Layered Earth Research Articles

Research Progress and Application of Layered Rare Earth Hydroxides, a Class of Inorganic Layered Compounds with Photoluminescence

Research Progress and Application of Layered Rare Earth Hydroxides, a Class of Inorganic Layered Compounds with Photoluminescence

Facile synthesis of nanoflowers of immobilized enzyme using layered rare earth hydroxides as carriers and their application for detection of H2O2 and phenol

This study reports a simple method for synthesizing the nanoflower-immobilized enzyme (LYH-HRP) using horseradish peroxidase (HRP) as the bioenzyme and layered yttrium hydroxide (LYH) as the inorganic carrier. Utilizing the structural advantage of LYH and the catalytic properties of HRP, a nanoflower-based colorimetric platform was newly designed and applied for sensitively detecting H2O2 and phenol with a detection time of as fast as 5 min. The limits of detection (LODs) for H2O2 and phenol are as low as 0.046 μM and 0.778 μM, respectively. The activity and stability tests showed that the activity of LYH-HRP was 1.52 times that of free HRP, and it maintained 75% of the initial activity after 60 days.

Mg-modified layered erbium hydroxides promoting glucose transformation to lactic acid

Layered rare earth hydroxides (LREHs) with unique layer structure and tunable properties have shown attractive potentials as heterogeneous catalyst, but is still challenging in biomass valorization towards valuable chemical production due to the poor catalytic activity. Herein, Mg-modified erbium hydroxides (Mg-LErHs) with well-constructed layered structure have been first fabricated, where the properties and structure of Mg-LErHs significantly depend on the proportion of Mg. The results of catalyst characterizations reveal that Mg introduction increases the interlayer spacing and the content of Er(III)-O. Mg modification also hinders the desorption of crystallized H2O and dehydroxylation, thereby increasing the degree of crystallinity and promoting the stability of the catalyst. The activity test indicate that Mg modification greatly promotes the production of lactic acid from monosaccharides, where Mg(5.8)-LErHs affords the highest lactic acid yield of 60.9 %. Mg-LErHs also outperform other Mg-LREHs catalysts for the production of lactic acid. The highest catalytic activity of Mg(5.8)-LErHs are possibly attributed to its highest degree of crystallinity, and the increased layer spacing after Mg modification might have an advantage in facilitating the entry of substrate. The increased Er(III)-O content with high Lewis acidity might facilitate the combination with electronic-rich carbonyl oxygen in substrate. This research may provide a novel strategy to design the layered rare earth catalysts with tunable catalytic activity for biomass valorization.

A comprehensive solid-state NMR and theoretical modeling study to reveal the structural evolution of layered yttrium hydroxide upon calcination

Layered rare earth hydroxides (LREHs) are a new family of ion-exchangeable layered metal hydroxides, which have extensive applications in various fields due to the unique properties of rare earth cations in the layered structure and the anion exchange capacity. The transformation of layered metal hydroxides to new layered phases that can be restored through the memory effect is critical for their chemistry and applications. However, the structure details of these new phases such as the coordination environments of rare earth cations/counterions and their evolution as a function of calcination temperature remain unclear to date. Herein, a comprehensive 89Y/35Cl solid-state NMR (ssNMR) and theoretical modeling approach was used to reveal the structural evolution of a representative LREH, namely LYH-Cl, upon calcination. We first identified partial decomposition products of Y3O(OH)5Cl2 and Y(OH)3 during the dehydration stage, then uncovered the preferential removal of hydroxide ions on yttrium sites coordinated with chlorine during the dehydroxylation stage, and finally determined the preferential removal of chlorine exposed to the surface of layers during the dechlorination stage. The coordination environments of Y3+ and Cl− undergo significant changes upon calcination, revealed by ssNMR experiments. These findings thus help us to overcome the obstacles impeding the rational design and synthesis of LREH-based functional materials via memory effect, underscoring the vast potential of ssNMR in deepening the understanding of layered metal hydroxides and related materials.

