Experimental study on strain field evolution around a simulated thrust fault

Earthquakes result from continuous geodynamic processes. A topic of significant interest for the scientific community is to elaborate on the phenomena governing the faulting and fracturing of crustal rocks. Therefore, in this study, uniaxial compressive shear failure experiments were conducted on Fangshan marble rock samples with a prefabricated slot to simulate thrust faulting. The center of each marble plate (105 mm × 80 mm × 5 mm) was engraved with a 30-mm long double-sided nonpenetrating slot (depth: 2 mm, width: 0.5 mm). The deformation and destruction processes of the rock surface were recorded using a high-speed camera. The digital image correlation method was used to calculate the displacement and strain distribution and variation at different loading stages. The accumulative and incremental displacement fields u and v , strain field e_x and e_y, and shear strain e_xy were analyzed. When the loading level reached its ultimate value, the strain field was concentrated around the prefabricated slot. The concentration reached a maximum at the ends of the prefabricated slot. The magnitude of shear strain reached 0.1. This experiment contributes to our understanding of the dynamic process of active faulting.     

Range imaging: a new method for high‐resolution topographic measurements in small‐ and medium‐scale field sites

Topographic measurements are essential for the study of earth surface processes. Three‐dimensional data have been conventionally obtained through terrestrial laser scanning or photogrammetric methods. However, particularly in steep and rough terrain, high‐resolution field measurements remain challenging and often require new creative approaches. In this paper, range imaging is evaluated as an alternative method for obtaining surface data in such complex environments. Range imaging is an emerging time‐of‐flight technology, using phase shift measurements on a multi‐pixel sensor to generate a distance image of a surface. Its suitability for field measurements has yet not been tested. We found ambient light and surface reflectivity to be the main factors affecting error in distance measurements. Low‐reflectivity surfaces and strong illumination contrasts under direct exposure to sunlight lead to noisy distance measurements. However, regardless of lighting conditions, the accuracy of range imaging was markedly improved by averaging multiple images of the same scene. For medium ambient lighting (shade) and a light‐coloured surface the measurement uncertainty was approximately 9 mm. To further test the suitability of range imaging for field applications we measured a reach of a steep mountain stream with a horizontal resolution of approximately 1 cm (in the focal plane of the camera), allowing for the interpolation of a digital elevation model on a 2 cm grid. Comparison with an elevation model obtained from terrestrial laser scanning for the same site revealed that both models show similar degrees of topographic detail. Despite limitations in measurement range and accuracy, particularly at bright ambient lighting, range imaging offers three‐dimensional data in real time and video mode without the need of post‐processing. Therefore, range imaging is a useful complement or alternative to existing methods for high‐resolution measurements in small‐ to medium‐scale field sites. Copyright © 2012 John Wiley & Sons, Ltd.     

Observations of fluid‐dependent shear‐wave splitting in synthetic porous rocks with aligned penny‐shaped fractures‡

P‐ and S‐wave velocity and attenuation coefficients (accurate to ±0.3% and ±0.2 dB/cm, respectively) were measured in synthetic porous rocks with aligned, penny‐shaped fractures using the laboratory ultrasonic pulse‐echo method. Shear‐wave splitting was observed by rotating the S‐wave transducer and noting the maximum and minimum velocities relative to the fracture direction. A block of synthetic porous rock of fracture density 0.0201 ± 0.0068 and fracture size 3.6 ± 0.38 mm (measured from image analysis of X‐ray CT scans) was sub‐sampled into three 20–30 mm long, 50 mm diameter core plugs oriented at 0°, 45° and 90° to the fracture normal (transversely isotropic symmetry axis). Full waveform data were collected over the frequency range 500–1000 kHz for both water and glycerin saturated cores to observe the effect of pore fluid viscosity at 1 cP and 100 cP, respectively. The shear‐wave splitting observed in the 90° core was 2.15 ± 0.02% for water saturated and 2.39 ± 0.02% for glycerin saturated, in agreement with the theory that suggests that the percentage splitting should be 100 times the fracture density and independent of the saturating fluid. In the 45° core, by contrast, splitting was 0.00 ± 0.02% for water saturation and ?0.77 ± 0.02% for glycerin saturation. This dependence on fracture orientation and pore fluid viscosity is consistent with the poro‐visco‐elastic theory for aligned, meso‐scale fractures in porous rocks. The results suggest the possible use of shear‐ or converted‐wave data to discriminate between fluids on the basis of viscosity variations.     

