Similar Waveforms Research Articles

Discriminative Method for Crack Detection Signals in Balanced-Field Electromagnetic Technique Based on Amplitude-Phase Composite Figure.

The balanced-field electromagnetic technique is an effective in-line inspection method for pipeline cracks. To address the problem that the interference signal generated by the tilt jitter of the sensor during the detection process affects the judgment of cracks, this paper proposes a method to differentiate the crack detection signal from the sensor jitter signal by using an amplitude-phase composite figure. The generation principle of the detection signal was analyzed by using the mutual inductance model, and the amplitude-phase composite figure was constructed by using the components of the detection signal after quadrature demodulation. The feasibility of using the phase as a signal discrimination feature was illustrated by finite element simulations, and the characteristics of the amplitude-phase composite figure were determined. The validity of the proposed method was verified experimentally. The results show that the crack detection signal and the signal generated by the sensor jitter are of the same frequency with similar waveforms and significantly different phases. The phase base value of the crack detection signal ranges from 35° to 55°, and the phase base value of the jitter signal is −4°. In terms of the characteristics of the amplitude-phase composite figure, the crack detection signal distribution is symmetrical about the origin in the first and third quadrants, and the axial crack is closer to the Y-axis than the circumferential crack; the jitter signal is distributed in the second and fourth quadrants and has a very small angle to the X-axis. In addition, the proposed method effectively weakens the observation of the phase noise region in the detection signal of the balanced-field electromagnetic technique.

Using Machine Learning Techniques with Incomplete Polarity Datasets to Improve Earthquake Focal Mechanism Determination

Abstract Earthquake focal mechanisms are traditionally produced using P-wave first-motion polarities and commonly require well-recorded seismicity. A recent approach that is less dependent on high signal-to-noise exploits similar waveforms to produce relative polarity measurements between earthquake pairs. Utilizing these relative polarity measurements, it is possible to produce composite focal mechanisms for clusters within microseismic sequences using regional networks. However, missing or low-confidence polarity measurements still limit our ability to calculate high-quality composite focal mechanisms. Here, we replaced unreliable polarity measurements with estimates using iterative random forests, an unsupervised ensemble machine learning method. Using the imputed (“replaced”) polarity data, we then categorically clustered the events into families. As a case study, we applied this modified composite mechanism workflow to a multistation template matched catalog of an earthquake swarm that occurred during 2020 near the Maacama fault in northern California. We found that our modified methodology produced higher-quality earthquake families and improved composite focal mechanisms, with fault-plane uncertainties <35° for 94% of the families compared with 34% of families using the previous methodology.

Monitoring the 2021 Mw 8.2 Alaska Earthquake by an Offshore Seismic and Fluid Pressure Observation Network and Implications for Ocean‐Crust Dynamic Coupling

AbstractGround shaking caused by earthquakes is accompanied by seafloor and sub‐seafloor formation fluid pressure variations in offshore areas, but there have been few collocated observations of these signals. In this work, we report seismic and high‐sampling‐rate fluid pressure records of the 2021 Mw 8.2 Alaska earthquake by the Ocean Networks Canada (ONC) NEPTUNE observatory at an epicentral distance of ∼2,200 km in the northeast Pacific Ocean. The system comprises observatory nodes in various tectonic environments, with each node including buried broadband seismometers, seafloor pressure sensors, and, at two nodes, borehole pressure sensors. Seismic and tsunami waveforms of the Mw 8.2 earthquake were documented in detail. Seismic seafloor pressure variations (Psf) were dominated by Rayleigh waves of periods between 5 and 50 s, with peak amplitudes of 3–4 kPa at most sites. Waveform similarity and the linear scaling between Psf and vertical ground acceleration indicate forced acceleration of the water column being dominant in governing Psf during long‐period surface‐wave arrivals, with an additional component of elastic oscillation occurring at higher frequencies (>0.1 Hz) causing extra pressure signals. Analysis of formation pressure variations due to various types of ocean loading of distinctly different frequencies (e.g., tides, tsunami, and infragravity waves) shows stable one‐dimensional vertical loading efficiencies that depend on lithology at each borehole site, with loading response being strongly influenced by the presence of free gas at shallow depths within the Cascadia accretionary prism. Inter‐site comparisons of seismic and seafloor pressure waveforms demonstrate a key role of sediment thickness in the amplification of surface wave amplitudes.

