Enhancing Low-Frequency Microwave Absorption Through Structural Polarization Modulation of MXenes

Two-dimensional carbon-based materials have shown promising electromagnetic wave absorption capabilities in mid-and high-frequency ranges,but face challenges in low-frequency absorption due to limited control over polarization response mecha-nisms and ambiguous resonance behavior.In this study,we pro-pose a novel approach to enhance absorption efficiency in aligned three-dimensional(3D)MXene/CNF(cellulose nanofibers)cavities by modifying polarization properties and manipulating resonance response in the 3D MXene architecture.This controlled polarization mechanism results in a significant shift of the main absorption region from the X-band to the S-band,leading to a remarkable reflection loss value of-47.9 dB in the low-frequency range.Furthermore,our findings revealed the importance of the oriented electromagnetic coupling in influencing electromagnetic response and microwave absorption properties.The present study inspired us to develop a generic strategy for low-frequency tuned absorption in the absence of magnetic element participation,while orientation-induced polarization and the derived magnetic resonance coupling are the key controlling factors of the method.

Suppression of low-frequency ultrasound broadband vibration using star-shaped single-phase metamaterials

In order to suppress the low-frequency ultrasound vibration in the broadband range of 20 k Hz—100 k Hz,this paper proposes and discusses an acoustic metamaterial with low-frequency ultrasound vibration attenuation properties,which is configured by hybrid arc and sharp-angle convergent star-shaped lattices.The effect of the dispersion relation and the bandgap characteristic for the scatterers in star-shaped are simulated and analyzed.The target bandgap width is extended by optimizing the geometry parameters of arc and sharp-angle convergent lattices.The proposed metamaterial configured by optimized hybrid lattices exhibits remarkable broad bandgap characteristics by bandgap complementarity,and the simulation results verify a 99%vibration attenuation amplitude can be obtained in the frequency of20 k Hz—100 k Hz.After the fabrication of the proposed hybrid configurational star-shaped metamaterial by 3D printing technique,the transmission loss experiments are performed,and the experimental results indicate that the fabricated metamaterial has the characteristics of broadband vibration attenuation and an amplitude greater than 85%attenuation for the target frequency.These results demonstrate that the hybrid configurational star-shaped metamaterials can effectively widen the bandgap and realize high efficiency attenuation,which has capability for the vibration attenuation in the application of highprecise equipment.

A low-frequency pure metal metamaterial absorber with continuously tunable stiffness

To address the incompatibility between high environmental adaptability and deep subwavelength characteristics in conventional local resonance metamaterials,and overcome the deficiencies in the stability of existing active control techniques for band gaps,this paper proposes a design method of pure metal vibration damping metamaterial with continuously tunable stiffness for wideband elastic wave absorption.We design a dual-helix narrow-slit pure metal metamaterial unit,which possesses the triple advantage of high spatial compactness,low stiffness characteristics,and high structural stability,enabling the opening of elastic flexural band gaps in the low-frequency range.Similar to the principle of a sliding rheostat,the introduction of continuously sliding plug-ins into the helical slits enables the continuous variation of the stiffness of the metamaterial unit,achieving a continuously tunable band gap effect.This successfully extends the effective band gap by more than ten times.The experimental results indicate that this metamaterial unit can be used as an additional vibration absorber to absorb the low-frequency vibration energy effectively.Furthermore,it advances the metamaterial absorbers from a purely passive narrowband design to a wideband tunable one.The pure metal double-helix metamaterials retain the subwavelength properties of metamaterials and are suitable for deployment in harsh environments.Simultaneously,by adjusting its stiffness,it substantially broadens the effective band gap range,presenting promising potential applications in various mechanical equipment operating under adverse conditions.

A seismic elastic moduli module for the measurements of low-frequency wave dispersion and attenuation of fluid-saturated rocks under different pressures

