Inverse Q filtering via synchrosqueezed wavelet transform

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. V121-V132 ◽  
Author(s):  
Ya-Juan Xue ◽  
Jun-Xing Cao ◽  
Xing-Jian Wang
Keyword(s):  
Wavelet Transforms ◽  
Ambient Noise ◽  
Real Data ◽  
Dispersive Media ◽  
Time Frequency ◽  
Effective Components ◽  
Text Filtering ◽  
Inverse Q Filtering ◽  
The Time Domain ◽  
Amplitude Compensation

We have developed and applied an inverse [Formula: see text]-filter formulation using synchrosqueezed wavelet transforms for the compensation of attenuating and dispersive media. A damping criterion concerning the reconstruction of the effective components for controlling noise amplification and the separation of the noise and signal in the synchrosqueezed wavelet domain is generated. The proposed method provides stable attenuation compensation without decreasing the seismic vertical and lateral resolution. The best property of the proposed method, unlike conventional inverse [Formula: see text]-filtering methods, is that it carries out amplitude compensation for the effective components located at some time samples in the time-frequency domain. The spectral reconstruction contributes to the reconstruction of the trace in the time domain and suppresses the ambient noise located at high frequencies at later times, especially suppressing the ambient noise within the main frequency band. It is not a noise-level-dependent method. We validated our approach with synthetic and real data. The comparison of the proposed method with the conventional stabilized inverse [Formula: see text]-filtering method is also carried out to illustrate the particular features of the proposed method. The examples demonstrate that our proposed method can effectively compensate for the amplitude attenuation by suppressing the ambient noise and further provide seismic images at high resolution while highlighting the effective details. Furthermore, it is a robust and easily tunable algorithm.

High-resolution gathers by inverse Q filtering in the wavelet domain

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. V53-V61 ◽  
Author(s):  
Igor L. S Braga ◽  
Fernando S. Moraes
Keyword(s):  
Synthetic Data ◽  
Structural Features ◽  
Natural Increase ◽  
Dispersive Media ◽  
Amplitude Variation With Offset ◽  
Time Frequency ◽  
Before And After ◽  
Text Filtering ◽  
Inverse Q Filtering ◽  
Definition Of

We have developed and applied an inverse [Formula: see text] filter formulation using the continuous wavelet transform (CWT), which provides a natural domain for time-variant operations, such as compensation for propagation in attenuating and dispersive media. The well-known linear attenuation model, given as a function of time and frequency, was applied very efficiently over wavelet coefficients in the time-frequency domain to correct for amplitude and phase distortions, as necessary. The inverse CWT yields the recovered trace with a broader bandwidth. The process works on a trace-by-trace basis, making no distinction if the data is pre- or poststack. Our motivation was to develop gather conditioning tools to enhance prestack interpretation techniques such as amplitude variation with offset (AVO) analysis and inversion — a technique that is often compromised by tuning and other propagation related issues that degrade seismic resolution. Thus, we investigated the AVO fidelity of our filter and the sensitivity of the results to incorrect values of [Formula: see text], using real and synthetic data. Our synthetic data experiments clearly showed that AVO anomalies are recovered and preserved in a stable manner, even with values of [Formula: see text] off by 50% of its correct value. The application in time-migrated gathers shows a very natural increase in the vertical definition of the events, especially due to the partial elimination of the tuning effect. The benefits for imaging are also evidenced by comparing stacked sections before and after inverse [Formula: see text] filtering. The higher resolution of seismic sections leads to a better definition of smaller scale stratigraphic and structural features.

An improved method to estimate Q based on the logarithmic spectrum of moving peak points

2019 ◽  
Vol 7 (2) ◽  
pp. T255-T263 ◽  
Author(s):  
Yanli Liu ◽  
Zhenchun Li ◽  
Guoquan Yang ◽  
Qiang Liu
Keyword(s):  
Seismic Waves ◽  
Wave Attenuation ◽  
Real Data ◽  
Peak Frequency ◽  
Seismic Reflection Data ◽  
The Real ◽  
Time Frequency ◽  
Reflection Data ◽  
Text Filtering ◽  
The Impact

