Numerical wavelets scheme to complex partial differential equation arising from Morlet continuous wavelet transform

2020 ◽  
Author(s):  
Vijay Kumar Patel ◽  
Somveer Singh ◽  
Vineet Kumar Singh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Partial Differential ◽  
Morlet Continuous Wavelet Transform

Relative acoustic impedance from wavelet transform

2014 ◽  
Vol 2 (1) ◽  
pp. SA107-SA118 ◽  
Author(s):  
Marcílio Castro de Matos ◽  
Rodrigo Penna ◽  
Paulo Johann ◽  
Kurt Marfurt
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Real Data ◽  
Velocity Model ◽  
Continuous Wavelet ◽  
Reconstruction Process ◽  
Seismic Wavelet ◽  
Morlet Continuous Wavelet Transform

Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that remove an estimated seismic wavelet from seismic data. We assume that seismic trace subtle discontinuities are associated with acoustic impedance contrasts and can be characterized by wavelet transform spectral ridges, also called modulus maxima lines (WTMML), allowing us to improve seismic resolution by using the wavelet transform. Specifically, we apply the complex Morlet continuous wavelet transform (CWT) to each seismic trace and compute the WTMMLs. Then, we reconstruct the seismic trace with the inverse continuous wavelet transform from the computed WTMMLs with a broader band complex Morlet wavelet than that used in the forward CWT. Because the reconstruction process preserves amplitude and phase along different scales, or frequencies, the result looks like a deconvolution method. Considering this high-resolution seismic representation as a reflectivity approximation, we estimate the relative acoustic impedance (RAI) by filtering and trace integrating it. Conventional deconvolution algorithms assume the seismic wavelet to be stochastic, while the CWT is implicitly time varying such that it can be applied to both depth and time-domain data. Using synthetic and real seismic data, we evaluated the effectiveness of the methodology on detecting seismic events associated with acoustic impedance changes. In the real data examples, time and in-depth RAI results, show good correlation with real P-impedance band-pass data computed using more rigorous commercial inversion software packages that require well logs and low-frequency velocity model information.

scholarly journals Fringe pattern analysis using a one-dimensional modified Morlet continuous wavelet transform

2008 ◽  
Author(s):  
Abdulbasit Z. Abid ◽  
Munther A. Gdeisat ◽  
David R. Burton ◽  
Michael J. Lalor ◽  
Hussein S. Abdul-Rahman ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Fringe Pattern ◽  
Pattern Analysis ◽  
Continuous Wavelet ◽  
One Dimensional ◽  
Morlet Continuous Wavelet Transform ◽  
Fringe Pattern Analysis

De-Noising Method for Partial Discharge Signal Based on Wavelet Transform and Partial Differential Equation

2014 ◽  
Vol 529 ◽  
pp. 444-447 ◽  
Author(s):  
Jian Zhang ◽  
Fu Jiang Mo ◽  
Feng Yao ◽  
Xiao Jian Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wavelet Transform ◽  
Noise Suppression ◽  
Partial Discharge ◽  
Interference Signal ◽  
Partial Differential ◽  
Calculation Results ◽  
Low Distortion

In order to solve the noise suppression problem in partial discharge (PD) signals detection, this paper proposes a de-noising method based on wavelet transform and partial differential equation (PDE). Compared the effect of proposed method with traditional wavelet threshold de-noising method, simulation and calculation results both show that paper’s method can remove the interference signal, retain the better edge detail of signal and low distortion when taking the appropriate iteration times.

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