Knowledge about the seismic elastic modulus dispersion,and associated attenuation,in fluid-saturated rocks is essential for better interpretation of seismic observations taken as part of hydrocarbon identification and time-lapse seismic surveillance of both conventional and unconventional reservoir and overburden performances.A Seismic Elastic Moduli Module has been developed,based on the forced-oscillations method,to experimentally investigate the frequency dependence of Young's modulus and Poisson's ratio,as well as the inferred attenuation,of cylindrical samples under different confining pressure conditions.Calibration with three standard samples showed that the measured elastic moduli were consistent with the published data,indicating that the new apparatus can operate reliably over a wide frequency range of f∈[1-2000,10^(6)]Hz.The Young's modulus and Poisson's ratio of the shale and the tight sandstone samples were measured under axial stress oscillations to assess the frequency-and pressure-dependent effects.Under dry condition,both samples appear to be nearly frequency independent,with weak pressure dependence for the shale and significant pressure dependence for the sandstone.In particular,it was found that the tight sandstone with complex pore microstructure exhibited apparent dispersion and attenuation under brine or glycerin saturation conditions,the levels of which were strongly influenced by the increased effective pressure.In addition,the measured Young's moduli results were compared with the theoretical predictions from a scaled poroelastic model with a reasonably good agreement,revealing that the combined fluid flow mechanisms at both mesoscopic and microscopic scales possibly responsible for the measured dispersion.

Current optimization-based control of dual three-phase PMSM for low-frequency temperature swing reduction

In this paper,a control scheme based on current optimization is proposed for dual three-phase permanent-magnet synchronous motor(DTP-PMSM)drive to reduce the low-frequency temperature swing.The reduction of temperature swing can be equivalent to reducing maximum instantaneous phase copper loss in this paper.First,a two-level optimization aiming at minimizing maximum instantaneous phase copper loss at each electrical angle is proposed.Then,the optimization is transformed to a singlelevel optimization by introducing the auxiliary variable for easy solving.Considering that singleobjective optimization trades a great total copper loss for a small reduction of maximum phase copper loss,the optimization considering both instantaneous total copper loss and maximum phase copper loss is proposed,which has the same performance of temperature swing reduction but with lower total loss.In this way,the proposed control scheme can reduce maximum junction temperature by 11%.Both simulation and experimental results are presented to prove the effectiveness and superiority of the proposed control scheme for low-frequency temperature swing reduction.

Dynamic characteristics of coal specimens with varying static preloading levels under low-frequency disturbance load

The mechanical properties of residual coal pillars under the influence of upward mining disturbances significantly affect the safety of residual mining activities on working faces.This study conducted low-frequency disturbance dynamic uniaxial compression tests on coal specimens using a self-developed dynamic-static load coupling electro-hydraulic servo system,and studied the strength evolutions,surface deformations,acoustic emission(AE)characteristic parameters,and the failure modes of coal specimens with different static preloading levels were studied.The disturbance damage is positively correlated with the coal specimen static preload level.Specifically,the cumulative AE count rates of the initial accelerated damage stage for the coal specimens with static preloading level of 60%and 70%of the uniaxial compressive strength(UCS)were 2.66 and 3.19 times that of the 50%UCS specimens,respectively.Macroscopically,this behaviour manifested as a decrease in the compressive strength,and the mean strengths of the disturbance-damaged coal specimens with 60%and 70%of UCS static preloading decreased by 8.53%and 9.32%,respectively,compared to those of the specimens under pure static loading.The crack sources,such as the primary fissures,strongly control the dynamic response of the coal specimen.The difference between the dynamic responses of the coal specimens and that of dense rocks is significant.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

The suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications.To address this concern,a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed.By combining Bloch’s theorem with the finite element method,the band structure is calculated.Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz,with a bandgap ratio exceeding 50%.The first bandgap spans from 169.57 Hz to 216.42 Hz.To reveal the formation mechanism of the bandgap,a vibrational mode analysis is performed.Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations.Additionally,detailed parametric analyses are conducted to investigate the effect ofθ,i.e.,the angle between the protruding corner of the structure and the horizontal direction,on the band structures and the total effective bandgap width.It is found that reducingθis conducive to obtaining lower frequency bandgaps.The propagation characteristics of elastic waves in the structure are explored by the group velocity,phase velocity,and wave propagation direction.Finally,the transmission characteristics of a finite periodic structure are investigated experimentally.The results indicate significant acceleration amplitude attenuation within the bandgap range,confirming the structure’s excellent low-frequency vibration suppression capability.