Development of an ANN-Based Technique for Inversion of Seismic Refraction Travel Times

Non-uniqueness in the inversion of seismic data can be considered the main challenge for the application of such data. Prior information, such as downhole data, can be used to control this problem. However, in most cases, prior information is not available; accordingly, geophysicists/analysts have to suppose a primary model for the observed data and then find the final adequate layered earth model through trial and error. In this study, a new technique was developed based on the artificial neural network (ANN) for the inversion of seismic refraction data in the absence of prior information. In this regard, a sequential multilayer perceptron (SMLP) was proposed, which integrates the sequential information of the model parameters to predict a reasonable layered earth model. In fact, at first, a multilayer perceptron (MLP) (First-MLP) was trained by synthetic data; then, a layered earth model, i.e., the primary model, was predicted for the observed data. Next, using the primary model, a range for each of the model parameters, i.e., thickness and P-wave velocity, for each layer was defined. Subsequently, new synthetic samples were generated based on the determined ranges. Finally, using another MLP (Second-MLP), which was trained by the new synthetic samples, the final model for the observed data was estimated. The proposed method was also tested by employing different synthetic data with and without noise. Moreover, the SMLP inversion technique was used to analyze the experimental seismic refraction dataset at a dam construction site. The results for both synthetic and experimental data confirmed the reliability of the proposed SMLP inversion technique.

Geoelectric Modelling Based on Bessel Functions Integral and Damped Least-Square Inversion for Layered Earth Models

Apparent resistivity formulations of a geoelectric method for layered Earth have been obtained analytically in the Bessel functions integral. This formulation is obtained through the application of two boundary conditions. First, the current density is zero at the Earth's surface. Second, current density and electric potential are continuous at the boundary between the layers. Geoelectric modelling can be done using several model parameters through this formulation. The modelling results show that apparent resistivity formulations based on Bessel function integrals can simulate apparent resistivity curves for layered earth models. The inversion process uses the apparent resistivity formulation based on Bessel function integrals. In this study, the inversion process uses a dumped Least-squared inversion method. The first step begins by testing the inversion program using synthetic data. After that, the inversion program is used in field data. The inversion results using field data from geoelectric data in Mount Pandan, East Java, show that the program was well done, with a minimal error value of 1.24%.

Analysis of sensor parameters for ultra close range lateral penetration of subway tunnel full section sand layer soil pressure shield tunneling

In order to solve the problem of large disturbance to the stratum caused by shield tunneling in the full face sand layer geology by using the earth pressure balance full bin tunneling technology in the subway tunnel shield construction, this paper presents a parameter analysis of the ultra close side penetration of the full face sand layer earth pressure shield in the subway tunnel. By analyzing the monitoring data of surface settlement caused by subway shield construction, it is concluded that the law of surface horizontal settlement basically conforms to peak settlement theory, and the law of surface vertical settlement basically shows a steady downward trend. Through the mathematical modeling of the cumulative settlement data affected by the shield passing of the right line tunnel at the surface monitoring point, the influence of the shield passing of the left line tunnel on the surface settlement is predicted, and the prediction result is accurate. The experimental results show that the maximum deviation is 1.47 mm and the minimum deviation is 0.03 mm. The prediction accuracy is high and meets the accuracy requirements of practical engineering. Under the same geological conditions and construction parameters, the disturbance law of tunnel shield construction on the ground surface has important guiding significance in practical engineering.

Imparting Stable and Ultrahigh Proton Conductivity to a Layered Rare Earth Hydroxide via Ion Exchange.

Proton conductors are essential functional materials with a wide variety of potential applications in energy storage and conversion. In order to address the issues of low proton conductivity and poor stability in conventional proton conductors, a simple and valid ion-exchange method was proposed in this study for the introduction of stable and ultrahigh proton conductivity in layered rare earth hydroxides (LRHs). Test analyses by solid-state nuclear magnetic resonance, Fourier transform infrared spectroscopy, and powder X-ray diffraction revealed that the exchange of H2PO4- not only does not disrupt the layered structure of LRHs, but also creates more active proton sites and channels necessary for proton transport, thereby creating a high-performance proton conductor (LRH-H2PO4-). By utilizing this ion-exchange method, the proton conductivity of LRHs can be significantly enhanced from a low level to an ultrahigh level (>10-2 S·cm-1), while maintaining excellent long-term stability. Moreover, through methodically manipulating the guest ions and molecules housed within the interlayers of LRHs, a comprehensive explanation has been presented regarding the proficient mechanism of proton conduction in LRH-H2PO4-. As a result, this investigation presents a feasible and available approach for advancing proton conductor.

Synthesis and Thermal Decomposition of High-Entropy Layered Rare Earth Hydroxychlorides.

