基于逆散射理论的地震波速度正则化反演

Regularized seismic velocity inversion based on inverse scattering theory

本文基于逆散射理论利用正则化有限差分对比源反演算法对地震波传播速度进行反演,该方法是基于波动方程的频率域波形反演算法,利用非线性共轭梯度法,通过最小化目标优化函数不断迭代更新速度模型.由于地球物理反演问题的病态性和不稳定性,通过基于反演参数总变差的正则化处理,使反演问题变为良性问题且算法具有较强的抗噪声干扰能力.反演过程中使用了频率-空间域9点差分正演算子以及PML吸收边界条件.与其他反演算法相比,由于背景模型在反演迭代过程中保持不变,可以避免在每次迭代过程中重新构造正演算子及矩阵分解等相关计算过程,使得该算法非常适合于大规模三维反演计算.此外,本文采用基于MPI的并行计算,进一步提高了反演计算的效率.二维CSEG模型反演结果表明该方法可以反演得到高分辨率的地震波速度重建结果,为地震勘探数据处理及解释提供准确的速度信息.

In this paper, the regularized finite difference contrast source inversion algorithm based on inverse scattering theory is utilized to invert the seismic velocity distribution in the underground medium, and this algorithm is a waveform inversion method in frequency domain based on wave equation. Velocity distribution is updated iteratively by minimizing the cost function using the nonlinear conjugate gradient method. The geophysical inversion problem has the characters of ill-posedness and instability, we handle this problem by adding an additional regularization item based on total variation of inversion parameter, making the inversion problem become a well-posed problem, and the algorithm has the ability of anti-noise interference. In the inversion process we use the frequency-space domain 9-point difference propagation operator under PML absorption boundary condition. Compared with other inversion algorithm, the construction of forward modeling operator and other matrix factorization calculation process can be avoided in each iterative step because the background medium remains unchanged throughout the inversion process, this makes the algorithm more suitable for large-scale three-dimensional inversion. In addition, the MPI parallel computation is applied, by which the efficiency of inversion process is improved greatly. The two-dimensional CSEG model inversion results show that this algorithm can obtain high resolution seismic velocity reconstruction, and provide an accurate velocity information for seismic data processing and interpretation.