Equation Method Research Articles

Characteristics of spatial and temporal changes in ecosystem service value and threshold effect in Henan along the Yellow River, China

Ecosystem services (ES), which serve as the link between human activities and natural ecosystems, are crucial for maintaining ecological balance and supporting economic development. The Ecosystem Services Value (ESV) is an indicator used to quantifying ecosystem services. Accurately estimating the dynamics of ESV and the threshold effects of influencing factors is of great importance for the sustainable development of the region. This study constructs an ESV valuation model based on the equivalent factor method, incorporating construction land, and corrects the initial valuation results in three dimensions. By constructing a random forest model and integrating partial dependence analysis, Elevation, Evapotranspiration, Normalized Difference Vegetation Index, and the proportion of built-up land area were identified as significant factors in determining ecologically vulnerable areas within the study region. The results show that: (1) The total ESV in Henan along the Yellow River in 2000, 2005, 2010, 2015, and 2020 was 204.612 billion yuan, 249.775 billion yuan, 239.100 billion yuan, 234.868 billion yuan and 202.767 billion yuan, respectively. The overall trend of change is first growth and then decline, with spatial features remaining relatively stable, and ESV polarization becoming more pronounced. (2) The spatial clustering characteristics of ESV in Henan along the Yellow River are remarkable, and the cold and hot spot areas show a bidirectional expansion trend. The cold spot areas expand substantially around the construction land, whilethe hot spot areas show a small expansion around the western mountain areas and the vegetation areas along the Yellow River, but the overall growth is slower. (3) The main factors affecting ESV include three natural factors and one anthropogenic factor, namely evapotranspiration (ET), the proportion of built-up land area (POB), normalized vegetation index (NDVI) and elevation (ELEV). ESV is at a high level when ELEV>718 m, ET<90 mm, NDVI>0.7, and POB<25.67 % approximately. The study results can provide an important theoretical basis for the development of comprehensive ecological protection measures. Furthermore, they can contribute to the sustainable development of the Yellow River Basin.

A model of cement grout flow in a fracture network system

Understanding the mechanism of cement grout flow in fractured rocks is essential for controlling seepage in the construction of hydraulic projects. However, simulating grouting in fractured rocks is complex due to random fracture distribution and non-Newtonian grout flow. This study proposes a numerical model for simulating cement grout flow, considering the hydro-mechanical coupled process in a three-dimensional fracture network system based on the unified pipe-network method. A pipe-network equivalence method is used to derive equivalent pipes for the process of grouting displacement, and the flow field can be solved in unified pipe networks. The hydro-mechanical coupled process is achieved by incorporating an analytical solution for the stress distribution of the center borehole model on an infinitely large plane and a constitutive model for the estimation of the fracture aperture. The time-varying property of the cement grout flow is also considered in the simulation of grouting. The reliability of the numerical model is verified by comparing with analytical solutions for grout flow in a water-saturated fracture. Grouting experiments in fracture networks are also performed to demonstrate the applicability of the proposed method. The influence of various factors on the propagation of cement grout is further investigated in three-dimensional fracture network models.

Power Dissipation of Uniaxial Anisotropic/Interacting Polar Molecules with Linear Reaction Dynamics in an Alternating Electric Field.

The influence of anisotropic potential energy and interaction between polar molecules on power absorption in chemical reactions with linear reaction dynamics in a weak alternating electric field is studied theoretically according to the reaction-diffusion equation. The expression for transient power loss is derived using two methods, electrodynamic method and equivalent circuit method, based on the electric energy conservation equation. Numerical calculations are carried out, and the results show that both the anisotropic potential energy and the interaction between polar molecules have a strong impact on energy dissipation and storage. For the anisotropic potential energy, when the applied dimensionless anisotropy is equal to 1, the power loss density increases about 32% at a low reaction rate and 27% at a high reaction rate compared to the case without anisotropic potential energy. When the dimensionless anisotropy is equal to -1, the power loss is suppressed and is reduced about 27% and 24% at low and high reaction rates, respectively. On the other hand, for the interaction between polar molecules, the power loss density decreases about 10% and 30% with low and high interaction potential energies, respectively. In addition, if the reaction rate is relatively high, the power loss will quickly decrease due to the end of the reaction process.

