none 10.1190/geo2021-0768.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 137955356 5981 2025121211393883400 10.1190 2025-12-12T16:39:44Z 2022-06-12T07:17:32Z 1 Geophysics 0016-8033 1942-2156 09 01 2022 87 5 Shibo Xu Kyoto University 1 , Department of Civil and Earth Resources Engineering, Kyoto, Japan. shibo.xu@tansa.kumst.kyoto-u.ac.jp http://orcid.org/0000-0001-8570-3677 Alexey Stovas Norwegian University of Science and Technology 2 , Department of Geoscience and Petroleum, Trondheim, Norway. alexey.stovas@ntnu.no http://orcid.org/0000-0002-2294-9626 Xingguo Huang Jilin University 3 , College of Instrumentation and Electrical Engineering, Changchun, China. xingguohuang@jlu.edu.cn (corresponding author) http://orcid.org/0000-0001-9719-6297 ABSTRACT In seismic data processing, compensation for geometric spreading along the raypath is necessary. The accurate approximation of the relative geometric spreading is critical because the traveltime parameters in the approximation can be estimated from velocity analysis. Two approximation types (direct and indirect) are generalized based on the procedure to derive the explicit expression. We develop perturbation-based approximations of the relative geometric spreading for P and S waves with these two types in the elastic transversely isotropic media with a vertical symmetry axis (VTI). The rational approximation and the general moveout approximation counterparts are compared to verify the superiority of our approach. Our study compares the performance of direct and indirect approximations for optimal selection under different cases. In the numerical examples, we apply the error sensitivity in the layer depth, anellipticity value, and vertical velocity ratio. It is found that the P-wave case is much more accurate than the S-wave case, and the direct type obtains relatively higher accuracy than the indirect one. In addition, the perturbation coefficients for the acoustic VTI model are derived not only with a much simpler expression but also achieve a highly accurate result that is recommended for the P-wave seismic processing. 07 20 2022 09 01 2022 06 09 2022 C99 C109 Geophysical Computational Imaging and Instrumentation Group at Jilin University 1 10.1190/crossmark-policy library.seg.org true 2021-11-26 2022-05-20 2022-05-22 2022-07-20 Geophysical Computational Imaging and Instrumentation Group at Jilin University 10.1190/geo2021-0768.1 https://pubs.geoscienceworld.org/geophysics/article/87/5/C99/615722/The-approximation-for-relative-geometric-spreading https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/87/5/C99/5697859/geo-2021-0768.1.pdf https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/87/5/C99/5697859/geo-2021-0768.1.pdf https://pubs.geoscienceworld.org/geophysics/article/87/5/c99/615722/the-approximation-for-relative-geometric-spreading 0016-8033 Geophysics Abedi 85 5 C163 2020 10.1190/geo2020-0005.1 Rational approximation of P-wave kinematics — Part 1: Transversely isotropic media 0016-8033 Geophysics Abedi 86 3 C65 2021 10.1190/geo2020-0415.1 Large-offset P-wave traveltime in layered transversely isotropic media 0016-8033 Geophysics Abedi 86 6 C173 2021 10.1190/geo2021-0215.1 Approximations for traveltime, slope, curvature, and geometric spreading of elastic waves in layered transversely isotropic media Quantitative seismology: Theory and methods, vol. 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