The quality factor ([Formula: see text]) is an important parameter for measuring the attenuation of seismic waves. Reliable [Formula: see text] estimation and stable inverse [Formula: see text] filtering are expected to improve the resolution of seismic data and deep-layer energy. Many methods of estimating [Formula: see text] are based on an individual wavelet. However, it is difficult to extract the individual wavelet precisely from seismic reflection data. To avoid this problem, we have developed a method of directly estimating [Formula: see text] from reflection data. The core of the methodology is selecting the peak-frequency points to linear fit their logarithmic spectrum and time-frequency product. Then, we calculated [Formula: see text] according to the relationship between [Formula: see text] and the optimized slope. First, to get the peak frequency points at different times, we use the generalized S transform to produce the 2D high-precision time-frequency spectrum. According to the seismic wave attenuation mechanism, the logarithmic spectrum attenuates linearly with the product of frequency and time. Thus, the second step of the method is transforming a 2D spectrum into 1D by variable substitution. In the process of transformation, we only selected the peak frequency points to participate in the fitting process, which can reduce the impact of the interference on the spectrum. Third, we obtain the optimized slope by least-squares fitting. To demonstrate the reliability of our method, we applied it to a constant [Formula: see text] model and the real data of a work area. For the real data, we calculated the [Formula: see text] curve of the seismic trace near a well and we get the high-resolution section by using stable inverse [Formula: see text] filtering. The model and real data indicate that our method is effective and reliable for estimating the [Formula: see text] value.

scholarly journals Detection of Patterns in Pressure Signal of Compressed Air System Using Wavelet Transform

2021 ◽  
pp. 61-67
Author(s):  
Mohamad Thabet ◽  
David Sanders ◽  
Nils Bausch
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Compressed Air ◽  
Learning Tools ◽  
Time Frequency ◽  
Pressure Signal ◽  
Operating Modes ◽  
Air System ◽  
The Time Domain ◽  
Future Work

AbstractThis paper investigates detecting patterns in the pressure signal of a compressed air system (CAS) with a load/unload control using a wavelet transform. The pressure signal of a CAS carries useful information about operational events. These events form patterns that can be used as ‘signatures’ for event detection. Such patterns are not always apparent in the time domain and hence the signal was transformed to the time-frequency domain. Three different CAS operating modes were considered: idle, tool activation and faulty. The wavelet transforms of the CAS pressure signal reveal unique features to identify events within each mode. Future work will investigate creating machine learning tools for that utilize these features for fault detection in CAS.

Absorption-compensation method by l1-norm regularization

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. V107-V114 ◽  
Author(s):  
Shoudong Wang ◽  
Xiaohong Chen
Keyword(s):  
Integral Equation ◽  
Seismic Wave ◽  
Fredholm Integral Equation ◽  
Seismic Data ◽  
Real Data ◽  
Compensation Method ◽  
L1 Norm ◽  
Text Filtering ◽  
The Time Domain ◽  
Attenuation And Dispersion

Absorption in subsurface media greatly reduces the resolution of seismic data. Absorption not only dissipates the high-frequency components of the wave, but it also distorts the seismic wavelet. The inverse [Formula: see text]-filtering method is an effective method to correct the attenuation and dispersion of the seismic wave. We evaluated an absorption compensation method based on [Formula: see text]-norm regularization. Forward modeling in the absorption medium is described by a Fredholm integral equation in the time domain, and the absorption compensation comes down to solving the Fredholm integral equation. The solutions of the Fredholm integral equation are extremely unstable. Generally, [Formula: see text]-norm regularization can be used to seek stable solutions of the Fredholm integral equation, but it makes the solutions smooth and reduces the resolution of seismic data. We used [Formula: see text]-norm regularization to overcome instability of solving the integral equation; it makes the solutions have a higher resolution than [Formula: see text]-norm regularization. The iteratively reweighted method is used to solve the minimization problem. Tests on synthetic and real data examples showed that the absorption compensation method that we evaluated can effectively correct the attenuation and dispersion of the seismic wave.

Separating Multiple Moving Sources by Microphone Array Signals for Wayside Acoustic Fault Diagnosis

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Wei Xiong ◽  
Qingbo He ◽  
Zhike Peng
Keyword(s):  
Fault Diagnosis ◽  
Time Domain ◽  
Feature Matching ◽  
Matching Pursuit ◽  
Microphone Array ◽  
Time Frequency ◽  
Moving Sources ◽  
The Time Domain ◽  
Envelope Spectrum ◽  
Threshold Setting

Wayside acoustic defective bearing detector (ADBD) system is a potential technique in ensuring the safety of traveling vehicles. However, Doppler distortion and multiple moving sources aliasing in the acquired acoustic signals decrease the accuracy of defective bearing fault diagnosis. Currently, the method of constructing time-frequency (TF) masks for source separation was limited by an empirical threshold setting. To overcome this limitation, this study proposed a dynamic Doppler multisource separation model and constructed a time domain-separating matrix (TDSM) to realize multiple moving sources separation in the time domain. The TDSM was designed with two steps of (1) constructing separating curves and time domain remapping matrix (TDRM) and (2) remapping each element of separating curves to its corresponding time according to the TDRM. Both TDSM and TDRM were driven by geometrical and motion parameters, which would be estimated by Doppler feature matching pursuit (DFMP) algorithm. After gaining the source components from the observed signals, correlation operation was carried out to estimate source signals. Moreover, fault diagnosis could be carried out by envelope spectrum analysis. Compared with the method of constructing TF masks, the proposed strategy could avoid setting thresholds empirically. Finally, the effectiveness of the proposed technique was validated by simulation and experimental cases. Results indicated the potential of this method for improving the performance of the ADBD system.