Investigation into the Variation Law of Network Fracture Conductivity in Unconventional Oil and Gas Reservoirs

The network fracturing technique is a key technology for increasing effective reservoir volume and enhancing production in shale oil and gas. The fracture network’s conductivity is one of the crucial factors affecting the efficient development of shale gas. To evaluate the variation patterns and influencing factors of the conductivity of network fractures, this study employed a proppant conductivity evaluation system and an equivalent theory testing method. It investigated the conductivity of propped and self-propped fractures under different angles and numbers of fractures. Experimental results showed that fractures with proppant support had higher conductivity than unsupported fractures. Smaller angles between secondary and main fractures resulted in greater conductivity. The conductivity of multi-fracture structures increased with the number of fractures. Under low-closure pressure conditions, self-propped fractures exhibited significantly higher conductivity than propped fractures, but this trend reversed under high closure pressure. This experimental research provides guidance for constructing network fractures with high conductivity in unconventional oil and gas reservoir fracturing.

Reconstruction of nonstationary sound field based on group sparsity time domain equivalent source method

To improve the accuracy and stability of reconstruction of nonstationary sound field, a novel time domain equivalent source method based on non-convex overlapping group sparsity (NOGS-TESM) is proposed. In the proposed NOGS-TESM, the time-varying pressure in the near field is first modeled by a set of equivalent sources positioned inside the vibrating structure. Then, the NOGS regularization is applied for solving the inverse problem, and a novel algorithm derived on the basis of Majorize-Minimization theory is utilized to obtain the optimal solution of equivalent sources strengths. Finally, the optimal equivalent sources strengths at all times are substituted into a time-domain convolution to calculate the time-varying pressure of reconstruction surface. The proposed NOGS-TESM enriches the prior information by considering the group sparsity of spatial pressure distribution, and enhances the accuracy of estimated equivalent sources strength via its alternative calculation of l0−norm. A vibrating plate to produce a nonstationary sound field, which is designed as a numerical simulation, and the time-varying pressures of measurement surface are input into the proposed NOGS-TESM. The quantitative and qualitative comparisons confirm that the proposed NOGS-TESM can greatly reconstruct the non-stationary sound field in time–space domains, and its reconstruction accuracy is higher than that of TESM with Tikhonov regularization (TR-TESM). Meanwhile, several parameters, for example, the noise and position of equivalent source surface, are discussed in detail, and the superiorities of the proposed NOGS-TESM in terms of stability and robustness are proved by comparing to TR-TESM. The predominance of the proposed NOGS-TESM is further validated by conducting one experiment on the vibrating steel plate.

Quantitative Determination of Partial Voxel Compositions with X-ray CT Image-Based Data-Constrained Modelling

X-ray CT imaging is an important three-dimensional non-destructive testing technique, which has been widely applied in various fields. However, segmenting image voxels as discrete material compositions may lose information below the voxel size. In this study, six samples with known volume fractions of compositions were imaged using laboratory micro-CT. Optical microscopic images of the samples reveal numerous small particles of compositions smaller than the CT voxel size within the samples. By employing the equivalent energy method to determine the X-ray beam energy for sample imaging experiments, data-constrained modelling (DCM) was used to obtain the volume fractions of different compositions in the samples for each voxel. The results demonstrated that DCM effectively captured information about compositions occupying CT voxels partially. The computed volume fractions of compositions using DCM closely matched the known values. The results of DCM and four automatic threshold segmentation algorithms were compared and analyzed. The results showed that DCM has obvious advantages in processing those samples containing a large number of particles smaller than the CT voxel size. This work is the first quantitative evaluation of DCM for laboratory CT image processing, which provides a new idea for multi-scale structure characterization of materials based on laboratory CT.

The Impact of Source Time Function Complexity on Stress-Drop Estimates

ABSTRACT Earthquake stress drop—a key parameter for describing the energetics of earthquake rupture—can be estimated in several different, but theoretically equivalent, ways. However, independent estimates for the same earthquakes sometimes differ significantly. We find that earthquake source complexity plays a significant role in why theoretically (for simple rupture models) equivalent methods produce different estimates. We apply time- and frequency-domain methods to estimate stress drops for real earthquakes in the SCARDEC (Seismic source ChAracteristics Retrieved from DEConvolving teleseismic body waves, Vallée and Douet, 2016) source time function (STF) database and analyze how rupture complexity drives stress-drop estimate discrepancies. Specifically, we identify two complexity metrics—Brune relative energy (BRE) and spectral decay—that parameterize an earthquake’s complexity relative to the standard Brune model and strongly correlate with the estimate discrepancies. We find that the observed systematic magnitude–stress-drop trends may reflect underlying changes in STF complexity, not necessarily trends in actual stress drop. Both the decay and BRE parameters vary systematically with magnitude, but whether this magnitude–complexity relationship is real remains unresolved.

