Vertical Component Of Displacement Research Articles

Three-dimensional surface deformation from multi-track InSAR and oil reservoir characterization: A case study in the Liaohe Oilfield, northeast China

Oil productions can result in pore pressure drop in the reservoir, generating an increase in effective stress and leading to reservoir compaction. The compaction in the subsurface reservoir translates to the earth's surface, which is manifested as a loss of elevation (land subsidence), causing damages to oil production facilities and surface infrastructures. The Liaohe oilfield, located in Liaohe River Delta (LRD), northeast of China, is one of the most significant subsidence areas in China as a direct consequence of oil extraction from the reservoir. Previous studies carried out in this area assumed the oil production-induced displacement retrieved from Interferometric Synthetic Aperture Radar (InSAR) corresponds only to vertical deformation. In this work, for the first time, we proposed a method to retrieve the full three-dimensional (3D) displacement field over the oilfield. We retrieved the vertical and east-west displacement components by combining the multiple-geometry InSAR line-of-sight (LOS) observations and retrieved the north-south component based on the assumption of a physical relationship between the horizontal and vertical displacement. Two ascending and two descending datasets from Sentinel-1 satellite covering the area were processed by an InSAR time series analysis over the 2017 to 2021 period, providing consistent displacement rate maps and displacement time series in the LOS direction. Spatial local-scale land subsidence was found in several producing fields over the deltaic region, including Shuguang, Huanxiling, and Jinzhou oilfields. The 3D displacement decomposition was then conducted in Shuguang oilfield. The derived 3D displacement field exhibit a circular subsidence bowl with a maximum subsiding rate reaching 212 mm/year, accompanied by a centripetal pattern of horizontal displacements with maximum rates up to 50–60 mm/year moving towards the subsidence center. The retrieved 3D displacements are in good agreement with predictions from the geomechanical modeling by assuming a disk-shaped reservoir subject to a uniform reduction in pore fluid pressure. Finally, we show the importance of knowing both the vertical and horizontal displacement in characterizing the lateral boundary of the subsurface reservoir.

Analytical solution for diffraction of magnetoelastic plane waves by a rigid strip in self-reinforced medium: a contour integration method

This study analytically addresses the diffraction of magnetoelastic plane waves by a rigid strip in a self-reinforced infinite elastic medium. Formulation of the studied model includes mixed type boundary value problem and has been solved by the method of integral equation. The expressions of vertical diffracted displacement and normal stress are established in the closed form by employing the contour integration technique. For the sake of validation, the deduced expressions of vertical diffracted displacement and normal stress are reduced to the special cases, such as without magnetoelastic coupling as well as anisotropy and matched with the pre-established results. The diffraction patterns for the vertical displacement component in the considered material medium are calculated numerically, and its dependence on various affecting parameters viz. magnetoelastic coupling parameter, phase velocity, wave number of the propagating magnetoelastic plane wave, and distance has been depicted graphically for self-reinforced and isotropic materials. Moreover, the influence of anisotropy of the infinite medium has been portrayed remarkably by the comparative study.

SPAMS: A new empirical model for soft soil surface displacement based on meteorological input data

We present SPAMS: Simple Parameterization for the Motion of Soils, a model to describe the motion of deformable soils in the Vadose zone, mainly peat and clay, herein called shallow soft soils. The SPAMS model estimates the reversible and irreversible vertical component of surface displacement to within sub-centimetre RMSE, using only four parameters: three scaling factors and an integration time. Requiring only meteorological data as an input, its lightweight nature and simple implementation make it a powerful tool when used as a first approximation in inverse problems like those encountered in remote sensing. It has been validated against in-situ data from five test sites in The Netherlands with different Holocene soil strata.

