Accurate Jacobian Matrix Using the Exact Zoeppritz Equations and Effects on the Inversion of Reservoir Properties in Porous Media

Liu, Xiaobo; Chen, Jingyi; Liu, Fuping; Wang, Anling; Zhao, Zhencong

doi:10.1007/s00024-018-1969-8

Cited by 5 publications

(3 citation statements)

References 35 publications

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“…Reflection and transmission of only P-wave incidence at an interface between two elastic media [11]. n is the normal direction.…”

Section: Figurementioning

confidence: 99%

“…To accurately invert the dry rock parameters, the most important step is to derive the Jacobian matrix (partial derivatives of PP and PS reflection coefficients with respect to dry rock moduli). Letting m j represent the unknown parameters K d1 , K d2 , µ d1 and µ d2 , the partial derivatives of the Zoeppritz equations with respect to m j can be expressed as Liu et al, [11] A…”

Section: The Partial Derivatives Of P-and S-wave Velocities With Respmentioning

confidence: 99%

“…The most widely used classical approximations are proposed by Aki-Richards and Shuey [7,8]. These classical approximations, however, are only valid for weak elastic contrasts and relatively small incidence angles [9][10][11]. Actually, there are many target zones that have strong elastic contrast interfaces or long-offset seismic data used.…”

Section: Introductionmentioning

confidence: 99%

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An Accurate Jacobian Matrix with Exact Zoeppritz for Elastic Moduli of Dry Rock

2019

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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.

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“…Reflection and transmission of only P-wave incidence at an interface between two elastic media [11]. n is the normal direction.…”

Section: Figurementioning

confidence: 99%

Section: The Partial Derivatives Of P-and S-wave Velocities With Respmentioning

confidence: 99%