Research on the water flooding front based on dynamic and static data inversion – a case study

To clarify the movement of the water flooding front in fluvial reservoirs, this research takes the BZ oilfield as an example. By considering the equivalent flow resistance theory for oil–water two-phase flow, the horizontal micro-element equivalent method and the strong heterogeneity of fluvial facies reservoir comprehensively, a calculation model for a non-piston water flooding front in a horizontal well pattern was established. First, five horizontal injection–production well groups in the BZ oilfield were taken as examples to calculate the water breakthrough time for the oil wells. The calculation results are in good agreement with the actual production performance. In detail, the advancing speed of the water flooding front in the high-permeability strip was 0.8–1.6 m/day, and the speed in the low-permeability strip was 0.12–0.35 m/day. When water is seen in the oil well, the advancing speed in the low-permeability strip is reduced, resulting in uneven displacement and the formation of non-dominant potential areas. In addition, the water flooding front advancing distance was simulated to be 300–450 m by establishing a reservoir numerical simulation model, which is close to the result of the proposed model, indicating that the calculation method is reliable. This research is of great significance for predicting the water breakthrough time of horizontal production wells, judging the weak affected area on the mainstream line, and optimizing water injection and tapping reservoir potential in good time.

Calculation Method of New Assembled Corrugated Steel Initial Support Structure of Highway Tunnel

The assembled corrugated steel initial support structure is a new prefabricated structure in highway tunnel engineering, achieving a balance between economy and safety. This study proposes a simplified calculation method and elucidates the mechanical mechanisms of assembled corrugated steel initial support structures. Firstly, the stiffness characteristics of corrugated steel plates were studied based on full-scale tests. A general equivalent stiffness coefficient table was established. Numerical simulations of corrugated steel flange joints were conducted to explore their bending mechanical properties. A two-stage rotational stiffness model for corrugated steel flange joints was proposed. Finally, a plane strain-spring simplified calculation method for the assembled corrugated steel initial support structure was developed, and the monitoring data from the Qipanshan Tunnel validated the correctness and reliability of the proposed method. The results demonstrate that (1) the plane strain-spring simplified model consists of the planar strain equivalent calculation method for corrugated steel plates and the two-line stiffness equivalent spring of the corrugated steel flange joint. The simplified model was validated as effective by monitoring data. (2) Corrugated steel plates exhibit two stages under loading, namely gap elimination and elastic stages. The elastic stage stiffness of corrugated steel plates decreases with increasing ratio of depth to pitch (RDP), positively correlating with plate thickness when the RDP exceeds 0.333 and otherwise negatively correlated. (3) Corrugated steel lining flange joints exhibit distinct elastic and plastic stages in their linear moment–rotation curves under loading.

Efficient implementation of equivalent medium parameterization in finite-difference seismic wave simulation methods

Summary Grid point discretization of the model has a significant impact on the accuracy of finite-difference seismic waveform simulations. Discretizing the discontinuous velocity model using local point medium parameters can lead to artifact diffraction caused by the stair-step representation and inaccuracies in calculated waveforms due to interface errors, particularly evident when employing coarse grids. To accurately represent model interfaces and reduce interface errors in finite-difference calculations, various equivalent medium parametrization methods have been developed in recent years. Most of these methods require volume-integrated averaging calculations of the medium parameter values within grid cells. The simplest way to achieve this volume averaging is to apply numerical integration averaging to all grid cells. However, this approach demands considerable computational time. To address this computational challenge, we propose employing a set of auxiliary grids to identify which grid cells intersected by the welded interface and perform volume averaging only on these specific cells, thereby reducing unnecessary computational overhead. Additionally, we present a three-dimensional tilted transversely isotropic equivalent medium parameterization method, which effectively suppresses interface errors and artefact diffraction under the application of coarse grids. We also provide an approach for computing the normal direction of the interface, which is essential for the tilted transversely isotropic equivalent medium parameterization. Numerical tests validate the accuracy of the tilted transversely isotropic equivalent medium parameterization method and demonstrate the practicality of the implementation proposed in this paper for complex models.