Shape Dynamic Time Warping for Seismic Waveform Inversion

ABSTRACT We illustrate shape dynamic time warping (ShapeDTW) for 1D structure waveform inversion with examples from Tanzania, East Africa, and Northeastern Oklahoma. Seismograms of the Mw 5.9 Lake Rukwa, Tanzania, earthquake (18 August 1994) recorded by regional broadband seismographic stations of the Tanzania Broadband Seismic Experiment are used to demonstrate the method. We also test the inversion through solving for 1D crustal velocity structure of the Cherokee Platform in Oklahoma using seismograms of the 2011 Mw 5.7 Prague, Oklahoma, earthquake recorded by the EarthScope Transportable Array. Dynamic time warping (DTW) bypasses the time expense required for manual identification of seismic phases and shows potential for linking discrete seismic phases between two similar waveforms. ShapeDTW improves inversion performance by characterizing the character of the time series near each amplitude point. Applying Sakoe-Chiba band limits to ShapeDTW and an additional amplitude constraint improves the overfitting problem that occurs with the classic DTW method. We apply ShapeDTW to estimate optimal time shifts between observed and synthetic waveforms with time shifts reduced through inversion. The crustal velocity model of Tanzania found using ShapeDTW is close to that found using “phase time inversion” of numerous regional seismic phases observed in the three-component waveforms in a previous study but avoids the necessity of isolating and interpreting different seismic phases in the waveforms. Reducing the ShapeDTW functional misfits can overcome the cycle-skipping problem that often occurs with direct comparison of amplitudes in waveform inversion. This method may be useful in generating starting models for other 1D and 3D inversion methods.

Characterization of vertical and longitudinal gusts generated by twin pitching airfoils

An experimental investigation is performed to characterize vertical and longitudinal gusts generated by a gust generator device in a low-speed water tunnel. The device is composed of two pitching airfoils with adjustable motion modes, namely, in-phase and out-of-phase. Phase-locked two-dimensional particle image velocimetry is used to measure the velocity field downstream of the airfoils. When the two airfoils pitch in phase, periodic vertical gusts dominate the flow field, while periodic longitudinal gusts dominate when the two airfoils pitch out of phase. A waveform similarity coefficient is proposed to quantify the spatial uniformity of the gust fields, which measures how similar gust profiles are at different spatial locations. For the two types of gusts, various airfoil spacings, pitching amplitudes, and reduced frequencies are considered to examine the effects of parameters on the downstream gust characteristics. The results show that a smaller airfoil spacing produces a larger gust amplitude; however, the region with a better uniformity is reduced. As the pitching amplitude increases, the gust amplitude increases linearly, and the uniformity of the measurement region improves. The slope between the gust amplitude and pitching amplitude increases with a reduced frequency, but further larger reduced frequencies could result in poor gust uniformity. Excluding the cases with poor uniformity, this device delivers a vertical gust amplitude up to 6.7% of the free-stream velocity with reduced frequencies of k = 0.2–0.6 and a longitudinal gust amplitude of 10% of the free-stream velocity with reduced frequencies of k = 0.2–0.8.

Validity and reliability of accelerations and orientations measured using wearable sensors during functional activities

Wearable sensors may enable the assessment of movement in a real-world setting, but they are not yet a standard practice in the analysis of movement due to the unknown accuracy and reliability with respect to different functional activities. Here, we established the concurrent validity and test–retest reliability of accelerations and orientations measured using affordable novel sensors during squats, jumps, walking and stair ambulation. In this observational study, participants underwent three data collection sessions during one day. Accelerations and orientations from sacrum, thigh and shank were collected using these sensors and already validated gold-standard sensors as the criterion method. We assessed validity by comparing the similarity of signal waveforms with the Linear Fit Method and by comparing mean differences in range values with the Bland–Altman plots. Reliability was assessed by calculating interclass correlation coefficient and standard error of measurements of the range values. Concurrent validity was from fair to excellent in 91% of the cases for accelerations and in 84.4% for orientations. Test–retest reliability of accelerations was from fair to excellent in 97% of cases when the sensors were attached by a researcher, and in 84.4% of cases when the sensors were attached by participants. Test–retest reliability of orientations was from fair to excellent in 88.9% of cases when the sensors were attached by a researcher, and in 68.9% of cases when the sensors were attached by participants. In conclusion, the new affordable sensors provide accurate measures of accelerations and orientations during multiple functional activities in healthy adults. Reliability of the orientations may depend on the ability to replicate the same position of the sensor under test–retest conditions.

