面波频散能量谱计算方法

面波频散能量谱成像精度是近地表横波速度计算的重要影响因素，有效提取面波频散曲线是后续反演地层结构及介质物性参数的重要环节。文中论述了τ-p变换法（τ为垂直波慢度，p为水平波慢度）、高分辨率线性Radon变换法、频率分解法、相移法、f-k变换法（f为频率，k为波数）、SFK变换法和矢量波数变换法等7种不同面波频散能量谱计算方法的基本原理；通过上述方法，对三层速度递增水平层状介质模型正演模拟合成Rayleigh波记录进行频散能量谱计算，并与理论频散曲线进行比较；根据所得频散能量谱，分析不同方法在数据处理过程中的特点与应用差异。结果表明：在提取频散曲线过程中，高分辨率线性Radon变换法和矢量波数变换法提取精度较高，f-k变换法提取精度最低，低频信息与高频信息无法有效识别；SFK变换法、矢量波数变换法、高分辨率线性Radon变换法抗噪性能强；τ-p变换法、f-k变换法、相移法计算速度优于其他方法。

Energy Spectrum Calculation of Surface Wave Dispersion

The energy spectrum precision of surface wave dispersion is an important factor affecting the acquisition of near-surface cross-wave velocity, and the effective extraction of surface wave dispersion curve is an important link of the subsequent inversion stratigraphic structures and medium physical parameters. The article discusses the basic principle of seven different wave dispersive energy spectrum methods, including τ-p transform, high resolution linear Radon transform, frequency decomposition, phase shift transform, frequency wavenumber transform, slant frequency wavenumber (SFK) transform, and vector wavenumber transformation methods. Through the modeling with a three-layer horizontal layered models with velocity increasing with depth and by using the above-mentioned methods to generate surface wave dispersive energy imaging, the energy spectra are calculated and compared with the theoretical dispersion curves. According to the obtained scattered energy spectra, the characteristics and applications of different methods in data processing are analyzed. The results show that the precision of dispersion curve extracted by high-resolution linear Radon transform and vector wavenumber transformation method is better; the precision of the dispersion curve extracted by frequency wavenumber transform is the lowest,  the low-frequency information and the high-frequency information cannot be effectively identified; the SFK transform and high resolution linear Radon transform have strong anti-noise performance; the calculation of τ-p transform, frequency wavenumber transform and phase shift transform is shorter than that using other methods.