Thin-bed Reflectivity Inversion Based On Sparse Optimization

Improving the resolution of seismic data has been a very important research direction in the field of geophysical exploration, and the prediction of thin layers has become a hot research topic. Thin-bed reflectivity inversion is a recently developed effective method which could identify fine thin layers. Based on seismic data Fourier transform with windows to obtain frequency and domain information of seismic data inversion reflectivity. In the frequency domain, high resolution time domain reflectivity can be obtained, The effective identification of thin reservoir can be realized by this method.This paper for thin-layer reflectivity inversion method carried out a series of studies, in-depth study of the theory of thin bed reflectivity inversion, A relatively complete inversion algorithm processes is established. The main work and achievements include:(1) The seismic convolution model is studied, and the seismic wavelet, reflectivity and seismic record are discussed in detail. The time and frequency domain representation of the model and the principle of the Fourier transform in the inversion of seismic records are discussed in the paper.(2) The definition of seismic thin layer under the different resolution limit criterion is discussed, the effect of the seismic response and the influence of the odd and even parts of reflectivity on the resolution in inversion is studied.(3) Method of extracting statistical wavelet is studied, focuses on two methods wavelet extraction, the constant phase wavelet extraction and minimum phase wavelet extraction. This paper presents a flowchart of the algorithm and uses theoretical models and real data to verify the correctness of the algorithm.(4) The objective function of the inversion of thin layer reflectivity is derived. The objective function of two simple reflectivity and the objective function of multiple reflectivity are derived.Finally, the inversion process of thin layer reflectivity is presented(5) Sparse optimization algorithm in thin layer reflectivity inversion is studied, and several typical inversion optimization algorithms are discussed. Focus on the basis pursuit de-noising algorithm, the principle and algorithm flow are presented.(6) Through a variety of theoretical model and the real data test, verify the correctness of the proposed algorithm and the inversion effect, Finally the effect of noise on the inversion is tested.