Wavelet Estimate Based On Robust Adaptive Conjugate Gradient Algorithms

In seismic exploration, the deconvolution of seismic data, wave impedance inversion, AVO inversion, the establishment of the forward modeling works are dependent on the precision of seismic wavelet. In the actual process, the seismic wavelet is often unknown. We extracts the real wavelet through the existing seismic data. The accuracy of the estimated seismic wavelet will effect the result of seismic inversion and forward model, and the interpretation of the seismic data. Conventional wavelet extraction methods have the direct method, deterministic method and statistical method:the direct method is to use the detector directly extract seismic wavelet, determine method is under the condition that the logging data is known, stratum reflection coefficient is calculated from logging data, and then extracting the seismic wavelet according to the seismic convolution model, its advantage is that can directly obtain wavelet by logging data and seismic trace record, but larger dependent on the accuracy of well logging data;Statistical wavelet estimation method is only through seismic trace their second order or higher order statistical feature of the seismic trace to extract seismic wavelet, this method does not need log data, but need to make some assumptions to the underlying reflection coefficients and seismic wavelet.This article mainly discusses extracting wavelet from the logging and well seismic trace. In the condition of known well logging data, using well logging data to calculate the actual stratum reflection coefficient to determine the wavelet estimation. Thought about the seismic convolution model, we can understand the process of seismic record as, stratum reflection coefficient of dilute signals after wavelet filtering system to get the output signal which is the seismic records, and regard the wavelet estimation problem under convolution model as the system identification problem in adaptive signal processing, estimated the optimal wavelet from the perspective of the adaptive filtering algorithm. In adaptive algorithms, LMS algorithm has the characteristics of simple calculation, low complexity, but its convergence speed is slowly, RLS algorithm convergence speedly, but its computational complexity is higher, need larger storage space for matrix operations, and numerical instability. Conjugate gradient algorithm is a kind of between LMS and RLS algorithm, it has a convergence speed compare to RLS algorithm and computational complexity between LMS and RLS. Therefore, in this article, we choose conjugate gradient filter algorithms to study the seismic wavelet estimation problem.Through the study of existing wavelet estimation method, according to actual problem of wavelet estimate, put forward the corresponding solutions. For seismic wavelet length is uncertain, the reflection coefficient for the non gaussian sequence, using higher order accumulated amount is roughly judge wavelet length; because the data length is limited, we use the recursive block data model to improve convergence of the conjugate gradient algorithm and make the algorithm can convergent in the limited time iteration; Traditional wavelet estimation methods are often in the assumption of white and color background noise, because of the complex seismic environment and the existence of impulse noise, in view of the non-gaussian noise, we propose robust wavelet estimation methods combined with the M-estimation algorithm; Observetion the actual wave shape, wavelet energy concentration and there is a longer zero interval, here we regard wavelet as sparse signal or half-sparse signal, adding the sparse constraint to the objective function to improve algorithm performance and precision of the wavelet. Theoretical model of simulation and actual seismic data processing show that the proposed algorithm can effectively suppress gaussian and non-gaussian noise, fast and efficient to extract the accurate wavelet.