Displacement‐based seismic analysis for out‐of‐plane bending of unreinforced masonry walls

This paper addresses the problem of assessing the seismic resistance of brick masonry walls subject to out‐of‐plane bending. A simplified linearized displacement‐based procedure is presented along with recommendations for the selection of an appropriate substitute structure in order to provide the most representative analytical results. A trilinear relationship is used to characterize the real nonlinear force–displacement relationship for unreinforced brick masonry walls. Predictions of the magnitude of support motion required to cause flexural failure of masonry walls using the linearized displacement‐based procedure and quasi‐static analysis procedures are compared with the results of experiments and non‐linear time‐history analyses. The displacement‐based procedure is shown to give significantly better predictions than the force‐based method. Copyright © 2002 John Wiley & Sons, Ltd.     

Subaerial gravel size measurement using topographic data derived from a UAV‐SfM approach

Accurate and reliable methods for quantifying grain size are important for river science, management and in various other sedimentological settings. Remote sensing offers methods of quantifying grain size, typically providing; (a) coarse outputs (c. 1 m) at the catchment scale where individual grains are at subpixel level, or; (b) fine resolution outputs (c. 1 mm) at the patch scale. Recently, approaches using unmanned aerial vehicles (UAVs) have started to fill the gap between these scales, providing hyperspatial resolution data (< 10 cm) over reaches a few hundred metres in length, where individual grains are at suprapixel level. This ‘mesoscale’ is critical to habitat assessments. Most existing UAV‐based approaches use two‐dimensional (2D) textural variables to predict grain size. Validation of results is largely absent however, despite significant differences in platform stability and image quality obtained by manned aircraft versus UAVs. Here, we provide the first quantitative assessment of the accuracy and precision of grain size estimates produced from a 2D image texture approach. Furthermore, we present a new method which predicts subaerial gravel size using three‐dimensional (3D) topographic data derived from UAV imagery. Data is collected from a small gravel‐bed river in Cumbria, UK. Results indicate that our new topographic method gives more accurate measures of grain size (mean residual error ‐0.0001 m). Better results for the image texture method may be precluded by our choice of texture measure, the scale of analysis or the effects of image blur resulting from an inadequate camera gimbal. We suggest that at our scale of assessment, grain size is more strongly related to 3D variation in elevation than to the 2D textural patterns expressed within the imagery. With on‐going improvements, our novel method has potential as the first grain size quantification approach where a trade‐off between coverage and resolution is not necessary or inherent. Copyright © 2017 John Wiley & Sons, Ltd.     

Implementation of a second‐order paraxial boundary condition for a water‐saturated layered half‐space in plane strain

A half‐space finite element and a transmitting boundary are developed for a water‐saturated layered half‐space using a paraxial boundary condition. The exact dynamic stiffness of a half‐space in plane strain is derived and a second‐order paraxial approximation of the stiffness is obtained. A half‐space finite element and a transmitting boundary are then formulated. The development is verified by comparison of the dynamic stiffness of impermeable and permeable rigid strip foundations with other published results. The advantage of using the paraxial boundary condition in comparison with the rigid boundary condition is examined. It is shown that the paraxial boundary condition offers significant gain and the resulting half‐space finite element and transmitting boundary can represent the effects of a water‐saturated layered half‐space with good accuracy and efficiency. In addition, the numerical method described herein maintains the strengths and advantages of the finite element method and can be easily applied to demanding problems of soil–structure interaction in a water‐saturated layered half‐space. Copyright © 2010 John Wiley & Sons, Ltd.     