Low-frequency oscillation of train-network system considering traction power supply mode

The low-frequency oscillation(LFO)has occurred in the train-network system due to the introduction of the power electronics of the trains.The modeling and analyzing method in current researches based on electrified railway unilateral power supply system are not suitable for the LFO analysis in a bilateral power supply system,where the trains are supplied by two traction substations.In this work,based on the single-input and single-output impedance model of China CRH5 trains,the node admittance matrices of the train-network system both in unilateral and bilateral power supply modes are established,including three-phase power grid,traction transformers and traction network.Then the modal analysis is used to study the oscillation modes and propagation characteristics of the unilateral and bilateral power supply systems.Moreover,the influence of the equivalent inductance of the power grid,the length of the transmission line,and the length of the traction network are analyzed on the critical oscillation mode of the bilateral power supply system.Finally,the theoretical analysis results are verified by the time-domain simulation model in MATLAB/Simulink.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

Diagnosing ratio of electron density to collision frequency of plasma surrounding scaled model in a shock tube using low-frequency alternating magnetic field phase shift

A non-contact low-frequency(LF)method of diagnosing the plasma surrounding a scaled model in a shock tube is proposed.This method utilizes the phase shift occurring after the transmission of an LF alternating magnetic field through the plasma to directly measure the ratio of the plasma loop average electron density to collision frequency.An equivalent circuit model is used to analyze the relationship of the phase shift of the magnetic field component of LF electromagnetic waves with the plasma electron density and collision frequency.The applicable range of the LF method on a given plasma scale is analyzed.The upper diagnostic limit for the ratio of the electron density(unit:m^(-3))to collision frequency(unit:Hz)exceeds 1×10^(11),enabling an electron density to exceed 1×10^(20)m^(-3)and a collision frequency to be less than 1 GHz.In this work,the feasibility of using the LF phase shift to implement the plasma diagnosis is also assessed.Diagnosis experiments on shock tube equipment are conducted by using both the electrostatic probe method and LF method.By comparing the diagnostic results of the two methods,the inversion results are relatively consistent with each other,thereby preliminarily verifying the feasibility of the LF method.The ratio of the electron density to the collision frequency has a relatively uniform distribution during the plasma stabilization.The LF diagnostic path is a loop around the model,which is suitable for diagnosing the plasma that surrounds the model.Finally,the causes of diagnostic discrepancy between the two methods are analyzed.The proposed method provides a new avenue for diagnosing high-density enveloping plasma.

Altered spontaneous brain activity patterns in hypertensive retinopathy using fractional amplitude of low-frequency fluctuations:a functional magnetic resonance imaging study

AIM:To study functional brain abnormalities in patients with hypertensive retinopathy(HR)and to discuss the pathophysiological mechanisms of HR by fractional amplitude of low-frequency fluctuations(fALFFs)method.METHODS:Twenty HR patients and 20 healthy controls(HCs)were respectively recruited.The age,gender,and educational background characteristics of the two groups were similar.After functional magnetic resonance imaging(fMRI)scanning,the subjects’spontaneous brain activity was evaluated with the fALFF method.Receiver operating characteristic(ROC)curve analysis was used to classify the data.Further,we used Pearson’s correlation analysis to explore the relationship between fALFF values in specific brain regions and clinical behaviors in patients with HR.RESULTS:The brain areas of the HR group with lower fALFF values than HCs were the right orbital part of the middle frontal gyrus(RO-MFG)and right lingual gyrus.In contrast,the values of fALFFs in the left middle temporal gyrus(MTG),left superior temporal pole(STP),left middle frontal gyrus(MFG),left superior marginal gyrus(SMG),left superior parietal lobule(SPL),and right supplementary motor area(SMA)were higher in the HR group.The results of a t-test showed that the average values of fALFFs were statistically significantly different in the HR group and HC group(P<0.001).The fALFF values of the left middle frontal gyrus in HR patients were positively correlated with anxiety scores(r=0.9232;P<0.0001)and depression scores(r=0.9682;P<0.0001).CONCLUSION:fALFF values in multiple brain regions of HR patients are abnormal,suggesting that these brain regions in HR patients may be dysfunctional,which may help to reveal the pathophysiological mechanisms of HR.

A bio-inspired spider-like structure isolator for low-frequency vibration

This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

Permeability evolution mechanism and the optimum permeability determination of uranium leaching from low-permeability sandstone treated with low-frequency vibration

