Non-gaussian Inversion Method For Elastic Parameters Of Shale Reservoir

A large number of shale reservoir petrophysical research results at home and abroad show that the key indexes of reservoir prediction,such as total organic carbon content,brittleness,and mineral content,are closely related to elastic parameters such as shale density,Poisson's ratio,and Young's modulus.Based on the rock physical relationship,elastic parameters such as Poisson's ratio and Young's modulus can be obtained by joint calculation of the velocity and density of longitudinal and transverse waves.The core of the calculation of the key indicators of shale reservoirs is to accurately obtain the three parameters of vertical and horizontal wave velocity and density.Based on high-precision pre-stack seismic data,the simultaneous pre-stack seismic three-parameter(vertical and horizontal wave velocity and density)inversion is one of the effective ways to obtain the vertical and horizontal wave velocity and density of shale.The traditional pre-stack simultaneous three-parameter inversion algorithm is based on the assumption that the inversion parameters and the seismic data noise obey Gaussian distribution.This assumption basically satisfies the inversion of post-stack seismic data with high signal-to-noise.However,due to the low signal-to-noise of pre-stack seismic data,especially shale reservoirs with small changes in lithology differences,the assumption of Gaussian model and Gaussian noise are often difficult to meet the needs of actual elastic parameter inversion.To this end,this paper firstly analyzes the source of non-Gaussian characteristics in shale reservoir inversion based on logging data and actual seismic data,and then constructs reflection coefficients,noise,etc.that are subject to nonGaussian based on Bayesian inversion framework and generalized extreme value distribution theory.The distributed shale reservoir elastic parameter inversion equation finally uses the numerical model and actual data to verify the effectiveness and practicability of the method.The main work and contributions of the paper mainly include the following three aspects:1)Source analysis of non-Gaussian characteristics in pre-stack seismic inversion of shale reservoirs: based on the longitudinal wave velocity,shear wave velocity,density and actual seismic data measured by logging,and by means of skewness,kurtosis,histogram and normal probability graph,the reflection coefficient of shale reservoir and the non-Gaussian characteristics in actual seismic data are analyzed based on the theoretical basis of the Zoeppritz's equation.The analysis results show that the four measurement indexes of the pre-stack reflection coefficient of shale reservoirs have a typical non-Gaussian probability distribution with sharp peaks and thick tail(right tail);the statistical characteristics of the noise in the pre-stack seismic data of shale reservoirs are asymmetric and thick-tailed,which are characterized by typical non-gaussian distribution.2)Study on the inversion method of the elastic parameters of shale reservoir in which the seismic reflection coefficient of shale reservoir following the non-Gaussian distribution is only considered: based on the Bayesian inversion framework,this method uses the generalized extremum distribution to characterize the non-Gaussian characteristics of the pre-stack reflection coefficient of shale reservoirs,constructs the objective function of three parameters simultaneous inversion of shale reservoirs based on the Bayesian framework that follows the generalized extremum distribution,and uses the simulated anneal-particle swarm optimization algorithm to solve the generalized extremum distribution parameters.Both the model calculation and the inversion results of the actual seismic data prove that this method is stronger than the traditional threeparameter simultaneous inversion algorithm(reflection coefficients follow Gaussian distribution)to obtain the noise resistance of shale reservoir longitudinal wave velocity and density.3)Study on the inversion method of elastic parameters of shale reservoir in which the pre-stack seismic reflection coefficient and the noise in the pre-stack seismic data that obey the non-gaussian distribution are simultaneously considered:based on the same idea and related theory that only consider the non-Gaussian distribution of pre-stack seismic reflection coefficients of shale reservoirs,the objective function of threeparameter simultaneous inversion of the shale reservoir is constructed based on the Bayesian framework of generalized extremum distribution(both the pre-stack reflection coefficients and the pre-stack seismic data noise are subject to the generalized extremum distribution).The model trial calculation and the inversion results of actual seismic data verify the correctness of the method and the reliability of the algorithm.Compared with the previous algorithm,the inversion method of elastic parameters of shale reservoir in which the reflection coefficient and the noise that both obey non-Gaussian distribution in the pre-stack seismic data are considered simultaneously can gain higher precision of vertical and horizontal wave velocity,density,but weak robustness to noise.And the particle swarm optimization algorithm is used to solve the parameters of double generalized extremum distribution with low efficiency.