block and an uplift of the southeastern block, which is consistent with the thrust-dominated focal mechanism of the Wushi earthquake in Xinjiang. A distinct boundary of vertical motion can be clearly identified in the figure. The spatial extent of this boundary aligns well with the main seismogenic fault and surface rupture zone interpreted from high-resolution optical remote sensing imagery, providing mutual validation between image-based structural interpretation and displacement field analysis.

4.2. Spatial Distribution of Near-Fault Co-Seismic Vertical Displacement

Based on the three measurement methods proposed in Section 3.4 (Figure 9), we extracted and calculated near-fault co-seismic vertical displacement values (within 250 m of the fault trace) along the main fault from the northwest to the northeast. As shown in Figure 10, an analysis of sample data within the 0–4600 m distance range reveals that all three methods consistently indicate a decreasing trend in displacement magnitude toward both ends of the fault, with localized uplift occurring in the central segment. Taking the line fitting-based method as an example, the overall vertical displacement values range from approximately 0.2 m to 1.4 m. Notably, peak displacement differences between the hanging wall and footwall are observed in three specific intervals: 2000–2300 m, 2500–2700 m, and 3000–3300 m, each followed by a sudden drop in displacement magnitude. These features suggest that the initiation and termination points of surface rupture or zones of localized stress concentration may be located along these segments of the fault. Further analysis reveals a maximum vertical displacement of ~1.46 m at approximately 3200 m, situated north of the Qialemati River, near the tectonic boundary between the alluvial fan and the bedrock region along the mountain front. All measured vertical displacements are positive, indicating uplift of the hanging wall and subsidence of the footwall, consistent with the thrust-dominated focal mechanism of the Wushi earthquake.

For the mean value difference method and the fault-parallel buffer zone method, both yield broadly consistent displacement trends within the 0–2800 m range, corresponding to the southwestern bedrock segment of the fault. However, in the central portion of the fault where it crosses the fan surface and the Qialemati River catchment, significant divergence appears in the estimated vertical displacement patterns. Although all three methods detect a maximum displacement near 3200 m, the fault-parallel buffer zone method exhibits more pronounced fluctuations in this segment. Error bar analysis further indicates that the mean value difference method demonstrates greater stability and reliability within the same interval.

5. Discussion

5.1. Selection of Window Size and Step Length in the ICP Algorithm

During the implementation of the ICP algorithm, it is essential to perform grid-based segmentation of the pre- and post-earthquake point cloud datasets. The choice of window size and step length has a significant impact on the accuracy and reliability of the derived co-seismic displacement field. When these parameters are set too small, the resulting displacement field may appear overly detailed, increasing its susceptibility to noise. Moreover, excessively fine-scale topographic variations within a small window may hinder precise point matching between the datasets, leading to deviation from true displacement values. Conversely, if the parameters are set too large, the method may overly smooth or even filter out fine-scale fault-zone features, causing displacement discontinuities or masking actual spatial variations in the near-fault region. Therefore, the appropriate selection of window size and step length is critical for capturing an accurate and geologically meaningful representation of the displacement field.

Although the study area is largely free from vegetation, anthropogenic structures, or buildings that could interfere with displacement estimation, it encompasses a range of geomorphic units, including alluvial fans and bedrock zones. Moreover, displacement data in river channel regions are often incomplete or missing. To systematically evaluate the effects of window size and step length, we selected four circular test areas—two on each side of the fault within the fan and bedrock domains—where the vertical displacement field is relatively uniform (Figure 11). Within each test area, 200 evenly distributed sample points were generated, and their vertical displacement values were extracted to compute the local mean. In addition, Monte Carlo error analysis was applied to each test area with 150 simulations, allowing the estimation of uncertainty ranges associated with each computed mean.

As shown in Figure 11, a homogeneity test of vertical co-seismic displacement values under different window and step length configurations reveals that displacement values within the same area are relatively stable and uniform when the window size ranges between 30–50 m and the step length falls within 15–25 m. Balancing the trade-off between capturing large-scale topographic structures and preserving fine-scale near-fault deformation features, we ultimately selected a window size of 30 m and a step length of 15 m as the optimal parameter configuration. The displacement field derived under this setting exhibits the highest degree of consistency and accuracy, and it was adopted as the basis for subsequent analysis of fault slip characteristics.

