Research On VMD-based Homomorphic Deconvolution Method

In seismic exploration,obtaining high-resolution seismic data is of great significance for the development of oil and gas reservoirs.Deconvolution is a commonly used method in seismic data processing.It aims to improve the resolution of seismic data by compressing the seismic wavelets,extracting the sequence of reflection coefficients,and broadening the frequency band of seismic data.Various deconvolution methods have certain restrictions when used,for example,assuming the minimum phase of the wavelet,the known wavelet,the sparse reflection coefficient.Later,a homomorphic deconvolution method has been proposed,which can be applied to any wavelet unnecessary to be known in advance,but affected by the noise,the wavelet obtained by the homomorphic deconvolution method has poor stability,and the reflection coefficient and the wavelet are aliased seriously in the same state domain.Aiming at how to better separate the wavelet and reflection coefficient in the homomorphic domain and obtain high-resolution seismic data,a method of variational mode decomposition in the homomorphic domain is proposed to improve the homomorphic deconvolution.This paper first introduces the principle of zero-phase homomorphic deconvolution and statistical homomorphic deconvolution,and explains their application defects in practical processing.Aiming at the problems of homomorphic deconvolution,the idea of using modal decomposition to separate reflection coefficient and wavelet separation is proposed.The paper also introduces the principles of each modal decomposition method,including empirical mode decomposition(EMD),set empirical mode decomposition(EEMD),complete set empirical mode decomposition(CEEMD),and variational mode decomposition(VMD).The advantages of the variational mode decomposition method are verified by analog signal experiments.The paper introduces the principle of homomorphic deconvolution method based on VMD in detail,and analyzes each step in detail through theoretical model data.In order to verify the applicability of this method,the seismic sequence is synthesized by mixing phase wavelet,minimum phase wavelet and time-varying wavelet,and the noise of different intensity is added to the single track recording.The results show that the algorithm has better resistance.The noise decomposing method,which can adapt to the data deconvolution in the case of time-varying wavelets,is a deconvolution method suitable for any wavelet.Further analysis of the actual data processing shows that the algorithm significantly improves the resolution of seismic data and verifies the applicability of the homomorphic deconvolution method based on VMD.The paper further discusses the influence of key parameters in VMD processing on the processing effect.Aiming at the problem that the VMD can not directly determine the number of decomposition layers,an algorithm for determining the number of decomposition layers by using the instantaneous frequency mean of each component is proposed.The homomorphic deconvolution method based on VMD achieves the purpose of effectively separating wavelet and reflection coefficient sequences by using VMD to decompose the homomorphic spectrum of seismic records.In the experiments of theoretical and practical data,good processing results have been achieved,which is an effective algorithm for improving resolution.