Characteristics Of Wave Field Research Articles

Research on the random generation model of 2D irregular aggregates in concrete based on fast grid region division method and its ground penetrating radar characteristics

Concrete can be regarded as a composite material with aggregates embedded in hardened slurries. The size, shape and distribution of aggregates directly affect multiple properties of concrete, including mechanical properties, ultrasonic field characteristics of concrete and ground penetrating radar (GPR) wave field characteristics. Therefore, conducting in-depth research on the random generation model of two-dimensional irregular aggregates is particularly important. This article introduces a fast grid region division method (FGRDM), which is an efficient reconstruction algorithm designed for two-dimensional concrete aggregate models. The algorithm takes into consideration the random micro-aggregate structure of concrete. A two-dimensional random distribution model of irregular aggregates in concrete was successfully established by generating concrete models with different particle size distributions and aggregate contents. Furthermore, the finite difference time domain method was used to analyze the GPR wave field of the random model. The significant influence of aggregate shape and distribution on the GPR wave field was discussed. Compared with existing two-dimensional irregular aggregate random generation models, the FGRDM proposed in this paper avoids computational redundancy and generates irregular aggregates at an increasingly fast speed. In the analysis of GPR data, electromagnetic waves are greatly affected by the shape and distribution of aggregates, highlighting the critical role of two-dimensional random distribution models in GPR data analysis. The paper uses FGRDM to generate random irregular aggregates to simulate the distribution of aggregates in actual concrete. Different diameter glass fiber reinforced polymer (GFRP) bars are inserted into the actual concrete and the numerical model to investigate the effect of aggregate size on the recognition of different diameter GFRP bars. The simulation results are generally consistent with the experimental results.

Study on ground-penetrating radar wave field characteristics for earth dam disease considering the medium randomness

Ground-Penetrating Radar (GPR) has been widely used for non-destructive testing of earth dam disease. However, the forward simulation of GPR for earth dam disease often employs layered homogeneous models, neglecting the influence of medium randomness on its wave field characteristics. Therefore, considering the randomness of the medium, a geoelectrical model for earth dam disease is established, which is based on the mixed-type autocorrelation function and the finite element time-domain method. The influence of random medium model parameters on the single-channel wave of GPR is analyzed. The electromagnetic wave propagation characteristics under different medium models are explored. The forward simulation of GPR for earth dam disease such as panel voiding, concentrated seepage, and loosening are performed. The differences in propagation characteristics for earth dam disease between uniform medium model and random medium model are compared. Compared to the calculation results of the uniform medium model, the propagation speed and amplitude of electromagnetic waves in the random medium model changes, and a number of diffraction waves are present. When performing forward simulation of GPR for earth dam disease, considering medium randomness can deepen the understanding of the GPR section view and help improve the accuracy of image interpretation.

Identification and Application of Wave Field Characteristics of Channel Waves in Extra-Thick Coal Seams

Channel wave seismic activity often occurs with thin and medium-thick coal seams being the main target layer. To address the problem of channel wave applicability detection in extremely thick coal seams, the propagation and identification characteristics of channel waves remain the focus of research. Therefore, this paper takes the in-seam wave exploration of a 27 m extremely thick coal seam as an example and uses the staggered mesh finite difference method to construct a three-dimensional medium model for numerical simulation. An analysis of the physical parameters of coal and rock, along with the dispersion characteristics of channel waves in extra-thick coal seams, is utilized, through the Zoeppritz equation and the total reflection propagation method, to calculate the imaging. We found the following: (1) The dispersion areas and weak dispersion areas along the detection direction are extremely thick coal seams. (2) There are apparent channel waves in extra-thick coal seams, with a waveform similar to body waves; the length of the wave train is shorter than that of the conventional channel wave, and the arrival time can be estimated accurately. The amplitude of the apparent channel wave is affected by the degree of dispersion, with lower attenuation and higher resolution. The characteristic of total reflection in extremely thick coal seams is that the incident angle is equal to the critical angle, and the dispersion characteristics are weak. (3) The channel waves with weak dispersion characteristics in extra-thick coal seams are mainly Love-type waves.

