The Study On Forward Modeling And Inversion Based On The Anisotropic Theory In Fracture Media

Fracture is the important reservoir space and migration channel of special lithology reservoir(carbonate,shale,etc.),so the study on forward modeling and inversion in fracture media has great theoretical and realistic significance to deeply understanding geologic structure,explorating complex reservoir and predicting geologic hazard.This paper focus on forward modeling and inversion based on the anisotropic theory in fracture media.In this paper the precise and approximate expression of the fracture propagation seismic wave characteristics are proposed,qP wave equation finite difference numerical simulation algorithm is established and the inversion strategies and methods are studied in the fracture media.The parameterized model using the equivalent linear sliding theory is the theoretical basis of forward modeling and inverse.This paper using the equivalent theory and considering the existence of the underground pressure which makes the fissure medium is usually high and steep dip angle cracks,a single set fracture is equivalented to HTI medium,two groups of vertical orthogonal fracture can be equivalent to orthogonal anisotropic media and two groups of vertical oblique fracture can be equivalent to monoclinic anisotropic media.This paper also deduces the equivalent anisotropic parameter quantitative expression in the three kinds of different fracture media,then the weak anisotropy approximation is deduced based on the thomsen parameters which establish the foundation inversion theory.Seismic wave propagation characteristics(velocity and polarization direction)is the core of the research on forward modeling and inverse.Seismic wave propagation velocity is an important parameter for study seismic wave propagation law and description medium characteristics,mainly including the phase velocity and group velocity.This paper derived christoffel equation in fracture media based on generalized hook's law?motion differential equilibrium equation and geometric equation,besides got phase velocity and polarization direction in fracture media by eigenvalue and eigenvector solution method,moreover,got group velocity based on berryman equation.And using the thomsen parameters to obtain the weakly anisotropic approximation of phase velocity and the polarization direction.qP wave seismic forward modeling is the important methods to study of seismic wave propagation law and the response of seismic characteristics.This paper derived elastic wave equation in fracture media based on generalized hook's law?motion differential equilibrium equation and geometric equation,and derived q P wave equation in fracture media based on acoustic approximation assumption which the shear velocity is zero.q P wave differential equation can transform to difference equation based on finite difference method and derive PML boundary difference equation on the condition of completely matched layer boundary.Selects the layered model and sag model forward modeling was verified the precision and accuracy of the method,study the seismic response characteristics of different patterns fissure medium,study the different fracture parameters(crack density and crack length,crack width and crack fillings)relationship with the characteristics of seismic wavefield,and further using the reverse-time migration results to verify the correctness of the forward modeling method.Prestack seismic inversion is the effective method to obtain fracture parameters and cognitive ground crack.Based on the elastic wave phase velocity and the polarization direction,set up the incident wave and reflected wave and transmission wave of wave function,combined with the snell's law and medium interface stress and displacement boundary conditions in a row,the elasticity quasi Zoeppritz equation was bulided.According to the weakly anisotropic approximation with elastic interface similar approximate the reflection coefficient and analyzed the AVOZ characteristics of the fracture parameters.On the basis of using the least squares inversion strategy,based on the two azimuth seismic data to inverse the fracture parameters,and then the p-wave velocity in the background was inversed by waveform inversion method.