Homogeneous Model Research Articles

Cosmic and thermodynamic analysis of parameterized torsion gravity

We examine the cosmic evolution of an accelerating universe within the framework of the Einstein–Cartan–Sciama–Kibble theory, employing a flat, homogeneous and isotropic model. In this context, various parameterizations of the equation of state parameter, denoted as ω, are considered with respect to the redshift function. We analyze the behavior of cosmological parameters such as deceleration, Om-diagnostic, statefinder and squared speed of sound. It is found that these cosmological parameters are consistent with the current cosmic scenario and recent Planck data from 2018. Additionally, we examine the validity of the generalized second law of thermodynamics at the apparent horizon, taking into account the Bekenstein–Hawking entropy and find it valid for specific choices of constants.

Multimillion Atom Simulations of Di-8-ANEPPS Chromophores Embedded in a Model Plasma Membrane: Toward the Investigation of Realistic Dyed Cell Membranes.

A multistep computational approach has been employed to study a multimillion all-atom dyed plasma membrane, with no less than 42 different lipid species spanning the major head groups and a variety of fatty acids, as well as cholesterol, with the objective of investigating its structure and dynamics, as well as its impact on the embedded di-8-ANEPPS dyes. The latter are commonly used as bioimaging probes and serve as local microscopes. So, they provide information on membrane morphology via their second harmonic nonlinear optical (NLO) responses, which have the advantage of being specific to interface regions and sensitive to the chromophore environment. In previous studies, this chromophore has only been studied in simpler membrane models, far from the complexity of real lipid bilayers, while, owing to the ever-increasing computational resources, multimillion lipid bilayers have been studied, giving access to the effects of its heterogeneity. First, using molecular dynamics (MD) simulations, it is found that the combination of lipids produces a more ordered and denser membrane compared to its homogeneous model counterparts, while the local environment of the embedded dyes becomes enriched in phosphatidylcholine. Subsequently, the second harmonic first hyperpolarizability of the probes was calculated at the TDDFT level on selected frames of MD, highlighting the influence of the lipid environment. Due to the complexity of the system, machine learning (ML) tools have been employed to establish relationships between the membrane structural parameters, the orientation of the probes, and their NLO responses. These ML approaches have revealed influential features, including the presence of diacylglycerol lipids close to the dye. On the whole, this work provides a first step toward understanding the cooperation, synergy, and interactions that occur in such complex guest-host environments, which have emerged as new targets for drug design and membrane lipid therapy.

Türkiye’de Bölgesel Kayıt Dışı İstihdam ve Makroekonomik Değişkenler Arasındaki Karşılıklı Dinamik İlişkiler: Bir Panel VAR Analizi

The presence of the informal economy and unregistered employment engenders adverse working conditions and job insecurity and diminishes tax revenues. Post-2000, Türkiye has placed considerable emphasis on fighting the informal economy and unregistered employment. Nevertheless, current data from the Social Security Institution reveals a 29% unregistered employment rate. Numerous factors affect the informal economy, with their impact contingent on the developmental status of economies. In Türkiye, characterized by substantial regional disparities, policymakers must account for regional heterogeneities. Within this context, an examination of the dynamic relationship between unregistered employment and key economic indicators such as growth, unemployment, and inflation in the Turkish economy is conducted using a homogeneous panel VAR model. Moreover, the study delves into gender-specific distinctions in unemployment rates and their relationship with unregistered employment. Utilizing annual data spanning 2009 to 2021 from NUTS 2 of TURKSTAT, the findings underscore the necessity for unregistered employment policies to address regional variations. Significantly, the interdependence between registered and unregistered economies underscores the guiding role of the unregistered sector within the registered economy. Hence, it is suggested that fighting unregistered employment may require a fundamental redesign of the current economic production structure to mitigate its prevalence.

Application of Hashin–Shtrikman bounds homogenization model for frequency analysis of imperfect FG bio-composite plates

Despite abundant theoretical investigations on the dynamic behavior of functionally graded (FG) structures, the study on frequency analysis of FG bio-composite structures is limited. FG bio-composite materials due to their biocompatibility potentials and good material properties can be applied in biomedical applications, especially dental implants. In this investigation, a natural frequency response of the FG bio-composite plate is analyzed within the framework of the newly developed refined higher-order shear deformation plate theory. Additionally, the imperfection impact on frequency behavior is evaluated while three imperfection distribution patterns are taken into account. The constitutive materials of FG bio-composite plate are Hydroxyapatite and Titanium. The effective material properties of the structure are determined with the help of the upper Hashin–Shtrikman bounds homogenization model. In continuation, to solve the derived governing equations of imperfect FG bio-composite plate, Galerkin's analytical method is employed. Also, the precision of the used theory is validated, the obtained outcomes are compared and an acceptable matching is found. Later, the sensitivity of different considerable variables is comprehensively assessed and discussed.