Characterization of fault-karst reservoirs based on deep learning and attribute fusion

AbstractThe identification of fault-karst reservoir is crucial for the exploration and development of fault-controlled oil and gas reservoirs. Traditional methods primarily rely on well logging and seismic attribute analysis for karst cave identification. However, these methods often lack the resolution needed to meet practical demands. Deep learning methods offer promising solutions by effectively overcoming the complex response characteristics of seismic wave fields, owing to their high learning capabilities. Therefore, this research proposes a method for fault-karst reservoir identification. Initially, a comparative analysis between the improved U-Net++ network and traditional deep convolutional networks is conducted to select appropriate training parameters for separate training of karst caves and faults. Subsequently, the trained models are applied to actual seismic data to predict karst caves and faults within the research area, followed by attribute fusion to acquire data on fault-karst reservoirs. The results indicate that: (1) The proposed method effectively identifies karst caves and faults, outperforming traditional seismic attribute and coherence methods in terms of identification accuracy, and slightly surpassing U-Net and FCN; (2) The fusion of predicted karst caves and faults yields clear delineation of the relationship between top karst caves and bottom fractures within the research area. In summary, the proposed method for fault-karst reservoirs identification and characterization provides valuable insights for the exploration and development of fault-controlled oil and gas reservoirs in the region.

A model for the hydrothermal tremor source of the Mefite d’Ansanto (Italy) CO2 non-volcanic emissions in the intermediate frequency band (1–15 Hz)

In the Summer 2021 a seismic passive survey was carried out at Mefite d’Ansanto (Italy), well-known for the cold non-volcanic and lethal CO2 emissions. Mefite is located close to that part of Irpinia region hosting the large historical earthquakes’ faults, that generated the destructive magnitude 6.8 earthquake of 1980 and have been related to the CO2 leakage by the scientific community. The survey was conducted by installing a small short-period seismic array with the purpose of determining the wavefield features and detecting the possible signature of the regional stress variations. By analyzing the acquired data, we have determined the properties of the seismic wavefield associated with the emission vents, in the intermediate frequency band, 1–15 Hz, which was found to be composed of a stationary background component and an intermittent higher energy one. Basing on our results, considerations on the medium properties and the deep source available information, we have depicted a schematic model of the shallow seismic source: the background components are linked to the shallower activity of the hydrothermal system, e.g. the bubbling, while the intermittent ones are likely generated by the passage of the overpressured gas, trapped in the first-tens-meters’ layers, after overcoming the internal cohesion charge. The characteristics of the wavefield that we have defined, refer to a condition in which no regional earthquakes occurred and could be considered as a basis to identify possible significant variations linked to CO2 emissions and to the regional stress changes.

Underwater Bubble Plume Recognition Algorithm Based on Multi-Feature Fusion Understanding

Underwater bubble plume images contain a wealth of information on wave field and flow characteristics, which can provide valuable research data for marine development, environmental protection, and underwater surveys. However, based on fusing image features and wave field environment features, identifying accurately the underwater bubble plume is still very difficult. In order to improve the accuracy and robustness of bubble plume identification in complex underwater environments, an underwater bubble plume recognition algorithm based on multi-feature fusion understanding is proposed. In this paper, a weight-independent dual-channel residual convolutional neural network (CNN) for feature extraction of the original optical images and the nonsubsampled contourlet transform (NSCT) low-frequency images, and the multi-scale composite feature map groups are generated. Then adaptive fusion is performed based on the feature contribution of the target in different types of images. Next, logical region of interest (ROI) masks are generated by the attention mechanism and superimposed on the fused image to further highlight the target features. Finally, the multi-scale dual-channel fused feature maps containing ROI masks are used for underwater bubble plume target recognition. The experimental results show that the designed recognition network can effectively fuse the features of the original optical images and the NSCT low-frequency imagers, improve the depth of information fusion, and retain the target texture features and the morphological features while reducing the interference of the background information, and have good recognition accuracy and robustness for multi-scale bubble targets in the underwater environment.

A fast amplitude preserving three-parameter 3D parabolic Radon transform and its application on multiple attenuation