The synthesis of multicomponent and high-entropy compounds has become a rapidly developing field in advanced inorganic chemistry, making it possible to combine the properties of multiple elements in a single phase. This paper reports on the synthesis of a series of novel high-entropy layered rare earth hydroxychlorides, namely, (Sm,Eu,Gd,Y,Er)2(OH)5Cl, (Eu,Gd,Tb,Y,Er)2(OH)5Cl, (Eu,Gd,Dy,Y,Er)2(OH)5Cl, and (Eu,Gd,Y,Er,Yb)2(OH)5Cl, using a homogeneous hydrolysis technique under hydrothermal conditions. Elemental mapping proved the even distribution of rare earth elements, while luminescence spectroscopy confirmed efficient energy transfer between europium and other rare earth cations, thus providing additional evidence of the homogeneous distribution of rare earth elements within the crystal lattice. The average rare earth cation radii correlated linearly with the unit cell parameters (0.868 < R2 < 0.982) of the high-entropy layered rare earth hydroxychlorides. The thermal stability of the high-entropy layered rare earth hydroxychlorides was similar to that of individual hydroxychlorides and their binary solid solutions.

Impacts of Local Green's Functions on Modeling Atmospheric Loading Effects for GNSS Reference Stations

AbstractThe Green's function approach is well‐established and widely used for modeling the surface mass loading displacements. Global mean Green's functions (MGFs) are commonly applied without considering local variations of the crustal structure. Derived from the modified layered Earth structure, the local Green's functions (LGFs) are theoretically beneficial to generate more accurate deformation, since they consider interior information of the local crust. This paper analyzed the differences among MGFs from Gutenberg–Bullen A model and two sets of LGFs derived from modified PREM Earth models consolidating with two crust models TEA12 and CRUST1.0, hereafter called PREMTEA and PREMCRU, respectively. Utilizing MGFs and two sets of LGFs, we modeled the corresponding 3D atmospheric loading displacements for 984 ITRF2014 stations and compared them with the ITRF2014 residuals. The results show that LGFs from PREMTEA and PREMCRU perform well in further promoting scatter reduction for ∼72%, ∼56%, and ∼85% of stations for the Up, East and North components, respectively. The improvements for the North components are significant (up to 3.6%). In particular, stations in the east coastal areas of North America and the west edge of Greenland exhibit further promoting scatter reduction for the East components (up to ∼2.5%), while those located in west coastline of North America show better performance for the North components. Nevertheless, there are significant anomalies in northern Europe for PREMCRU, the mutation margin of which should be carefully considered when using a resolution higher than 1°. In the area around station MORP (358.31°W, 55.21°N, sited at coastline of Britain), we suggest using PREMTEA model.

Theoretical magnetotelluric response of stratiform earth consisting of alternative homogeneous and transitional layers

Abstract The magnetotelluric (MT) responses are explicitly solved for a stratiform earth containing multiple transitional layers in which the conductivity varies linearly with depth. In the model under consideration, any one homogeneous layer with constant conductivity or transitional one may be absent in the geometry. The traditional one-dimensional (1D) models with sharp boundaries will be obtained if all the transitional layers are absent in the geometry, while a special 1D model consisting of a sequence of contiguous transitional layers may be obtained if all the homogeneous layers (except the basement layer) are removed from the geometry. The tangential electric and magnetic fields as well as the surface impedance are analytically expressed by Airy functions. The analytical formula is validated in three theoretical examples by comparing with the results from available codes. The apparent resistivity and impedance phase on the surface of three different transitional models are illustrated to analysis the influence of the transitional layers on MT responses. The new formula provides an alternative way to obtain the analytic MT responses for the special layered earth.

Mass and strain field mediated low thermal conductivity for enhanced thermoelectric properties in Zn substituted SnS

Tin Sulfide (SnS) is widely recognized as a promising material for thermoelectrics owing to its layered structure, anharmonicity, earth abundance, and minimal toxicity. This study focuses on controlling the hole...

