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<p>Improving the accuracy of velocity analysis is crucial to ensure the precision of subsequent data processing and interpretation. Especially for seismic data containing multiples, extracting primary velocity information requires a high-resolution velocity spectrum. We propose a high-resolution hyperbolic Radon transform velocity analysis method based on nonconvex <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({L}_{{q}_{1}}-{L}_{{q}_{2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <msub> <mi>q</mi> <mn>1</mn> </msub> </msub> <mo>-</mo> <msub> <mi>L</mi> <msub> <mi>q</mi> <mn>2</mn> </msub> </msub> </mrow> </math></EquationSource> </InlineEquation> mixed regularization sparse inversion that can handle this problem. In this way, we improve the resolution of the velocity spectrum while eliminating the interference of multiples. To address the difficult problem of nonconvex optimization, we use an improved alternating direction method of multipliers algorithm approximation and provide the convergence condition. To study the stability of method, we analyzed the impact of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({q}_{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({q}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> on the results. And we compare the proposed method with the velocity curve picked manually, the traditional and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({L}_{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> regularization method, and the results of synthetic and actual data show the effectiveness of our proposed method.</p>

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Velocity Analysis Using High-resolution Hyperbolic Radon Transform with \({L}_{{q}_{1}}-{L}_{{q}_{2}}\) Regularization

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Qiuying Wu,
  • Bin Hu,
  • Cai Liu,
  • Junming Zhang

摘要

Improving the accuracy of velocity analysis is crucial to ensure the precision of subsequent data processing and interpretation. Especially for seismic data containing multiples, extracting primary velocity information requires a high-resolution velocity spectrum. We propose a high-resolution hyperbolic Radon transform velocity analysis method based on nonconvex \({L}_{{q}_{1}}-{L}_{{q}_{2}}\) L q 1 - L q 2 mixed regularization sparse inversion that can handle this problem. In this way, we improve the resolution of the velocity spectrum while eliminating the interference of multiples. To address the difficult problem of nonconvex optimization, we use an improved alternating direction method of multipliers algorithm approximation and provide the convergence condition. To study the stability of method, we analyzed the impact of \({q}_{1}\) q 1 and \({q}_{2}\) q 2 on the results. And we compare the proposed method with the velocity curve picked manually, the traditional and \({L}_{1}\) L 1 regularization method, and the results of synthetic and actual data show the effectiveness of our proposed method.