Multiscale Method Research Articles

Spatially and temporally high-order dynamic nonlinear variational multiscale methods for generalized Newtonian flows

Non-Newtonian fluids are of interest in industrial sectors, biological problems and other natural phenomena. This work proposes rheologically-dependent, spatially and temporally high-order non-residual stabilized finite element formulations. The accuracy of the methods is assessed by tackling highly-convective time-dependent power-law flows. The spatial approximation uses Lagrangian finite elements up to fourth order. The temporal integration is done via backward differentiation formulas of order one, two and three. A key aspect of our work is using a non-residual orthogonal variational multiscale (VMS) formulation to stabilize dominant convection and to allow equal-order interpolation of velocity and pressure. Our VMS method uses dynamic nonlinear subscales, which have not been tested so far for generalized Newtonian fluids. In this work, the use of high-order temporal discretizations for the subscale components is systematically evaluated. Numerical experiments consider the flow over a confined cylinder for Reynolds numbers between 40 and 400 and power-law indices between 0.4 and 1.8. Numerical testing demonstrates the method to be stable in all combinations of spatial and temporal orders. Our results show that using high-order spatial discretizations more accurately approximates boundary layers and viscosity fields. Moreover, higher temporal orders allow using larger time steps while still capturing highly dynamic behaviors with better resolution in frequency spectra.

Implicit unified gas-kinetic scheme for steady state solution of hypersonic thermodynamic non-equilibrium flows

The unified gas-kinetic scheme (UGKS), designed to solve Boltzmann equation and its model equations, aims to accurately resolve multi-scale flow problems within a single computation framework. In this study, an implicit UGKS is proposed for the steady state solution of diatomic gas flows based on a multiple-temperature Boltzmann model equation with non-equilibrium among translational, rotational and vibrational modes (Zhang et al., 2023), utilizing a novel hybrid Cartesian-unstructured discrete velocity space (DVS) mesh approach. The multiple-temperature macroscopic equations corresponding to the Boltzmann model equation are simultaneously solved implicitly to address the stiffness and nonlinearity of the collision operator encountered when solving the Boltzmann model equation in isolation. Both macroscopic equations and Boltzmann model equation are solved by using the point relaxation symmetric Gauss–Seidel method to achieve a fast convergence rate. The efficiency of the implicit UGKS can be improved by about two orders of magnitude compared to the explicit one. Moreover, the hybrid Cartesian-unstructured DVS achieves a noteworthy reduction in both CPU-hours and memory consumption, requiring only 15%∼23% of the advanced unstructured DVS. It effectively alleviates the dimensional crisis of UGKS in solving three-dimensional hypersonic flows, and can be extended to other DVS-based methods. As a result, UGKS extends its applicable regime to simulations of hypersonic thermodynamic non-equilibrium flows with Mach numbers up to 30, achieving three-dimensional flow simulations of complex geometrical configurations with relatively low computational resources. A series of test cases, including normal shock structures, two-dimensional hypersonic flows around cylinder, blunt wedge and flat plate, and three-dimensional hypersonic flows around a sphere and an X38-like configuration vehicle, are conducted to validate the implicit UGKS with hybrid Cartesian-unstructured DVS. Overall, the proposed method shows advantages of unified multi-scale methods in terms of computational efficiency and capturing multi-scale solution of hypersonic thermodynamic non-equilibrium flows.

