时间二阶积分波场的全波形反演

通过对波场的时间二阶积分运算以增强地震数据中的低频成分,提出了一种可有效减小对初始速度模型依赖性的地震数据全波形反演方法—时间二阶积分波场的全波形反演方法.根据散射理论中的散射波场传播方程,推导出时间二阶积分散射波场的传播方程,再利用一阶Born近似对时间二阶积分散射波场传播方程进行线性化.在时间二阶积分散射波场传播方程的基础上,利用散射波场反演地下散射源分布,再利用波场模拟的方法构建地下入射波场,然后根据时间二阶积分散射波场线性传播方程中散射波场与入射波场、速度扰动间的线性关系,应用类似偏移成像的公式得到速度扰动的估计,以此建立时间二阶积分波场的全波形迭代反演方法.最后把时间二阶积分波场的全波形反演结果作为常规全波形反演的初始模型可有效地减小地震波场全波形反演对初始模型的依赖性.应用于Marmousi模型的全频带合成数据和缺失4Hz以下频谱成分的缺低频合成数据验证所提出的全波形反演方法的正确性和有效性,数值试验显示缺失4Hz以下频谱成分数据的反演结果与全频带数据的反演结果没有明显差异.

Full waveform inversion of the second-order time integral wavefield

We proposed a new full waveform inversion (FWI) method, namely full waveform inversion of the second-order time integral wavefield, by enhancing low-frequency components of seismic data with a second-order time integration to seismic wavefield, which can efficiently reduce the initial model dependence of FWI. According to the propagation equation of scattering wavefield in scattering theory, we derived a propagation equation for the scattering wavefield with second-order time integral, and used the leading order Born approximation for the linearization to the propagation equation. Based on this equation, using the scattering wavefield to inverse the distribution of scattering sources in subsurface, and using wavefield modeling to construct the incident wavefield, and according to the linear relationship between the scattering wavefield and incident wavefield, velocity perturbation in the linear propagation equation for the scattering wavefield with second-order time integral, we applied a formula similar to the imaging formula of migration to estimate velocity perturbation, and established an iterative inversion method for the full waveform inversion of second-order integral wavefield. Applying the inversion result of full waveform inversion of second-order integral wavefield as the initial velocity model for the conventional FWI can efficiently reduce the initial model dependence of FWI. Numerical tests using synthetic data of the Marmousi model demonstrate the validity and feasibility of the proposed method. The final results of the new method can obtain much improved results than the conventional FWI. Furthermore, to test the independence to the seismic frequency-band, we used a low-cut source wavelet (cutting from 4Hz below) to generate the synthetic data. The inversion results by our new method show no appreciable difference from the full-band source results.