Groundwater Storage Variations in the Main Karoo Aquifer Estimated Using GRACE and GPS

The Gravity Recovery and Climate Experiment (GRACE) provided valuable insights into variations in Groundwater Storage (GWS). However, the sensitivity of utilizing Global Positioning System (GPS) time series displacement data for detecting changes in GWS remains a subject of ongoing discussion. In order to estimate the spatiotemporal GWS, we selected a vertical displacement from 65 GPS stations located in the Main Karoo Aquifer (MKA). We performed total water storage (TWS) inversion on GPS vertical displacement components; after that, we deducted surface water components based on the Global Land Data Assimilation System (GLDAS) from January 2013 to December 2021. Additionally, for validation, we compared our GWS estimates with the GRACE-derived GWS and observed GWS values derived from the WaterGAP Global Hydrology Model (WGHM) compartments. We discovered that the TWS and GWS trends derived from GPS and GRACE exhibited similar behaviors with trend values overestimated by GRACE and WGHM. Our findings demonstrate relatively typical behavior between GPS and GRACE in the first and second principal component behaviors (PCs) and empirical orthogonal function (EOF) loadings (or spatial patterns). With a contribution of 71.83% to GPS-derived GWS variability and 68.92% to GRACE-derived GWS variability, EOF-1 is a relatively potent factor. For Principal Components PC1 and PC2, the GRACE and GPS PCs have correlation coefficients of 0.75 and 0.84, respectively. Finally, with higher temporal resolution, GPS can perform the same task as GRACE in hydrological applications. In addition, GPS can add important and valuable information to assess regional GWS change.

Soil–pile interaction in vertical vibration in inhomogeneous soils

AbstractThis paper develops a novel reference analytical solution for axially loaded piles in inhomogeneous soils, extending the pioneering elastodynamic model of Nogami and Novak (1976) to piles embedded in vertically inhomogeneous soils. Following the classical earlier model, the pile is modelled as a rod, using the strength‐of‐materials solution, and the soil layer as an approximate continuum, which rest on rigid rock. The approximation lies in reducing the number of dependent variables by eliminating certain stresses and displacements in the governing elastodynamic equations: the vertical normal and vertical shear stresses in the soil are controlled exclusively by the vertical component of the soil displacement. Soil inhomogeneity is introduced via a power law variation of shear modulus with depth, and perfect bonding is assumed at the soil–pile interface. The proposed generalized formulation treats two types of inhomogeneity by employing pertinent eigen expansions of the dependent variables over the vertical coordinate. The response is expressed in terms of generalized Fourier series and includes: (i) displacements and stresses along the pile and the pile–soil interface; and (ii) displacement and stress in the soil. Contrary to available models for homogeneous soils, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered.

Theoretical investigation of Rayleigh surface acoustic wave propagation characteristics in c-axis-zigzag ScAlN film/silicon substrate structure

Surface acoustic wave (SAW) resonators are key components of mobile communication systems, and the development of wideband SAW resonators is especially required because next-generation mobile communication systems require high-speed data transmission using wide frequency bands. In this study, two layered structures—(i) a c-axis-tilted ScAlN bilayer film/silicon substrate and (ii) a c-axis-zigzag ScAlN film/silicon substrate—are proposed for highly coupled SAW resonators, and the electromechanical coupling coefficient K2 of the non-leaky Rayleigh-mode SAW propagating in these structures is investigated theoretically. With a proper c-axis tilt angle and thickness selection of the ScAlN film, the first-mode Rayleigh SAW in the c-axis-tilted ScAlN bilayer film/silicon substrate and c-axis-zigzag ScAlN film/silicon substrate offers high K2. The maximum K2 was 9.56%, obtained in the c-axis-zigzag ScAlN film/silicon substrate structure, which was 2.5 times the maximum K2 in the c-axis-tilted ScAlN monolayer film/silicon substrate structure; this is because the c-axis-zigzag ScAlN films increase the shear vertical component of the SAW particle displacement, most of which is concentrated in the c-axis-zigzag ScAlN film on the silicon substrate. It is also important that the second-mode SAW (Sezawa wave) in the c-axis-zigzag ScAlN film/silicon substrate structure is not excited when the K2 value of the first-mode SAW is maximized. The techniques for fabricating a c-axis-tilted ScAlN film and a c-axis-zigzag ScAlN film have been reported, and well-established micromachining technology related to silicon semiconductors offers significant advantages in the manufacturing and processing of SAW resonators. Therefore, the c-axis-zigzag ScAlN film/silicon substrate structure has significant potential for SAW device applications.