Application of scalable sensor-assisted multi-scale computational methods in the simulation of micro mechanical behavior of composite materials

Micro mechanics involves the examination of the mechanical behavior of heterogeneous materials, taking into account inhomogeneities such as voids, fractures, and inclusions, and building on mathematical models developed. Composites bring engineering design barriers despite their strengths. Composite manufacturing and processing need specialized equipment, strategies, and labor, ensuring they are challenging and expensive. Mechanical behavior deals with how a composite material performs if faced with mechanical effects and action. Scalable sensor-assisted multi-scale computational Methods (SS-MSCM) are used to investigate topics ranging from the molecular basis of soot production in combustion to how molecule-level flaws influence macroscopic mechanical qualities. Carbon fiber reinforced polymers (CFRP) are generated by mixing graphene fiber with a resin, like vinyl ester and epoxy, to render a composite material with superior performance to the component ingredients. Hence, SS-MSCM-CFRP has Improved mechanical qualities achieved by incorporating nano-reinforcements, including carbon nanofibers and graphene nanoplates, into the CFRP matrix: enhanced flexural and compressive strengths, energy absorption upon impact, toughness to fracture, and interlaminar bonding. Composite materials feature excellent mechanical qualities like high strength and stiffness, fatigue resistance, and durability. It is possible to insert scalable sensors throughout the manufacturing process, which enables real-time monitoring of structural health, strain, and other factors. Scalable sensor-assisted multi-scale computational methods offer enhanced accuracy, real-time monitoring, and cost-effectiveness by integrating sensor data with computational models, improving predictions and failure mechanism insights. However, they face limitations like sensor dependency, computational complexity, data integration challenges, and high implementation costs, leading to potential discrepancies between simulation and experimental results. Important qualities include corrosion resistance, thermal conductivity, and electrical conductivity. As the composite materials develop to satisfy the established mechanical stress and temperature conditions, they offer high durability and strength.

An Efficient Multi-Scale Wavelet Approach for Dehazing and Denoising Ultrasound Images Using Fractional-Order Filtering

Ultrasound imaging is widely used in medical diagnostics due to its non-invasive and real-time capabilities. However, existing methods often overlook the benefits of fractional-order filters for denoising and dehazing. Thus, this work introduces an efficient multi-scale wavelet method for dehazing and denoising ultrasound images using a fractional-order filter, which integrates a guided filter, directional filter, fractional-order filter, and haze removal to the different resolution images generated by a multi-scale wavelet. In the directional filter stage, an eigen-analysis of each pixel is conducted to extract structural features, which are then classified into edges for targeted filtering. The guided filter subsequently reduces speckle noise in homogeneous anatomical regions. The fractional-order filter allows the algorithm to effectively denoise while improving edge definition, irrespective of the edge size. Haze removal can effectively eliminate the haze caused by attenuation. Our method achieved significant improvements, with PSNR reaching 31.25 and SSIM 0.905 on our ultrasound dataset, outperforming other methods. Additionally, on external datasets like McMaster and Kodak24, it achieved the highest PSNR (29.68, 28.62) and SSIM (0.858, 0.803). Clinical evaluations by four radiologists confirmed its superiority in liver and carotid artery images. Overall, our approach outperforms existing speckle reduction and structural preservation techniques, making it highly suitable for clinical ultrasound imaging.

A Multi-Scale Numerical Simulation Method Considering Anisotropic Relative Permeability

Most of the oil reservoirs in China are fluvial deposits with firm reservoir heterogeneity, where differences in fluid flow capacity in individual directions should not be ignored; however, the available commercial reservoir simulation software cannot consider the anisotropy of the relative permeability. To handle this challenge, this paper takes full advantage of the parallelism of the multi-scale finite volume (MsFV) method and establishes a multi-scale numerical simulation approach that incorporates the effects of reservoir anisotropy. The methodology is initiated by constructing an oil–water black-oil model considering the anisotropic relative permeability. Subsequently, the base model undergoes decoupling through a sequential solution, formulating the pressure and transport equations. Following this, a multi-scale grid system is configured, within which the pressure and transport equations are progressively developed in the fine-scale grid domain. Ultimately, the improved multi-scale finite volume (IMsFV) method is applied to mitigate low-frequency error in the coarse-scale grid, thereby enhancing computational efficiency. This paper introduces two primary innovations. The first is the development of a multi-scale solution method for the pressure equation incorporating anisotropic relative permeability. Validated using the Egg model, a comparative analysis with traditional numerical simulations demonstrates a significant improvement in computational speed without sacrificing accuracy. The second innovation involves applying the multi-scale framework to investigate the impact of anisotropy relative permeability on waterflooding performance, uncovering distinct mechanisms by which absolute and relative permeability anisotropy influence waterflooding outcomes. Therefore, the IMsFV method can be used as an effective tool for high-resolution simulation and precise residual oil prediction in anisotropic reservoirs.

