基于交叉梯度约束的地震初至纵波与瑞雷面波联合反演

本文提出了一种初至纵波（P波）与瑞雷面波的交叉梯度联合反演策略.通过对初至P波进行全波形反演可以获得近地表P波速度结构；通过对仅含瑞雷面波信息的地震数据转换到频率-波数域进行加窗振幅波形反演（Windowed-Amplitude Waveform Inversion，w-AWI）可获得近地表横波（S波）速度结构.在二者反演的目标函数中均加入P波速度和S波速度的交叉梯度作为正则化约束项，使得在反演过程中P波速度和S波速度相互制约，相互约束，从而实现对地震初至P波与瑞雷面波的联合反演.数值模拟结果表明交叉梯度联合反演可以提高S波速度反演分辨率，而P波速度反演结果并没有得到提高.实际资料的反演结果表明，交叉梯度联合反演能够获得更加可信的近地表速度结构.

Joint inversion of first arrival P waves and Rayleigh waves based on cross-gradient constraint

In seismic exploration, knowledge of the near-surface velocity can improve the construction of an accurate geological model. Until recently, most surface-wave inversion approaches assumed a layered model, which is not justified in a complex geological environment.#br#To overcome this 1D limitation, researchers have begun to explore the benefits of 2D waveform inversion of surface waves. Windowed-Amplitude waveform inversion is a replacement to classical Full Wave form Inversion (FWI), which has faster convergence, however, lower spatial resolution in the tomogram is deduced. To partly recover this lost resolution, we propose a joint inversion of first arrival P-wave data and Rayleigh wave data that uses the cross-product between the P-velocity and S-velocity gradients as a regularization term. First, the P-velocity model is inverted by the full waveform inversion method, in which the first arrivals are those of the refraction and direct arrivals. Then, the amplitude spectra of the surface waves in the frequency-wavenumber domain are inverted for the S-velocity model with a cross-product constraint. This constraint regularization insists that the S-velocity gradient is closely parallel to that of the P-velocity gradient. Results show that cross-product regularization provides a significant reduction in artifacts in the S-velocity tomogram. In this case the less robust inversion of surface waves is combined with high resolution P-wave tomography to achieve better spatial resolution of the S-wave velocity tomogram.