Co-seismic deformation for the 2015 M_(W)7.8 Gorkha earthquake(Nepal)using near-field GPS data

Seasonal variations and common mode errors affect the precision of the Global Positioning System(GPS)time series.In this paper,we explore to improve the precision of coordinate time series,thereby providing a better detection of weak or transient deformation signals,particularly co-seismic signals.Based on 97 GPS stations,including the campaign and continuous GPS stations in Nepal and southern Tibet,we first consider seasonal variations and common errors,then obtain co-seismic deformation of the 2015 Gorkha earthquake in Nepal and southern Tibet.Our co-seismic rupture model is characterized by a shallow ramp and a deeper detachment fault,in agreement with the relocated aftershock sequence.Our results indicate that the earthquake rupture is mainly distributed in the upper-crustal fault,and the maximum slip is up to 8.0 m at~15.0 km depth located in the approximate-80 km east of the epicenter.The average slip is more than 5 m,and the total modelled magnitude is M_(W)7.84,consistent with the observed seismic moment.Our rupture model for the 2015 Gorkha earthquake suggests that the rupture zone is not only in the upper crustal Main Himalayan Thrust(MHT),but also spreads to the northern segment of the MHT.

Modeling Near-Field Impulsive Waves Generated by Deformable Landslide Using the HBP Model Based on the SPH Method

Landslide-generated impulsive waves(LGWs)in reservoir areas can seriously threaten waterway safety as well as hu-man life and properties around the two side slopes.The risk reduction and mitigation of such a hazard require the accurate prediction of near-field wave characteristics,such as wave amplitude and run-up.However,near-field LGW involves complicated fluid-solid interactions.Furthermore,the wave characteristics are closely related to various aspects,including the geometry and physical features of the slide,river,and body of water.However,the empirical or analytical methods used for rough estimation cannot derive accurate results,especially for deformable landslides,due to their significant geometry changes during the sliding process.In this study,the near-field waves generated by deformable landslides were simulated by smoothed particle hydrodynamics(SPH)based on multi-phase flow.The deformable landslides were generalized as a kind of viscous flow by adopting the Herschel-Bulkley-Papanastasiou(HBP)-based nonNewtonian rheology model.The HBP model is capable of producing deformable landslide dynamics even though the high-speed sliding process is involved.In this study,an idealized experiment case originating from Lituya LGW and a practical case of Gongjiafang LGW were reproduced for verification and demonstration.The simulation results of both cases show satisfactory consistency with the experiment/investigation data in terms of landslide movement and near-field impulsive wave characteristics,thus indicating the applicability and accuracy of the proposed method.Finally,the effects of the HBP model’s rheological parameters on the landslide dynamics and near-field wave characteristics are discussed,providing a parameter calibration method along with sug-gestions for further applications.

Deformation and Stress Analysis of the Deepwater Steel Lazy Wave Riser Subjected to Internal Solitary Waves

The dynamic response of the steel lazy wave riser(SLWR)subjected to the internal solitary wave is a key to assessing its application feasibility.The innovation of this paper is to study the dynamic response properties of the SLWR with large deformation characteristics under internal wave excitation.A numerical scheme of the SLWR is constructed using the slender-rod theory,and the internal solitary wave(ISW)with a two-layer seawater model is simulated by the extended Korteweg-deVries equation.The finite element method combined with the Newmark-βmethod is applied to discretize the equations and update the time integration.The ISW excitation combined with vessel motion on the dynamic deformation and stress of the SLWR is investigated,and extensive simulations of the ISW parameters,including the interface depth ratio and density difference,are carried out.Case calculation reveals that the displacement of the riser in the lower interface layer increases significantly under the ISW excitation,and the stresses at a part of both ends grow evidently.Moreover,the mean value of riser responses under a combination of vessel motion and ISW coincides with the ISW-induced ones.Furthermore,the dynamic responses along the whole riser,including the displacement amplitudes,bending moment amplitudes,and stress amplitudes,almost increase with the increase in interface depth ratios and density differences.

