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<p>Full waveform inversion (FWI) has achieved significant advances under isotropic assumptions. However, real subsurface media are often anisotropic, and vertically transversely isotropic (VTI) media are widely used in practice. Multi-parameter FWI in VTI media suffers from strong nonlinearity, parameter trade-offs, and cycle skipping. In this study, the optimal transport distance based on the Kantorovich–Rubinstein (KR) norm is introduced into multi-parameter FWI in VTI media. This approach improves robustness to time shifts of seismic data and enhances the convexity of the objective function, thereby mitigating cycle skipping. The computationally efficient pure qP-wave equation is used, and the corresponding adjoint-state equation and gradient expressions are derived. Radiation pattern analysis is used to reveal the sensitivity and trade-off characteristics of anisotropic parameters under different parameterizations, and to select an optimal parameterization <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left[{v}_{nmo},\eta ,\delta \right]\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="]" open="["> <msub> <mi>v</mi> <mrow> <mi mathvariant="italic">nmo</mi> </mrow> </msub> <mo>,</mo> <mi>η</mi> <mo>,</mo> <mi>δ</mi> </mfenced> </math></EquationSource> </InlineEquation> for inversion. Numerical experiments demonstrate that the proposed method reduces dependence on the initial model and improves both the accuracy and robustness of multi-parameter FWI in VTI media.</p>

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Multi-parameter full waveform inversion based on optimal transport distance in VTI media

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Shuo Wei,
  • Bingshou He,
  • Mingqian Wang,
  • Yuzhao Lin

摘要

Full waveform inversion (FWI) has achieved significant advances under isotropic assumptions. However, real subsurface media are often anisotropic, and vertically transversely isotropic (VTI) media are widely used in practice. Multi-parameter FWI in VTI media suffers from strong nonlinearity, parameter trade-offs, and cycle skipping. In this study, the optimal transport distance based on the Kantorovich–Rubinstein (KR) norm is introduced into multi-parameter FWI in VTI media. This approach improves robustness to time shifts of seismic data and enhances the convexity of the objective function, thereby mitigating cycle skipping. The computationally efficient pure qP-wave equation is used, and the corresponding adjoint-state equation and gradient expressions are derived. Radiation pattern analysis is used to reveal the sensitivity and trade-off characteristics of anisotropic parameters under different parameterizations, and to select an optimal parameterization \(\left[{v}_{nmo},\eta ,\delta \right]\) v nmo , η , δ for inversion. Numerical experiments demonstrate that the proposed method reduces dependence on the initial model and improves both the accuracy and robustness of multi-parameter FWI in VTI media.