走时层析成像的迭代Tikhonov正则化反演研究

Study of travel time tomography by iterative Tikhonov regularization inversion

针对反问题求解常遇到不适定的困难,采用奇异值分析的方法探讨了层析成像反演方程的不适定特征,研究了利用迭代Tikhonov正则化方法求解二维走时层析成像问题.该方法是一种拟线性化的反演算法,采用 L曲线法确定最优正则参数,拟定了四个有效的反问题迭代收敛准则,得到在残差范数和解的范数之间取最优折衷的解.核心异常数值化模型的计算结果表明,该方法比传统的联合迭代重建算法(SIRT)收敛快、精度高.

Ill-posed problem is the bottleneck to solution of inversion. The singular value decomposition (SVD) technique was applied to analyze the characteristic of inversion equations. The iterative Tikhonov regularization method was studied to solve 2D acoustic travel time tomography. It was a quasi-linear inversion algorithm, and the L-curve method was proposed for finding the optimal regularization parameter to avoid aimless random trial calculations. Four convergence criteria were also suggested for guiding the inversion iterations. The tomography results of the numerical simulation model with an abnormal core showed that the solutions had optimal balance between the solution norm and the corresponding residual norm. Compared with the conventional simultaneous iterative reconstruction techniques (SIRTs), the iterative Tikhonov regularization method has better precision and convergence efficiency.