Real‐Time Seismogeodetic Earthquake Magnitude Estimates for Local Tsunami Warnings

AbstractWe estimate a seismogeodetic earthquake moment magnitude using unclipped, broadband velocity and displacement waveforms from collocated Global Navigation Satellite Systems and seismic stations located within 800 km epicentral distance for nine 7.2 < < 9.1 earthquakes. We consider the vertical component of seismogeodetic displacement as an approximate source time function and integrate the associated time series to obtain the seismic moment. By continuing to integrate vertical displacement beyond the initial P‐waves, we obtain rapid estimates of that are within 0.2 magnitude units for 8 thrust faulting events and within 0.3 units for the single normal faulting event. Because our estimates of the seismic moment are based on the maximum value of integrated displacement, no regression against other source parameters, or distance, is necessary. Our new method shows promise for integration into earthquake and local tsunami early warning systems, including tsunami earthquakes characterized by relatively slow moment release over a longer rupture time, and earthquakes with complex source time functions.

Modelling and prediction of GNSS time series using GBDT, LSTM and SVM machine learning approaches

Global navigation satellite system (GNSS) site coordinate time series provides essential data for geodynamic and geophysical studies, realisation of a regional or global geodetic reference frames, and crustal deformation research. The coordinate time series has been conventionally modelled by least squares (LS) fitting with harmonic functions, alongside many other analysis methods. As a key limitation, the traditional modelling approaches simply use the functions of time variable, despite good knowledge of various underlying physical mechanisms responsible for the site displacements. This paper examines the use of machine learning (ML) models to reflect the effects or residential effects of physical variables related to Sun and the Moon ephemerides, polar motion, temperature, atmospheric pressure, and hydrology on the site displacements. To form the ML problem, these variables are constructed as the input vector of each ML training sample, while the vertical displacement of a GNSS site is regarded as the output value. In the evaluation experiments, three ML approaches, namely the gradient boosting decision tree (GBDT) approach, long short-term memory (LSTM) approach, and support vector machine (SVM) approach, are introduced and evaluated with the time series datasets collected from 9 GNSS sites over the period of 13 years. The results indicate that all three approaches achieve similar fitting precision in the range of 3–5 mm in the vertical displacement component, which is an improvement in over 30% with respect to the traditional LS fitting precision in the range of 4–7 mm. The prediction of the vertical time series with the three ML approaches shows the precision in the range of 4–7 mm over the future 24- month period. The results also indicate the relative importance of different physical features causing the displacements of each site. Overall, ML approaches demonstrate better performance and effectiveness in modelling and prediction of GNSS time series, thus impacting maintenance of geodetic reference frames, geodynamics, geophysics, and crustal deformation analysis.

Analysis of the Influence of Motors Installed in Passenger Car Wheels on the Torsion Beam of the Rear Axle Suspension

The influence of mounting motors in wheels’ hubs and flexibility of the twist beam rear suspension on their dynamics and strength is presented in the paper. The international roughness indicator (IRI) is applied to assess the overcoming of road unevenness. This indicator is a combination of a shape of the road unevenness and of overcoming velocity. The movement of a wheel’s axis during obstacles overcoming is described. For the needs of the dynamics analysis, the mathematical model of the rear suspension system with embedded motors is developed using the MSC.Adams-ANSYS interface. The discrete model of the twist beam is prepared in the ANSYS software, which is used in the next step to construct the dynamics model of the rear suspension system using the MSC.Adams program. The vertical components of displacement and acceleration of the wheel’s centre, forces in the suspension’s springs and dampers, as well as forces in the joints are analyzed. The analysis of the suspension beam’s stress during the road unevenness overcoming is also carried out.