Neural Network-Based Aggregated Equivalent Modeling of Distributed Photovoltaic External Characteristics of Faults

Distributed power networks have a large number of photovoltaic power sources. The bidirection of power flow, different transient control strategies, and installation locations make the transient characteristics highly complex and unpredictable. The vast network of the distribution system makes it almost impossible to predict the electrical quantities of each branch. Reasonable aggregation modeling of the distribution network can greatly simplify the network topology, facilitating transient control and the setting of relay protection settings. An aggregated equivalent modeling method based on the LSTM neural network for distributed PV fault external characteristics is proposed. This method equates the complex distribution network to a highly nonlinear but controllable current source. The method can output the I–V curves of equivalent PV system parallel points under any output power and is able to predict the fault characteristics of the equivalent system after a voltage drop at the parallel point. Compared to traditional mechanistic modeling, this method does not require specific modeling of complex physical systems and is able to accurately map the strong nonlinear inputs and outputs of distribution networks. The established LSTM model first uses a one-dimensional convolutional layer for feature extraction of the PV power coefficients (input), and then two hidden layers are utilized to process the sequence data; the vectors are mapped into a sequence of external characteristic curves (output) in a fully connected layer. A typical distribution network is built based on the traditional PV power model, and a large number of different output combinations are selected for simulation to provide an effective training set and validation set data for LSTM model training. By using the training set data, the weights and offset coefficients of each layer of the LSTM are continuously optimized until the model with the smallest overall error is obtained, which is the optimal model. Finally, the optimal model is utilized to establish an equivalent distribution network system, different degrees of voltage drops are set up at the grid-connected points, the fault characteristics are compared with those of the complete model, and the simulation results can prove the reliability and practicality of the proposed method.

Evaluation of Fine Particulate Matter (PM2.5) Concentrations Measured by Collocated Federal Reference Method and Federal Equivalent Method Monitors in the U.S.

Evaluation of Fine Particulate Matter (PM2.5) Concentrations Measured by Collocated Federal Reference Method and Federal Equivalent Method Monitors in the U.S.

Intralingual Understanding of Zakat, Infaq, alms, and Gifts in Islamic Economics In Aceh

The implementation of Islamic economics in Aceh has a positive impact on society. Aceh Province is a region in Indonesia that has an influence on poverty issues because it has been hit by social conflict that has been going on for a very long time so that access to work is not conducive for the people of Aceh. ). Aceh Province with the implementation of Islamic law has a role to play in resolving and minimizing poverty problems. The method used by Aceh Province is to foster the management of zakat, infaq and alms because they are sources of eternal funds. Supporting the importance of previous research on zakat, infaq and alms, this study wants to determine the ability to understand interlingual terminology about zakat, alms and infaq plus one other terminology, namely gifts. This research was a descriptive-qualitative research. The data used are 4 terminologies in Islamic economics, namely alms, zakat, infaq and gifts to be translated interlingually. The four terms to be translated were analyzed using the intralingual equivalence method. The sample is 50 students from the Faculty of Economics who have studied science related to Islamic economics courses. The findings obtained that related to the terminology of zakat, all participants as many as 50 students or 100% of participants managed to answer intralingually. Then, there were the same results between the terminology of infak, sedekah, and hadiah, namely 47 students managed to answer correctly but insignificantly there were only 3 students who answered incorrectly.

Torque Performance Analysis of Asymmetric Magnetic Pole Permanent Magnet Synchronous Motor for New Energy Vehicles

In view of the problem of large torque ripple and poor output performance of permanent magnet synchronous motor, a new topology of asymmetric magnetic pole permanent magnet synchronous motor is proposed, and the torque ripple of this motor structure and the suppression method are analyzed. First, the equivalent magnetic circuit method and Lorentz force law are used to derive the analytical formula of torque ripple of the motor. Then, based on the analytical formula, the parameters of permanent magnet of the asymmetric magnetic pole permanent magnet synchronous motor are optimized and verified by finite element software simulation; on this basis, the method of rotor eccentricity is used to further weaken the torque ripple of the motor, and the optimal eccentricity distance is analyzed. The research shows that when the parameters of the magnetic pole of the asymmetric magnetic pole permanent magnet synchronous motor is appropriate, the harmonic content of the air gap magnetic density of the optimized motor is greatly reduced, and the motor has good output characteristics, and the torque ripple is reduced to 5.4%. Finally, the prototype is trial‐manufactured and tested. The results show that after optimization, the cogging torque of the motor is reduced, the torque output performance is improved, and the overall motor performance is improved. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Определение вязкости и диэлектрической проницаемости жидкости методом эквивалентных схем с помощью резонатора с поперечным электрическим полем