Multi-scale Decomposition of Co-seismic Deformation from High Resolution DEMs:a Case Study of the 2004 Mid-Niigata Earthquake

Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imagery analyses only provide the displacement in the Line-of-Sight （LOS） direction or elevation changes. The 2004 Mid-Niigata earthquake in Japan provides lessons on how to decompose co-seismic deformation from two sets of DEMs. If three adjacent points undergo a rigid-body-translation movement, their co-seismic deformation can be decomposed by solving simultaneous equations. Although this method has been successfully used to discuss tectonic deformations, the algorithm needed improvement and a more rigorous algorithm, including a new definition of nominal plane, DEMs comparability improvement and matrix condition check is provided. Even with these procedures, the obtained decomposed displacement often showed remarkable scatter prompting the use of the moving average method, which was used to determine both tectonic and localized displacement characteristics. A cut-off window and a pair of band-pass windows were selected according to the regional geology and construction activities to ease the tectonic and localized displacement calculations, respectively. The displacement field of the tectonic scale shows two major clusters of large lateral components, and coincidently major visible landslides were found mostly within them. The localized displacement helps to reveal hidden landslides in the target area. As far as the Kizawa hamlet is concerned, the obtained vectors show down-slope movements, which are consistent with the observed traces of dislocations that were found in the Kizawa tunnel and irrigation wells. The method proposed has great potential to be applied to understanding post-earthquake rehabilitation in other areas.

Co-seismic changes of Wenchuan Ms8.0 earthquake and six aftershocks recorded by four deformation instruments at Xuzhou seismostation

Co-seismic changes of Wenchuan Ms8.0 earthquake and six strong aftershocks were recorded by 4 digital deformation instruments at Xuzhou seismostation at an cpicentral distance of 1392 km. The result shows that the straln-step changes and wave motions are caused by the arrival of the corresponding surface waves. The shape and size of the step changes and the response time were different for different instruments, even they were located in the same rock body only 7.65 m to 10.57 m apart. This difference is probably a reflection of different instrument properties, such as sensitivity and frequency response. The earthquake-caused stress changes, which were mainly compression in Xuzhou, had an important triggering effect on far-field strain changes

Lithospheric structure and deformation in SE Tibet revealed by ambient noise and earthquake surface wave tomography: Recent advances and perspectives

High-resolution lithospheric structure is essential for understanding the tectonic evolution and deformation patterns of the southeastern Tibetan plateau. This is now possible due to recent advances in ambient noise and earthquake surface wave tomography, and great improvements in data coverage from dense portable array stations deployed in SE Tibet. In this review paper, I first give a brief overview of the tomographic methods from ambient noise and earthquake surface waves, and then summarize the major findings about the lithospheric structure and deformation in SE Tibet revealed by ambient noise and earthquake surface wave tomography as well as by other seismic and geophysical observations. These findings mainly include the 3-D distribution of mechanically weak zones in the mid-lower crust, lateral and vertical variations in radial and azimuthal anisotropy, possible interplay of some fault zones with crustal weak zones, and importance of strike-slip faulting on upper crustal deformation. These results suggest that integration of block extrusion in the more rigid upper-middle crust and channel flow in the more ductile mid-lower crust will be more compatible with the current geophysical observations. Finally I discuss some future perspective researches in SE Tibet, including array-based tomography, joint inversion using multiple seismic data, and integration of geodynamic modeling and seismic observations.

Three kinds of nonlinear dispersive waves in elastic rods with finite deformation

On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.

NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD

A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.