Influence of temperature on the elastic properties of graphene and graphene-like nanosheets based on the asymptotic homogenization method

In this paper, the effective elastic properties of hexagonal monolayers such as graphene, boron nitride, silicon carbide, and aluminum nitride are evaluated using the asymptotic homogenization method taking into account temperature changes. The effective properties are determined analytically by considering temperature, force constants, bond lengths, and thickness, using atomic interactions within the context of the unit cell problem. The relationship between environmental temperature and the coefficient of thermal expansion is established by considering changes in the values ​​of bond stretching, bond angle bending, and torsion resistance constants at different temperatures from 0 to 1800 K. The results provided by the proposed homogeneous model are consistent with the valid findings of other researchers in the literature. It is found that these different hexagonal nanosheets exhibit isotropic temperature-dependent properties and their Young's and shear modulus decrease almost linearly as the temperature rises, considering a constant coefficient of thermal expansion. However, Poisson's ratio is found to be independent of temperature. Furthermore, the temperature-dependent elastic properties of these nanosheets become nonlinear when the variation of the coefficient of thermal expansion with temperature is taken into account. The Young and shear moduli of the nanosheets increase as the coefficient of thermal expansion decreases and vice versa. The highest elastic modulus values are obtained when the thermal expansion is close to its minimum threshold. However, it is recognized that the elastic modulus of graphene and boron nitride nanosheets is higher than that of silicon carbide and aluminum nitride at any temperature. As an alternative to lengthy computer modeling or rigorous testing, the homogeneous models provided can be used to simulate nanosheets.

Conventionalism, Cosmology and Teleparallel Gravity

We consider homogeneous and isotropic cosmological models in the framework of three geometrical theories of gravitation. In Einstein’s general relativity, they are given in terms of the curvature of the Levi-Civita connection in torsion-free metric spacetimes; in the teleparallel equivalent of general relativity, they are given in terms of the torsion of flat metric spacetimes; and in the symmetric teleparallel equivalent of general relativity, they are given in terms of the nonmetricity of flat torsion-free spacetimes. We argue that although these three formulations seem to be different, the corresponding cosmological models are in fact equivalent and their choice is conventional.

Development of a complex model for processing various data

The object of the research is intelligent decision-making support systems. The scientific problem that is solved in the research is the development of a comprehensive model for processing various types of data in intelligent decision-making support systems (DMSS). The relevance of the research lies in the fact that in intelligent DMSS circulate different in origin and units of measurement data obtained from various technical devices of obtaining information. The essence of the integrated approach in modeling is that two partial models are proposed: a model for processing different types of data in intelligent decision-making support systems and a model for processing homogeneous data in intelligent decision-making support systems. Analysis of the intelligent DMSS model for processing different types of data allows to draw such a conclusion. While solving the problem of processing different types of data, a model of intelligent DMSS is proposed, in contrast to traditional, even for the process of solving partial problems incorrectly started by experts with the help of self-organization, expressed in the coordination of partial tasks of the decision maker, striving for an ideal solution to the problem of processing different types of data, which increases the efficiency of finding an acceptable result for processing different types of data. The homogeneous data processing model is based on the idea that the same processing of homogeneous data in intelligent DMSS can be solved in parallel by different functional elements. Element integration relationships arise as internal non-verbal images in the user's memory, which can compare the dynamics of modeling a task for processing different types of data in intelligent DMSS from different points of view, which allows to see what modeling does not give using one model. The direction of further research should be considered the improvement of information processing methods in intelligent decision-making support systems.