scholarly journals Interpolation in wavelet spaces and the HRT-conjecture

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Eirik Berge
Keyword(s):  
Compact Group ◽  
Wavelet Transforms ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Space Structure ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Positive Type ◽  
Time Frequency ◽  
Hrt Conjecture

AbstractWe investigate the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })\subset L^{2}(G)$$ W g ( H π ) ⊂ L 2 ( G ) arising from square integrable representations $$\pi :G \rightarrow \mathcal {U}(\mathcal {H}_{\pi })$$ π : G → U ( H π ) of a locally compact group G. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong restrictions. Moreover, we use this to derive consequences for wavelet transforms related to convexity and functions of positive type. Motivated by the reproducing kernel Hilbert space structure of wavelet spaces we examine an interpolation problem. In the setting of time–frequency analysis, this problem turns out to be equivalent to the HRT-conjecture. Finally, we consider the problem of whether all the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })$$ W g ( H π ) of a locally compact group G collectively exhaust the ambient space $$L^{2}(G)$$ L 2 ( G ) . We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.

scholarly journals Ultrasonic Assessment of Thickness and Bonding Quality of Coating Layer Based on Short-Time Fourier Transform and Convolutional Neural Networks

Coatings ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 909
Author(s):  
Azamatjon Kakhramon ugli Malikov ◽  
Younho Cho ◽  
Young H. Kim ◽  
Jeongnam Kim ◽  
Junpil Park ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Coating Layer ◽  
Ultrasonic Pulse ◽  
Short Time Fourier Transform ◽  
Coating Materials ◽  
Time Frequency ◽  
High Attenuation ◽  
Bonding State ◽  
The Time Domain ◽  
Short Time

Ultrasonic non-destructive analysis is a promising and effective method for the inspection of protective coating materials. Offshore coating exhibits a high attenuation rate of ultrasonic energy due to the absorption and ultrasonic pulse echo testing becomes difficult due to the small amplitude of the second echo from the back wall of the coating layer. In order to address these problems, an advanced ultrasonic signal analysis has been proposed. An ultrasonic delay line was applied due to the high attenuation of the coating layer. A short-time Fourier transform (STFT) of the waveform was implemented to measure the thickness and state of bonding of coating materials. The thickness of the coating material was estimated by the projection of the STFT into the time-domain. The bonding and debonding of the coating layers were distinguished using the ratio of the STFT magnitude peaks of the two subsequent wave echoes. In addition, the advantage of the STFT-based approach is that it can accurately and quickly estimate the time of flight (TOF) of a signal even at low signal-to-noise ratios. Finally, a convolutional neural network (CNN) was applied to automatically determine the bonding state of the coatings. The time–frequency representation of the waveform was used as the input to the CNN. The experimental results demonstrated that the proposed method automatically determines the bonding state of the coatings with high accuracy. The present approach is more efficient compared to the method of estimating bonding state using attenuation.

A New Method for Characterizing Replacement Rate Variation in Molecular Sequences: Application of the Fourier and Wavelet Models to Drosophila and Mammalian Proteins

Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 381-395
Author(s):  
Pavel Morozov ◽  
Tatyana Sitnikova ◽  
Gary Churchill ◽  
Francisco José Ayala ◽  
Andrey Rzhetsky
Keyword(s):  
Wavelet Transforms ◽  
Parametric Bootstrap ◽  
Real Data ◽  
New Method ◽  
Rate Variation ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Ratio Test ◽  
Replacement Rate ◽  
New Models

Abstract We propose models for describing replacement rate variation in genes and proteins, in which the profile of relative replacement rates along the length of a given sequence is defined as a function of the site number. We consider here two types of functions, one derived from the cosine Fourier series, and the other from discrete wavelet transforms. The number of parameters used for characterizing the substitution rates along the sequences can be flexibly changed and in their most parameter-rich versions, both Fourier and wavelet models become equivalent to the unrestricted-rates model, in which each site of a sequence alignment evolves at a unique rate. When applied to a few real data sets, the new models appeared to fit data better than the discrete gamma model when compared with the Akaike information criterion and the likelihood-ratio test, although the parametric bootstrap version of the Cox test performed for one of the data sets indicated that the difference in likelihoods between the two models is not significant. The new models are applicable to testing biological hypotheses such as the statistical identity of rate variation profiles among homologous protein families. These models are also useful for determining regions in genes and proteins that evolve significantly faster or slower than the sequence average. We illustrate the application of the new method by analyzing human immunoglobulin and Drosophilid alcohol dehydrogenase sequences.

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