Construction of Optimal Basic Wavelet via AIDNN and Its Application in Seismic Data Analysis

Tian, Yajun; Gao, Jinghuai; Liu, Naihao; Chen, Daoyu

doi:10.1109/lgrs.2020.2997339

Cited by 10 publications

(11 citation statements)

References 19 publications

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“…As explained in the study of Tian et al [103], an adequate wavelet selection can influence the obtained results while analyzing seismic data. Likewise, Walenczykowska et al [91] also studied the effects of Morse wavelet parameters when analyzing radar waveforms.…”

Section: Discussionmentioning

confidence: 99%

Applications of the Generalized Morse Wavelets: A Review

et al. 2023

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The study of signals, processes, and systems has motivated the development of different representations that can be used to analyze and understand them. Classical ways of studying the behavior of signals are the time domain and frequency domain representations. For the analysis of non-stationary signals, time-frequency representations have become an essential tool to understand how the frequency content of signals changes with time. A common time-frequency technique employed in the literature is the wavelet transform. Nevertheless, selecting an adequate mother wavelet to perform the wavelet transform has become challenging due to the diverse available wavelet families. This paper reviews the applications and uses of a particular class of wavelet basis known as the Generalized Morse Wavelets. This class of wavelet family provides a systematic framework to choose and generate a wavelet for general-purpose use. This study reviews the application of Generalized Morse Wavelets in biomedical engineering, dynamical systems analysis, electrical engineering, geophysics, and communication systems. Moreover, the parameters of the Generalized Morse Wavelets used in each study are presented. The results of this study reveal that Generalized Morse Wavelets have proven helpful in studying signals, systems, and processes in areas ranging from biomedical engineering to geophysics. Nonetheless, the parameters of the Generalized Morse Wavelets are yet to be chosen through a rigorous methodology and argumentation. Therefore, there is an opportunity to generate methods for selecting the parameters of the Generalized Morse Wavelets based on the characteristics of the signals, systems, or processes under research.INDEX TERMS Generalized Morse wavelets, mother wavelet selection, continuous wavelet transform, applications, time-frequency analysis.

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Section: Discussionmentioning

confidence: 99%

Applications of the Generalized Morse Wavelets: A Review

et al. 2023

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“…In this paper, the basic wavelet 𝜓 of the synchrosqueezing transform is the optimal basic wavelet (OBW) (Tian et al, 2021). The OBW can best match the seismic wavelet estimated by Equation ( 6) because it uses the three-parameter wavelet to fit the seismic wavelet.…”

Section: Synchrosqueezing Optimal Basic Wavelet Transformmentioning

confidence: 99%

“…n denotes the additive noise. Then, the inversion problem of the seismic wavelet can be defined as (Tian et al., 2021)

\begin{equation}\hat{J} = \min \left[ {\frac{1}{2}{\Vert{{\bf s}} - {{\bf Wr}}\Vert}_2^2 + \Phi ({{\bf r}}) + \Psi ({{\bf w}})} \right],\end{equation}

where w is vector of seismic wavelet ω . Φ ( r ) and Ψ ( w ), respectively, indicate the convex regularization function of r and w .…”

Section: Theorymentioning

confidence: 99%

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Upscaling method based on sedimentary cycle prior and its application to well‐to‐seismic tie

Tian

Stovas

Gao

2023

Geophysical Prospecting

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A well‐to‐seismic tie is a typical upscaling problem. The traditional well‐to‐seismic tie methods often use the velocity log directly to tie well logs to seismic data without considering the upscaling problem led by the velocity dispersion due to thin beds. We propose an upscaling method based on the Backus average method to upscale the well‐log velocity to seismic velocity and apply it to a well‐to‐seismic tie problem. For Backus average method, choosing an appropriate average window is a crucial issue. We introduce a synchrosqueezing optimal basic wavelet transform to calculate an average window. The synchrosqueezing optimal basic wavelet transform is a time–frequency representation method, which can extract the sedimentary cycle information from seismic data. Considering the relationship between the sedimentary cycle and the thin‐bed thickness, we propose a workflow to estimate the instantaneous thin‐bed thickness based on synchrosqueezing optimal basic wavelet transform and determine the window length of the Backus average at each depth point. Then, the Backus average is used to estimate the effective velocity, which is further used to calculate the initial time–depth function and transfer the reflection coefficients from the depth domain to the time domain. Choosing an appropriate seismic wavelet is another fundamental problem for the well‐to‐seismic tie process. This paper introduces an alternating iterative deep neural network‐based method to estimate the seismic wavelet. Thus realistic synthetic seismograms can be computed by convolving the estimated seismic wavelet and the reflection coefficient, which can be stretched or squeezed to match the near‐well seismic trace. We show that the proposed workflow effectively reduces the errors in a well‐to‐seismic tie procedure caused by velocity dispersion of thin beds.

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“…Compared with the Fourier transform method used in

\sin \omega t

\cos \omega t

{e}^{j\omega t}

as basic functions, wavelet transform used in the wavelet functions are not unique, such as Daubechies (DB), Biorthogonal (Bior), Meyer, and so forth 20 . Their specific properties are shown in Table 1.…”

Section: Experiments Of Detection Sensormentioning

confidence: 99%

A near‐infrared CO₂ detection system for greenhouse gas based on PCA‐DNN

Liu

et al. 2022

Micro & Optical Tech Letters

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Carbon dioxide (CO 2 ) gas is one of the main greenhouse gases. The detection of CO 2 gas content is of great significance to the study of the greenhouse effect. The CO 2 detection system based on the principle of tunable diode laser absorption spectroscopy (TDLAS) was demonstrated. A distributed feedback (DFB) laser with a central wavelength of 1580 nm was used as the laser source, multipass gas cell (MPGC) was used as gas cell, and indium gallium arsenic (IGA) photodetector was used to complete photoelectric conversion, and the original extracted second harmonic signal was smooth and denoised by wavelet transform. The signal-to-noise ratio (SNR) of the wavelet-filtered spectrum improved from 6.88 to 13.87 dB, an improvement of 2.02 times. Principal component analysis was used to reduce the complexity of the data by compressing the spectrum from 800 dimensions to 2 dimensions. For the concentration inversion, the back-propagation deep neural network (BP-DNN) model was used to perform standard gas concentration step experiments and compared with the back-propagation neural network (BPNN). The experimental results show that the BP-DNN inversion of CO 2 concentration has improved computational accuracy and the root mean square error (RMSE) is 3.55 times lower than that of the traditional BPNN, showing favorable application prospects.

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Construction of Optimal Basic Wavelet via AIDNN and Its Application in Seismic Data Analysis

Cited by 10 publications

References 19 publications

Applications of the Generalized Morse Wavelets: A Review

Applications of the Generalized Morse Wavelets: A Review

Upscaling method based on sedimentary cycle prior and its application to well‐to‐seismic tie

A near‐infrared CO₂ detection system for greenhouse gas based on PCA‐DNN

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Construction of Optimal Basic Wavelet via AIDNN and Its Application in Seismic Data Analysis

Cited by 10 publications

References 19 publications

Applications of the Generalized Morse Wavelets: A Review

Applications of the Generalized Morse Wavelets: A Review

Upscaling method based on sedimentary cycle prior and its application to well‐to‐seismic tie

A near‐infrared CO2 detection system for greenhouse gas based on PCA‐DNN

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Product

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A near‐infrared CO₂ detection system for greenhouse gas based on PCA‐DNN