A waveform-similarity-based protection scheme for the VSC-HVDC transmission lines

The protection for the voltage source converter based high voltage direct current (VSC-HVDC) transmission lines must detect the faulty DC lines and faulty poles within a few milliseconds, because the fault current rises quickly. The traditional protections are easily influenced by fault resistance and signal noise. What is worse, the double-pole-to-ground (DPG) fault with its positive-pole fault resistance unequal to negative-pole fault resistance cannot be detected accurately. To solve the problems, a non-unit protection scheme based on the waveform similarity and wavelet transform modulus maximum (WTMM) theories for the VSC-HVDC lines is proposed in this paper. A four-terminal VSC-HVDC power network is modeled in PSCAD to verify the protection. Extensive simulations of various fault situations prove that the protection scheme can detect high-fault-resistance, DPG, and remote faults. Moreover, it is insensitive to the sampling frequency, signal noise, smoothing reactor, and start delay. Furthermore, it can meet the rapidity requirement. Therefore, the proposed protection can identify the DC faults accurately, which minimizes the disturbance to power grids and improves system security and stability.

The use of weighted self-organizing maps to interrogate large seismic data sets

SUMMARY Modern microseismic monitoring systems can generate extremely large data sets with signals originating from a variety of natural and anthropogenic sources. These data sets may contain multiple signal types that require classification, analysis and interpretation: a considerable task if done manually. Machine learning techniques may be applied to these data sets to expedite and improve such analysis. In this study, we apply an unsupervised technique, the Self-Organizing Map (SOM), to high-volume data recorded by an in-mine microseismic network. This represents a good example of a large seismic data set that contains a wide range of signals, owing to the diversity of source processes occurring within the mine. The signals are quantified by extracting a number of features (temporal and spectral) from the waveforms which are provided as input data for the SOM. We develop and implement a weighted variant of the SOM in which the contributions of various different features to the training of the map are allowed to evolve. The standard and weighted SOMs are applied to the data, and the output maps compared. Both variants are able to separate source types based on the waveform characteristics, allowing for rapid, automatic classification of signals and the ability to find sources with similar waveforms. Fast classification of such signals provides practical benefit by automatically discarding waveforms associated with anthropogenic sources within the mine while seismic signals originating from genuine microseismic events, which constitute a small fraction of all signals, can be prioritized for subsequent processing and analysis. The weighted variant provides an exploratory tool through quantification of the contribution of different features to the clustering process. This helps to optimize the performance of the SOM through the identification of redundant features. Furthermore, those features that are assigned large weights are considered to be more representative of the source generation processes as they contribute more to the cluster separation process. We apply weighted SOMs to data from a mine recorded during two different time periods, corresponding to different stages of the mine development. Changes in feature importance and in the observed distribution of feature values indicate evolving source generation processes and may be used to support investigatory analysis. The weighted SOM therefore represents an effective tool to help manage and investigate large seismic data sets, providing both practical benefit and insight into underlying event mechanisms.

A new subsequence similarity retrieval method based on inverted index in EAST

The analysis technology of massive experimental data is one of the important concerns in the field of nuclear fusion research, and the waveform similarity retrieval is the basis of realizing data mining of discharge experiment. In this work, we proposed an efficient subsequence retrieval method for matching a selected waveform segment in the discharge signal waveform. This method accurately represents the waveform characteristics based on the slope of segment and the drop distance of segment head (DDSH). In order to improve the retrieval efficiency, an inverted index method based on the slope of segment was adopted to filter the discharge signal waveforms and then perform fine retrieving. The retrieval algorithm was implemented based on Python, and was verified with the plasma density and stored energy signals of historical experimental data from EAST mdsplus database. The test results show the retrieval efficiency is improved by 43.6% on average after using slope inverted index.

