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<p>Full-waveform inversion (FWI) is a high-precision geophysical imaging method with significant applications in oil and gas exploration, deep structure detection, and other fields. However, Hessian-related uncertainty estimation in large-scale 3D problems has long been a key challenge for this method. In this study, based on a vector-version Square-Root Variable Metric (SRVM) algorithm, we apply it to the 3D elastic FWI by storing only one SRVM vector of the model size and one SRVM scalar per iteration. After completing the SRVM-based elastic FWI, we obtain the posterior covariance by sampling the inverse data-misfit Hessian from the stored SRVM vectors and scalars. To facilitate posterior analysis and sampling, we probe the stored SRVM vectors and scalars using a randomized singular value decomposition (SVD) method. Due to the involvement of millions of model parameters (<i>V</i><sub><i>p</i></sub> and <i>V</i><sub><i>s</i></sub> defined on every GLL point in 3D), this 3D SRVM-based elastic FWI and uncertainty estimation study was conducted on the Shaheen II supercomputing platform. The results demonstrate that the proposed method can effectively invert subsurface velocity structures and accurately characterize the uncertainty of inversion results in a modified 3D Marmousi model, providing important methodological support and technical references for the practical application of future large-scale 3D elastic FWI.</p>

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3D square-root variable-metric-based elastic full-waveform inversion and uncertainty estimation

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Qiancheng Liu,
  • Ling Chen

摘要

Full-waveform inversion (FWI) is a high-precision geophysical imaging method with significant applications in oil and gas exploration, deep structure detection, and other fields. However, Hessian-related uncertainty estimation in large-scale 3D problems has long been a key challenge for this method. In this study, based on a vector-version Square-Root Variable Metric (SRVM) algorithm, we apply it to the 3D elastic FWI by storing only one SRVM vector of the model size and one SRVM scalar per iteration. After completing the SRVM-based elastic FWI, we obtain the posterior covariance by sampling the inverse data-misfit Hessian from the stored SRVM vectors and scalars. To facilitate posterior analysis and sampling, we probe the stored SRVM vectors and scalars using a randomized singular value decomposition (SVD) method. Due to the involvement of millions of model parameters (Vp and Vs defined on every GLL point in 3D), this 3D SRVM-based elastic FWI and uncertainty estimation study was conducted on the Shaheen II supercomputing platform. The results demonstrate that the proposed method can effectively invert subsurface velocity structures and accurately characterize the uncertainty of inversion results in a modified 3D Marmousi model, providing important methodological support and technical references for the practical application of future large-scale 3D elastic FWI.