Low-frequency vibrations can effectively improve natural sandstone permeability,and higher vibration frequency is associated with larger permeability.However,the optimum permeability and permeability evolution mechanism for uranium leaching and the relationship between permeability and the change of chemical reactive rate affecting uranium leaching have not been determined.To solve the above problems,in this study,identical homogeneous sandstone samples were selected to simulate lowpermeability sandstone;a permeability evolution model considering the combined action of vibration stress,pore water pressure,water flow impact force,and chemical erosion was established;and vibration leaching experiments were performed to test the model accuracy.Both the permeability and chemical reactions were found to simultaneously restrict U6þleaching,and the vibration treatment increased the permeability,causing the U6þleaching reaction to no longer be diffusion-constrained but to be primarily controlled by the reaction rate.Changes of the model calculation parameters were further analyzed to determine the permeability evolution mechanism under the influence of vibration and chemical erosion,to prove the correctness of the mechanism according to the experimental results,and to develop a new method for determining the optimum permeability in uranium leaching.The uranium leaching was found to primarily follow a process consisting of(1)a permeability control stage,(2)achieving the optimum permeability,(3)a chemical reactive rate control stage,and(4)a channel flow stage.The resolution of these problems is of great significance for facilitating the application and promotion of lowfrequency vibration in the CO_(2)+O_(2) leaching process.

Observation of low-frequency oscillation in argon helicon discharge

We present here a kind of low-frequency oscillation in argon helicon discharge with a half helical antenna.This time-dependent instability shows a global quasi-periodic oscillation of plasma density and electron temperature,with a typical frequency of a few tens of Hz which increases with external magnetic field as well as radiofrequency(RF)power.The relative oscillation amplitude decreases with magnetic field and RF power,but the rising time and pulse width do not change significantly under different discharge conditions.The oscillation can only be observed in some specific conditions of low magnetic fields and low RF power when the gas flows in from one end of the discharge area and out from another end.This global instability is suggested to be attributed to the pressure instability of neutral depletion,which is the result of compound action of gas depletion by heating expansion and gas replenishment from upstream.There are two kinds of oscillations,large and small amplitude oscillations,occurring in different discharge modes.This study could be a good verification of and complement to earlier experiments.This kind of spontaneous pulse phenomenon is also helpful in realizing a pulsing plasma source without a pulsed power supply.

Method for measuring the low-frequency sound power from a complex sound source based on sound-field correction in a non-anechoic tank

Similar to air reverberation chambers, non-anechoic water tanks are important acoustic measurement devices that can be used to measure the sound power radiated from complex underwater sound sources using diffusion field theory. However,the problem of the poor applicability of low-frequency measurements in these tanks has not yet been solved. Therefore,we propose a low-frequency acoustic measurement method based on sound-field correction(SFC) in an enclosed space that effectively solves the problem of measuring the sound power from complex sound sources below the Schroeder cutoff frequency in a non-anechoic tank. Using normal mode theory, the transfer relationship between the mean-square sound pressure in an underwater enclosed space and the free-field sound power of the sound source is established, and this is regarded as a correction term for the sound field between this enclosed space and the free field. This correction term can be obtained based on previous measurements of a known sound source. This term can then be used to correct the mean-square sound pressure excited by any sound source to be tested in this enclosed space and equivalently obtain its free-field sound power. Experiments were carried out in a non-anechoic water tank(9.0 m × 3.1 m × 1.7 m) to confirm the validity of the SFC method. Through measurements with a spherical sound source(whose free-field radiation characteristics are known),the correction term of the sound field between this water tank and the free field was obtained. On this basis, the sound power radiated from a cylindrical shell model under the action of mechanical excitation was measured. The measurement results were found to have a maximum deviation of 2.9 d B from the free-field results. These results show that the SFC method has good applicability in the frequency band above the first-order resonant frequency in a non-anechoic tank. This greatly expands the potential low-frequency applications of non-anechoic tanks.

A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

We find that the perturbed Lagrangian derived from the drift-kinetic equation in[Porcelli F et al 1994 Phys.Plasmas 1470]is inconsistent with the ordering for the low-frequency large-scale magnetohydrodynamic(MHD).Here,we rederive the expression for the perturbed Lagrangian within the framework of nonideal MHD using the ordering system for the low-frequency largescale MHD in a low-beta plasma.The obtained perturbed Lagrangian is consistent with Chen's gyrokinetic theory[Chen L and Zonca F 2016 Rev.Mod.Phys.88015008],where the terms related to the field curvature and gradient are small quantities of higher order and thus negligible.As the perturbed Lagrangian has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency MHD applications,this finding may have a significant impact on the understanding of the kinetic driving and dissipative mechanisms of MHD instabilities and the plasma response to electromagnetic perturbations in fusion plasmas.

