The Research Of Spatiotemporal 2-D Time-frequency Peak Filtering For Seismic Random Noise Suppression

Seismic prospecting is the most important geophysical method to obtain the information of petroleum and gas resources. It utilizes the seismic wave generated by artificial excitation to obtain geological information, and then to cognitive the underground geological structure and locate the gas and minerals. However, with the global increasing demand for the oil, gas and mineral resources, the development exploration technology will gradually facing unknown and more complex deep areas. Thus the exploration will more and more difficulty. Accordingly, the influence of such factors as complex environment, man-made and instrument make the seismic waves which carry geological information always distorted by a large amount of random noise. This kind of noise is a random irregular and the adjacent channel is unrelated that caused serious impact to seismic data analysis and interpretation. At present, the geophysicists have proposed many effective methods for random noise suppression. But in strong random noise(lower than 0d B) environment, it is difficult to identify the reflection events which even be covered,then some existing methods is not ideal in treatment the noisy signal. After filtering, the amplitude of the signal will attenuated. Therefore, effectively simultaneous denoising and protect the amplitude of seismic signal, and to improve the signal-to-noise ratio, resolution,and fidelity, is the top priority and key steps of the seismic signal processing, and also is the premise of understanding the geological condition, not only in the seismic data processing aspect but also from an economic perspective.The fractal conservation law is based on a partial differential equation model. The main advantage of the equation is combined use of fractal anti-diffusion and classical Laplace diffusion which are two antagonistic terms. The anti-diffusion is used to enhance the contrast, whereas the diffusion is used to reduce the noise. The tuning of the filter can be achieved by controlling the fractal exponent, the amount of anti-diffusion and diffusion. In2012, it is first proposed by Pascal Azerad and successfully applied to the electrocardiogram(ecg) signal. It proves that it is a fast and effective to simultaneous denoising and enhancement of signals. This paper first applied this new filtering method for the seismic signal processing, aimed at to obtain a better effect in the random noise suppression and the events protection of the seismic data.The research and the innovation points of this thesis can be include the following three parts:1. The FCL algorithm is first introduced into the seismic random noise reduction.Because the filtering algorithm is based on a partial differential equation, in this paper, we analysis the characteristics of denoising and enhancement of the equation in detail and presented two methods of numerical implementation: the Finite difference method and the Fourier transform method. The finite difference method to discrete the equation directly.According to the initial conditions of the signal(the noisy signal), the subsequent status of the signal can be calculate through the iterative arithmetic. The numerical experiment using this scheme is simple to understand, and can be observed the filtering process directly of a noisy signal. But it is not obtain the strict stability using this scheme, and can only get the approximate solution, thus, there inevitable exists the errors; iterative operation seriously affect the calculation speed, and it makes the processing efficiency very low, not suitable for the application of actual seismic data. So this scheme only takes one dimensional seismic wavelet as the experimental object. The purpose is intuitive to understanding the process of FCL algorithm for signal denoising and enhancement, and also to verify the feasibility the method in random noise reduction and enhance or maintain the signal. In Fourier transform scheme, by using an integral formula, which is based on Taylor-Poisson’s formula and Fubini’s theorem for an anti-diffusive term, and then taking the fast Fourier transform of the PDE, the filter in the frequency domain can be derived. The study showed that this filter eliminates the high frequencies, amplifies the medium frequencies, and preserves the low frequencies. With the frequency response, the filtering process can be realized in the frequency domain for computational efficiency. The FCL algorithm is tested using synthetic and field seismic data. The experimental results illustrate the superior performance of FCL in the recovery of seismic events by removing random noise and enhancing valid signal. Usually, these features are flattened by other denoising methods.2. The adaptive FCL algorithm is first presented. For traditional FCL, The performance of FCL depends on the shape of the frequency response which is fixed, then it will has some limitations on the filtering. Aiming at this lack, the adaptive FCL method is proposed. According to the frequency response under different parameters to filter noise seismic record, and can be get a set of filtering results. Thus at each sampling point will get a set of filter estimate, and then find out the maximum and minimum value and establish a continuous bounded closed interval. We Introduced a penalized least squares criterion as the objective function. Using Viterbi algorithm to find the objective function in the global scope to achieve the minimum point which is the best. The main strategy of theadaptive method is to find the best filter at each sample point adaptively. The adaptive FCL is tested on synthetic seismic data which contains a complex geometry and the actual common shot point record, and compared this method with conventional FCL algorithm,the well known wavelet denoising method and F-X convolution method. We know the adaptive FCL method achieving better random noise reduction and higher continuity and clarity of the reflection events.3. The Radon-FCL algorithm is first presented. By Radon transform we develops the conventional 1-D FCL to the spatiotemporal 2-D. Due to the seismic data has 2-D features,the lateral correlation between the seismic events have important research value. Therefore there is a great advantage over the 1-D FCL about the random noise suppression. Using the space and time characteristics of the Radon transform, to stack the original seismic data along appropriate trajectories(linear, parabolic, etc.) to transform the original data into the Radon domain. The reflection events of the original seismic records are focused as energy wavelets with different locations in Radon domain. Thus, the Radon transform change the structure of the original seismic data. That is to say, the Radon transform plays a role in indicating the direction of seismic events and providing a direction for FCL. By performing the FCL method along the direction of the slope or curvature parameters in the Radon domain, which is equivalent to do FCL filter on multiple directions in the original domain, and not along the direction of the seismic trace for time dimension filtering.Utilize the space information of the signal to perform FCL filtering in the Radon domain,the signal submerged by strong noise can be recovered through the correlations between time- and space- domain. Thereby the 2-D filtering will improve the continuity of the events. Since the random noise has no correlation on the space, it is easier to remove in the Radon domain. The two-dimensional FCL method utilizes the space characteristic of the Radon transform and the frequency characteristic of the FCL method, and provides a fast and efficient new way for the random noise reduction and events protection of the seismic data.