A multi-scale deep residual network-based guided wave imaging evaluation method for fatigue crack quantification

Abstract As a promising structural health monitoring (SHM) technology, guided wave (GW) imaging is gaining increasing attention for crack monitoring of aircraft structures. However, actual fatigue crack propagation is a complex dynamically evolving process affected by various variabilities. It is still challenging to accurately track and quantify the dynamic fatigue crack propagation with GW imaging methods. Therefore, in order to achieve more accurate fatigue crack quantification, this paper proposes a multi-scale deep residual network-based GW imaging evaluation method. A convolutional neural network (CNN) is utilized to evaluate the entire pixel distribution of GW imaging maps to fuse damage-related information from multiple GW monitoring paths. By designing multi-scale convolutional kernels and deep residual learning, a robust quantitative image feature extraction is ensured with the dynamic evolution process of fatigue crack growth and the performance degradation is avoided as the CNN goes deeper, thereby improving the quantification accuracy. The method is validated on a fatigue test of landing gear beams, which are important load-carrying aircraft structural components. The results demonstrate that the proposed method can extract multi-scale crack length-related features and accurately track fatigue crack propagations. For batch specimens, the maximum quantification error is reduced from the original 6.1mm to 1.6mm, marking a significant improvement.

Stochastic Schrödinger equation for hot-carrier dynamics in plasmonic systems

We present a multiscale method coupling the theory of open quantum systems with real-time ab initio treatment of electronic structure to study hot-carrier dynamics in photoexcited plasmonic systems. We combine the Markovian Stochastic Schrödinger equation with an ab initio GW coupled to the Bethe–Salpeter (BSE) equation description of the electronic degrees of freedom, interacting with a metallic nanoparticle modeled classically according to the polarizable continuum model. We apply this methodology to study the effect of relaxation (T1) and pure dephasing (T2) times on the hot-carrier dynamics in a system composed of a quantum portion described at GW/BSE level, i.e., a CHO fragment adsorbed on a vertex of a rhodium nanocube, and of the rest of the nanocube, treated classically, when irradiated with a 2.7 eV light pulse, inspired by the experimental results on plasmon-driven CO2 photoreduction. A net hole injection from rhodium to CHO is observed, with and without the classical portion of the nanocube. The nanocube effect is to enhance the generated charge population by two orders of magnitude. The nonradiative decay, via a relaxation time T1 based on the energy-gap law, produces a rapid decrease of the charge population. Results with T2 only show that a charge injection retarded with respect to the pulse, which is present in the coherent dynamics, disappears when coherence is erased.

Segment Anything Model Combined with Multi-Scale Segmentation for Extracting Complex Cultivated Land Parcels in High-Resolution Remote Sensing Images