The paper presents a method for determining the viscosity and permittivity of a liquid using the equivalent circuit method. The parameters of the Mason equivalent circuit were found for a piezoelectric resonator with a lateral electric field made of PZT-19 ceramics. The frequency dependences of the real and imaginary parts of the electrical impedance of a resonator loaded with liquid samples with different viscosity and permittivity were measured. The fitting of the theoretical frequency dependences of the real and imaginary parts of the electrical impedance of a resonator loaded with mixtures of “water - isopropyl alcohol” and “water - glycerin” to the measured dependences was carried out. As the result the dependence of the permittivity of the liquid on the additional capacitance (determined from the Mason scheme) and the dependence of the shear fluid viscosity on the imaginary part of the mechanical impedance of the fluid load (determined from the Mason scheme) were built. These dependences can be used as calibration curves to determine dielectric constant and viscosity.

Infrared radiation characteristics simulation of exhaust suppression type ships

An equivalent calculation method for the infrared-suppressed ship’s infrared radiation is carried out, which couples thermal characteristics of the ship surface and the exhaust system. Firstly, a refined physical model for the infrared suppressed exhaust system is proposed, which considers the processes of convective heat transfer and radiative heat transfer. The model generates the equivalent heat flow boundary conditions of the internal heat source through the numerical calculation of Computational Fluid Dynamics (CFD), and combines with the energy balance physical model. The energy balance model on the ship surface is developed, which considers external thermal environment conditions including itself radiation, solar radiation, atmospheric radiation, and reflective radiation among surface elements. The temperature calculation model for the ship with a jet exhaust system is formed. Subsequently, an exhaust-suppressed ship infrared radiation calculation model is formed based on the infrared radiation rendering of solid targets and the narrow spectral principle of exhaust plumes, which considers the spontaneous radiation and environmental radiation of ships. Finally, the infrared simulation results are compared and verified based on experimental data. The results indicate that the infrared radiation error on the ship’s typical parts is less than 30 %. Additionally, 90.1 % of the cabin walls using exhaust suppression systems have a temperature difference of less than 3 K under different operating conditions. It suggests that the exhaust suppression system is effective in reducing the temperature of the cabin wall. The calculation method for ship infrared characteristics constructed in this paper has reasonable results, and it can be used for infrared characteristic analysis of exhaust suppression ships.

Fundamental Physical Parameter Fitting via Electrochemical Impedance Spectroscopy

Electrochemical impedance spectroscopy (EIS) is a non-destructive technique that plays a crucial role in the investigations of batteries. EIS enables to analyze essential information regarding what is happening in a battery. The most important information that can be obtained from an EIS data is the effects of kinetic and diffusion related events. Having an idea about these physical events enables doing battery diagnostics and development. Therefore, several methods of EIS data analysis had been developed in order to clearly understand what is underlying an EIS spectra.One of the developed methods for EIS data analysis is using equivalent circuits. The very first example was done by Randles in 1947[1]. In his paper, he was able to separately obtain kinetic and diffusion-related parameters with the equivalent circuit method. However, he focused on just one reaction in a single interface using a three-electrode setup. Therefore, by lowering the complexity of the system, he was able to separately identify kinetic and diffusion related events. However, the systems that are currently investigated are much more complicated. Therefore, using the equivalent circuit method is plagued by ambiguity and multivalued fits.On the other hand, in 2018, Murbach and Schwartz published on a new way of analysis[2]. They have simulated 38800 impedance spectra with variety of physical constants and tried to match the experimentally provided impedance spectra. However, this method suffers from the above-mentioned ambiguity. That is, several impedance spectra calculated with very different physical constants fitted the experimental data equally well. Therefore, reducing or eliminating this ambiguity of EIS data is essential.Temperature-dependent EIS is one of the ways to reduce this ambiguity. In our group, we have previously shown that even with equivalent circuits, it is possible to distinguish diffusion and kinetic-related events with temperature-dependent EIS[3]. Kinetic events such as lithium-ion transfer has a strong dependence of temperature. Therefore, we were able to separate the kinetic and diffusion events by varying the temperature and looking the Arrhenius plots.In addition to the temperature dependence, non-linear impedance can further reduce the complexity of the EIS data. Again, in our group, we have shown that higher harmonics contain valuable information about redox reactions happening in the system[4]. Also, non-linear impedance response, especially the second harmonic, provides crucial information regarding the diffusion parameters at the low frequency region which is also showed by Murbach and Schwartz [5]. Therefore, we will show that using temperature-dependent linear and non-linear EIS can unlock the secrets of an EIS spectrum.In the current study, we will report temperature-dependent linear and non-linear simulations on an Li-ion battery with the NMC/Graphite chemistry. Here, we will show that temperature-dependent impedance measurements will enhance the discernibility of various kinetic parameters. Also, non-linear impedance response will improve the discernibility of diffusion related events. Combination of temperature dependence and non-linear response is collected in an objective function. The derived objective function is employed for the analysis of variations between experimental and simulated data, considering weights assigned to each parameter during the calculation process.By monitoring the value of this difference as a function of various fundamental parameters, we will show that meticulously adjusted weights can further improve the objective function to converge proper values. Ultimately, we will show that it is possible to correctly separate and identify the physical constants related to kinetic and diffusion events with temperature-dependent linear and non-linear EIS in an unequivocal manner.