Compressive study on recycled concrete: experiment and numerical homogenization modelling

This paper describes a study of recycled concrete under compressive loads. The study was conducted in two main parts. In the first part, experimental tests were carried out on concrete samples with varying levels of substitution (25%, 50%, and 75%) with recycled aggregate in order to measure the mechanical properties of the recycled concrete. In the second part of the study, a nonlinear homogenization model was developed on the basis of a classical secant approach to predict the behavior of recycled concrete. In this model, we assume that the behavior of the mortar phase, the concrete, and the recycled aggregates follow Mazars damage law. Comparison with the experimental data shows that the proposed homogenization model is accurate and efficient in predicting the correct nonlinear behavior of the recycled concrete. By better understanding the properties and behavior of recycled concrete, it will be possible to develop more effective methods for incorporating recycled materials into concrete structures.

Simulation study of key cross-sectional area dimensions of CO2 ejector on performance

In this paper, based on the homogeneous equilibrium model, the effects of nozzle inlet cross-sectional area, nozzle throat cross-sectional area, pre-mixing chamber cross-sectional area, mixing chamber cross-sectional area, and diffusion chamber outlet cross-sectional area on the performance of the ejector of a CO2 transcritical refrigeration system are analyzed by using Ansys Fluent. The simulation results show that the primary flow rate of the ejector is sensitive only to the nozzle throat cross-sectional area, while the entrainment ratio is strongly influenced by the nozzle throat and the mixing chamber cross-sectional area, and there is an optimum value. The nozzle inlet cross-sectional area has no significant effect on the performance of the ejector. The pre-mixing and diffusion chamber outlet cross-sectional areas do not have a significant effect on the performance within a limited range, but deviating too much from the optimum value can also lead to degradation of ejector performance.

Comparison of diffuse correlation spectroscopy analytical models for measuring cerebral blood flow in adults.

Although multilayer analytical models have been proposed to enhance brain sensitivity of diffuse correlation spectroscopy (DCS) measurements of cerebral blood flow, the traditional homogeneous model remains dominant in clinical applications. Rigorous in vivo comparison of these analytical models is lacking. We compare the performance of different analytical models to estimate a cerebral blood flow index (CBFi) with DCS in adults. Resting-state data were obtained on a cohort of 20 adult patients with subarachnoid hemorrhage. Data at 1 and 2.5cm source-detector separations were analyzed with the homogenous, two-layer, and three-layer models to estimate scalp blood flow index and CBFi. The performance of each model was quantified via fitting convergence, fit stability, brain-to-scalp flow ratio (BSR), and correlation with transcranial Doppler ultrasound (TCD) measurements of cerebral blood flow velocity in the middle cerebral artery (MCA). The homogeneous model has the highest pass rate (100%), lowest coefficient of variation (CV) at rest (median [IQR] at 1Hz of 0.18 [0.13, 0.22]), and most significant correlation with MCA blood flow velocities (, ) compared with both the two- and three-layer models. The multilayer model pass rate was significantly correlated with extracerebral layer thicknesses. Discarding datasets with non-physiological BSRs increased the correlation between DCS measured CBFi and TCD measured MCA velocities for all models. We found that the homogeneous model has the highest pass rate, lowest CV at rest, and most significant correlation with MCA blood flow velocities. Results from the multilayer models should be taken with caution because they suffer from lower pass rates and higher coefficients of variation at rest and can converge to non-physiological values for CBFi. Future work is needed to validate these models in vivo, and novel approaches are merited to improve the performance of the multimodel models.

Geodetic slip rate partitioning in the central Anninghe and Daliangshan faults: Effects of fault geometry, elastic heterogeneity, and viscoelastic rheology

Geodetic measurements can be employed to estimate the secular slip rates and locking depths of crustal faults, two key parameters which influence assessment of long-term seismic hazard presented by a fault. However, this process requires making assumptions about the rheological properties of the Earth's crust and lithosphere, as well as the fault geometry at depth. Previous geodetic studies have inferred widely varying slip rates and locking depths for the central Xianshuihe-Xiaojiang Fault System, located along the southeastern margin of the Tibetan plateau. In this study, we use updated GNSS measurements, including 13 new velocities, to explore the effects of assumed rheology and fault geometry on the inferred slip rates and locking depths of the subparallel Anninghe (ANH) and Daliangshan (DLS) faults in this region. We demonstrate that only models taking into account the viscoelastic relaxation of the lower crust can resolve the apparent discrepancies. Models assuming a fully elastic rheology suggest very deep locking depths (∼35 km) and a lower slip rate on the ANH fault (∼5 mm/yr) than the DLS fault (∼7 mm/yr). Neither the relative slip rates nor the locking depths agree with seismic or geologic observations. We also consider models assuming a heterogeneous elastic rheology, but find they are indistinguishable from the homogeneous models. Modifying the fault geometry can impact the relative slip rates of the two faults but does not produce a reasonable locking depth either. In contrast, viscoelastic models accounting for seismic cycle effects indicate a faster ANH slip rate (∼5–7 mm/yr), a slower DLS rate (∼4–5 mm/yr), and a shallower locking depth for both faults (∼18 km), all of which are more consistent with independent seismic and geological observations. Our study suggests that steady long-term motion on these faults is modulated by long-lasting viscoelastic effects over a relatively broad region.