Transient creep‐fatigue crack growth in creep‐brittle materials: Application to Alloy 718

AbstractThis study presents incremental finite element computations of creep‐fatigue crack growth in Alloy 718 at in air. Alloy 718 is representative of creep‐brittle materials, in which viscoplastic deformation is restricted near the tip of a growing crack. The computations predict crack growth using a unique combination of an irreversible cohesive zone formulation and a strain gradient viscoplastic material model based on the Kocks–Mecking formulation. Cohesive zone damage parameters are estimated using sustained loading and constant‐amplitude cyclic loading experiments. Computations of crack extension under three different waveforms containing overloads all predict post‐overload retardation. The amount of retardation depends strongly on the overload ratio, consistent with experiments in the literature using similar waveforms. Analysis of the crack‐tip fields demonstrates retardation is associated with unloading in the highly deformed material near the advancing crack tip. Dynamic recovery and geometrically necessary dislocations are shown to significantly influence post‐overload crack extension.

A Python Code for Detecting True Repeating Earthquakes from Self-Similar Waveforms (FINDRES)

AbstractSeismic data are generally scrutinized for repeating earthquakes (REs) to evaluate slip rates, changes in the mechanical properties of a fault zone, and accelerating nucleation processes in foreshock and aftershock sequences. They are also used to study velocity changes in the medium, earthquake physics and prediction, and for constraining creep rate models at depth. For a robust detection of repeaters, multiple constraints and different parameter configurations related to waveform similarity have been proposed to measure cross-correlation values at a local seismic network and evaluate the location of overlapping sources. In this work, we developed a Python code to identify REs (FINDRES), inspired by previous literature, which combines both seismic waveform similarity and differential S-P travel time measured at each seismic station. A cross-spectral method is applied to evaluate precise differential arrival travel times between earthquake pairs, allowing a subsample precision and increasing the capacity to resolve an overlapping common source radius. FINDRES is versatile and works with and without P- and S-wave phase pickings, and has been validated using synthetic and real data, and provides reliable results. It would contribute to the implementation of open-source Python packages in seismology, supporting the activities of researchers and the reproducibility of scientific results.

Faulty Section Location Method Based on Dynamic Time Warping Distance in a Resonant Grounding System

When a single-phase grounding fault occurs in a resonant grounding system, the determination of the fault location remains a significant challenge due to the small fault current and the instability of the grounding arc. In order to solve the problem of low protection sensitivity when a high-resistance grounding fault occurs in a resonant grounding system, this paper proposes a fault location method based on the combination of dynamic time warping (DTW) distance and fuzzy C-means (FCM) clustering. By analyzing the characteristics of the zero-sequence current upstream and downstream of the fault point when a single-phase grounding fault occurs in the resonant grounding system, it is concluded that the waveform similarity on both sides of the fault point is low. DTW distance can be used to measure the similarity of two time series, and has the characteristics of good fault tolerance and synchronization error tolerance. According to the rule that the DTW value of faulty section is much larger than that of nonfaulty sections, FCM clustering is used to classify the DTW value of each section. The membership degree matrix and cluster centers are obtained. In the membership degree matrix, the section corresponding to the data in a class of their own is the faulty section, and all other data correspond to the nonfaulty section; otherwise, it is a fault occurring at the end of the line. The simulation results of MATLAB/Simulink and the field data test show that the method can accurately locate the faulty section.

Geomagnetic Detection of the Atmospheric Acoustic Resonance at 3.8 mHz During the Hunga Tonga Eruption Event on 15 January 2022

AbstractModeling studies have predicted that the acoustic resonance of the atmosphere during geophysical events such as earthquakes and volcanos can lead to an oscillation of the geomagnetic field with a frequency of about 4 mHz. However, observational evidence is still limited due to scarcity of suitable events. On 15 January 2022, the submarine volcano Hunga Tonga‐Hunga Ha'apai (20.5°S, 175.4°W, Tonga) erupted in the Pacific Ocean and caused severe atmospheric disturbance, providing an opportunity to investigate geomagnetic effects associated with acoustic resonance. Following the eruption, geomagnetic oscillation is observed at Apia, approximately 835 km from Hunga Tonga, mainly in the Pc 5 band (150–600 s, or 1.7–6.7 mHz) lasting for about 2 hr. The dominant frequency of the oscillation is 3.8 mHz, which is consistent with the frequency of the atmospheric oscillation due to acoustic resonance. The oscillation is most prominent in the eastward (Y) component, with an amplitude of ∼3 nT, which is much larger than those previously reported for other events (<1 nT). Comparably large oscillation is not found at other stations located further away (>2700 km). However, geomagnetic oscillation with a much smaller amplitude (∼0.3 nT) is observed at Honolulu, which is located near the magnetic conjugate point of Hunga Tonga, in a similar wave form as at Apia, indicating interhemispheric coupling. This is the first time that geomagnetic oscillations due to the atmospheric acoustic resonance are simultaneously detected at magnetic conjugate points.