Accurate cultivated land parcel data are an essential analytical unit for further agricultural monitoring, yield estimation, and precision agriculture management. However, the high degree of landscape fragmentation and the irregular shapes of cultivated land parcels, influenced by topography and human activities, limit the effectiveness of parcel extraction. The visual semantic segmentation model based on the Segment Anything Model (SAM) provides opportunities for extracting multi-form cultivated land parcels from high-resolution images; however, the performance of the SAM in extracting cultivated land parcels requires further exploration. To address the difficulty in obtaining parcel extraction that closely matches the true boundaries of complex large-area cultivated land parcels, this study used segmentation patches with cultivated land boundary information obtained from SAM unsupervised segmentation as constraints, which were then incorporated into the subsequent multi-scale segmentation. A combined method of SAM unsupervised segmentation and multi-scale segmentation was proposed, and it was evaluated in different cultivated land scenarios. In plain areas, the precision, recall, and IoU for cultivated land parcel extraction improved by 6.57%, 10.28%, and 9.82%, respectively, compared to basic SAM extraction, confirming the effectiveness of the proposed method. In comparison to basic SAM unsupervised segmentation and point-prompt SAM conditional segmentation, the SAM unsupervised segmentation combined with multi-scale segmentation achieved considerable improvements in extracting complex cultivated land parcels. This study confirms that, under zero-shot and unsupervised conditions, the SAM unsupervised segmentation combined with the multi-scale segmentation method demonstrates strong cross-region and cross-data source transferability and effectiveness for extracting complex cultivated land parcels across large areas.

A photovoltaic cell defect detection model capable of topological knowledge extraction

As the global transition towards clean energy accelerates, the demand for the widespread adoption of solar energy continues to rise. However, traditional object detection models prove inadequate for handling photovoltaic cell electroluminescence (EL) images, which are characterized by high levels of noise. To address this challenge, we developed an advanced defect detection model specifically designed for photovoltaic cells, which integrates topological knowledge extraction. Our approach begins with the introduction of a multi-scale dynamic context-based feature extraction method, capable of generating static context by thoroughly capturing the local texture and structural information of multi-scale defects. This static context is then combined with dynamic context to produce fine-grained local features. Subsequently, we developed a centralized feature pyramid structure, enhanced by spatial semantics, which models the explicit visual center. This structure effectively elucidates the relationship between local and global features in defect images, thereby improving the representation of defect characteristics. Finally, we implemented a feature enhancement strategy grounded in spatial semantic knowledge extraction. This strategy uncovers potential correlations among defect targets by constructing a spatial semantic topology of features, mapping these features to a higher-order representation, and ultimately delivering precise defect detection results.

A higher order multiscale method for the wave equation

Abstract In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher order extension of the localized orthogonal decomposition method combined with a higher order time stepping scheme and present rigorous a priori error estimates in the energy-induced norm. We find that in the very general setting without additional assumptions on the coefficient beyond boundedness arbitrary orders of convergence cannot be expected, but that increasing the polynomial degree may still considerably reduce the size of the error. Under additional regularity assumptions higher orders can be obtained as well. Numerical examples are presented that confirm the theoretical results.

An investigation of dynamic droplet wetting within the smoothed dissipative particle dynamics (SDPD) multi-scale modeling framework

The multi-scale numerical procedure proposed in our previous work based on smoothed dissipative particle dynamics (SDPD) is employed, and a new multi-phase interaction model based on the inter-particle force (IPF) that includes a consistent repulsion force is presented and verified. A comparative investigation utilizing smoothed particle hydrodynamics (SPH), SDPD, and our multi-scale methods is then carried out and the computational efficiency, droplet morphology, wetting flow field, and advantages of the multi-scale method are demonstrated. In addition, the droplet thickness is derived from the Navier–Stokes equations with a stochastic force, demonstrating the effect of thermal fluctuations on the mesoscopic scale. Finally, the wetting states are simulated at different surface roughness values, and the transition of states and some new mechanisms are clarified. When the roughness scale is smaller than the interaction range between particles, the wetting state may change significantly, and this effect becomes weaker when the roughness scale exceeds the interaction range. The results also show that the horizontal roughness (direction of droplet spreading) is more decisive than vertical one (perpendicular to the direction of droplet spreading), usually leading to a transition of the wetting states, while the vertical roughness usually plays a reinforcing role.