Seismic wavefields propagate through three-dimensional (3D) space, and their precise characterization is crucial for understanding subsurface structures. Traditional 2D algorithms, due to their limitations, are insufficient to fully represent three-dimensional wavefields. The classic 3D Radon transform algorithm assumes that the wavefield's propagation characteristics are consistent in all directions, which often does not hold true in complex underground media. To address this issue, we present an improved 3D three-parameter Radon algorithm that considers the wavefield variation with azimuth and provides a more accurate wavefield description. However, introducing new parameters to describe the azimuthal variation also poses computational challenges. The new Radon transform operator involves five variables and cannot be simply decomposed into small matrices for efficient computation; instead, it requires large matrix multiplication and inversion operations, significantly increasing the computational load. To overcome this challenge, we have integrated the curvature and frequency parameters, simplifying all frequency operators to the same, thereby significantly improving computation efficiency. Furthermore, existing transform algorithms neglect the lateral variation of seismic amplitudes, leading to discrepancies between the estimated multiples and those in the data. To enhance the amplitude preservation of the algorithm, we employ orthogonal polynomial fitting to capture the amplitude spatial variation in 3D seismic data. Combining these improvements, we propose a fast, amplitude-preserving, 3D three-parameter Radon transform algorithm. This algorithm not only enhances computational efficiency while maintaining the original wavefield characteristics, but also improves the representation of seismic data by increasing amplitude fidelity. We validated the algorithm in multiple attenuation using both synthetic and real seismic data. The results demonstrate that the new algorithm significantly improves both accuracy and computational efficiency, providing an effective tool for analyzing seismic wavefields in complex subsurface structures.

Thin Copper Plate Defect Detection Based on Lamb Wave Generated by Pulsed Laser in Combination with Laser Heterodyne Interference Technique.

Thin copper plate is widely used in architecture, transportation, heavy equipment, and integrated circuit substrates due to its unique properties. However, it is challenging to identify surface defects in copper strips arising from various manufacturing stages without direct contact. A laser ultrasonic inspection system was developed based on the Lamb wave (LW) produced by a laser pulse. An all-fiber laser heterodyne interferometer is applied for measuring the ultrasonic signal in combination with an automatic scanning system, which makes the system flexible and compact. A 3-D model simulation of an H62 brass specimen was carried out to determine the LW spatial-temporal wavefield by using the COMSOL Multiphysics software. The characteristics of the ultrasonic wavefield were extracted through continuous wavelet transform analysis. This demonstrates that the A0 mode could be used in defect detection due to its slow speed and vibrational direction. Furthermore, an ultrasonic wave at the center frequency of 370 kHz with maximum energy is suitable for defect detection. In the experiment, the size and location of the defect are determined by the time difference of the transmitted wave and reflected wave, respectively. The relative error of the defect position is 0.14% by averaging six different receiving spots. The width of the defect is linear to the time difference of the transmitted wave. The goodness of fit can reach 0.989, and it is in good agreement with the simulated one. The experimental error is less than 0.395 mm for a 5 mm width of defect. Therefore, this validates that the technique can be potentially utilized in the remote defect detection of thin copper plates.

Analytical solutions for dispersions and waveforms of acoustic logging in a cased hole

Acoustic logging is one of the most promising methods for the quantitative evaluation of cement bond conditions in cased holes. However, inefficient use of full-wave information yields unsatisfactory interpretation accuracy. Fundamentally, this is because the wavefield characteristics have not been thoroughly investigated under various cement bonding conditions. Thus, this study derives analytical solutions of wavefields for a single-cased-hole model and emphasizes the dispersion calculation algorithm. To solve the dispersion equation when solving for the poles of the propagating modes with real wavenumbers, we renormalize the Bessel function related to the borehole fluid by multiplying it with an attenuation factor. For leaky modes with complex wavenumbers, we develop a novel method to find local peaks of the matrix condition number (LPMCN) in the frequency domain to determine dispersion poles, avoiding the local optimization issues resulting from the traditional Gauss-Newton iteration method. Combining these two methods, we establish a fast and accurate workflow for evaluating the dispersion of all modes in cased holes using a relatively fast bisection method to manage the dispersion of the propagating modes and using the LPMCN method to derive the dispersion curves of leaky modes. Furthermore, all propagating modes are individually investigated in the monopole measurement by evaluating the residues of the real poles in a casing-free model. The analysis demonstrates that the first-order pseudo-Rayleigh wave (PR1) and inner Stoneley wave (ST1) are the two strongest modes. Finally, we focus on the waveforms and dispersion characteristics of the outer Stoneley wave (ST2) related to the fluid channel in the cement annulus. The results reveal that as the fluid thickness increases, the phase velocity of the ST2 mode decreases, and its amplitude increases. Therefore, the ST2 mode can potentially evaluate the thickness of the fluid channel in a cement annulus if an effective weak-signal-extraction method is used.