The Hiccup of Villarrica volcano (Chile) during the 2015 eruption and its expression in LP activity and VLP ground motion

SUMMARY Volcano seismology is an essential tool for monitoring volcanic processes in the advent and during eruptions. A variety of seismic signals can be recorded at volcanoes, of which some are thought to be related to the migration of fluids which is of primary importance for the anticipation of imminent eruptions. We investigate the volcanic crises at Villarrica volcano in 2015 and report on a newly discovered very-long-period (VLP) signal that accompanies phases of periodic long period (LP) signal burst. Despite their low amplitude emergent character, we can locate the source region of the 1 Hz LP signals to the close vicinity of the volcano using a network-based correlation method. The source of the VLP signal with a period of about 30–100 s appears to locate in the vicinity of two stations a few kilometres from the summit. Both stations record very similar VLP waveforms that are correlated with the envelope of the LP bursts. A shallow magma reservoir was inferred by Contreras from surface deformation as the source of inflation following the eruption in 2015. Cyclic volume changes of 6 m3 in this reservoir at 3 km depth can explain the observed amplitudes of the vertical VLP signal. We propose that the LP signal is generated by the migration of gas or gas-rich magma that is periodically released from the inflating reservoir through a non-linear valve structure which modulates the flux, and thereby causes bursts of flow-related LP signals and pressure changes observed as VLP deformation. Our model predicts that the correlated occurrence of LP bursts and VLP surface motion depends on the intensity of the fluid flux. A weaker flux of fluids may not exceed the opening pressure of valve structure, and higher rates might maintain pressure above the closing pressure. In both cases, the VLP signal vanishes. Our observation provides constrains for models of fluid transport inside volcanoes. At Villarrica the VLP signal, and its relation to the LP activity, reveal additional information about fluxes in the magmatic reservoir that might aide forecasting of volcanic activity.

Viscoelastic and Viscoplastic Glucose Theory (VGT #22): Applying the Concepts of Viscoelasticity, Viscoplasticity and Perturbation Theories to Predict Cancer Risk Percentages using the overall Lifestyle Scores and Calculated Cancer Risk Change Rates with Corresponding Lifestyle Scores as the Respective Viscosity Factors along with Studying the Relationship between Cancer Risks and Diabetic Glucoses Based on the GH-Method: Math-Physical Medicine (No. 601)

Viscoelastic and Viscoplastic Glucose Theory (VGT #22): Applying the Concepts of Viscoelasticity, Viscoplasticity and Perturbation Theories to Predict Cancer Risk Percentages using the overall Lifestyle Scores and Calculated Cancer Risk Change Rates with Corresponding Lifestyle Scores as the Respective Viscosity Factors along with Studying the Relationship between Cancer Risks and Diabetic Glucoses Based on the GH-Method: Math-Physical Medicine (No. 601)

Waveform Similarity-Based Robust Pilot Protection for Transmission Lines

This paper proposes a robust pilot protection scheme based on waveform similarity that restricts the influence of outliers in fault line identification. By comparing two refactoring currents constructed using the time-domain sampling values of currents at the two terminals of a transmission line, a waveform similarity algorithm called the Kendall's Tau coefficient (KTC) is employed to distinguish two different datasets of a protected transmission line. A reliable fault identification is realized under different fault types, distances, and resistances. Proposed criteria that are robust against to current transformer saturation, synchronization error, and noise are proposed. The KTC is based on simply the rank order instead of the metric value and thus limits outliers to a moderate level, ensuring protection safety in cases where outliers that cannot be eliminated completely are included in the current waveforms. The simulation results demonstrate the excellent performance of the proposed robust pilot protection scheme.