Nighttime large-field video image change detection based on adaptive superpixel reconstruction and multi-scale singular value decomposition fusion

With the development of technology and the needs of social governance, surveillance equipment has been widely used. It is very mature to detect the change of surveillance video images in conventional scenes through video image change detection algorithms. However, in the large field of view environment at night, there are complex random noise and low signal-to-noise ratio in surveillance video images, which makes it difficult for people to find small moving targets. To this end, we propose a new method for nighttime large-field surveillance video image change detection based on adaptive superpixel reconstruction and multi-scale singular value decomposition fusion. The proposed method consists of two parts. On the one hand, an adaptive superpixel reconstruction method is used to reconstruct the two denoised difference images by selecting different segmentation parameters, and the edge information of the two reconstructed difference images is significantly enhanced. On the other hand, a multi-scale singular value decomposition fusion method is used to fuse the two difference images. The multi-scale singular value decomposition fusion obtains a robust difference image by selecting fusion rules at different scales and using the complementary information of different difference images, and the Fuzzy c-means (FCM) clustering algorithm is used to obtain the final changed image. Experimental results on a self-built nighttime large-field video image dataset with two resolutions show that the proposed method is superior to other algorithms in terms of detection accuracy and robustness.

Numerical Assessment of Effective Elastic Properties of Needled Carbon/Carbon Composites Based on a Multiscale Method

Needled carbon/carbon composites contain complex microstructures such as irregular pores, anisotropic pyrolytic carbon, and interphases between fibers and pyrolytic carbon matrices. Additionally, these composites have hierarchical structures including weftless plies, short-cut fiber plies, and needled regions. To predict the effective elastic properties of needled carbon/carbon composites, this paper proposes a novel sequential multiscale method. At the microscale, representative volume element (RVE) models are established based on the microstructures of the weftless ply, short-cut fiber ply, and needled region, respectively. In the microscale RVE model, a modified Voronoi tessellation method is developed to characterize anisotropic pyrolytic carbon matrices. At the macroscale, an RVE model containing hierarchical structures is developed to predict the effective elastic properties of needled carbon/carbon composites. For the data interaction between scales, the homogenization results of microscale models are used as inputs for the macroscale model. By comparing these against the experimental results, the proposed multiscale model is validated. Furthermore, the effect of porosity on the effective elastic properties of needled carbon/carbon composites is investigated based on the multiscale model. The results show that the effective elastic properties of needled carbon/carbon composites decrease with the increase in porosity, but the extent of decrease is different in different directions.

Dynamic and modal analysis of nearly incompressible structures with stabilised displacement-volumetric strain formulations

This paper presents a dynamic formulation for the simulation of nearly incompressible structures using a mixed finite element method with equal-order interpolation pairs. Specifically, the nodal unknowns are the displacement and the volumetric strain component, something that makes possible the reconstruction of the complete stain at the integration point level and thus enables the use of strain-driven constitutive laws. Furthermore, we also discuss the resulting eigenvalue problem and how it can be applied for the modal analysis of linear elastic solids. The article puts special emphasis on the stabilisation technique used, which becomes crucial in the resolution of the generalised eigenvalue problem. In particular, we prove that using a variational multiscale method assuming the sub-grid scales to lie in the finite element space orthogonal to that of the approximation, namely the Orthogonal Sub-Grid Scales (OSGS), results in a convenient linear and symmetric generalised eigenvalue problem. The correctness, convergence and performance of the method are proven by solving a series of two- and three-dimensional examples.

Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model

For nonlinear Cosserat elasticity, we consider multiscale methods in this paper. In particular, we explore the generalized multiscale finite element method (GMsFEM) to solve an isotropic Cosserat problem with strain-limiting property (ensuring bounded linearized strains even under high stresses). Such strain-limiting Cosserat model can find potential applications in solids and biological fibers. However, Cosserat media with naturally rotational degrees of freedom, nonlinear constitutive relations, high contrast, and heterogeneities may produce challenging multiscale characteristics in the solution, and upscaling by multiscale methods is necessary. Therefore, we utilize the offline and residual-based online (adaptive or uniform) GMsFEM in this context while handling the nonlinearity by Picard iteration. Through various two-dimensional experiments (for perforated, composite, and stochastically heterogeneous media with small and big strain-limiting parameters), our numerical results show the approaches' convergence, efficiency, and robustness. In addition, these results demonstrate that such approaches provide good accuracy, the online GMsFEM gives more accurate solutions than the offline one, and the online adaptive strategy has similar accuracy to the uniform one but with fewer degrees of freedom.

