Singularity detection of the thin bed seismic signals with wavelet transform

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.

Singularity Detection of Signals Based on their Wavelet Transform

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.

Research on the detecting methods of singularity in deformation signal based on two kinds of wavelet entropy

There are various influencing factors that affect the deformation observation, and deformation signals show differ- ent characteristics under different scales. Wavelet analysis possesses multi-scale property, and the information entropy has great representational capability to the complexity of information. By hamming window to the wavelet coefficients and windowed wavelet energy obtained by multi-resolution analysis （MRA）, it can be achieved to measure the wavelet time entropy （WTE） and wavelet energy entropy （WEE）. The paper established deformation signals, selected the parameters, and compared the sin- gularity detection ability and anti-noise ability of two kinds of wavelet entropy and applied them to the singularity detection at the GPS continuously operating reference stations. It is shown that the WTE performs well in weak singularity information de- tection in finite frequency components signals and the WEE is more suitable for detecting the singularity in the signals with complex, strong background noise.

Cycle-slip Detection of GPS Carrier Phase with Methodology of SA4 Multi-wavelet Transform

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.