Land subsidence surrogate models for normally consolidated sedimentary basins

This article presents a methodology for building a computationally-fast “surrogate model” to simulate land subsidence due to fluid extraction from normally consolidated sedimentary basins. The model relies on the extension of the classic nucleus of strain solution (NoS) in a homogeneous semi-infinite continuum to heterogeneous basins, in which the uniaxial vertical compressibility cM varies along the depth z following either a power or an exponential law. The NoS solution represents the horizontal and vertical components of the surface displacement associated with a unit volume at a given depth c in which a unit change of pore pressure occurs. The modified NoS solution is obtained by fitting the horizontal and vertical components of the surface displacement calculated using a finite-element (FE) numerical model. This is achieved through a regression algorithm that identifies four fitting parameters. By repeating such a regression over a set of combinations of the coefficients of the basin compressibility model cM(z), it is possible to identify four functions that emulate the variability of the four fitting parameters with respect to the compressibility model coefficients. The surrogate land subsidence model is then built by integrating the modified NoS equations within the subsurface region (e.g. an aquifer) where a change in pore pressure occurs due to fluid abstraction. Such formulation results in an explicit “response-matrix” approach, where the forcing terms depend on the pore pressure variations, and the matrix coefficients account for the selected basin compressibility model. The implementation approach is quite straightforward and powerful, as it allows, for example, to easily construct a land subsidence package “online” over any groundwater flow model, or estimate “offline” the land surface displacement associated with any simulated or observed 3D pore pressure change field. The surrogate land subsidence model is tested with a series of numerical experiments, and is shown to produce accurate results within the working assumptions of the model.

Propagation behavior of Love-type waves in poro-elastic medium using staggered grid finite difference Scheme

The analysis of the propagation behaviour of seismic waves in porous medium requires a mathematical backup. That is pictured here. The present study investigates the propagation behavior of Love-type waves in poro-elastic medium. A staggered grid finite-difference (SFD) scheme in time-space domain formulation for the Biot’s equation of poro-elasticity, is presented and applied to the problem. Complete theoretical seismograms for the horizontal and vertical components of displacement are obtained. The dispersion curves are evaluated considering the material parameters of different models. The stability analysis of the above numerical scheme is deliberated. From different graphs, it is noticed that there is difference in phase velocity for various models. By observing the curves behaviour, we can understand the nature of the composite structure. Our outcomes also endorse the finite difference modeling is an important numerical tool to acquire knowledge about the transmission of seismic waves in porous medium. The agreement is excellent.

Interseismic Deformation From Sentinel‐1 Burst‐Overlap Interferometry: Application to the Southern Dead Sea Fault

AbstractInterferometric Synthetic Aperture Radar (InSAR) data are increasingly being used to map interseismic deformation with ascending and descending‐orbit observations allowing for resolving the near‐east and vertical displacement components. The north component has, however, been difficult to retrieve due to the limited sensitivity of standard InSAR observations in that direction. Here, we address this problem by using time‐series analysis of along‐track interferometric observations in burst‐overlap areas of the Terrain Observation with Progressive Scan imaging mode of the Sentinel‐1 radar satellites. We apply this method to the southern part of the near‐north striking Dead Sea transform fault to show that the ∼5 mm/year relative motion is well recovered. Furthermore, the results indicate the locking depth of the fault decreases toward the south as it enters the transtensional Gulf of Aqaba basin. Our results show that time‐series analysis of burst‐overlap interferometric observations can be used to obtain meaningful interseismic deformation rates of slow‐moving and northerly striking faults.

New modification of the acoustic Lamb waves and its application for liquid and ice sensing

Using quartz plates as an example existance of the new modification of the Lamb waves is demonstrated. The waves have small vertical displacement, large shear-horizontal and longitudinal components, and elliptic polarization which is oriented parallel to the plate faces. Numerical calculations of the surface displacements and depth profiles show the particular polarization is maintained at any depth from free faces and for all plate thickness in the range h/λ = 0–1.7 (h - thickness, λ - wave length). Results of the measurements accomplished for four new modes and three plate thickness h/λ confirm that radiation of the waves into adjucent liquid (which is proportional to vertical displacement) is small, while viscoelestic loss of the same the waves (which is proportional to in-plane components) is large. This property makes the modified waves suitable for sensing liquids and ices. In particular, responses of the waves towards liquid viscosity and water-to-ice transformation are larger than those are for common Lamb waves approaching 27 and 50 dB, respectively, at about 30 MHz, 1500 cP, and 10 mm propagation path.