Dependence of resistivity of natural rock samples on humidity

Rock resistivity measurements under non-wet conditions are essential for interpreting subsurface shallow resistivity structure. This study investigated the resistivity of rock samples collected from several locations around the Nakadake craters of Aso Volcano, Japan. The resistivity of rock samples exhibited a logarithmically linear relationship with changes in absolute humidity, corresponding to possible seasonal variations and correlating with the porosity of rocks. As the samples maintained an identical cylindrical shape and size, the observed variations in humidity were unrelated to the external surface area but were caused by the internal pore structure of rocks. Furthermore, the external surface area of homogeneous granite was artificially varied using slits and its measured resistivity did not vary in the presence of slits. The measured distribution of electrical potential was well explained by a homogeneous model, and less so by a two-layer model, indicating that the region of resistivity change was not restricted to the surface of the sample, but rather covered the entire sample. Further, changes in resistivity in response to absolute humidity were caused by the adsorption of water molecules onto minerals at internal pore surfaces, as evidenced by the measured temporal scale of resistivity change based on a simple concentration–diffusion process of gaseous water molecules caused by humidity changes in the external environment. These findings imply significant variations in the resistivity of shallow subsurfaces owing to humidity changes; thus, the consideration of humidity is important for the interpretation of subsurface shallow resistivity structures.

DEM simulation of subsoiling for soil disturbance as affected by soil layering and working speed

Although the discrete element method (DEM) has been used to simulate soil-subsoiler interactions, the degree of soil heterogeneity along the depth profile has not been well documented. Models of a layered soil structure were developed using the DEM, and they were a heterogeneous soil model (HeS Model) with seven layers, a semi-heterogeneous soil model (SHeS Model) with three layers, and a homogeneous soil model (HoS Model) with one layer. The models simulated the soil dynamic behavior resulting from a subsoiler travelling at speeds from 2 to 6 km h−1. Simulations were compared with field measurements. Results showed that soil particles flow in front of the subsoiler formed three distinguished zones: “pushing”, “rising”, and “passive” zones, with the “pushing” zone having the highest particle velocities. Compared with the measurements, the overall relative errors of the simulated soil disturbance widths (W) within the range of working speed from 2 to 6 km h−1 were below 20 % for all three models. Whereas the overall relative errors of the simulated soil surface flatness (F) were larger than 20 % for all three models. These suggest that all three models are suitable for predicting W, but not for predicting F, if a 20 % relative error was used as the judging criterion. The overall relative errors of the simulated elevated soil area (A) were 11.1 %, 18.8 %, and 25.7 % for the HeS, SHeS, and HoS Models, respectively, which suggest that HeS Model had the highest accuracy in predicting A. This study provides critical information for determining the degree of soil heterogeneity in simulations of the dynamics of soil-subsoiler interaction.

Optical parameters estimation in inhomogeneous turbid media using backscattered light: for transcutaneous scattering measurement of intravascular blood.

In our earlier research, a technique was developed to estimate the effective attenuation coefficient of subcutaneous blood vessels from the skin surface using the spatial distribution of backscattered near-infrared (NIR) light. The scattering effect in surrounding tissues was suppressed through the application of a differential principle, provided that the in vivo structure is known. In this study, a new method is proposed enabling the separate estimation of both scattering and absorption coefficients using NIR light of different wavelengths. The differential technique is newly innovated to make it applicable to the subcutaneous structure without requiring explicit geometrical information. Suppression of the scattering effect from surrounding tissue can be incorporated into the process of estimating the scattering and absorption coefficients. The validity of the proposed technique can be demonstrated through Monte Carlo simulations using both homogeneous and inhomogeneous tissue-simulating models. The estimated results exhibit good coherence with theoretical values (r2 = 0.988-0.999). Moreover, the vulnerability and robustness of the proposed technique against different measurement errors are verified. Optimal conditions for practical measurement are specified under various light-detection conditions. Separate estimation of scattering and absorption coefficients improves the accuracy of turbidity measurements and spectroscopy in biomedical applications considerably, particularly for noninvasive measurements and analysis of blood, lipids, and other components in subcutaneous blood vessels.