A Precoding Approach for Dual-Functional Radar-Communication System With One-Bit DACs

In this paper, we investigate the precoder design for multiple-input multiple-output (MIMO) dual-functional radar-communication (DFRC) system with one-bit digital-to-analog converters (DACs). In order to form the dual-functional beam-pattern, we formulate the precoding problem as a weighted optimization problem with the constant modulus constraint, which aims at minimizing the average error power and guaranteeing radar waveform similarity. The problem is divided into three sub-problems corresponding to the multiple variables, i.e., the precoding factor, transmit signal matrix, and radar waveform matrix. Due to the discrete and non-convex properties of the optimization problem, we propose a multi-variable alternating minimization (MVAM) framework to achieve the near-optimal solutions. The precoding factor and radar waveform can be solved in closed-forms. For the transmit signal matrix, we devise a binary particle swarm optimization-simulated annealing (BPSO-SA) algorithm to obtain it under the MVAM framework. Extensive simulations validate the effectiveness of the proposed approach under various scenarios, including the case without perfect channel state information. The simulation results show that, compared with existing non-linear precoders, the proposed approach achieves 7dB SNR gain at the bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> in the 8-antenna system, and the gain of SNR is 0.2dB in the massive MIMO system with 128 antennas.

Optimization and Quality Assessment of Arrival Time Picking for Downhole Microseismic Events.

Arrival-time picking is a critical step in microseismic data processing, and thus the quality control of arrival results is necessary. Conventional picking methods may be inaccurate or inconsistent due to varied signal-to-noise ratios (SNR) and waveform patterns of the events recorded in different time sections. To address this issue, we propose a quality assessment method based on waveform similarity coefficients to evaluate arrival results and also a global optimization algorithm based on iterative cross-correlation to refine arrival times. The recordings after moveout correction are applied to calculate the intra-event and inter-event waveform coefficients for the quality assessment of arrival results. The residual time differences of intra-event and inter-event traces are calculated sequentially using an enhanced iterative cross-correlation method. In addition, the stacked waveform of each event after the intra-event residual time correction is introduced for global optimization to obtain the inter-event residual time discrepancies. We use both synthetic data and field data to validate the proposed method. The results indicate that the proposed method yields more robust and reliable results. The quality assessment of the optimized arrivals is greatly enhanced compared to the adjusted picks obtained from single event-based processing methods.

Comparison of marker-less and marker-based motion capture for baseball pitching kinematics

ABSTRACT The purpose of this study was to compare baseball pitching kinematics measured with marker-less and marker-based motion capture. Two hundred and seventy-five fastball pitches were captured at 240 Hz simultaneously with a 9-camera marker-less system and a 12-camera marker system. The pitches were thrown by 30 baseball pitchers (age 17.1 ± 3.1 years). Data for each trial were time-synchronised between the two systems using the instant of ball release. Coefficients of Multiple Correlations (CMC) were computed to assess the similarity of waveforms between the two systems. Discrete measurements at foot contact, during arm cocking, and at ball release were compared between the systems using Bland-Altman plots and descriptive statistics. CMC values for the five time series analysed ranged from 0.88 to 0.97, indicating consistency in movement patterns between systems. Biases for discrete measurements ranged in magnitude from 0 to 16 degrees. Standard deviations of the differences between systems ranged from 0 to 14 degrees, while intraclass correlations ranged from 0.64 to 0.92. Thus, the marker-based and marker-less motion capture systems produced similar patterns for baseball pitching kinematics. However, based on the variations between the systems, it is recommended that a database of normative ranges be established for each system.

Low-frequency seismic random noise attenuation based on EPLL-TV under double prior constraints

The expected patch log likelihood (EPLL) method utilizes the learned Gaussian mixture model (GMM) as a prior for white Gaussian noise removal, so that every patch from noisy data is likely under the prior and the global morphology is remained along with denoising. For suppressing the low-frequency seismic random noise having similar waveforms to the signals, we propose an Expected Patch Log Likelihood-Total Variation (EPLL-TV) algorithm, which is constrained by the EPLL prior and the total variation (TV) prior. In the denoising process, the TV prior introduces the structural features of the current data and restrains the random noise by enhancing the gradient sparsity of seismic data. Hence, the EPLL-TV algorithm is able to choose the Gaussian component which is closest to the features of signals from pre-learned general prior of EPLL, although the features in the patch are severely disturbed by the low-frequency noise. Then the seismic events with complex structures can be accurately restored by the chosen Gaussian component, which provides more reliable structures for denoising via the TV prior. We use the alternating direction method of multipliers (ADMM) to solve the proposed optimization model with double constraints and reconstruct the data in Fourier domain to reduce computational complexity. The results of the synthetic and field seismic data demonstrate that the proposed EPLL-TV method is superior to the other methods mentioned in our paper in terms of recovering the seismic events with complex structures and suppressing the low-frequency seismic random noise which has similar waveforms to the signals.