Coupled poroelastic and gravitational deformation of a layered spherical Earth – I: load Love numbers

SUMMARY In this paper, we propose a fully coupled two-phase poroelastic deformation theory for a spherically layered and self-gravitating Earth. The earth model consists of a solid inner core, a fluid outer core and poroelastic mantle and crust. The boundary-value problems are posed in the Laplace-transformed domain using the spherical system of vector functions, and analytical solutions are obtained in each layer using the dual-variable and position matrix method. As an application, the surface loading problem is considered. The undrained and drained limits are discussed with the corresponding governing equations, which are different from the conventional ones where body force is ignored. Numerical examples show that the poroelastic effect can be significant since the difference between the results for undrained and drained limits are large with obvious time-dependent deformation. This newly derived theory for the coupled boundary-value problem will have broad applications, such as displacement and gravity change due to groundwater depletion, poroelastic rebound after an earthquake and risk evaluation of earthquakes induced by water injection.

Reconstruction of Co-Seismic and Post-Seismic Processes for the February 6, 2023 Earthquake in Turkey from Data of Satellite SAR Interferometry

Using different methods for processing SAR images from the Sentinel-1A satellite, the displacement fields were determined in the region of the East Anatolian Fault Zone (EAFZ) and the Sürgü-Çardak faults, as well as a small fault on the continuation of the East Hatay fault zone, which rupture initiated a series of catastrophic earthquakes in Turkey on February 6, 2023. DInSAR and offset methods were applied. The most detailed data on the displacements were obtained by the offset method using images from the descending orbit. When constructing the model from the available SAR data, the data with the maximum signal-to-noise ratio were selected. For the northern part of the region, above 37.4° N, the range displacements obtained by the offset method from a descending orbit were used. South of parallel 37.0° N, we used azimuth displacements from the same descending orbit. The model of the seismic rupture was constructed on the basis of solution of (Pollitz, 1996) of the problem of deformations at the surface of a layered spherical Earth caused by along dip and strike displacements on a rectangular fault located inside the planet. Pollitz (1996) demonstrated that ignoring the radial layering of the planet leads to errors up to 20%, with the largest errors occurring in the presence of a large strike-slip component. Ignoring sphericity also introduces an error when using the solution in the framework of the idealization of an elastic homogeneous half-space with a flat free surface (Okada, 1985) which was used when constructing USGS and (Barbot et al., 2023) models. In our model the surfaces of seismic rupture are approximated by 19 rectangular elements along the strike, divided into three levels along the dip. Another element approximated a rupture along the extension of the East Hatay Fault Zone. As in the models of other authors (USGS; Barbot et al., 2023), in our model in the southern part of the EAFZ, the displacements increase from south to north, and are mainly concentrated in the upper part of the Earth’s crust to a depth of 10 km. At the southern end of this rupture, displacements in our model with an amplitude of up to 2 m are obtained at the lower levels of the model, and at its upper level, the displacements were only 0.11 m, and in this area on February 20, 2023 an earthquake of magnitude 6.3 occurred with a hypocenter depth of 11.5 km. The main displacements on the EAFZ are determined on its central segment. Here, the displacements go to a greater depth, their value reaches 10.2 m. On the Sürgü-Çardak fault, significant displacements occurred down to a depth of 20 km; displacements exceeded 10.2 m. In our model, at the northeast end of the seismic rupture along the EAFZ, a displacement area of 6.8 m overlaps with the southwest end of the seismic rupture model of the Doğanyol-Sivrice earthquake of January 24, 2020 with Mw 6.7, published on the USGS website. Therefore, our model does not confirm the hypothesis of the presence of a seismic gap here, which, according to (Barbot et al., 2023), is a zone of a possible nearest earthquake.

Reconstruction of Co-Seismic and Post-Seismic Processes for the February 6, 2023 Earthquake in Turkey from Data of Satellite SAR Interferometry

