基于混合快速共轭梯度法的有限差分对比源反演

Finite-difference contrast source inversion based on hybrid fast conjugate gradient method

有限差分对比源反演(FDCSI)是一种解决逆散射问题的方法,该方法在反演中背景模型保持不变,只进行一次全正演计算,减少了计算量。FDCSI将逆散射问题转化为优化问题,采用常规共轭梯度法优化目标泛函,但收敛速度较慢,影响反演效率。为此,在研究频率域声波方程有限差分对比源反演方法的基础上,提出了基于混合快速共轭梯度法的有限差分对比源反演方法,提高了反演效率。混合快速共轭梯度法是在快速迭代收缩阈值算法基础上改进得到的优化方法,该方法适用于有限差分对比源反演,在不增加单次迭代计算量的基础上加速目标泛函收敛,保证了对比源反演算法的快速稳定收敛。

Finite-difference contrast source inversion(FDCSI)is a solution to inverse scattering.The background model remains unchanged in the inversion,and forward modeling is performed for only one time;this reduced the workload of computation.FDCSI translates the problem of inverse scattering into a problem of optimization.The cost function is optimized using the conjugate gradient method,which suffers from small convergence rate and low efficiency.After the study of FDCSI using acoustic wave equation in frequency domain,we develop a FDCSI algorithm based on a hybrid fast conjugate gradient method to improve the efficiency of inversion.The hybrid fast conjugate gradient method is modified from the fast iterative shrinkage thresholding algorithm and is feasible for FDCSI.The cost function could converge quickly without more computation in a single iteration;this guarantees fast and robust convergence of FDCSI.