Torque and Eddy Current Behavior of a Magnet Rotating Axial Disk Type Magnetic Coupler: Analysis and Experimental Verification

This research explored the impact of air gap on torque and eddy current behavior of a magnet-north-pole rotating axial disk-type magnetic coupler using the magnetic equivalent circuit method. A magnetic equivalent circuit (MEC) model was developed to analyze the torque and induced eddy current behavior for the magnetic N-pole rotation angle 0° to 30° axial disk type magnetic coupler (MC). Torque equations were derived by combining Kirchhoff's law and the integral method, whereas induced eddy current equations were derived using Ampere's law. Flux leakage reluctance equations were obtained using an integral method. Furthermore, the study conducted 2D finite element simulations, and the results were validated against experimental data to ensure the accuracy and reliability of the proposed MEC model. Finally, the research findings suggested that an air gap length of 4 mm was an optimum length to obtain maximum torque and minimum magnetic saturation effects for a proposed MEC model of N-pole rotating axial disk type MC.

Spatio-temporal Pattern of Ecosystem Service Value Evolution in the Yihe River Basin in the Context of Land Use Change

In this study, the modified equivalent factor method was applied to account for the long time series ecosystem service value （ESV） of the Yihe River Basin from 1975 to 2020 in the context of land use change, and the cold hot spot analysis and topographic position analysis methods were introduced to explore the characteristics of its spatial pattern. The results showed that： ① From 1975 to 2020, the land use type of the Yihe River Basin was dominated by arable land, and the land use changes were characterized by the rapid decrease of arable land and the continuous expansion of construction land, a slight increase in the area of forest land and grassland, a contraction of the water body area, and little change in the area of unused land. ② The modified equivalent factor method was more suitable for accounting for the ESV in the basin. From 1975 to 2020, the overall ESV of the basin showed an upward spiral trend （33.369-33.816 billion CNY）, dominated by the regulating services. The ESV of arable land was the highest with a decreasing trend, whereas the ESV of unused land was the lowest. ③ In the horizontal spatial pattern, the hot spot of ESV was near mountains and reservoirs, and the cold spot of ESV was near urban areas. In terms of vertical spatial patterns, with growing topographic gradient, vertical changes in ESV for all land use types showed an increasing trend followed by a decreasing trend. The results of the study revealed the spatial and temporal patterns of ecosystem service values in the Yihe River Basin in the context of land use change and provide a scientific basis for optimizing the land use structure and spatial pattern and enhancing ecosystem services.

Time-Domain Analysis for Rayleigh Wave Scattering by Complex Terrain of Alpine Valley

ABSTRACT In this paper, a time-domain solution for Rayleigh wave scattering from a complex site of Alpine Valley is presented based on the scaled boundary finite element method (SBFEM). Both the near-field region and the far-field region are assumed to be homogeneous, isotropic linear elastomers, where the near-field region is discretized using the quadtree method and the far-field region is simulated with a displacement unit impulse response function. The input of Rayleigh waves is solved by the equivalent loading method. The scattering behavior of seismic waves in alpine valleys is comprehensively analyzed, and the results are of theoretical significance for site safety evaluation and seismic defenses.