Abstract—Using different methods for processing SAR images from the Sentinel-1A satellite, the displacement fields were determined in the region of the East Anatolian Fault Zone (EAFZ) and the Sürgü-Çardak faults, as well as a small fault on the continuation of the East Hatay fault zone, which rupture initiated a series of catastrophic earthquakes in Turkey on February 06, 2023. DInSAR and offset methods were applied. The most detailed data on the displacements were obtained by the offset method using images from the descending orbit. When constructing the model from the available SAR data, the data with the maximum signal-to-noise ratio were selected. For the northern part of the region, above 37.4° N, the range displacements obtained by the offset method from a descending orbit were used. South of parallel 37.0° N, we used azimuth displacements from the same descending orbit. The model of the seismic rupture was constructed on the basis of solution of (Pollitz, 1996) of the problem of deformations at the surface of a layered spherical Earth caused by along dip and strike displacements on a rectangular cut located inside the planet. Pollitz (1996) demonstrated that ignoring the spherical layering of the planet leads to errors up to 20%, with the largest errors occurring in the presence of a large strike-slip component. Ignoring sphericity also introduces an error when using the solution in the framework of the idealization of an elastic homogeneous half-space with a flat free boundary (Okada, 1985) which was used when constructing USGS and (Barbot et al., 2023) models. In our model the surfaces of seismic rupture are approximated by 19 rectangular elements along the strike, divided into three levels along the dip. Another element approximated a rupture along the extension of the East Hatay Fault Zone. As in the models of other authors (USGS; Barbot et al., 2023), in our model in the southern part of the EAFZ, the displacements increase from south to north, and are mainly concentrated in the upper part of the Earth’s crust to a depth of 10 km. At the southern end of this rupture, displacements in our model with an amplitude of up to 2 m are obtained at the lower levels of the model, and at its upper level, the displacements were only 0.11 m, and in this area on February 20, 2023 an earthquake of magnitude 6.3 occurred with a hypocentre depth of 11.5 km. The main displacements on the EAFZ are determined on its central segment. Here, the displacements go to a greater depth, their value reaches 10.2 m. On the Sürgü-Çardak fault, significant displacements occurred down to a depth of 20 km; displacements exceeded 9.8 m. In our model, at the northeast end of the seismic rupture along the EAFZ, a displacement area of 6.8 m overlaps with the southwest end of the seismic rupture model of the Doğanyol-Sivrice earthquake of January 24, 2020 with Mw 6.7, published on the USGS website. Therefore, our model does not confirm the hypothesis of the presence of a seismic gap here, which, according to (Barbot et al., 2023), is a zone of a possible nearest earthquake.

Seismic prompt gravity strain signals in a layered spherical Earth

Seismic waves generated by an earthquake can produce dynamic perturbations in the Earth’s gravity field before the direct arrival of P-waves. Observations of these so-called prompt elasto-gravity signals by ground-based gravimeters and broadband seismometers have been reported for some large events, such as the 2011 MW9.1 Tohoku earthquake. Recent studies have introduced prompt gravity strain signals (PGSSs) as a new type of observable seismic gravity perturbation that can be used to measure the spatial gradient of the perturbed gravity field. Theoretically, these types of signals can be recorded by in-development instruments termed gravity strainmeters, although no successful detection has been reported as yet. Herein, we propose an efficient approach for PGSSs based on a multilayered spherical Earth model. We compared the simulated waveforms with analytical solutions obtained from a homogeneous half-space model, which has been used in earlier studies. This comparison indicates that the effect of the Earth’s structural stratification is significant. With the help of the new simulation approach, we also demonstrated how the PGSSs depend on the magnitude of the seismic source. We further conducted synthetic tests estimating earthquake magnitude using gravity strain signals to demonstrate the potential application of this type of signal in earthquake early warning systems. These results provide essential information for future studies on the synthesis and application of earthquake-induced gravity strain signals.

Cinnamate-Intercalated Layered Yttrium Hydroxide: UV Light-Responsive Switchable Material.

In recent years, there has been an increasing interest in stimuli-responsive host-guest materials due to the high potential for their application in switchable devices. Light is the most convenient stimulus for operating these materials; a light-responsive guest affects the host structure and the functional characteristics of the entire material. UV-transparent layered rare earth hydroxides intercalated with UV-switchable anions are promising candidates as stimuli-responsive host-guest materials. The interlayer distance in the layered rare earth hydroxides depends on the size of the intercalated anions, which could be changed in situ, e.g., via anion isomerisation. Nevertheless, for layered rare earth hydroxides, the possibility of such changes has not been reported yet. A good candidate anion that is capable of intercalating into the interlayer space is the cinnamate anion, which undergoes UV-assisted irreversible trans-cis isomerisation. In this work, both trans- and cis-cinnamate anions were intercalated in layered yttrium hydroxide (LYH). Upon UV-irradiation, the interlayer distance of trans-cinnamate-intercalated layered yttrium hydroxide suspended in isopropanol changed from 21.9 to 20.6 Å. For the first time, the results obtained demonstrate the possibility of using layered rare earth hydroxides as stimuli-responsive materials.