Vertical vibration analysis of rolling interface based on dynamic rolling force with variable friction characteristics

This study investigates the impact of variable friction characteristics at the rolling interface on the vertical vibration of plate and strip rolling mills. Based on the optimized Karman equilibrium theory, a dynamic rolling force model considering the front and back tension, elastic stretching, and rolling speed was established. The amplitude-frequency response equation of rolling mill system is solved by multi-scale method, and the influence of main parameters on vertical vibration of rolling mill system is analyzed. The results show that the increase of the first stiffness coefficient of dynamic rolling force leads to the decrease of the principal common amplitude of the system. On the contrary, when the third stiffness coefficient increases, the system exhibits a jump phenomenon. When the third stiffness coefficient of dynamic rolling force is reduced within a certain range, a stable and unique solution is obtained without jumping phenomenon. Moreover, the smaller the damping coefficient of the upper and lower roller system is, the larger the vibration amplitude is and the jump phenomenon occurs. Decreasing the external disturbance force can effectively reduce the system’s vertical vibration amplitude and suppress the resonance. In addition, with the change of external disturbance force, the roll system of the rolling mill shows a variety of complex motion states, such as periodic motion, double-periodic motion, and chaotic motion. The research results provide an effective theoretical reference for the suppression of vertical vibration of rolling mill.

Multi-scale analysis of ultimate bearing capacity in composite hull joints: failure mechanism and numerical simulation

ABSTRACT Progressive failure analysis method is the main method to analyse the ultimate bearing capacity and failure mode of composite structures. Multi-scale method can effectively reduce the dependence of damage mode and stiffness degradation analysis on material parameters. Based on the multi-scale method, from micro-scale to mesoscale and then to macro-scale, the equivalent modulus and equivalent strength of fibre bundles, single-layer laminates and multi-directional laminates were predicted respectively, and the prediction method of ultimate bearing capacity of large-scale composite structures from material level to structure level was constructed. The mechanical properties of standard composite materials and the ultimate bearing capacity of full-scale composite joints were tested respectively, and the ultimate bearing capacity and failure mode of L-joints were predicted by numerical method. The results show that the numerical simulation method based on multi-scale can accurately predict the ultimate bearing capacity and failure mode of large-scale joints of the hull.

A study on the mechanisms and influencing factors of interfacial physicochemical interactions between asphalt and mineral aggregates based on multiscale evaluation methods

The elucidation of interfacial physicochemical mechanisms between asphalt and mineral aggregates is vital for comprehending the interface formation in asphalt mixtures and enhancing their performance. To this end, multiscale evaluation methods were used to investigate the mechanisms and influencing factors of interfacial physicochemical interactions between asphalt and mineral aggregates (IPIAMA). Initially, the dynamic shear rheometer (DSR) was used to measure the complex shear modulus (G*) of various asphalt mastics. Subsequently, the interface film thickness was calculated using G* in conjunction with the Hashin and Mori-Tanaka (MT) micromechanical models. This indicator facilitated quantitative assessments and the analysis of influencing factors. The results indicated that the MT model underestimated the interface film thickness by approximately 0.08–0.29 % compared to the Hashin model, a discrepancy attributable to assumptions regarding aggregate particle interlocking. Moreover, the interface film thickness systematically varied with factors such as aggregate content, type of aggregate, and type of asphalt, ranging from 0.24 to 0.53 μm. To further elucidate the IPIAMA mechanisms behind these variations, the fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), x-ray photoelectron spectroscopy (XPS), and the ultraviolet test (UV) testing were conducted. FTIR tests demonstrated that the primary components of mineral aggregates—dolomite, calcite, and quartz—contributed to the physical adsorption increments on asphalt functional groups by 0.0185, 0.0509, and 0.004, respectively. SEM images revealed that dolomite and calcite possessed more surface fissures and pores than quartz. XPS tests showed that calcium carbonate and magnesium carbonate chemically reacted with asphalt, resulting in electron shifts of 0.9 eV and 1.1 eV, respectively, while silicon oxide only exhibited electron shifts when combined with a silane coupling agent-modified asphalt. UV tests demonstrated that lighter asphalt fractions were preferentially absorbed into the pores and micro-cracks of mineral aggregates. Consequently, the complex IPIAMA involved physical adsorption, chemical reactions, and selective absorption, strongly correlating with factors such as mineral composition, surface morphology, and asphalt type.

