Research Of Seismic Signal Spectral Decomposition Based On Sparse Inverse Algorithm

In seismic interpretation, spectral decomposition is widely applied in the area of reservoir characterization, detection of low-frequency shadow of hydrocarbons and reservoir prediction. The accuracy of seismic interpretation is influenced by the resolution of the result of spectral decomposition. To improve the resolution of spectral decomposition has a significant meaning for the research of hydrocarbon reservoirs. The conventional spectral decomposition methods cannot satisfy the accuracy and resolution that today’s seismic interpretation requires, each one of them has some flaws and may even cause wrong conclusions.The conventional spectral decomposition methods are the basics to study for higher resolution spectral decomposition. In this paper, we review some spectral decomposition methods that are mostly used, including Short Time Fourier Transform(STFT), Gabor Transform, Continuous Wavelet Transform(CWT), S Transform, Wigner-Ville Distribution(WVD), Matching Pursuit(MP) and Hilbert-Huang Transform(HHT). But these methods are limited on the aspect of time-frequency resolution. Seismic signal spectral decomposition based on sparse inverse algorithm as a new method, has its advantage on the aspect of resolution. On the purpose of improving the time resolution and frequency resolution of spectral decomposition result, an alternative way is to describe the signal spectral decomposition as an inverse problem. Through the seismic non-stationary convolution model, we can view the seismic signal as the convolution result by the dictionary of Ricker wavelets with central frequency and the pseudo-reflectivity sequences. Portniaguine et al.(2004)proposed that spectral decomposition can be described as a geophysics inverse problem and this problem is undetermined, thus it needs sparse inverse algorithms to constrain the results.In this paper, we will discuss the inverse problem and rephrase it as Basis Pursuit De-noising(BPDN) problem. And we introduce two sparse inverse algorithms(SPGL1 and FISTA) to solve this problem, they are the mathematical basics for the sparse inverse spectral decomposition which will be discussed later on.Then we put inverse spectral decomposition and Gabor Transform into comparison, the former one has much higher time-frequency resolution. And did some research on the real and imaginary part of time-frequency map and the time-frequency phase map. In the comparison of two sparse inverse algorithms, although they both have high time-frequency resolution, due to the difference on the way of building the wavelet dictionary, they have huge gap on the aspect of time consuming. In the process of FISTA spectral decomposition, we use CWT forward and inverse as operator to build the wavelet dictionary, it is proved that in this way we will get the result much quicker compared with SPGL1 spectral decomposition as SPGL1 spectral decomposition needs to build the wavelet dictionary as a matrix. And in this way, we can easily reconstruct the signal form time-frequency domain, then we can use this advantage to accomplish the goal of signal de-noising from the time-frequency domain, and the synthetic data has approved its feasibility.At last, we apply Gabor Transform, SPGL1 and FISTA to a single trace of real seismic data to obtain the time-frequency map, and the results show that these two sparse inverse algorithms have their advantages over the conventional methods when applied in practice. And another example of applying them in the real offshore seismic data has shown that the sparse inverse algorithms spectral decomposition has much higher time-frequency resolution and it can show the position of hydrocarbons clearly with more accurate results.