Research On Spectral Decomposition Method Of Thin Layer Based On Basis Pursuit

With the deepening of oil and gas exploration and development,subtle oil and gas reservoirs have gradually become the focus of exploration.The sand bodies of these reservoirs are thin,narrow and small,and are mostly under seismic resolution,it is difficult to characterize the spatial distribution of narrow channel in thin interbed reflection wave,which leads to the difficulty of effective exploration and development in this kind of reservoirs.Spectral decomposition based on Basis Pursuit is an effective method to analyze the time-frequency response characteristics of seismic signals in both time-domain and frequency-domain,it is very suitable for the analysis of time-frequency response characteristics and variation rules of thin layer and thin interlayer,and the over-complete dictionary construction is the core and key of the decomposition method,on the basis of previous research,this paper makes some exploration and practice.This article first considers the changes in the main frequency of seismic wavelet excitation,the polarity and magnitude of the reflection coefficient,and investigates the effect of the thin-layer top and bottom reflection coefficient parity decomposition on the resolution limit of the single-frequency dictionary spectrum inversion,and whether it is suitable for promotion to the spectral decomposition method based on multi-frequency dictionary.The study found that the spectrum inversion method based on the reflection coefficient parity decomposition not only has a large amount of calculation,but also has limited ability to improve the resolution of the spectrum inversion,which is not suitable for popularization and application to the spectrum decomposition method.Based on the principle of Basis Pursuit,this paper implements two spectral decomposition methods based on the real Ricker wavelet dictionary and the complex Ricker wavelet dictionary.Compared with the complex Ricker wavelet dictionary spectral decomposition method,the real Ricker wavelet dictionary spectral decomposition method has higher time resolution,but the frequency resolution is relatively low.In order to improve the above two methods,this paper proposes a dictionary based on impulse response spectral decomposition method.This method uses wave equation forward modeling to obtain single-interface reflected pulses as dictionary atoms,translates along the main diagonal of the square matrix to construct a convolution matrix,and arranges the convolute on matrices with different dominant frequencies in sequence to form an impulse response dictionary.The spectral decomposition method based on impulse response dictionary not only has higher time resolution,but also the frequency focus is improved by 3times.This paper uses the spectral decomposition method based on the impulse response dictionary to carry out the research on the time-frequency response characteristics of single sand layers,equal thickness thin interbeds,and cyclic thin interbeds.The top and bottom interface of the layer is separable on the time-frequency diagram,which can indicate the existence of a single sand layer;as the thickness of the interbedded single layer of equal thickness increases,the time spectrum gradually shows a discrete distribution of equal frequency with slightly higher head and tail energy cluster frequencies;When the interlayer is thin,the frequency spectrum is distributed in discrete strips,with the frequency characteristics of thin rise and thick fall.The top interface of independent different deposition units has obvious time-frequency characteristics that are different from those inside the deposition unit,and the time-frequency characteristics are relatively stable,which is helpful for the identification of a single thin layer on the top interface of the thin interlayer.When the number of interlayers is large,the thickness of the single layer is large,the time frequency diagram of the thin interlayer of equal thickness and the cyclic thin interlayer clearly shows the internal structure characteristics of the thin interlayer and the change of the thickness of the single layer;and the thin layers of different thickness intervals,etc.Thick and thin interlayers and cyclic thin interlayers have different morphological characteristics,which are helpful for the qualitative interpretation and division of different types of thin interlayers,and are not affected by random changes in the thickness of small layers,reflection coefficients and high-frequency noise,and have good stability.Using the high-precision time-frequency spectrum obtained based on the impulse response dictionary spectrum decomposition method,the time thickness and instantaneous frequency of a single thin layer,a single layer of equal thickness and thin interlayers are extracted,and it is found that the two have a good linear relationship in the coordinate system?~2-1/f_p~2.The peak frequency is used to predict the thickness of a thin sand layer and a single-layer sand body of equal thicknes.In summary,the spectral decomposition method based on the impulse response dictionary has higher time resolution and better frequency focusing characteristics,which can better show the time-frequency variation of thin layers and the internal structural characteristics of various thin interlayers,which is beneficial to thin layers qualitative division of equivalent thin layer and quantitative prediction of thickness.