The crack propagation behaviors, microstructure and mechanical properties of T-welded joints for TIGW with crystal plasticity model and XFEM

In view of the significant impact of welding defects on the fracture behaviors involving the strength, stress concentration and bearing capacity of welded joint, etc., the propagation behaviors and mechanical properties of welded joints with porosity and micro crack are deeply investigated using a multiscale method. In this work, a crack nucleation and propagation model based on crystal plasticity theory, combined with the extended finite element method (XFEM), is established for the T-welded joint. The maximum slip on the predominant slip system method is applied to predict the crack propagation path of pores and micro cracks in the weld zone (WZ), and the effect of crystal orientation on crack growth is explored. Then, a continuous model is used to analyze the micro and macro fracture behaviors near the weld under tensile load, combined with the maximum principal stress method. The WZ and heat affected zone (HAZ) are observed using electron backscatter diffraction (EBSD) to study the microstructure evolution. Considering grain boundaries, the image information of crystal morphology is processed through binary image analysis for FE modeling. The local mechanical properties testing is carried out using micro-specimens of HAZ and WZ to calibrate the crystal plastic parameters. The results show that the resolved shear stress of the predominant slip system of crack initiation and propagation elements is increased by pore and crack defects. The fracture positions of tensile specimens through numerical simulation are in good agreement with the macroscopic experimental results. It will provide an analysis basis for preventing fracture failure and improving the service performance of thin-walled structures in future.

Three-dimensional interseismic crustal deformation in the northeastern margin of the Tibetan Plateau using GNSS and InSAR

The nature of the crustal deformation of the northeastern margin of the Tibetan Plateau is vital for elucidating the expansion mechanism of the plateau. We installed 21 continuous GNSS stations and obtained a horizontal velocity field with high spatial resolution. We also acquired a line-of-sight(LOS)velocity field with Sentinel-1 images covering the study area from 2014 to 2022. A multi-scale spherical wavelet method was employed to unify the reference frames of GNSS and InSAR data. After unifying the reference frame, the two data types achieve high consistency. Combining GNSS and InSAR velocities yielded the three-dimensional interseismic velocity field in the northeastern margin of the Tibetan Plateau. Furthermore, we analyzed the crustal deformation characteristics based on the three-dimensional deformation field. The crustal deformation exhibits a pronounced northeastward shift relative to the Ordos block, whereas the interior of the Ordos block remains remarkably stationary, behaving as a rigid unit. The Liupanshan fault is primarily characterized by uplift, devoid of any notable horizontal deformation across the fault. The left-lateral strike-slip mainly characterizes the Haiyuan fault.. The maximum east–west deformation velocity on the southern side of the fault is approximately 3.9 mm/yr, decreasing to about 1.0 mm/yr at the eastern end of the fault. The western segment of the West Qinling fault exhibits a minor east–west motion. Our result provides essential data for further study of the crustal deformation patterns.