Traditional approaches of using dispersion curves for S-wave velocity reconstruction have limitations, principally, the 1D-layered model assumption and the automatic/manual picking of dispersion curves. At the same time, conventional full-waveform inversion (FWI) can easily converge to a non-global minimum when applied directly to complicated surface waves. Alternatively, the recently introduced wave equation dispersion spectrum inversion method can avoid these limitations, by applying the adjoint state method on the dispersion spectra of the observed and predicted data and utilizing the local similarity objective function to depress cycle skipping. We apply the wave equation dispersion spectrum inversion to three real datasets of different scales: tens of meters scale active-source data for estimating shallow targets, tens of kilometers scale ambient noise data for reservoir characterization and a continental-scale seismic array data for imaging the crust and uppermost mantle. We use these three open datasets from exploration to crustal scale seismology to demonstrate the effectiveness of the inversion method. The dispersion spectrum inversion method adapts well to the different-scale data without any special tuning. The main benefits of the proposed method over traditional methods are that (1) it can handle lateral variations; (2) it avoids direct picking dispersion curves; (3) it utilizes both the fundamental and higher modes of Rayleigh waves, and (4) the inversion can be solved using gradient-based local optimizations. Compared to the conventional 1D inversion, the dispersion spectrum inversion requires more computational cost since it requires solving the 2D/3D elastic wave equation in each iteration. A good match between the observed and predicted dispersion spectra also leads to a reasonably good match between the observed and predicted waveforms, though the inversion does not aim to match the waveforms.

使用频散曲线进行 S 波速度重建的传统方法存在局限性，主要是一维分层模型假设和频散曲线的自动/手动选取。同时，当直接应用于复杂的表面波时，传统的全波形反演 (FWI) 可以很容易地收敛到非全局最小值。或者，最近引入的波动方程色散谱反演方法可以避免这些限制，通过对观测和预测数据的色散谱应用伴随状态方法，并利用局部相似性目标函数来抑制循环跳跃。我们将波动方程色散谱反演应用于三个不同尺度的真实数据集：用于估计浅层目标的数十米尺度的活动源数据，用于储层表征的数十公里尺度环境噪声数据和用于对地壳和最上地幔进行成像的大陆尺度地震阵列数据。我们使用这三个从勘探到地壳尺度地震学的开放数据集来证明反演方法的有效性。色散谱反演方法可以很好地适应不同尺度的数据，无需任何特殊的调谐。与传统方法相比，所提出的方法的主要优点是（1）它可以处理横向变化；(2)避免了直接拾取色散曲线；(3) 它利用了瑞利波的基模和高模，以及 (4) 可以使用基于梯度的局部优化来解决反演问题。与传统的一维反演相比，色散谱反演需要更多的计算成本，因为它需要在每次迭代中求解 2D/3D 弹性波方程。观察到的和预测的色散光谱之间的良好匹配也会导致观察到的和预测的波形之间相当好的匹配，尽管反演的目的不是匹配波形。