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Approximate equation for calculating P-wave traveltime in horizontally layered VTI media |
WEI Jian, SUN Xiang'e |
School of Electronics and Information, Yangtze University, Jingzhou, Hubei 434023, China |
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Abstract The calculation accuracy of P-wave traveltime equations based on the Taylor series is affected by the transverse isotropy medium with vertical symmetry axis(VTI). In order to improve this situation, a calculation method based on square processing and coefficient matching is proposed. In this method, the square processing is used to transform the traveltime equation of the non-square form based on the Taylor series into the square form containing high-order terms, and then the coefficient matching method is used to deal with the high-order terms of the traveltime square equation so that the highest order of the equation offset is the commonly used fourth order. Then, on the basis of simplifying the form of parameters and optimizing the traveltime square equation, a new coefficient y, which is related to the anisotropic parameter, is obtained. Finally, a fourth-order P-wave traveltime calculation method with y based on square processing and coefficient matching is formed. The experimental results based on the horizontally layered VTI medium model show that compared with the rational approximation method, the generalized moveout approximation method based on three rays, and the extended generalized moveout approximation method, this method has smaller errors, and the calculation ability at the far offset is improved to some extent, which provides more options for the applications based on traveltime equations.
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Received: 17 July 2022
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