A commercial finite element approach to modelling Glacial Isostatic Adjustment on spherical self-gravitating compressible earth models

SUMMARYThis paper presents a method that modifies commercial engineering-oriented finite element packages for the modelling of Glacial Isostatic Adjustment (GIA) on a self-gravitating, compressible and spherical Earth with 3-D structures. The approach, called the iterative finite element body and surface force (FEMIBSF) approach, solves the equilibrium equation for deformation using the ABAQUS finite element package and calculates potential perturbation consistently with finite element theory, avoiding the use of spherical harmonics. The key to this approach lies in computing the mean external body forces for each finite element within the Earth and pressure on Earth's surface and core–mantle boundary (CMB). These quantities, which drive the deformation and stress perturbation of GIA but are not included in the equation of motion of commercial finite element packages, are implemented therein. The method also demonstrates how to calculate degree-1 deformation directly in the spatial domain and Earth-load system for GIA models. To validate the FEMIBSF method, loading Love numbers (LLNs) for homogeneous and layered earth models are calculated and compared with three independent GIA methodologies: the normal-mode method, the iterative body force method and the spectral-finite element method. Results show that the FEMIBSF method can accurately reproduce the unstable modes for the homogeneous compressible model and agree reasonably well with the Love number results from other methods. It is found that the accuracy of the FEMIBSF method increases with higher resolution, but a non-conformal mesh should be avoided due to creating the so-called hanging nodes. The role of a potential force at the CMB is also studied and found to only affect the long-wavelength surface potential perturbation and deformation in the viscous time regime. In conclusion, the FEMIBSF method is ready for use in realistic GIA studies, with modelled vertical and horizontal displacement rates in a disc load case showing agreement with other two GIA methods within the uncertainty level of GNSS measurements.

A stable analytical expression for magnetotelluric/radiomagnetotelluric impedances in anisotropic layered Earth models

Previous closed-form solutions of impedances on layered Earth models were only available for the anisotropic conductivity case under the plane wave electromagnetic incidence. Here, we have developed a numerically stable impedance formula for both magnetotelluric and radiomagnetotelluric problems in layered media with arbitrarily anisotropic conductivity and dielect permittivity. Maxwell equations are first transformed into a set of coupled second-order partial differential equations with the horizontal components of electric field as the variables. Then, the recursive formula of surface impedance is obtained by using the general solutions of the second-order partial differential equations and the tangential continuity condition of electromagnetic fields at each layer interface. To avoid the numerical overflow in both the nominator and denominator of the recursive impedance formula due to large layer thickness or high working frequency, an artificial exponential function with positive exponential factor is used to regularize both the nominator and denominator. It leads numerically stable recursive formula for any layer thickness and working frequency. At the end, a four layered magnetotelluric model with anisotropic conductivities is adopted to validate the newly derived analytical formula and another two synthetic layered Earth models are used to study the effects of conductive anisotropy and dielectric anisotropy on radiomagnetotelluric responses.

Periodic surface loading using GRACE data for a layered viscoelastic earth model based on a direct relationship between geoid and displacement

SUMMARY Loading theory is fundamental in explaining deformation resulting from surface mass changes. Although various theoretical methods, including the classical elastic loading theory by W. E. Farrell and I. M. Longman, have been proposed, a viscoelasticity-based theory may be required to address long timescale loading problems, such as annual and interannual deformation, as well as longer timescale loading effects. In this study, we use a semi-analytical approach to simulate the continuous periodic loading deformation of a viscoelastic, spherical, layered earth model with linear rheology profiles. We provide a series of formulas in the spectral domain for the spatiotemporal displacement, which establish connections between mass, geoid and displacement solely through the utilization of complex Love numbers and Stokes coefficients, thereby circumventing the need for viscoelastic Green's function. Using our newly proposed method, we investigate the viscoelastic loading deformation caused by annual cyclic mass loading, considering both steady-state creep and additional transient creep with a wide range of viscosities. The results indicate that when utilizing steady-state viscosity values constrained by GIA data, the viscoelastic effect is not evident in the annual cyclic load deformation. However, incorporating the Burgers model with transient creep mainly constrained by post-seismic deformation influences the amplitude and phase of the annual cyclic loading, highlighting the role of rheology. Furthermore, we observe that the horizontal displacement in periodic load deformation exhibits a higher sensitivity to the viscosity of the model compared to the geoid and vertical displacement, regardless of the rheological model used.