An automated salt‐tracing gauge for flow‐velocity measurement

This article introduces the SVG (salt‐velocity gauge), a novel automated technique for measuring flow velocity by means of salt tracing. SVG allows a high measuring rate (up to one every 2 seconds), short control section length (down to 10 cm), high accuracy (+[sol ]?1·5 cm s^?1), and unbiased calculation of the mean velocity in experimental conditions with turbulent, supercritical flow. A few cubic centimetres of saturated salt solution (NaCl) are injected into the flow at regular time intervals using a programmable solenoid valve. The tracer successively passes two conductivity probes placed a short distance downstream. The transformation of the signal between the two probes is modelled as a one‐dimensional diffusion wave equation. Model calibration gives an estimation of the mean velocity and the diffusion for each salt plume. Two implementations of the SVG technique are described. The first was an outdoors simulated rainfall experiment in Senegal (conductivity probes at 40 cm apart, 8 Hz measurement rate, salt injections at 10 second intervals). Mean velocity was estimated to range between 0·1 and 0·3 m s^?1. The second was a laboratory‐based flume experiment (conductivity probes at 10 cm apart, 32 Hz, salt injections at 2 second intervals). Another SVG with probes at 34 cm apart was used for comparison. An acoustic Doppler velocimeter (ADV) was also used to give an independent assessment of velocity. Using the 10 cm salt gauge, estimated mean velocity ranged from 0·6 to 0·9 m s^?1 with a standard deviation of 1·5 cm s^?1. Comparisons between ADV, 10 cm SVG and 34 cm SVG were consistent and demonstrated that the salt‐tracing results were unbiased and independent of distance between probes. Most peaks were modelled with r² > 90 per cent. The SVG technology offers an alternative to the dye‐tracing technique, which has been severely criticized in the literature because of the wide interval of recommended values for the correction factor α to be applied to the timings. This article demonstrates that a fixed value of α is inappropriate, since the correction factor varies with velocity, diffusion and the length of the control section. Copyright © 2005 John Wiley & Sons, Ltd.     

Kinematic transformations for planar multi‐directional pseudodynamic testing

The pseudodynamic (PSD) test method imposes command displacements to a test structure for a given time step. The measured restoring forces and displaced position achieved in the test structure are then used to integrate the equations of motion to determine the command displacements for the next time step. Multi‐directional displacements of the test structure can introduce error in the measured restoring forces and displaced position. The subsequently determined command displacements will not be correct unless the effects of the multi‐directional displacements are considered. This paper presents two approaches for correcting kinematic errors in planar multi‐directional PSD testing, where the test structure is loaded through a rigid loading block. The first approach, referred to as the incremental kinematic transformation method, employs linear displacement transformations within each time step. The second method, referred to as the total kinematic transformation method, is based on accurate nonlinear displacement transformations. Using three displacement sensors and the trigonometric law of cosines, this second method enables the simultaneous nonlinear equations that express the motion of the loading block to be solved without using iteration. The formulation and example applications for each method are given. Results from numerical simulations and laboratory experiments show that the total transformation method maintains accuracy, while the incremental transformation method may accumulate error if the incremental rotation of the loading block is not small over the time step. A procedure for estimating the incremental error in the incremental kinematic transformation method is presented as a means to predict and possibly control the error. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic model updating using a combined genetic‐eigensensitivity algorithm and application in seismic response prediction

A reliable computational model is necessary for evaluating the state and predicting the future performance of existing structures, especially after exposure to damaging effects such as an earthquake. A major problem with the existing iterative‐based model updating methods is that the search might be trapped in local optima. The genetic algorithms (GAs) offer a desirable alternative because of their ability in performing a robust search for the global optimal solution. This paper presents a GA‐based model updating approach using a real‐coding scheme for global model updating based on dynamic measurement data. An eigensensitivity method is employed to further fine‐tune the GA updated results in case the sensitivity problem arises due to restricted measurement information. The application on shear‐type frames reveals that with a limited amount of modal data, namely the lowest three natural frequencies and the first mode shape, it is possible to achieve satisfactory updating by the GA alone for cases involving a limited number of parameters (storey stiffness herein). With the incorporation of the eigensensitivity algorithm, the updating capability is extended to a sufficiently large number of parameters. In case the modal data contain errors, the GA is also shown to be able to update the model to a satisfactory accuracy, provided the required amount of modal data is available. An example is given in which a 6‐DOF stick model for an actual six‐storey RC frame is updated using the measured dynamic properties. The effectiveness of the updating is evaluated by comparing the measured and predicted seismic response using the updated model. Copyright © 2005 John Wiley & Sons, Ltd.     