5.2. Error Analysis of ICP-Derived Displacement Results

The ICP-derived displacement errors in this study originate collectively from four principal sources: (1) coordinate and elevation accuracy of the raw point cloud. These errors stem from the quality of the WorldView-2 stereo imagery, the satellite’s imaging geometry and sensor parameters, the degree of topographic relief, and the precision with which ground control points (GCPs) and tie points are defined and matched during DEM extraction. As demonstrated in Section 3.1 and by comparing field-survey benchmarks with our extracted DEM, the vertical error of the WorldView-2–derived DEM is less than 0.5 m. (2) Errors introduced during data preprocessing. Preprocessing steps such as denoising, filtering, smoothing, and rasterization can generate additional artifacts. However, the ICP algorithm implemented here operates directly on the raw point cloud to compute displacement vectors, thereby eliminating any bias or smoothing errors that might arise from using filtered or gridded DEMs. (3) Influence of terrain relief on ICP vector accuracy. From the theoretical basis of the ICP algorithm (see Figure 4), areas with pronounced topographic variation and well-defined geomorphic features improve tie-point matching and vector precision. Our study area comprises steep bedrock mountains, a piedmont alluvial fan, and the Qialemati River channel—each exhibiting significant relief—so any terrain-induced ICP error is effectively minimized. (4) Surface morphology changes and vegetation effects caused by the earthquake. Apart from the obvious ground ruptures adjacent to the fault trace, there are no other seismically triggered mass-wasting events (e.g., landslides or dammed lakes) within the study region. Moreover, the area’s extreme aridity, very sparse vegetation cover, and absence of anthropogenic structures (e.g., buildings or roads) mean that pre- and post-seismic point-cloud mismatches due to vegetation growth or human disturbance are effectively negligible.

When applying the ICP algorithm to extract and measure co-seismic vertical displacements, both the number of iterations and the convergence threshold are critical parameters that directly affect the final results. Too few iterations prevent full alignment of the pre- and post-seismic point clouds, yielding very large RMS errors for most pixels, often exceeding the prescribed convergence threshold. Conversely, once alignment is essentially achieved, an excessively high iteration count simply wastes computation and matching steps and can even crash the processing workflow, making displacement measurement impossible. To determine an optimal iteration count, we conducted comparative experiments varying iterations between 10 and 30. We found that, as the count increases from 10 to 15 and up to 20, the proportion of valid pixels (RMS < threshold) in the ICP-derived displacement field steadily rises and reaches its maximum at 20 iterations. Beyond 20 iterations, however, outlier pixels with high RMS persist, and overall field quality does not improve, so we fixed the iteration count at 20. The convergence threshold likewise governs the accuracy and reliability of the computed displacement field. Based on Equation (3) in Section 3.2, a too-large threshold allows many spurious displacement vectors and topographic variations to be accepted; by contrast, a too-strict threshold overconstrains the allowable point-to-plane distance, causing genuine displacements to be discarded. We tested thresholds between 0 and 15 m, comparing the resulting co-seismic vertical fields and their peak displacements, and we ultimately selected 10 m as the convergence threshold.

5.3. Influence of Different Measurement Methods on Co-Seismic Vertical Displacement Estimates

Based on the three co-seismic vertical displacement extraction methods described in Section 3.4, we conducted a comparative analysis between the estimated displacement values and field-measured displacements projected along the fault strike. As illustrated in Figure 12, all four datasets exhibit a consistent spatial pattern characterized by lower displacement magnitudes at both ends and higher values in the central segment, with several localized peak concentrations. The range of vertical displacements measured in the field falls approximately between 0.2 and 1 m, while the values derived from the displacement field calculations are generally higher than the field measurements. Only a few field data points exceed the computed values, and these anomalies tend to deviate from the overall trend of continuous spatial variation. This discrepancy may be attributed to the overreliance on prominent surface rupture features during field measurements, potentially leading to errors in identifying the correct reference plane or mistakenly interpreting cumulative displacement as purely co-seismic displacement. Moreover, during seismic events, energy released from deeper crustal levels may propagate toward the surface through fault branches over a broader area. Given that some vertical co-seismic displacement may occur below the surface, field measurements that only capture surface rupture expression could underestimate the true magnitude of the co-seismic deformation field.

Among the three vertical displacement extraction methods introduced in Section 3.4, the line-fitting-based method yielded displacement results with minimal outliers and greater continuity along the fault strike. When compared to field measurements, both the overall trend and the distribution of peak values show strong agreement. This method incorporates manual judgment for identifying fault width, fault location, and displacement contrast between the two sides of the fault for each profile, effectively filtering out noise and anomalous values in the displacement field. As a result, it provides the most geologically reasonable representation of the spatial distribution of co-seismic vertical displacement along the Wushi earthquake rupture zone.

