Ground roll extraction using the Karhunen-Loeve transform in the time-frequency domain

Geophysics ◽  
2021 ◽  
pp. 1-22
Author(s):  
Aleksander S. Serdyukov
Keyword(s):  
Surface Wave ◽  
Data Processing ◽  
Surface Waves ◽  
Frequency Domain ◽  
Band Frequency ◽  
Time Frequency ◽  
S Transform ◽  
Ground Roll ◽  
Karhunen Loeve Transform ◽  
Complex Valued

Ground roll suppression is critical for seismic reflection data processing. Many standard methods, i.e., FK filtering, fail when spatially aliased surface wave interference is present in the data. Spatial aliasing is a common problem; receiver spacing is often not dense enough to extract wavenumbers of low-velocity surface waves. It has long been known that the Karhunen-Loeve transform can be used to suppress aliased ground roll. However, the ground roll should be flattened before suppression, which is challenging due to the dispersion of surface wave velocities. I propose to solve this problem via the time-frequency domain. I apply the S-transform, which was previously shown to perform well in the multichannel analysis of surface waves. A simple complex-valued constant phase shift is a suitable model of surface wave propagation in common-frequency S-transform gathers. Therefore, it is easy to flatten the corresponding S-transform narrow-band frequency surface wave packet and extract it from the data by principal component analysis of the corresponding complex-valued data-covariance matrix. As the result, the proposed S-transform Karhunen-Loeve (SKL) method filters the aliased ground roll without damaging the reflection amplitudes. The advantages of SKL filtering have been confirmed by synthetic- and field-data processing.

THREE‐DIMENSIONAL SEISMIC MODEL STUDIES

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 19-32 ◽  
Author(s):  
F. K. Levin ◽  
H. C. Hibbard
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Wave ◽  
Surface Waves ◽  
Shear Waves ◽  
Three Dimensional ◽  
Seismic Model ◽  
Model Studies ◽  
Ground Roll ◽  
Detector Configurations

Elastic wave propagation in a two‐layer section has been studied with a solid two‐bed model and records resembling seismograms obtained for the four possible source‐detector configurations. Numerous events are identified. Among these, the shear waves are found to be surprisingly prominent. The amplitude of the ground roll falls off approximately as [Formula: see text] This is the amplitude‐range dependence expected for a surface wave. The ability of two in‐line detectors to reduce surface waves has been demonstrated.

Gear fault diagnosis based on time–frequency domain de-noising using the generalized S transform

2017 ◽  
Vol 24 (15) ◽  
pp. 3338-3347 ◽  
Author(s):  
Jianhua Cai ◽  
Xiaoqin Li
Keyword(s):  
Fault Diagnosis ◽  
Frequency Domain ◽  
Vibration Signal ◽  
Time Frequency ◽  
Transmission Modes ◽  
S Transform ◽  
Mining Machinery ◽  
Gear Fault ◽  
Generalized S Transform ◽  
Gear Fault Diagnosis

Gears are the most important transmission modes used in mining machinery, and gear faults can cause serious damage and even accidents. In the work process, vibration signals are influenced not only by friction, nonlinear stiffness, and nonstationary loads, but also by strong noise. It is difficult to separate the useful information from the noise, which brings some trouble to the fault diagnosis of mining machinery gears. The generalized S transform has the advantages of the short time Fourier transform and wavelet transform and is reversible. The time–frequency energy distribution of the gear vibration signal can be accurately presented by the generalized S transform, and a time–frequency filter factor can be constructed to filter the vibration signal in the time–frequency domain. These characteristics play an important role when the generalized S transform is used to remove the noise in the time–frequency domain. In this paper, a new gear fault diagnosis based on the time–frequency domain de-noising is proposed that uses the generalized S transform. The application principle, method steps, and evaluation index of the method are presented, and a wavelet soft-threshold filtering method is implemented for comparison with the proposed approach. The effectiveness of the proposed method is demonstrated by numerical simulation and experimental investigation of a gear with a tooth crack. Our analyses also indicate that the proposed method can be used for fault diagnosis of mining machinery gears.

scholarly journals Multi-Band Frequency Window for Time-Frequency Fault Diagnosis of Induction Machines

2019 ◽  
Author(s):  
Jordi Burriel-Valencia ◽  
Ruben Puche-Panadero ◽  
Javier Martinez-Roman ◽  
Angel Sapena-Bano ◽  
Martin Riera-Guasp ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Window ◽  
Early Stage ◽  
Induction Machines ◽  
Frequency Domain Analysis ◽  
Frequency Resolution ◽  
Good Time ◽  
Band Frequency ◽  
Time Frequency ◽  
Multi Band