A non‐baseline algorithm for damage locating in flexural structures using dynamic distributed macro‐strain responses

The concept of distributed strain‐sensing techniques has been proposed in our recent research, which was dedicated to utilizing the strain distributions throughout the full or partial areas of structures to detect arbitrary and unforeseen damage. An algorithm not requiring a detailed analytical model is presented for damage locating in flexural structures through the direct use of dynamic responses recorded by distributed long‐gauge strain sensors. The modal macro‐strain vector (MMSV), which has been proven to have a mapping relation with displacement mode shape, can be extracted directly from macro‐strain time‐series data, from which a damage evaluating index can be derived and used as an indicator for locating damage. Numerical examples are simulated to verify the sensitivity and effectiveness of the index in different cases. Furthermore, experimental investigations on a cantilevered beam with various long‐gauge fibre optic sensors placements are carried out to examine the feasibility and applicability of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessing the performance of structure‐from‐motion photogrammetry and terrestrial LiDAR for reconstructing soil surface microtopography of naturally vegetated plots

Soil microtopography is a property of critical importance in many earth surface processes but is often difficult to quantify. Advances in computer vision technologies have made image‐based three‐dimensional (3D) reconstruction or Structure‐from‐Motion (SfM) available to many scientists as a low cost alternative to laser‐based systems such as terrestrial laser scanning (TLS). While the performance of SfM at acquiring soil surface microtopography has been extensively compared to that of TLS on bare surfaces, little is known about the impact of vegetation on reconstruction performance. This article evaluates the performance of SfM and TLS technologies at reconstructing soil microtopography on 6 m × 2 m erosion plots with vegetation cover ranging from 0% to 77%. Results show that soil surface occlusion by vegetation was more pronounced with TLS compared to SfM, a consequence of the single viewpoint laser scanning strategy adopted in this study. On the bare soil surface, elevation values estimated with SfM were within 5 mm of those from TLS although long distance deformations were observed with the former technology. As vegetation cover increased, agreement between SfM and TLS slightly degraded but was significantly affected beyond 53% of ground cover. Detailed semivariogram analysis on meter‐square‐scale surface patches showed that TLS and SfM surfaces were very similar even on highly vegetated plots but with fine scale details and the dynamic elevation range smoothed out with SfM. Errors in the TLS data were mainly caused by the distance measurement function of the instrument especially at the fringe of occlusion regions where the laser beam intersected foreground and background features simultaneously. From this study, we conclude that a realistic approach to digitizing soil surface microtopography in field conditions can be implemented by combining strengths of the image‐based method (simplicity and effectiveness at reconstructing soil surface under sparse vegetation) with the high accuracy of TLS‐like technologies. Copyright © 2015 John Wiley & Sons, Ltd.     

RAPTOR‐UAV: Real‐time particle tracking in rivers using an unmanned aerial vehicle

