Methodologies Of Prestack Seismic Inversion For Cracked Media Based On Effective Medium Theory

The cracks are the important storage spaces and migration channels for hydrocarbon bearing carbonate and unconventioanal(tight oil and gas,shale oil and gas,etc.)reservoirs.The description of underground cracked media can be used to guide the exploration and development of cracked reservoirs.The effective medium theory(EMT)is the key to the characterization of cracked media using the seismic data,and an aligned inhomogeneous cracked medium can be equivalent to a homogeneously anisotropic medium wehn the crack length and spacing is much smaller than the seismic wavelength.Therefore,the elastic properties of a microscopic heterogeneous cracked medium can be studied through an equivalent macroscopic homogeneously anisotropic medium.Based on the EMT of cracked media,this paper focuses on three kinds of crack-induced static,quasi-static,and dynamic seismic anisotropic theory,and corresponding methodologies of prestack seismic inversion for cracked media.We intend to realize the inversion and prediction of crack characteristic parameters,providing the support of reasonable geophysical data for the exploration and development of cracked reservoirs.Based on the Schoenberg's static linear-slip theory(LST),the PP-wave weak-anisotropy(WA)reflection coefficients in cracke-induced static anisotropic media are derived,which establish the quantitative analytical relationship between the characteristic parameters of cracked media and the seismic response characteristics of single or multiple sets of cracks.Using the proposed parameterization of crakc quasi-weaknesses,the WA azimuthal elastic impedance(AEI)equations are also derived.We finally develop the iterative AEI inversion with the contrained regularizations under the Bayesian framework,and implement the inversion prediction of crack strength and orientation,as well as the description of fluids filling in cracks.Combining the low-frequency anisotropic Gassmann's equation with the crack-induced static LST,we consider the fluid flow effect between cracks and matrix pores,and derive the PP-wave WA reflection coefficients in cracke-induced quasi-static anisotropic media,establishing the quantitative relationship between cracked parameters and seismic response.In addition,we develop the iterative azimuthal amplitude variation with angle of incidence(AVA)inversion with the contrained regularizations under the Bayesian framework,and finally realize the inversion for the fluid indicator and crack characteristic parameters.Integrating the complex anisotropic Gassmann's equation and the modified Schonenberg's LST,we consider both the background intrinsic attenuration and crack-induced attenuration,and derive the PP-wave WA reflection coefficients and AEI equations in cracke-induced dynamic anisotropic media,which build the quantitative relationship between the dynamic characteristic parameters of cracks and the seismic response characteristics.Then an iterative Bayesian attunation AEI inversion method is proposed,and the fluid indicator,crack characteristic parameters and attenuative parameters are reasnonably estimated.