The mean value difference method follows a similar workflow, but instead of manual evaluation, it applies an automated averaging process after extracting displacement values from individual perpendicular profiles. While this significantly improves processing efficiency, its results show high consistency with both field data and the line-fitting-based estimates within the 1500–4600 m segment along the fault. However, in the southwestern bedrock region, where co-seismic vertical displacements are generally below 1 m, the close spatial proximity of point cloud values on either side of the fault increases the sensitivity of the mean calculation to extreme values. These local anomalies vary across profiles, making it difficult to define a unified filtering criterion or apply consistent smoothing. This limitation is also reflected in the Monte-Carlo-derived error bars, which indicate a wider uncertainty range for the 0–1500 m interval. In this segment, the spatial distribution of displacement values is more scattered, resulting in reduced stability and confidence in the calculated means. Therefore, the mean value difference method is more suitable in scenarios where displacements are relatively large, fault-related deformation is well-defined, and point cloud data are evenly distributed. In more diffuse deformation zones or where near-fault stress is poorly localized, additional manual filtering or displacement value selection may be necessary to improve accuracy.

The fault-parallel buffer zone method, widely used in previous studies—such as those on the 2008 Iwate earthquake and the 2011 Tohoku earthquake in Japan [36,49]—was also tested in this study. While the overall displacement trends are broadly consistent with the previous two methods, some anomalies were observed: in several segments, negative vertical displacements appeared, indicating that the hanging wall displaced downward relative to the footwall. This contradicts the thrust-dominated with left-lateral slip focal mechanism solution of the Wushi earthquake. In peak displacement zones, the results also exhibited local oscillations rather than a smooth variation. Although this method provides a straightforward comparison of the spatial distribution of displacement across the fault, it proved less suitable in this case. This may be attributed to the generally small displacement magnitudes (typically <1 m) observed in the Wushi earthquake. In the fault-parallel buffer zones, the low displacement gradients led to widely dispersed values within each computation window, making the average highly sensitive to outliers. Consequently, the associated uncertainties were also large. This method may therefore be more appropriate in seismic events where fault-parallel displacements or vertical offsets exceed several meters.

In summary, while the line fitting-based method requires the manual interpretation of displacement values on both sides of the fault, it provides the most reasonable and accurate estimates of co-seismic displacement. In cases where fault offsets are relatively large and point cloud data are evenly distributed, the mean value difference method offers comparable accuracy with a much higher degree of automation, while also enabling error quantification. For earthquakes with clearly expressed surface rupture and large-magnitude displacements, the fault-parallel buffer zone method provides a valuable balance of automation and spatial visualization capabilities, allowing for the intuitive representation of near-fault deformation and associated stress patterns.

6. Conclusions

This study generated high-resolution digital elevation models (DEMs) and point cloud datasets derived from WorldView-2 stereo imagery. The Iterative Closest Point (ICP) algorithm was then employed to determine the co-seismic deformation field induced by the Wushi earthquake. Based on the spatial distribution characteristics of this deformation field, three quantitative methods were utilized to extract near-fault co-seismic vertical displacements, followed by a comparative analysis of their results. The primary conclusions are summarized as follows:

• The co-seismic vertical deformation field of the Wushi earthquake indicates a predominant surface uplift near the fault, reflecting a distinct reverse-faulting mechanism characterized by differential vertical displacement between the hanging wall and footwall blocks. The vertical displacement profile along strike presents a systematic low–high–low variation, ranging from 0.2 to 1.4 m, including three prominent peaks interpreted as localized zones of high stress concentration along the seismogenic fault. The maximum observed vertical displacement (~1.46 m) is located north of the Qialemati River, within the mountain-front transitional zone at the interface between the alluvial fan deposits and bedrock terrain.
• Comparative analyses of displacement measurements from the three extraction methods demonstrate that selecting an optimal measurement technique should consider faulting style, deformation characteristics, and observed surface rupture conditions. In regions with subtle vertical displacement contrasts between fault blocks, manual filtering and selective displacement extraction methods yield enhanced accuracy. Conversely, automated averaging approaches prove more efficient and robust in areas characterized by distinct surface ruptures and substantial displacements, with the added benefit of facilitating quantitative error estimations to evaluate measurement reliability.
• The results of this study indicate that novel high-resolution optical satellites, such as WorldView-2, are capable of acquiring terrain data with sub-meter to meter-level resolution. Measurements derived from point cloud data achieve accuracies finer than the scale of co-seismic slip associated with large earthquakes. Moreover, this technique demonstrates distinct advantages in accumulating pre-earthquake baseline data, rapidly acquiring post-earthquake observations, and extensively covering surface deformation zones. Consequently, it enables rapid and timely construction of high-resolution, three-dimensional, near-field co-seismic displacement fields of earthquake surface ruptures, effectively overcoming the spatial coverage limitations near faults inherent to GNSS and InSAR observational techniques.