River system measurement and mapping using UAVs is both lean and agile, with the added advantage of increased safety for the surveying crew. A common parameter of fluvial geomorphological studies is the flow velocity, which is a major driver of sediment behavior. Advances in fluid mechanics now include metrics describing the presence and interaction of coherent structures within a flow field and along its boundaries. These metrics have proven to be useful in studying the complex turbulent flows but require time‐resolved flow field data, which is normally unavailable in geomorphological studies. Contactless UAV‐based velocity measurement provides a new source of velocity field data for measurements of extreme hydrological events at a safe distance, and could allow for measurements of inaccessible areas. Recent works have successfully applied large‐scale particle image velocimetry (LSPIV) using UAVs in rivers, focusing predominantly on surficial flow estimation by tracking intensity differences between georeferenced images. The objective of this work is to introduce a methodology for UAV based real‐time particle tracking in rivers (RAPTOR) in a case study along a short test reach of the Brigach River in the German Black Forest. This methodology allows for large‐scale particle tracking velocimetry (LSPTV) using a combination of floating, infrared light‐emitting particles and a programmable embedded color vision sensor in order to simultaneously detect and track the positions of objects. The main advantage of this approach is its ability to rapidly collect and process the position data, which can be done in real time. The disadvantages are that the method requires the use of specialized light‐emitting particles, which in some cases cannot be retrieved from the investigation area, and that the method returns velocity data in unscaled units of px/s. This work introduces the RAPTOR system with its hardware, data processing workflow, and provides an example of unscaled velocity field estimation using the proposed method. First experiences with the method show that the tracking rate of 50 Hz allows for position estimation with sub‐pixel accuracy, even considering UAV self‐motion. A comparison of the unscaled tracks after Savitzky–Golay filtering shows that although the time‐averaged velocities remain virtually the same, the filter reduces the standard deviation by more than 40% and the maxima by 20%. Copyright © 2017 John Wiley & Sons, Ltd.     

Axially equilibrated displacement‐based beam element for simulating the cyclic inelastic behaviour of RC members

Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance‐based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits because they directly relate to damage and are therefore less dependent on member geometry and boundary conditions. However, predicting accurately strain demands still represents a major simulation challenge. Tension shift effects, which induce a linear curvature profile in the plastic hinge region of RC columns and walls, are one of the main causes for the mismatch between experimental and numerical estimates of local level quantities obtained through force‐based formulations. Classical displacement‐based approaches are instead suitable to simulate such linear curvature profile. Unfortunately, they verify equilibrium only on an average sense due to the wrong assumption on the axial displacement field, leading to poor deformation and force predictions. This paper presents a displacement‐based element in which axial equilibrium is strictly verified along the element length. The assumed transversal displacement field ensures a linear curvature profile, connecting accurately global displacement and local strain demands. The proposed finite element is validated against two sets of quasi‐static cyclic tests on RC bridge piers and walls. The results show that curvature and strain profiles for increasing ductility demands are significantly improved when axially equilibrated rather than classical displacement‐based or force‐based elements are used to model the structural members. Copyright © 2017 John Wiley & Sons, Ltd.     

An improvement to linear‐elastic procedures for seismic performance assessment

An improved linear‐elastic analysis procedure is developed in this paper as a simple approximate method for displacement‐based seismic assessment of the existing buildings. The procedure is mainly based on reducing the stiffness of structural members that are expected to respond in the inelastic range in a single global iteration step. Modal spectral displacement demands are determined from the equal displacement rule. Response predictions obtained from the proposed procedure are evaluated comparatively by using the results of benchmark nonlinear response history analysis, and both the conventional and the multi‐mode pushover analyses. In comparative evaluations, a twelve‐story RC plane frame and a six‐story unsymmetrical‐plan RC frame are employed by using 91 ground motion components. It is observed that the proposed procedure estimates the flexural deformation demands in deformation‐controlled members and the shear forces in force‐controlled members with reasonable accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

The Kinect: a low‐cost,high‐resolution,short‐range 3D camera

We present a novel application of the Kinect?, an input device designed for the Microsoft® Xbox 360® video game system. The device can be used by Earth scientists as a low‐cost, high‐resolution, short‐range 3D/4D camera imaging system producing data similar to a terrestrial light detection and ranging (LiDAR) sensor. The Kinect contains a structured light emitter, an infrared camera (the combination of these two produce a distance image), a visual wavelength camera, a three‐axis accelerometer, and four microphones. The cost is ~ US $100, frame rate is 30 Hz, spatial and depth resolutions are mm to cm depending on range, and the optimal operating range is 0.5 to ~5 m. The resolution of the distance measurements decreases with distance and is ≤1 mm at 0.5 m and ~75 mm at 5 m. We illustrate data collection and basic data analysis routines in three experiments designed to demonstrate the breadth and utility of this new sensor in domains of glaciology, stream bathymetry, and geomorphology, although the device is applicable to a number of other Earth science fields. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance of a real‐time pseudodynamic test system considering nonlinear structural response

