The location of singularities may be detected by local maxima of the wavelet transform modulus. The digital modeling and focusing process to wavelet transform of the reflecting seismic signals have been done. It has b...The location of singularities may be detected by local maxima of the wavelet transform modulus. The digital modeling and focusing process to wavelet transform of the reflecting seismic signals have been done. It has been found that the locations of singularities after wavelet transform are only affected by two factors, their original locations and the seismic wavelet length, which says it does not matter with what shape the wavelet will be. The wavelet length can be determined according to the wavelet transform results and be eliminated thereafter so that we are able to detect thin bed seismic signal with resolution of l/32 wavelength. The singularities have been recovered with improved resolution of the seismic section by real data processing.展开更多
This paper introduces a multiresolution decomposition of signals based on their wavelet transform. The different behaviors of the wavelet transform between the signal and the noise are compared. An algorithm of singul...This paper introduces a multiresolution decomposition of signals based on their wavelet transform. The different behaviors of the wavelet transform between the signal and the noise are compared. An algorithm of singularity detection and processing in signals is proposed by the modulus maximum of the wavelet transform.展开更多
That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system （GPS）. In this paper, an algorithm based on le...That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system （GPS）. In this paper, an algorithm based on length-4 symmetric/anti-symmetric （SA4） orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements. Associated with the local singularity detection principle, cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform. Firstly, studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust （GHM）, Chui-Lian （CL） and SA4. Moreover, the mathematical characterization of singularities with Lipschitz exponents is explained, the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation. Finally, field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm. Because SA4 possesses the specific nature of good multi-filter properties （GMPs）, it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly, and for the half-cycle slip, it also remains better detection, location ability and the equal complexity of wavelet transform.展开更多
文摘The location of singularities may be detected by local maxima of the wavelet transform modulus. The digital modeling and focusing process to wavelet transform of the reflecting seismic signals have been done. It has been found that the locations of singularities after wavelet transform are only affected by two factors, their original locations and the seismic wavelet length, which says it does not matter with what shape the wavelet will be. The wavelet length can be determined according to the wavelet transform results and be eliminated thereafter so that we are able to detect thin bed seismic signal with resolution of l/32 wavelength. The singularities have been recovered with improved resolution of the seismic section by real data processing.
文摘This paper introduces a multiresolution decomposition of signals based on their wavelet transform. The different behaviors of the wavelet transform between the signal and the noise are compared. An algorithm of singularity detection and processing in signals is proposed by the modulus maximum of the wavelet transform.
基金National Natural Science Foundation of China (61153002)
文摘That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system （GPS）. In this paper, an algorithm based on length-4 symmetric/anti-symmetric （SA4） orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements. Associated with the local singularity detection principle, cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform. Firstly, studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust （GHM）, Chui-Lian （CL） and SA4. Moreover, the mathematical characterization of singularities with Lipschitz exponents is explained, the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation. Finally, field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm. Because SA4 possesses the specific nature of good multi-filter properties （GMPs）, it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly, and for the half-cycle slip, it also remains better detection, location ability and the equal complexity of wavelet transform.