A 17-point composite average-derivative optimal method for high-accuracy frequency-domain scalar wave modeling

The frequency-domain finite-difference (FD) technique, especially the average-derivative method (ADM), is widely utilized in wavefield modeling. However, conventional low-order FD techniques are insufficient for high-accuracy demands. Applying high-order FD operator and optimizing their coefficients are effective measures for improving the accuracy of seismic modeling. However, these approaches suffer from the limitations of constant density media and approximant perfectly matched layer (PML). To address this issue, we have developed a composite-ADM 17-point scheme for a scalar-wave equation. This novel scheme is based on the composition of ADM discretizations with different grid intervals, which successfully removes the above limitations and achieves high accuracy. To suppress the numerical dispersion, we take the L∞ norm to construct the objective function, which we minimize using the Grey Wolf Optimizer (GWO) and Particle Swarm Optimization (PSO) algorithms. Numerical analysis indicates that the composite-ADM greatly reduces phase velocity error compared with the traditional-ADM, requiring only 2.44 grid points per wavelength within a 1% phase velocity error. Using numerical examples in homogeneous and complex models, we demonstrate the accuracy and versatility of the composite-ADM 17-point scheme in variable density media with exact PML. Furthermore, we extend this optimal scheme to the case of 2D viscous and 3D scalar-wave equations, making it a more practical and versatile solution.

Heterogeneity and dynamics in network models

SummaryWe propose an empirical spatial modeling framework that allows for both heterogeneity and dynamics in economic network connections. We establish the model's stationarity and ergodicity properties and show that the model's implied filter is invertible. While highly flexible, the model is straightforward to estimate by maximum likelihood. We apply the model to three datasets for Eurozone sovereign credit risk over the period Dec‐2009 to Dec‐2022. Accounting for both heterogeneity and time‐variation turns out to be empirically important both in‐sample and out‐of‐sample. The new model uncovers intuitive patterns that would go unnoticed in either homogeneous and/or static spatial financial network models.

A single-surface multi-failure strength domain for masonry

In this paper, we propose a simple approach to derive a single-surface multi-failure strength domain for the in-plane behaviour of masonry. The approach, that lays the basis for homogeneous continuum model developments relies on micro-mechanical analyses employing a block-based model for masonry in which blocks, modelled as finite strength continuum bodies, interact through zero-thickness interfaces. In order to derive the strength domain, firstly three failure mechanism typologies are identified, namely crushing failure, joint failure and mixed joint-block failure. Then, the limit surface for each mechanism is obtained relying on limit equilibrium considerations, also introducing a novel rational treatment of the mixed mechanism. Accordingly, a multi-surface strength domain is built by intersecting all the limit surfaces. Finally, such multi-surface strength domain is reduced to a single-surface one exploiting the RealSoftMax function, which allows to preserve the multi-failure nature of the approach, i.e. the explicit distinction between all the failure mechanisms. Following the proposed procedure, the resulting strength domain inherits the material parameters characterizing the block-based model. A finite element block-based model and available experimental data are employed to validate the proposed strength domain. The good agreement obtained with reference results confirms the soundness of the approach.

Homogenization-based chemomechanical properties of dissipative heterogeneous composites under transient mass diffusion