This paper presents the implementation details of a real‐time pseudodynamic test system that adopts an implicit time integration scheme. The basic configuration of the system is presented. Physical tests were conducted to evaluate the performance of the system and validate a theoretical system model that incorporates the dynamics and nonlinearity of a test structure and servo‐hydraulic actuators, control algorithm, actuator delay compensation methods, and the flexibility of an actuator reaction system. The robustness and accuracy of the computational scheme under displacement control errors and severe structural softening are examined with numerical simulations using the model. Different delay compensation schemes have been implemented and compared. One of the schemes also compensates for the deformation of an actuator reaction system. It has been shown that the test method is able to attain a good performance in terms of numerical stability and accuracy. However, it has been shown that test results obtained with this method can underestimate the inelastic displacement drift when severe strain softening develops in a test structure. This can be attributed to the fact that the numerical damping effect introduced by convergence errors becomes more significant as a structure softens. In a real‐time test, a significant portion of the convergence errors is caused by the time delay in actuator response. Hence, a softening structure demands higher precision in displacement control. Copyright © 2007 John Wiley & Sons, Ltd.     

A novel predictor–corrector algorithm for sub‐structure pseudo‐dynamic testing

A new predictor–corrector (P–C) method for multi‐site sub‐structure pseudo‐dynamic (PSD) test is proposed. This method is a mixed time integration method in which computational components separable from experimental components are solved by implicit time integration method (Newmark β method). The experiments are performed quasi‐statically based on explicit prediction of displacement. The proposed P–C method has an important advantage as it does not require the determination of the initial stiffness values of experimental components and is thus suitable for representing elastic and inelastic systems. A parameter relating to quality of displacement prediction at boundaries nodes is introduced. This parameter is determined such that P–C method can be applicable to many practical problems. Error‐propagation characteristics of P–C method are also presented. A series of examples including linear and non‐linear soil–foundation–structure interaction problem demonstrate the performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd.     

A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

In this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.     

Time lapse structure‐from‐motion photogrammetry for continuous geomorphic monitoring

Recent advances are made in earth surface reconstruction with high spatial resolution due to SfM photogrammetry. High flexibility of data acquisition and high potential of process automation allows for a significant increase of the temporal resolution, as well, which is especially interesting to assess geomorphic changes. Two case studies are presented where 4D reconstruction is performed to study soil surface changes at 15 seconds intervals: (a) a thunderstorm event is captured at field scale and (b) a rainfall simulation is observed at plot scale. A workflow is introduced for automatic data acquisition and processing including the following approach: data collection, camera calibration and subsequent image correction, template matching to automatically identify ground control points in each image to account for camera movements, 3D reconstruction of each acquisition interval, and finally applying temporal filtering to the resulting surface change models to correct random noise and to increase the reliability of the measurement of signals of change with low intensity. Results reveal surface change detection with cm‐ to mm‐accuracy. Significant soil changes are measured during the events. Ripple and pool sequences become obvious in both case studies. Additionally, roughness changes and hydrostatic effects are apparent along the temporal domain at the plot scale. 4D monitoring with time‐lapse SfM photogrammetry enables new insights into geomorphic processes due to a significant increase of temporal resolution. Copyright © 2017 John Wiley & Sons, Ltd.     

基于多尺度球面小波解算GPS应变场的方法及应用

提出了利用多尺度球面小波解算GPS应变场的方法,该方法通过建立不规则分布的小波基函数以凸显测站非均匀分布的特征,获取不同空间尺度的应变场.通过对模拟数据进行对比分析验证该方法的有效性,模拟结果显示,多尺度球面小波应变计算方法稳健性较好.在位移场中加入高斯随机误差(均值为0.0mm,标准差为0.5mm)对应变计算结果的影响可忽略不计.从原有位移场随机抽取的60%的数据解算应变场时,仍然能够获取比较可靠的结果,但如果出现大范围的数据空缺,则会对应变结果产生明显影响.基于华北地区GPS测站原始观测数据,通过高精度数据处理方法解算了该区域GPS速度场,根据多尺度球面小波方法,解算了该区域的应变率场及其误差,并分析了其空间分布特征.