基于奇异值分解的岩溶区微动面波成像方法

    A microtremor surface wave imaging method for Karst areas based on singular value decomposition

    • 摘要: 在岩溶发育区采集的微动面波受复杂近地表条件影响,往往存在信噪比低、数据质量差的问题,制约了探测精度。为此,提出一种基于奇异值分解(SVD)的微动面波成像方法。该方法首先对互相关获取的单道虚源经验格林函数进行SVD重建,提取大奇异值信号重波场,有效压制噪声并提升面波信噪比;进而利用高信噪比重建信号构建虚源多道记录,通过F-K变换得到频散能量谱,其面波频散条带的分辨率和连续性得到显著改善;随后,从优化后的频散谱中提取频散曲线,并采用遗传算法与阻尼最小二乘联合反演策略,兼顾全局最优解与收敛效率,进一步提高成像精度;最终,整合研究区内所有测点的反演结果,构建二维横波速度剖面,揭示研究区地下结构特征及岩溶发育的空间展布规律。在某岩溶区的应用实例表明,该方法有效提升了岩溶区复杂近地表条件下的成像质量,为岩溶发育区的精细结构探测和地质解释提供了可靠的技术支撑。

       

      Abstract: The microtremor surface waves collected from karst areas, where near-surface conditions are complex, often show low signal-to-noise ratios (SNRs) and poor data quality, thus restricting the detection accuracy. Hence, this study proposed a microtremor surface wave imaging method based on singular value decomposition (SVD). First, the single-trace virtual-source empirical Green's function obtained by cross-correlation was reconstructed through SVD. The signal components corresponding to large singular values were extracted to reconstruct the wave field, thereby effectively suppressing the noise and improving the SNRs of surface waves. Second, the virtual-source multi-trace records were constructed using the reconstructed signal with high SNRs. The dispersion energy spectrum was derived through the F-K transform, obtaining significantly improved surface wave dispersion bands in terms of resolution and continuity. Third, the frequency dispersion curves were extracted from the optimized dispersion energy spectrum. The joint inversion strategy employing the genetic algorithm and damped least squares was used to further improve the imaging accuracy, considering the globally optimal solution and convergence efficiency. Fourth, by integrating the inversion results of all survey points in the study area, a two-dimensional shear wave velocity profile was constructed to reveal the underground structural characteristics and the spatial distribution of karsts in the study area. The practical application in a karst area demonstrates that the proposed method can effectively improve the imaging quality of the karst area with complex near-surface conditions, providing reliable technical support for the fine-scale structure detection and geological interpretation in karst areas.

       

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