The chemomechanical properties of heterogeneous composites under mass diffusion are of significance in modern advanced technology and engineering applications. A homogenization-based two-scale chemomechanical model is developed for heterogeneous composites undergoing chemical mass diffusion. A two-scale incremental variational formulation is established for heterogeneous composites consisting of multiconstituents featuring local dissimilar diffusion-deformation properties. The minimization problems for coupled chemomechanical behaviors are solved for both macrostructure and microstructure contexts, where the macroscopic material properties are extracted from the results of local boundary value problem on the nested representative volume elements (RVEs). Through a staggered finite element method (FEM) implementation procedure, the proposed homogenization-based two-scale solution algorithm is implemented in the FEM package ABAQUS (V6.14). The developed variational model and tangential algorithm is checked by solving chemomechanical properties of particles enforced composite, where several numerical examples are conducted applying two-scale solution algorithm and validated by full-scale simulations. Parametric studies are carried out on the size effects of RVEs, with respect to the ‘inertia effect’ associated with ‘moment of mass concentration’, and the coupling mechanisms are discussed for mechanical and chemical solutions. To the end, the inelastic dissipations are solved on subscale BVPs and their effects on the mechanical deformation and chemical mass diffusion are checked. The contributions of this work are mainly two-folds. One is the theoretical advance for self-consistent homogenization modeling of the coupled multi-physics of heterogeneous composites, and a rigorous FE2 solution procedure. The other is providing numerical reference for evaluation of approximation algorithm as well as advanced data-driven method, which is needed for high-efficient material design.

MATLAB-based innovative 3D finite element method simulator for optimized real-time hyperthermia analysis

Background and ObjectiveOwing to the significant role of hyperthermia in enhancing the efficacy of chemotherapy or radiotherapy for treating malignant tissues, this study introduces a real-time hyperthermia simulator (RTHS) based on the three-dimensional finite element method (FEM) developed using the MATLAB App Designer. MethodsThe simulator consisted of operator-defined homogeneous and heterogeneous phantom models surrounded by an annular phased array (APA) of eight dipole antennas designed at 915 MHz. Electromagnetic and thermal analyses were conducted using the RTHS. To locally raise the target temperature according to the tumor's location, a convex optimization algorithm (COA) was employed to excite the antennas using optimal values of the phases to maximize the electric field at the tumor and amplitudes to achieve the required temperature at the target position. The performance of the proposed RTHS was validated by comparing it with similar hyperthermia setups in the FEM-based COMSOL software and finite-difference time-domain (FDTD)-based Sim4Life software. ResultsThe simulation results obtained using the RTHS were consistent, both for the homogeneous and heterogeneous models, with those obtained using commercially available tools, demonstrating the reliability of the proposed hyperthermia simulator. The effectiveness of the simulator was illustrated for target positions in five different regions for both homogeneous and heterogeneous phantom models. In addition, the RTHS was cost-effective and consumed less computational time than the available software. The proposed method achieved 94% and 96% accuracy for element sizes of λ/26 and λ/36, respectively, for the homogeneous model. For the heterogeneous model, the method demonstrated 93% and 95% accuracy for element sizes of λ/26 and λ/36, respectively. The accuracy can be further improved by using a more refined mesh at the cost of a higher computational time. ConclusionsThe proposed hyperthermia simulator demonstrated reliability, cost-effectiveness, and reduced computational time compared to commercial software, making it a potential tool for optimizing hyperthermia treatment.

High-Accuracy Simulation of Rayleigh Waves Using Fractional Viscoelastic Wave Equation

The propagation of Rayleigh waves is usually accompanied by dispersion, which becomes more complex with inherent attenuation. The accurate simulation of Rayleigh waves in attenuation media is crucial for understanding wave mechanisms, layer thickness identification, and parameter inversion. Although the vacuum formalism or stress image method (SIM) combined with the generalized standard linear solid (GSLS) is widely used to implement the numerical simulation of Rayleigh waves in attenuation media, this type of method still has its limitations. First, the GSLS model cannot split the velocity dispersion and amplitude attenuation term, thus limiting its application in the Q-compensated reverse time migration/full waveform inversion. In addition, GSLS-model-based wave equation is usually numerically solved using staggered-grid finite-difference (SGFD) method, which may result in the numerical dispersion due to the harsh stability condition and poses complexity and computational burden. To overcome these issues, we propose a high-accuracy Rayleigh-waves simulation scheme that involves the integration of the fractional viscoelastic wave equation and vacuum formalism. The proposed scheme not only decouples the amplitude attenuation and velocity dispersion but also significantly suppresses the numerical dispersion of Rayleigh waves under the same grid sizes. We first use a homogeneous elastic model to demonstrate the accuracy in comparison with the analytical solutions, and the correctness for a viscoelastic half-space model is verified by comparing the phase velocities with the dispersive images generated by the phase shift transformation. We then simulate several two-dimensional synthetic models to analyze the effectiveness and applicability of the proposed method. The results show that the proposed method uses twice as many spatial step sizes and takes 0.6 times that of the GSLS method (solved by the SGFD method) when achieved at 95% accuracy.