Research On Seismic Wavelet Estimation Using Second-Order And High-Order Statistics

Seismic exploration is the most effective tools and is commonly applied to oil and gas exploration and development. While, the technology of seismic wavelet extraction is important to develop the resolution of seismic data. If the wavelet is known, the deconvolution process can maximize the resolution of seismic data and can get reflective coefficients. Based on the extracted wavelet and achieved reflective coefficients, the woks of channel integration and impedance inversion can be processed to get some important information about subterranean impedance, density and speed. So the work of extracting wavelet is of great importance, even can be considered:whether the extracted seismic wavelet is accurate or not, it has become a critical factor of success about the deconvolution, the impedance inversion and forward modeling of seismic data.Currently, the basic framework of seismic wavelet extraction is the convolution model, mainly including the statistical extraction method and the deterministic extraction method. The deterministic method requires seismic records to combine with the well logging data. The statistical methods are without the help of any logging data, but have to make the assumption that seismic wavelets and reflection coefficients should be satisfied with some kinds of certain distribution or properties. They can be classified into some categories, such as Higher-order Statistics Method, Second-order Statistics Method, Nonlinear Inversion Method and so on. But the method based on Higher-order Statistics assumes that the reflective coefficient should be satisfied with non-Gaussian random process. While, the Second-order Method based on SIMO system blind identification algorithm, requires the reflective coefficients to be the same as the others and the wavelets to be different from the others. In other words, it unreasonably assumes that all of the differences among seismic records are caused by multi-wavelets and have nothing to do with reflection coefficients.But different regions exist in variously geological conditions, and their reflective coefficients comply with the rules of different assumptions. So what kind of statistics method can be suitably applied into the destination area? Due to the statistical wavelet extraction methods in possession of different assumptions, this paper estimates the seismic wavelet via the analysis of those methods-Third-order Cumulant Spectrum. Fourth-order Cumulant Spectrum and Blind Channel Identification based on Subspace Sethod of Second-order Statistics-and undertakes the comparative study of noise immunity. On this basis, In order to solve the unstable problem in solving overdetermined equations of High-order Cumulant Method, author firstly cites a more robust algorithm than the original one. It is called that Damping Double Conjugate Gradient Algorithm (DDCGA), which contributes to get more stable and reliable results. Besides, in order to meet the problem of unsatiable assumptions in the way of identifing SIMO system blindly, and aiming at the character of seismic signal and using the thinking about Mallat algorithm of the Discrete Wavelet Transform, this paper makes a preliminary discussion about two methods of building Pseudo Single-Input Multi-Output System which has no limitation for any hypothesis, and then deduces the algorithm of extracting seismic wavelet with noise subspace method in PSIMO system. This method, belonging to the category of blind system identification, makes no assumptions about wavelets and reflective coefficients. It is ture that the adaptive degree of real data is better. Finally, all of the methods together applies into the data processing of the South China Sea and analyzes the results.Through the model test and actual application, we may draw some conclusions and cognition briefly. Firstly, the wavelet estimating algorithm of DDCGA based on high-order cumulant spectrum is more constant and accurate than inversion algorithm. Secondly, the antinoise ability of PSIMO system by the second approach which can overcome the irrational assumption is better than SIMO system. Thirdly, the estimated wavelets using the methods of Third-order and Fourth-order Cumulant Spectrum, PSIMO system by the second approach are closer to the situation of real wavelet on account of their better and high-resolution Decon-profiles. It denotes that these methods of seismic wavelet estimation are more suitable for processing this area’s seismic data than others.