Ground Deformation Modelling of the 2020 Mw6.9 Samos Earthquake (Greece) Based on InSAR and GNSS Data

Modelling of combined Global Navigation Satellite System (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) data was performed to characterize the source of the Mw6.9 earthquake that occurred to the north of Samos Island (Aegean Sea) on 30 October 2020. Pre-seismic analysis revealed an NNE–SSW extensional regime with normal faults along an E–W direction. Co-seismic analysis showed opening of the epicentral region with horizontal and vertical displacements of ~350 mm and ~90 mm, respectively. Line-of-sight (LOS) interferometric vectors were geodetically corrected using the GNSS data and decomposed into E–W and vertical displacement components. Compiled interferometric maps reveal that relatively large ground displacements had occurred in the western part of Samos but had attenuated towards the eastern and southern parts. Alternating motions occurred along and across the main geotectonic units of the island. The best-fit fault model has a two-segment listric fault plane (average slip 1.76 m) of normal type that lies adjacent to the northern coastline of Samos. This fault plane is 35 km long, extends to 15 km depth, and dips to the north at 60° and 40° angles for the upper and lower parts, respectively. A predominant dip-slip component and a substantial lateral one were modelled.

Cosine Integral Transform Method for Solving the Westergaard Problem in Elasticity of the Half-Space

The cosine integral transform method is applied to find the expressions for spatial variations of displacements and stresses in the Westergaard continuum under vertical concentrated loading, and distributed loadings acting over lines and geometric areas on the surface. The half-space is considered to be horizontally inextensible and the displacement field reduces to the vertical displacement component. The paper derives a displacement formulation of the equation of equilibrium in the vertical direction. Cosine integral transformation is applied to the formulated equation and the Boundary Value Problem (BVP) is found to simplify to Ordinary Differential Equation (ODE). The general solution of the ODE is obtained in the cosine integral transform space. The requirement of bounded solutions is used to obtain one integration constant. Inversion of the bounded solution gave the solution in the real problem domain space. The stress fields are obtained using the stress-displacement equations. The requirement of equilibrium of the vertical stress fields and the vertical point loading at the origin is used to determine the remaining integration constant, and thus the vertical deflections and the stresses. The solutions obtained are kernel functions employed to derive the expressions for solutions for line, and uniformly distributed loads applied over given geometric areas such as rectangular and circular areas. The vertical stresses are expressed in terms of dimensionless vertical stress influence factors and tabulated. The vertical displacements and stresses obtained are identical with Westergaard solutions obtained by stress function method. The solutions agree with results obtained by Ike using Hankel transform method.

An approach for retrieving complete three-dimensional ground displacement components from two parallel-track InSAR measurements

In the investigation and evaluation of geological hazards such as those caused by co-seismic displacement, displacement due to underground mining, landslides, volcanic eruptions, it is important to retrieve the complete three-dimensional ground displacement components. However, both conventional D-InSAR (differential synthetic aperture radar interferometry) and MT-InSAR (multi-temporal InSAR) can only measure the displacement component along the radar LOS (line of sight) direction, which greatly limits the application of InSAR technique. Over the past decades, great endeavors have been made to overcome its limitation of the one-dimensional LOS measurements, and several methods have been proposed to retrieve complete three-dimensional displacement components from InSAR measurements. On the whole, the commonality of the existing methods is characterized by using both ascending and descending SAR data. In this paper, we put forward an approach for retrieving complete three-dimensional ground displacement components from two parallel-track InSAR measurements and present the analytical expressions for the vertical, the North–South, the East–West displacement components. It reveals that the vertical displacement component is just a function of the two parallel-track InSAR LOS displacements, i.e., the vertical displacement component can be retrieved from the two parallel-track InSAR LOS displacements, while the North–South or the East–West displacement component is a function of both the two parallel-track InSAR LOS displacements and the azimuthal displacement. What is more, the proposed approach can effectively improve the accuracy of the azimuthal measurement by using a redundant measurement. As a result, the accuracies of the derived North–South and East–West displacement components are improved as well, which can provide more reliable results for characterizing ground movement associated with geological hazards. In terms of their geographic coverage, there is a strong complementary relationship between the proposed approach and the existing methods. Thus, they can be integratedly utilized in the practical applications. Finally, the approach is illustrated through the retrieval of the complete three-dimensional co-seismic displacement components in an area to the west of Bam, Iran, where a strong earthquake occurred in 2003.

