基于多点样条型旅行时插值的射线追踪方法研究及应用

Research and application of ray tracing method based on multi-spline traveltime interpolation

  • 摘要: 地震波的走时和射线路径是地震数据处理中的关键参数,其计算的精度、效率和稳定性直接影响地震波成像精度和解析能力。然而,传统算法在计算效率和精度上存在不足。为此,提出了一种基于多点样条型旅行时插值(Multipoint Spline Traveltime Interpolation,MSTI)的射线追踪方法。通过理论计算分析,MSTI方法的走时曲线与理论走时曲线高度吻合,显著优于传统的线性插值(Linear Traveltime Interpolation,LTI)方法和抛物型插值(Parabola Traveltime Interpolation,PTI)方法。在数值模拟中,构建了均匀介质和垂向渐变速度模型,其结果表明:① 基于MSTI方法计算的走时更接近理论走时,即使使用较少的节点数,其计算精度也优于LTI方法;② 当单元边界插值节点数相同时,随着离散单元的细化,计算精度得到提升;③ 当离散单元大小固定时,增加节点数有助于快速提升MSTI方法的走时精度,而对LTI方法的精度提升影响较小;④ 在垂向渐变速度模型中,使用Snell定律计算的走时与理论走时更为接近,增加节点数使MSTI方法的计算精度显著提升,而LTI方法的计算精度提高趋于停滞。为进一步验证该方法的有效性,对比分析了不同异常体的反演结果,基于MSTI方法的层析成像技术能够精准定位不同异常体,显示出该方法具有一定的优越性。现场试验结果表明:基于MSTI方法的弯曲射线追踪2.5维层析成像算法反演速度异常区与回采实际揭露断层空间位置基本一致,为煤矿的安全高效生产提供了强有力的技术支持。

     

    Abstract: The traveltime and ray path of seismic waves are key parameters in seismic data processing, and the accuracy, efficiency and stability of their calculation directly affect the imaging accuracy and analytical capabilities of seismic waves. However, traditional algorithms exhibit deficiencies in computational efficiency and accuracy. To address these deficiencies, a ray tracing method based on Multipoint Spline Traveltime Interpolation (MSTI) is introduced. Theoretical calculations and analyses show that the traveltime curve obtained through the MSTI method closely matches the actual traveltime curve, significantly outperforming traditional approaches such as Linear Traveltime Interpolation (LTI) and Parabola Traveltime Interpolation (PTI). In numerical simulation, both uniform and vertical gradient velocity models are constructed. The results indicate that: ① The traveltime calculated using the MSTI method is closer to the theoretical traveltime, and even with fewer nodes, the computational accuracy surpasses that of the LTI method; ② When the number of interpolation nodes at the element boundaries is the same, calculation accuracy improves as the discrete elements are refined; ③ When the size of the discrete element is fixed, increasing the number of nodes significantly enhances the traveltime accuracy of the MSTI method, while the improvement in the LTI method accuracy is marginal; ④ In the vertical gradient velocity model, the traveltime calculated using Snell's law is closer to the theoretical traveltime, and increasing the number of nodes significantly improves the accuracy of the MSTI method, while the improvement in the LTI method accuracy tends to stagnate. To further verify validate the effectiveness of the MSTI method, a comparative analysis of inversion results for different anomalies is conducted. The tomographic imaging technique based on the MSTI method accurately locates different anomalies, demonstrating the method's superiority. Field test results indicate that the inversion of velocity anomalies using the 2.5D curved ray tracing tomographic imaging algorithm based on the MSTI method closely matches the spatial positions of the faults exposed during mining practice, providing robust technical support for the safe and efficient production of coal mines.

     

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