Reconstructions of time-evolving sound-speed fields perturbed by deformed and dispersive internal solitary waves in shallow water

The high-fidelity reconstruction of sound speeds is crucial for predicting acoustic propagation in shallow water where internal solitary waves(ISWs)are prevalent.Mapping temperatures from time series to spatial fields is an approach widely used to reproduce the sound speed perturbed by deformed internal waves.However,wave-shape distortions are inherent in the modeling results.This paper analyzes the formation mechanism and dynamic behavior of the distorted waveform that is shown to arise from the mismatch between the modeled and real propagation speeds of individual solitons within an ISW packet.To mitigate distortions,a reconstruction method incorporating the dispersion property of an ISW train is proposed here.The principle is to assign each soliton a real speed observed in the experiment.Then,the modeled solitons propagate at their intrinsic speeds,and the packet disperses naturally with time.The method is applied to reconstruct the sound speed perturbed by ISWs in the South China Sea.The mean and median of the root-mean-square error between the reconstructed and measured sound speeds are below 2 m/s.The modeled shape deformations and packet dispersion agree well with observations,and the waveform distortion is reduced compared with the original method.This work ensures the high fidelity of waveguide-environment reconstructions and facilitates the investigation of sound propagation in the future.

GEOMETRICAL NONLINEAR WAVES IN FINITEDEFORMATION ELASTIC RODS

By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.

The Interaction of Oblique Flexural Gravity Waves With a Small Bottom Deformation on a Porous Ocean-Bed： Green＇s Function Approach

The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.

Reliability Analysis of Numerical Simulation of Sea-Crossing Bridge Deformation Under Wave Forces

To study on the numerical simulation calculation reliability of sea-crossing bridge under complex wave forces,the paper applied GPS deformation monitoring and numerical simulation calculation by researching Qingdao Jiaozhou Bay Sea-Crossing Bridge.The db3 wavelet three-layer decomposition was used on the horizontal movement of the sea-crossing bridge and the wind speed of the waves to analyze their correlation.The complex wave forces value of Qingdao Jiaozhou Bay Sea-Crossing Bridge was loaded on FLAC3D software successfully to make numerical simulation calculation of bridge deformation.Since the accuracy of the GPS deformation monitoring reaches millimeter level,it was used to monitor the exact value of the bridge deformation to judge the reliability of numerical simulation.The relative errors of displacement in X,Y and Z directions were between 33%and 41%through comparison.It could be seen that the numerical simulation error was relatively large,which was mainly due to various environmental factors and the deviation of applied wave forces.However,numerical simulation generally reflects the deformation law of the sea-crossing bridge under complex wave forces,providing an effectively technical support for the safe operation assessment of the sea-crossing bridge.

Scattering of Oblique Surface Waves by the Edge of Small Deformation on a Porous Ocean Bed

The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.

Finite element analysis of controlling the TC4 thin plate weldment wave-like deformation by welding with impacting rotation

The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of controlling the wave-like deformation. In order to know the development of internal thermal stress and strain, finite element method is utilized for- the stress and strain are difficult to be investigated by experimental methods during the welding process. Temperature field, thermal stress evolution and distortion of thin plate are compared with the test results such as weld thermal cycle, residual stress sectioning measurement, and the deflection of the thin plate respectively. By the finite element analysis and test results verification, the meehaaism of the technology to control the wave-like deformation is brought forward, non-uniform thermal elastic strain between compressive plastic region and elastic extensive region is diminished by a certain amount of extensive plastic deformation by welding with impacting rotation process.

SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD

A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.

Comparison of Excitation of Acoustic-Electromagnetic Wave in Piezoelecric Crystal and Crystal with Potential of Deformation

In this article, the comparison of excitation in high frequencies of acoustic-electromagnetic wave in piezoelecric crystal and crystal with potential of deformation GaAs is investigating. Possible mechanisms of coupling different hybrid waves are the piezoeffect and the deformation potential. As a model it is analyzing a film of crystal places between two symmetrical substrates with the other materials without an acoustic contact. This film includes 2D electron gas with a high negative differential conductivity and uniform initial distribution of electrons. The hybrid acoustic-electromagnetic wave and hybrid space charge wave interact. Amplification of space charge wave takes place due to negative differential conductivity in GaAs. This amplification of space charge waves is causing the amplification of acoustic-electromagnetic wave. It is to show that the symmetric modes, emerging as transverse ones, interact more effectively with the space charge waves. Another important result is the following: at the frequencies f ≈ 10 GHz, the excitation efficiency of acoustic-electromagnetic wave with transverse displacement due to piezoeffect is more effective, but at higher frequencies, the deformation potential is dominating.