Assembly Variation Analysis of Incompletely Positioned Macpherson Suspension Systems Considering Vehicle Load Change

Abstract The assembly precision of wheel alignment parameters is vital to vehicle handling stability. Due to the vertical wheel displacement and compliant components in suspension systems, it is difficult to assemble qualified vehicles with proper wheel alignment parameters. In the assembly shop of the automobile factory, the adjustment of wheel alignment parameters is the most time-consuming process because it relies on trial and error. In order to provide a theoretical guidance to the precision control of wheel alignment parameters, this paper extends the theory of equilibrium equations of incremental forces (EEIF) to 3D compliant mechanisms. Constraint equations of kinematic joints are adopted to express the spatial relationships of different parts. A couple of fixed and floating joint coordinate systems (CSs) are used together to represent deviations of compliant components. The impacts of suspension part deviations on vertical wheel displacement and assembly deformations are well illustrated by such approach. Accuracy of the proposed method is verified by comparing with ADAMS simulation. The results show that the error rates of the 3D EEIF method are less than 5%. Furthermore, statistical assembly variation analysis of a Macpherson suspension is accomplished by using the proposed method and an optimized process strategy is put forward.

Tectonic and non-tectonic crustal deformation in Kumaun Garhwal Himalaya

A detailed characterization of the crustal deformation in the Himalaya is important to understand the tectonic and non-tectonic deformation processes responsible for the strain build-up and transients in deformation. In the present work, we have characterised the present day tectonic and non-tectonic deformations in the Kumaun Garhwal Himalaya estimated from the continuous GPS measurements. We observed strong seasonal variations in the horizontal and vertical displacement components (i.e. North, East and Vertical). The transient surface deformation estimated from global hydrological models is found to explain ~40–60% of the observed seasonal variations at sites. Plate convergence rate, and variation of slip deficit on the Main Himalayan Thrust (MHT) are calculated using site velocity estimated after removal of seasonal variations from the GPS time series. We report an excessive compression with an average principal shortening rate of −0.09 μ strain/yr in the north-northeast direction. The derived plate convergence rate is 18 ± 1 mm/yr and the width of locked frontal part of MHT is 100 ± 15 km. The quiescence of major to great earthquakes in the region since at least past 200 years and high rate of strain build up make this region vulnerable for a potentially devastating earthquake of Mw ≥ 8 in near future.

Experimental study of cross-ice acoustic signal propagation

To obtain the channel characteristics of acoustic information across ice propagation, a field experimental was conducted involving of cross-ice acoustic (CIA) direct-sequence spread spectrum communication. In the experiment, three single-component geophones installed on the surface of the ice layer were used to measure the vertical component of the particle displacement. For comparison, two hydrophones were used to measure the sound pressure for under-ice acoustic (UIA) communication. The experimental results are used to compare and analyze the characteristics of the two communication methods. This paper uses the normal model theory to calculate the acoustic signal propagation characteristics. The calculation results explain why (i) the acoustic speed of the signal received by the geophone is less than that in the water and (ii) the frequency characteristics of the UIA and CIA communication channels differ. Finally, the communication performance based on differential energy detector is analyzed, and the feasibility of CIA direct-sequence spread spectrum communication is verified.

Sports bra but not sports footwear decreases breast movement during walking and running

Running is a modality that has a large number of adepts, including women. Therefore, it is important to understand how sportswear can help women, with special attention to the breast movement. The aim of this study was to analyse the effect of different combinations of breast support and footwear on the breast movement during walking and running. Twenty women performed treadmill walking (5 km/h) and running (7 and 10 km/h) combining different footwear (barefoot, minimalist, and traditional) and breast support conditions (bare breast, everyday bra, and sports bra). Three-dimensional data from breast and trunk markers were tracked for 10 stride cycles. Relative breast displacement was calculated and derived for velocity. An interaction effect was observed between support, footwear, and speed conditions. The bare breast conditions presented differences from the other conditions in the majority of the kinematic variables, presenting higher breast displacement and velocity values. On the other hand, the sports bra conditions presented the lowest values for the kinematics variables. In the vertical component of breast displacement during running (10 km/h) we verified that the sports bra presented reductions of 56% and 43% in relation to the bare breast and everyday bra conditions, respectively. Despite this, no differences were found between footwear within each breast support condition. A sports bra is efficient to decrease breast movement. In addition, neither of the tested footwear was able to decrease these movements.