Tracking Seismic Velocity Perturbations at Ridgecrest Using Ballistic Correlation Functions

Abstract We present results based on data of a dense nodal array composed of 147 stations, deployed in 2022 near the epicenter of the 2019 Mw 7.1 Ridgecrest earthquake to investigate characteristics of the seismic wavefields. Through array analyses, we identified two primary components. First, we observed far-field P waves dominating the 0.5–1.2 Hz frequency range, which are likely primarily generated by wind-driven oceanic swell activity. Second, we detected near-field body waves resulting from anthropogenic activities in the frequency range 2–8 Hz. We examined noise correlation functions derived from data of the dense deployment and regional stations to explore fault-zone seismic velocity changes using ballistic arrivals, with a focus on velocity perturbation shortly before and after the Ridgecrest earthquake sequence. Our findings exhibit distinct behavior compared to results obtained through standard coda-wave interferometry. Particularly, we observed a decrease in P-wave travel time on certain station pairs prior to the 2019 earthquake sequence. Supported by detailed investigation of the local seismic wavefields, we interpret the decreasing P-wave travel time as likely caused by a velocity increase away from the fault, possibly related to fluid migration. However, additional information is necessary to verify this hypothesis.

Binocular reconstruction of breaking ship bow waves in circulating water channel

This study conducts an experiment on the bow waves generated by a 1:80 KRISO container ship (KCS) model in a circulating water channel. The Froude numbers (characterized by the length of perpendiculars) reach high conditions of 0.377, 0.424, and 0.471. A binocular imaging system is employed to reconstruct three-dimensional configurations of the bow wave surface. The dynamic characteristics of bow wave fields are investigated by observing the standard deviation and employing the Proper Orthogonal Decomposition (POD) method. The power spectral density function presents a power-law relationship with frequency. A novel technique referred as Stereoscopic Foam Image Velocimetry (SFIV) is developed to extract the instantaneous three-dimensional velocity of the foam in breaking area. The velocity field obtained through SFIV defines the nominal time-averaged velocity and nominal turbulent energy. A correlation mapping from pixel coordinates to world coordinates is established to evaluate the actual physical uncertainty. The results demonstrate the superior spatiotemporal accuracy and resolution of binocular imaging technology in measuring the characteristics of bow waves. This research provides significant experimental data of surface three-dimensional configurations for the bow waves breaking issues at high Froude numbers.

Integrable turbulence and statistical characteristics of chaotic wave field in the Kundu-Eckhaus equation.

Integrable turbulence, as an irregular behavior in dynamic systems, has attracted a lot of attention in integrable and Hamiltonian systems. This article focuses on the studies of integrable turbulence phenomena of the Kundu-Eckhaus (KE) equationas well as the generation of rogue waves from the numerical and statistical viewpoints. First, via the Fourier collocation method, we obtain the spectral portraits of different analytical solutions. Second, we perform the numerical simulation on the KE equationunder the initial condition of a plane wave with random noise to simulate the chaotic wave fields. Then, we analyze the influences of standard deviation and correlation length on the integrable turbulence and amplitude of wave field. It's found that both of the two parameters have positive effects on the generation probability of rogue wave caused by the interactions. But only the variation of standard deviation can lead to the transition from the breather turbulence to soliton turbulence. Furthermore, by analyzing the effects of additional higher-order nonlinear terms on the chaotic wave field, we find that those two higher-order nonlinear effects in the KE equationcan lead to a larger amplitude of the chaotic wave field and a higher probability of generating rouge waves compared with the NLS equation.

Influence of wind and waves on ambient noise and bubble entrainment depth in the semi-enclosed Baltic Sea

Semi-enclosed, fetch-limited waters create unique conditions for wind wave development and breaking. Parameters of breaking waves influence bubble entrainment depth and associated noise, which is why they differ in semi-enclosed sea compared to open waters. While the established noise-wind speed relationship holds in oceanic conditions, it differs in land-constrained basins like the Baltic Sea. To explore noise level, bubble entrainment depth and wind speed relationships, we conducted noise and sub-surface bubble measurements, coupled with wind observations, in the selected area of the Baltic Sea during two consecutive summers. A novel method was employed to estimate bubble entrainment depth under conditions of strong backscatter. Model data of wave field parameters were employed to assess their influence on noise level and bubble entrainment depth. Results suggest stronger connections between noise level and wind speed, as well as wave height, compared to wave age and wind sea steepness. The same patterns hold true for the correlation between bubble entrainment depth and both wind speed and wave field parameters. The parameterized noise level-wind speed relationship differs from that obtained for oceanic conditions and also varies across measurement periods. Observed differences were shaped by varying wind-wave conditions, notably differences in wind speed, direction, wave height, and the presence of swell. The noise level-bubble entrainment depth relation is reported for the first time for Baltic Sea conditions. For a thorough analysis of the influence of these factors on noise and bubbles, longer measurements under diverse wind-wave conditions are required to account for site-specific wave field characteristics.