Stress wave propagation and incompatible deformation mechanisms in rock discontinuity interfaces in deep-buried tunnels

Complex weak structural planes and fault zones induce significant heterogeneity,discontinuity,and nonlinear characteristics of a rock mass.When an earthquake occurs,these characteristics lead to extremely complex seismic wave propagation and vibrational behaviors and thus pose a huge threat to the safety and stability of deep buried tunnels.To investigate the wave propagation in a rock mass with different structural planes and fault zones,this study first introduced the theory of elastic wave propagation and elastodynamic principles and used the Zoeppritz equation to describe wave field decomposition and develop a seismic wave response model accordingly.Then,a physical wave propagation model was constructed to investigate seismic waves passing through a fault,and dynamic damage was analyzed by using shaking table tests.Finally,stress wave attenuation and dynamic incompatible deformation mechanisms in a rock mass with fault zones were explored.The results indicate that under the action of weak structural planes,stress waves appear as a complex wave field decomposition phenomenon.When a stress wave spreads to a weak structural plane,its scattering may transform into a tensile wave,generating tensile stress and destabilizing the rock mass;wave dynamic energy is absorbed by a low-strength rock through wave scattering,which significantly weakens the seismic load.Wave propagation accelerates the initiation and expansion of internal defects in the rock mass and leads to a dynamic incompatible deformation.This is one of the main causes for large deformation and even instability within rock masses.These findings provide an important reference and guide with respect to stability analysis of rock mass with weak structural planes and fault zones.

A Note on the Solution of Water Wave Scattering Problem Involving Small Deformation on a Porous Channel-Bed

The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.

Large post-liquefaction deformation of sand:Mechanisms and modeling considering water absorption in shearing and seismic wave conditions

Large deformation of sand due to soil liquefaction is a major cause for seismic damage.In this study,the mechanisms and modeling of large post-liquefaction deformation of sand considering the significant influence of water absorption in shearing and seismic wave conditions.Assessment of case histories from past earthquakes and review of existing studies highlight the importance of the two factors.Based on the micro and macro scale mechanisms for post-liquefaction shear deformation,the mechanism for water absorption in shearing after initial liquefaction is revealed.This is aided by novel designed constant water-absorption-rate shear tests.Water absorption in shearing can be classified into three types,including partial water absorption,complete water absorption,and compulsory water absorption.Under the influence of water absorption in shearing,even a strongly dilative sand under naturally drained conditions could experience instability and large shear deformation.The mechanism for amplification of post-liquefaction deformation under surface wave load is also explained via element tests and theoretical analysis.This shows that surface wave–shear wave coupling can induce asymmetrical force and resistance in sand,resulting in asymmetrical accumulation of deformation,which is amplified by liquefaction.A constitutive model,referred to as CycLiq,is formulated to capture the large deformation of sand considering water absorption in shearing and seismic wave conditions,along with its numerical implementation algorithm.The model is comprehensively calibrated based on various types of element tests and validated against centrifuge shaking table tests in the liquefaction experiments and analysis projects(LEAP).The model,along with various numerical analysis methods,is adopted in the successful simulation of water absorption in shearing and Rayleigh wave-shear wave coupling induced large liquefaction deformation.Furthermore,the model is applied to high-performance simulation for large-scale soil-structure interaction in liquefiable ground,including underground structures,dams,quay walls,and offshore wind turbines.

Co-seismic displacements of 2011 Japan Mw9.0 earthquake recorded by far-field GPS stations

Co-seismic displacements of the 2011 Mw9.0 Japan earthquake recorded by GPS stations in China and surrounding areas showed a movement toward the epicenter. The horizontal displacements were up to 1 - 3 cm in northeastern China, 3 -8 mm in the North China, and 2 cm in the Korean peninsula. The vertical movements in China were small uplifts.