Research On Threshold Denoising Method Based On New Seislet Transform In The Condition Of Low SNR

Seismic data often contains a lot of random noise, such as the backgroundinterference and micro vibration, etc., To remove random noise and improve thesignal-to-noise ratio of seismic data is the key to seismic data processing. Combinedthe sparse transform with threshold denoising method, we can remove random noiseand enhance the signal-to-noise ratio.Wavelet-like transforms mainly use the direction features in the image, they havea wide range of applications in the seismic data processing and data analysis. TheSeislet transform is a digital wavelet-like transform tailored specifically forrepresenting seismic data. It is defined with the help of the wavelet lifting schemecombined with local plane-wave destruction. It analyzes seismic data by followingvariable slopes of seismic events across different scales. Generally, the classic digitalwavelet transform is simply a Seislet transform with a zero slope. Seislet transformcan provide more effectively compression ability of seismic data than classicalwavelet transform. In the discrete wavelet transform, the basic unit of transform isdata sample，however， in Seislet transform, the corresponding processing unit is aseismic trace. Using the local slope properties of corresponding seismic trace topredict and shift the events, the result is more suitable for the piecewise smoothassumptions of discrete wavelet transform. Here, the calculation of the local slopes isthe core of this method. There are many kinds of methods to calculate the local slopes.But in the condition of low signal-to-noise ratio (SNR), these methods have somelimitations.I propose a method that is suitable for low SNR based on the definition of theslopes of t-x relationship in CMP traces. Compared the slopes of t-x relationship inCMP traces with PWD method, we can see that the new method is more accurate incalculating the local slopes. Apply these slopes to Seislet frame, I establish a newSeislet transform that characterizes low SNR data. New Seislet transform can bettercompress seismic event under the condition of strong random seismic noise, while the random noise distribute in the whole transform domain. Therefore, the new Seislettransform provides an effective transform domain to separate signal and noise. Then,threshold along the scale direction (that is to keep transform coefficients of smallscale and zero transform coefficients of big scale) and do inverse transform. After theinverse transform, we can see that, events based on slopes of t-x relationship in CMPtraces are more reasonable than those based on slopes of PWD method. But there isstill so much noise left. So we denoise using threshold function method.The calculation of the threshold value is the core of threshold function method.In this work, I denoise using percentile. Generally, we determine the percentile clip bymany experiments. It cannot do quantitatively. In this work, we combine thresholdestimation model with percentile to get a more accurate percentile, then apply it tothreshold function method for denoising. The traditional hard-threshold method andsoft-threshold method both have some limitations. In seismic data processing, weintroduce two methods which were introduced in acoustic signals. Combined withnew Seislet transform, we propose two new threshold methods. From the analysis oftheoretical model and field data tests, the improved methods are not only suitable forseismic signals, but also better than the traditional hard-threshold method andsoft-threshold method in signal-to-noise ratio (SNR) and mean square error (MSE).The second improved threshold method is better than the other three methods insmoothness. The second improved threshold method has more advantages andeffectiveness.The processing results of theoretical model and field data show that the newSeislet transform can better follow hyperbolic time-distance relationship of event inseismic CMP gathers. It can also compress seismic event and provide sparsetransform domain to separate the signal and noise. By using improved thresholdmethod, we can separate signal and noise in CMP gathers reasonably. It confirms theeffectiveness of the method in this paper.