A fast algorithm for simulation and analysis of wavefields in acoustic single-well imaging of logging-while-drilling considering arbitrary types of sources

Acoustic single-well imaging (SWI) of logging-while-drilling (LWD) is an advanced logging method in reservoir exploration, which uses reflected waves to detect the around-borehole geologic structures and quickly determines the drilling direction for enhancing the drilling-encounter ratio and reducing the drilling risk. Forward acoustic modeling is a fundamental problem for SWI in LWD. Due to the complex structures, it is a challenge to simulate the wave propagation and investigate wavefield characteristics based on the forward model. Numerical modeling is a commonly used method for calculating wavefields; however, it is too computationally expensive. In this study, we develop a fast method for calculating the full reflected pressure and displacement waves (i.e., P-P, SV-SV, SH-SH, and P-SV/SV-P) in SWI of LWD considering different types of sources such as arcuate, monopole, and dipole transmitters. The analytical algorithm is developed by applying the reciprocity relation between the virtual force (displacement) sources located at the receiver position and the outside-borehole virtual forces that are equivalent to the reflections from the formation interfaces. Numerical experiments indicate that the analytical solutions agree well with the reference solutions from the 3D finite-difference time-domain method, demonstrating the accuracy and high efficiency of the analytical method. Based on the analytical solutions, we find that LWD reflected waves are much more sensitive to the azimuth than those in the wireline case, indicating that the availability of LWD is important for identifying the reflector azimuth. Furthermore, to enhance the reception efficiency of reflected waves, the LWD parameters are optimized. For slow formations, we suggest using a dipole source with dominant excitation-frequency band being from 1 kHz to 3 kHz. For fast formations, a dipole with wider excitation-frequency band from 1 kHz to 5 kHz is recommended. For all formations, recording pressure signals indicates much higher reception efficiency than the displacement signals.

Modified pure-viscoacoustic wave propagation and compensated reverse-time migration in transversely isotropic media

Previous studies demonstrated that seismic attenuation and anisotropy can significantly affect the kinematic and dynamic characteristics of wavefields. If these effects are not incorporated into seismic migration, the resolution of the imaging results will be reduced. Considering the anisotropy of velocity and attenuation, we derive a new pure-viscoacoustic wave equation to simulate P wave propagation in transversely isotropic (TI) attenuating media by combining the complex dispersion relation and modified complex modulus. Compared to the conventional complex modulus, the modified modulus is derived from the optimized relationship between angular frequency and wavenumber, which can improve the modeling accuracy in strongly attenuating media. Wavefield comparisons illustrate that our pure-viscoacoustic wave equation can simulate stable P wavefields in complex geological structures without S-wave artifacts and generate similar P wave information to the pseudo-viscoacoustic wave equation. During the implementation, we introduce two low-rank decompositions to approximate the real and imaginary parts and then use the pseudo-spectral method to solve this new equation. Since the proposed equation can simulate decoupled amplitude attenuation and phase dispersion effects, it is used to perform Q-compensated reverse-time migration (Q-RTM). Numerical examples demonstrate the accuracy and robustness of the proposed method for pure-viscoacoustic wavefield simulations and migration imaging in transversely isotropic attenuating media.

Development of a method for identifying cracks in permafrost rocks based on differentiation of GPR data

Relevance. The presence of cracks significantly affects the physical and mechanical properties of rocks, which must be taken into account when planning mining operations and building mining structures. In the conditions of the distribution of permafrost rocks, characteristic of the North-East of Russia, the study of fracturing is possible using the ground penetrating radar method, which is used to assess the structure of rock masses of placer deposits. The criteria for identifying cracks based on the characteristics of GPR wave fields are currently known, and the main problem preventing the full use of the GPR method for studying cracks in subsurface layers of rocks is the significant complexity of processing and interpreting GPR measurement data. The purpose of the work is to develop a method for processing the results of ground penetrating radar measurements to identify cracks in frozen rocks. Methods. Physical and computer modeling of GPR measurements of a rock mass with a fracture, differential calculus methods for analyzing the GPR wave field structure model. Results and their scope. As a result of the research, based on an early developed model of the structure of the GPR wave field, the use of the differentiation operation for identifying cracks in permafrost rocks was justified. Special cases of rectilinear inclined and horizontal axes of in-phase of ground penetrating radar signals are considered and corresponding formulas are obtained for them. The theoretical results obtained were tested on computer and physical modeling data, as well as on field measurement data. An analysis of the features of the signals after differentiation was carried out, and the features of the original radargrams were noted, which may interfere with the reliable interpretation of the results obtained. Conclusions. In the practice of processing data from ground penetrating radar measurements, the results of the research will make it possible to more quickly identify zones of increased fracturing in rocks. In the future, it is planned to develop an algorithm and software that implements it for mapping rock fractures using ground penetrating radar data.

