Wavelet transforms have been successfully used in seismic data processing with their ability for local time - frequency analysis. However, identification of directionality is limited because wavelet transform coeffici...Wavelet transforms have been successfully used in seismic data processing with their ability for local time - frequency analysis. However, identification of directionality is limited because wavelet transform coefficients reveal only three spatial orientations. Whereas the ridgelet transform has a superior capability for direction detection and the ability to process signals with linearly changing characteristics. In this paper, we present the issue of low signal-to-noise ratio （SNR） seismic data processing based on the ridgelet transform. Actual seismic data with low SNR from south China has been processed using ridgelet transforms to improve the SNR and the continuity of seismic events. The results show that the ridgelet transform is better than the wavelet transform for these tasks.展开更多
Noise has traditionally been suppressed or eliminated in seismic data sets by the use of Fourier filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific c...Noise has traditionally been suppressed or eliminated in seismic data sets by the use of Fourier filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific conditions, they may produce undesirable effects for the low signal to noise ratio data. In this paper, a new method, multi-scale ridgelet transform, is used in the light of the theory of ridgelet transform. We employ wavelet transform to do sub-band decomposition for the signals and then use non-linear thresholding in ridgelet domain for every block. In other words, it is based on the idea of partition, at sufficiently fine scale, a curving singularity looks straight, and so ridgelet transform can work well in such cases. Applications on both synthetic data and actual seismic data from Sichuan basin, South China, show that the new method eliminates the noise portion of the signal more efficiently and retains a greater amount of geologic data than other methods, the quality and consecutiveness of seismic event are improved obviously as well as the quality of section is improved.展开更多
The conventional discrete wavelet transform （DWT） introduces artifacts during denoising of images containing smooth curves. Finite ridgelet transform （FRIT） solved this problem by mapping the curves in terms of sm...The conventional discrete wavelet transform （DWT） introduces artifacts during denoising of images containing smooth curves. Finite ridgelet transform （FRIT） solved this problem by mapping the curves in terms of small curved ridges. However, blind application of FRIT all over an image is computationally heavy. Finite curvelet transform （FCT） selectively applies FRIT only to the tiles containing small portions of a curve. In this work, a novel curvelet transform named as 4-quadrant finite curvelet transform （4QFCT） based on a new concept of 4-quadrant finite ridgelet transform （4QFRIT） has been proposed. An image is band pass filtered and the high frequency bands are divided into small non-overlapping square tiles. The 4QFRIT is applied to the tiles containing at least one curve element. Unlike FRIT, the 4QFRIT takes 4 sets of radon projections in all the 4 quadrants and then averages them in time and frequency domains after denoising. The proposed algorithm is extensively tested and benchmarked for denoising of images with Gaussian noise using mean squared error （MSE） and peak signal to noise ratio （PSNR）. The results confirm that 4QFCT yields consistently better denoising performance quantitatively and visually.展开更多
基金This paper is supported by China Petrochemical Key Project in the"11th Five-Year"Plan Technology and the Doctorate Fund of Ministry of Education of China (No.20050491504)
文摘Wavelet transforms have been successfully used in seismic data processing with their ability for local time - frequency analysis. However, identification of directionality is limited because wavelet transform coefficients reveal only three spatial orientations. Whereas the ridgelet transform has a superior capability for direction detection and the ability to process signals with linearly changing characteristics. In this paper, we present the issue of low signal-to-noise ratio （SNR） seismic data processing based on the ridgelet transform. Actual seismic data with low SNR from south China has been processed using ridgelet transforms to improve the SNR and the continuity of seismic events. The results show that the ridgelet transform is better than the wavelet transform for these tasks.
基金supported by China Petrochemical key project during the 11th Five-year Plan as well as the Doctorate Fund of Ministry of Education of China (No.20050491504)
文摘Noise has traditionally been suppressed or eliminated in seismic data sets by the use of Fourier filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific conditions, they may produce undesirable effects for the low signal to noise ratio data. In this paper, a new method, multi-scale ridgelet transform, is used in the light of the theory of ridgelet transform. We employ wavelet transform to do sub-band decomposition for the signals and then use non-linear thresholding in ridgelet domain for every block. In other words, it is based on the idea of partition, at sufficiently fine scale, a curving singularity looks straight, and so ridgelet transform can work well in such cases. Applications on both synthetic data and actual seismic data from Sichuan basin, South China, show that the new method eliminates the noise portion of the signal more efficiently and retains a greater amount of geologic data than other methods, the quality and consecutiveness of seismic event are improved obviously as well as the quality of section is improved.
文摘The conventional discrete wavelet transform （DWT） introduces artifacts during denoising of images containing smooth curves. Finite ridgelet transform （FRIT） solved this problem by mapping the curves in terms of small curved ridges. However, blind application of FRIT all over an image is computationally heavy. Finite curvelet transform （FCT） selectively applies FRIT only to the tiles containing small portions of a curve. In this work, a novel curvelet transform named as 4-quadrant finite curvelet transform （4QFCT） based on a new concept of 4-quadrant finite ridgelet transform （4QFRIT） has been proposed. An image is band pass filtered and the high frequency bands are divided into small non-overlapping square tiles. The 4QFRIT is applied to the tiles containing at least one curve element. Unlike FRIT, the 4QFRIT takes 4 sets of radon projections in all the 4 quadrants and then averages them in time and frequency domains after denoising. The proposed algorithm is extensively tested and benchmarked for denoising of images with Gaussian noise using mean squared error （MSE） and peak signal to noise ratio （PSNR）. The results confirm that 4QFCT yields consistently better denoising performance quantitatively and visually.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60375021)教育部留学回国人员科研启动基金(The Project-Sponsored by SRF for ROCS+5 种基金SEM)湖南省杰出青年基金(the Fund of Hunan Province for Distinguished Young Scholarunder Grant No.05JJ10011)湖南省自然基金重点基金(No.04JJ20010)湖南省教育厅重点项目(the Research Project of Department ofEducation of Hunan ProvinceChina under Grant No.04A056No.05C092)。