Low-Frequency Oscillation Analysis of Grid-Connected VSG System Considering Multi-Parameter Coupling

With the increasing integration of new energy generation into the power system and the massive withdrawal of traditional fossil fuel generation,the power system is faced with a large number of stability problems.The phenomenon of low-frequency oscillation caused by lack of damping and moment of inertia is worth studying.In recent years,virtual synchronous generator(VSG)technique has been developed rapidly because it can provide considerable damping and moment of inertia.While improving the stability of the system,it also inevitably causes the problem of active power oscillation,especially the low mutual damping between the VSG and the power grid will make the oscillation more severe.The traditional time-domain state-space method cannot reflect the interaction among state variables and study the interaction between different nodes and branches of the power grid.In this paper,a frequency-domain method for analyzing low-frequency oscillations considering VSG parameter coupling is proposed.First,based on the rotor motion equation of the synchronous generator(SG),a secondorder VSG model and linearized power-frequency control loop model are established.Then,the differences and connections between the coupling of key VSG parameters and low-frequency oscillation characteristics are studied through frequency domain analysis.The path and influencemechanism of a VSG during low-frequency power grid oscillations are illustrated.Finally,the correctness of the theoretical analysis model is verified by simulation.

Development of a low-frequency magnetic lightning mapping system(LFM-LMS)in North China:validation and preliminary results

A low-frequency magnetic lightning mapping system(LFM-LMS)was built during the SHAndong Triggered Lightning Experiment(SHATLE),based on continuous measurements of magnetic field radiation from lightning.The hardware and source-mapping techniques used by the LFM-LMS were introduced;both Monte Carlo simulations and the observation of rocket-triggered lightning examples were employed to examine the location accuracy and detection effectiveness of the LFM-LMS.We estimated that the system’s location accuracy about 100−200 m horizontally and~200 m vertically.A natural intra-cloud lightning flash and a rocket-triggered lightning flash,both with intricate structures and discharging processes,were examined using the three-dimensional mapping results.The progressing path of negative lightning leaders is usually well-defined,and its propagation speed is estimated to be(0.5−1.4)×10^(6)m/s.In summary,the LFM-LMS can reconstruct the three-dimensional morphology of lightning flashes;this technology provides a efficient method for investigating the characteristics of lightning development,as well as the overall electrical strucuture of thunderstorms.

Understanding Lithium-ion Transport in Sulfolane- and Tetraglyme-Based Electrolytes Using Very Low-Frequency Impedance Spectroscopy

With the increasing interest in highly concentrated electrolyte systems,correct determination of the cation transference number is important.Pulsed-field gradient NMR technique,which measures self-diffusion coefficients,is often applied on liquid electrolytes because of the wide accessibility and simple sample preparation.However,since the assumptions of this technique,that is,complete salt dissociation,all ions participating in motion,and all of them moving independently,no longer hold true in concentrated solutions,the transference numbers,thus obtained are often over-estimated.In the present work,impedance spectroscopy at a frequency range of 1 MHz to 0.1 mHz was used to examine the concentration effect on lithium-ion transference number under anion-blocking conditions T abc Liþfor two electrolytes:lithium bis(fluorosulfonyl)imide(LiFSI)in sulfolane(SL)and lithium bis(trifluorosulfonyl)imide(LiTFSI)in tetraglyme(G4).The T abc Liþof the former was almost an order of magnitude higher than that of the latter.It also appeared to increase with increasing concentration while the latter followed an opposite trend.The faster Li^(+)transport in the SL system is attributed to the formation of a liquid structure consisting of extended chains/bridges of SL molecules and the anions,which facilitate a cation-hopping/ligand-exchanged-typed diffusion mechanism by partially decoupling the cations from the anions and solvent molecules.The G4 system,in contrast,is dominated by the formation of long-lived,stable[Li(G4)]+solvation cages that results in a sluggish Li+transport.The difference between the two transport mechanisms is discussed via comparison of the bulk ionic conductivity,viscosity,ion self-diffusion coefficients,and the Onsager transport coefficients.

Low-frequency data analysis and expansion

The use of low-frequency seismic data improves the seismic resolution, and the imaging and inversion quality. Furthermore, low-frequency data are applied in hydrocarbon exploration; thus, we need to better use low-frequency data. In seismic wavelets, the loss of low-frequency data decreases the main lobe amplitude and increases the first side lobe amplitude and results in the periodic shocking attenuation of the secondary side lobe. The loss of low frequencies likely produces pseudo-events and the false appearance of higher resolution. We use models to examine the removal of low-frequency data in seismic data processing. The results suggest that the removal of low frequencies create distortions, especially for steep structures and thin layers. We also perform low-frequency expansion using compressed sensing and sparse constraints and develop the corresponding module. Finally, we apply the proposed method to real common image point gathers with good results.