Abstract
Seismic velocities are related to the solid matrices and the pore fluids. The bulk and shear moduli of dry rock are the primary parameters to characterize solid matrices. Amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA) is the most used inversion method to discriminate lithology in hydrocarbon reservoirs. The bulk and shear moduli of dry rock, however, cannot be inverted directly using seismic data and the conventional AVO/AVA inversions. The most important step to accurately invert these dry rock parameters is to derive the Jacobian matrix. The combination of exact Zoeppritz and Biot–Gassmann equations makes it possible to directly calculate the partial derivatives of seismic reflectivities (PP-and PS-waves) with respect to dry rock moduli. During this research, we successfully derive the accurate partial derivatives of the exact Zoeppritz equations with respect to bulk and shear moduli of dry rock. The characteristics of these partial derivatives are investigated in the numerical examples. Additionally, we compare the partial derivatives using this proposed algorithm with the classical Shuey and Aki–Richards approximations. The results show that this derived Jacobian matrix is more accurate and versatile. It can be used further in the conventional AVO/AVA inversions to invert bulk and shear moduli of dry rock directly.
Highlights
IntroductionThe amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA)
The amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA)inverts from the measured amplitudes of seismic reflectivities to the rock properties [1,2,3]
We propose to combine the exact Zoeppritz equations with the Biot–Gassmann equations and derive the accurate Jacobian matrix for inverting dry rock moduli directly without any simplifications
Summary
The amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA). The best way to get an accurate elastic moduli of dry rock from seismic data is to use AVO/AVA inversion with exact Zeoppritz equations. The most difficult part of AVO/AVA inversion based on the exact Zoeppritz equations, is to obtain the accurate Jacobian matrix (partial derivatives of the reflection coefficients with respect to dry rock moduli) [34,35]. We propose to combine the exact Zoeppritz equations with the Biot–Gassmann equations and derive the accurate Jacobian matrix for inverting dry rock moduli directly without any simplifications. We derive the accurate partial derivatives of reflection coefficients with respect to dry rock parameters (bulk and shear moduli) through combining the exact Zoeppritz equations and the. We compare the partial derivatives and their errors using this proposed method with those from the classical Aki–Richards and Shuey approximations
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