Edge preserving filtering on 3‐D seismic data using complex wavelet transforms

In this paper, we introduce several methods of signal quantitative analysis using the perfect-translation-invariant complex wavelet functions (PTI complex wavelet functions), which are used in our proposed perfect-translation-invariant complex discrete wavelet transforms (PTI CDWTs) and can be designed by customization. First, using PTI complex wavelet functions, we define the continuous wavelet coefficient (CWC). Next, using orthonormal wavelet functions in the classical Hardy space, we analyze the CWC, and show that, using a CWC, we can measure the energy of a customizable frequency band, and additionally, using numbers of CWCs, we can measure the energy of the whole frequency band. Next, we introduce the fast calculation method of CWCs and show the applicability of the PTI CDWTs to digital signals. Based on them, we introduce some examples of signal quantitative analysis, including the methods to obtain instantaneous amplitude, instantaneous phase and instantaneous frequency. Additionally, we introduce the energy measurement of the whole frequency band using the PTI DT-CDWT, which is one of our proposed PTI CDWTs.

Download Full-text

ROBUST SVD FILTERING FOR LOW SIGNAL-TO-NOISE RATIO SEISMIC DATA

Geophysics ◽

10.1190/geo2020-0169.1 ◽

2021 ◽

pp. 1-51

Author(s):

Chao Wang ◽

Yun Wang

Keyword(s):

Seismic Data ◽

Signal To Noise Ratio ◽

Singular Values ◽

New Method ◽

Signal To Noise ◽

Coherent Noise ◽

Edge Preserving ◽

Singular Vectors ◽

Reduced Rank ◽

Noise Ratio

Reduced-rank filtering is a common method for attenuating noise in seismic data. As conventional reduced-rank filtering distinguishes signals from noises only according to singular values, it performs poorly when the signal-to-noise ratio is very low, or when data contain high levels of isolate or coherent noise. Therefore, we developed a novel and robust reduced-rank filtering based on the singular value decomposition in the time-space domain. In this method, noise is recognized and attenuated according to the characteristics of both singular values and singular vectors. The left and right singular vectors corresponding to large singular values are selected firstly. Then, the right singular vectors are classified into different categories according to their curve characteristics, such as jump, pulse, and smooth. Each kind of right singular vector is related to a type of noise or seismic event, and is corrected by using a different filtering technology, such as mean filtering, edge-preserving smoothing or edge-preserving median filtering. The left singular vectors are also corrected by using the filtering methods based on frequency attributes like main-frequency and frequency bandwidth. To process seismic data containing a variety of events, local data are extracted along the local dip of event. The optimal local dip is identified according to the singular values and singular vectors of the data matrices that are extracted along different trial directions. This new filtering method has been applied to synthetic and field seismic data, and its performance is compared with that of several conventional filtering methods. The results indicate that the new method is more robust for data with a low signal-to-noise ratio, strong isolate noise, or coherent noise. The new method also overcomes the difficulties associated with selecting an optimal rank.

Download Full-text

Applicataion of ormsby wavelet for generation of synthetic seismic signals

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i2.7.10980 ◽

2018 ◽

Vol 7 (2.7) ◽

pp. 794

Author(s):

E Sai Sumanth ◽

V Joseph ◽

Dr K S Ramesh ◽

Dr S Koteswara Rao

Keyword(s):

Wavelet Transform ◽

Seismic Data ◽

Wavelet Transforms ◽

Seismic Signal ◽

Core Structure ◽

Seismic Signals ◽

Seismic Reflections ◽

Input Wave

Investigation of signals reflected from earth’s surface and its crust helps in understanding its core structure. Wavelet transforms is one of the sophisticated tools for analyzing the seismic reflections. In the present work a synthetic seismic signal contaminated with noise is synthesized and analyzed using Ormsby wavelet[1]. The wavelet transform has efficiently extracted the spectra of the synthetic seismic signal as it smoothens the noise present in the data and upgrades the flag quality of the seismic data due to termers. Ormsby wavelet gives the most redefined spectrum of the input wave so it could be used for the analysis of the seismic reflections.

Download Full-text