Induction machines drive many industrial processes, and their unexpected failure can cause heavy production losses. The analysis of the current spectrum can identify online the characteristic fault signatures at an early stage, avoiding unexpected breakdowns. Nevertheless, frequency domain analysis requires stable working conditions, which is not the case for wind generators, motors driving varying loads, etc. In these cases an analysis in the time-frequency domain -such as a spectrogram- is required for detecting faults signatures. The spectrogram is built using the short frequency Fourier transform, but its resolution depends critically on the time window used to generate it: short windows provide good time resolution, but poor frequency resolution, just the opposite than long windows. Therefore, the window must be adapted at each time to the shape of the expected fault harmonics, by highly skilled maintenance personnel. In this paper, this problem is solved with the design of a new multi-band window, which generates simultaneously many different narrow-band current spectrograms, and combines them into a single, high resolution one, without the need of manual adjustments. The proposed method is validated with the diagnosis of bar breakages during the start-up of a commercial induction motor.

scholarly journals Time-Frequency Domain Deconvolution based on Synchrosqueezing Generalized S Transform

2021 ◽  
pp. 148-155
Author(s):  
Shulin Zheng ◽  
Zijun Shen
Keyword(s):  
Frequency Domain ◽  
Seismic Data ◽  
Oil And Gas ◽  
Amplitude Spectrum ◽  
Frequency Resolution ◽  
Good Effect ◽  
Time Frequency ◽  
S Transform ◽  
Convolution Model ◽  
Generalized S Transform

Complex geological characteristics and deepening of the mining depth are the difficulties of oil and gas exploration at this stage, so high-resolution processing of seismic data is needed to obtain more effective information. Starting from the time-frequency analysis method, we propose a time-frequency domain dynamic deconvolution based on the Synchrosqueezing generalized S transform (SSGST). Combined with spectrum simulation to estimate the wavelet amplitude spectrum, the dynamic convolution model is used to eliminate the influence of dynamic wavelet on seismic records, and the seismic signal with higher time-frequency resolution can be obtained. Through the verification of synthetic signals and actual signals, it is concluded that the time-frequency domain dynamic deconvolution based on the SSGST algorithm has a good effect in improving the resolution and vertical resolution of the thin layer of seismic data.

Sparsity-promoting method to estimate the dispersion curve of surface-wave group velocity

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. V33-V43 ◽  
Author(s):  
Reza Dokht Dolatabadi Esfahani ◽  
Roohollah Askari ◽  
Ali Gholami
Keyword(s):  
Surface Wave ◽  
Group Velocity ◽  
Energy Concentration ◽  
Wave Group ◽  
Velocity Range ◽  
S Wave ◽  
New Approach ◽  
Time Frequency ◽  
Gaussian Window ◽  
S Transform

Group velocity is an important characteristic of surface wave that is defined as the velocity of an envelope of frequencies. Although many studies have shown the promises of analyzing the group velocity to obtain subsurface S-wave velocity, the estimation of the group velocity is not straightforward due to the uncertainties of selecting an optimum envelope of frequencies. Conventional transformations or filtering algorithms used to define an optimum envelope usually give reasonable results just for a narrow frequency or velocity range. We introduced a new approach for the estimation of the group velocity using the sparse S transform (SST) and sparse linear Radon transform (SLRT). In SST, the width of the Gaussian window is optimally calculated by energy concentration to eliminate energy smearing in the time-frequency (TF) domain, and then the sparsity is applied to enhance the TF resolution. Compared with conventional methods for the estimation of the group velocity based on the generalized S transforms, SST does not require any adjustment to the Gaussian window and yields accurate estimates of the group velocity. We apply SST to each seismic trace of a seismic shot record to obtain a 3D cube of frequency, time, and offset. For any frequency, we obtain a common frequency gather of time and offset to which we apply SLRT to obtain the group velocity of the surface wave. Our approach is robust at calculating high-resolution distinguishable dispersion curves of the group velocity in particular when data are extremely sparse.

Surface wave attenuation based polarization attributes in time-frequency domain for multicomponent seismic data

2018 ◽  
Vol 15 (1) ◽  
pp. 99-110 ◽  
Author(s):  
Xuan-Lin Kong ◽  
Hui Chen ◽  
Zhi-Quan Hu ◽  
Jia-Xing Kang ◽  
Tian-Ji Xu ◽  
...  
Keyword(s):  
Surface Wave ◽  
Frequency Domain ◽  
Seismic Data ◽  
Wave Attenuation ◽  
Time Frequency ◽  
Multicomponent Seismic

Multichannel analysis of surface waves

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 800-808 ◽  
Author(s):  
Choon B. Park ◽  
Richard D. Miller ◽  
Jianghai Xia
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Dispersion Curve ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Frequency Component ◽  
Multichannel Recording ◽  
Phase Velocities ◽  
Ground Roll

The frequency‐dependent properties of Rayleigh‐type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface‐wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental‐mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source‐generated noise inhibits the reliability of shear‐wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental‐mode Rayleigh waves (noise) are body waves, scattered and nonsource‐generated surface waves, and higher‐mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear‐wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive trace‐to‐trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable‐frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real‐time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface‐wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single‐measurement surveying of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing random or nonlinear noise introduced during recording. A multichannel shot gather decomposed into a swept‐frequency record allows the fast generation of an accurate dispersion curve. The accuracy of dispersion curves determined using this method is proven through field comparisons of the inverted shear‐wave velocity ([Formula: see text]) profile with a downhole [Formula: see text] profile.

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