Frequency-dependent Q simulation and viscoacoustic reverse time migration based on the fractional Zener model

Seismic attenuation is a basic physical property of the earth, which significantly affects the characteristics of seismic wavefields. Accurately simulating wave propagation in the earth is essential to image subsurface structures. Some prevailing methods (e.g., the standard linear solid and fractional Laplacian equation) to describe seismic wave propagation in attenuating media are mainly based on the constant- Q model (CQM), which is valid at room temperature and pressure. However, laboratory measurements suggest that the quality factor Q is a function of frequencies in some regions. To simulate the frequency-dependent Q effect, we derive a viscoacoustic wave equation from the stress-strain relationship of the fractional Zener model (FZM) with variable fractional orders. During the implementation, we separate the real and imaginary parts of the modulus and introduce a low-rank decomposition method to solve the FZM equation. Because the amplitude dissipation and phase dispersion are decoupled, we establish a compensated reverse time migration ( Q-RTM) algorithm to mitigate adverse effects caused by seismic attenuation and improve the quality of seismic migration in frequency-dependent attenuating media. A two-layer model and the BP gas chimney model are used to perform Q-RTM tests. A low-pass filter with a Tukey window function is applied to suppress numerical instability during the compensation. Numerical results demonstrate that our FZM Q-RTM approach can produce high-resolution images with corrected reflector positions and amplitudes. Because the CQM equation ignores the frequency dependence of Q, it may lead to overcompensation in Q-RTM.

Description of Random Heterogeneity and Characteristic Analysis of Wave Field in Near-surface Medium

Random heterogeneity of near surface medium is caused by weathering layer, desert and gravel layer etc. For seismic exploration in this complex area, it is helpful to improve the exploration effect that detailed description of this heterogeneity and in-depth analysis the characteristics of seismic wave field in this medium. In order to figure out the above-mentioned issue, firstly, a regional multi-scale disturbance random medium modeling method in complex topographical conditions is proposed to describe the random heterogeneity of near-surface medium. Secondly, in the condition of undulating earth’s surface, the finite difference method (FDM) of wave equation numerical simulation is used to simulate the seismic wave field. Finally, some seismic wave characteristics in near-surface random heterogeneity are obtained by analyzing seismic snapshots and gathers.

Structure and Characteristics of Internal Wave Field in an Ocean Frontal Region East of Malta in Mediterranean

Structure and Characteristics of Internal Wave Field in an Ocean Frontal Region East of Malta in Mediterranean

Vibration isolation of infinitely periodic pile barriers for anti-plane shear waves: An exact series solution

The application of periodic pile barriers for isolating ambient vibrations has emerged as a significant research topic, which is essentially the problem of wave scattering by periodically distributed structures. This study presents an analytical series solution for anti-plane shear (SH) wave scattering by infinitely periodic pile barriers using the wave function expansion method, incorporating the wave field characteristics of infinitely periodic distributed scatterers subjected to plane waves. From the perspective of periodic theory, the wave fields around each scatterer are completely identical, differing only by a phase shift (frequency domain) or a time difference (time domain). As a result, as long as the boundary condition of one scatterer is satisfied, boundary conditions of the remaining scatterers can be satisfied simultaneously. This novel approach allows the selection of an arbitrary single pile as a reference in the infinitely periodic model to be solved, yielding accurate results without truncation errors and significantly reducing computational and storage requirements. A FORTRAN code is developed to achieve numerical evaluation of the theoretical formulation, followed by verification of the solution's accuracy using two degenerate examples. Numerical examples are conducted, focusing on the influence of pile stiffness, pile spacing, and pile type on the vibration isolation. The results demonstrate that decreasing the spacing between piles can effectively increase the bandgap width and reduce the displacement response. The screening effectiveness of solid piles is better than that of hollow pipe piles and filled pipe piles. In vibration mitigation design for engineering projects, the larger the shear stiffness ratio of the pile-soil is not always better, an economical and reasonable pile stiffness should be selected.