基于混合差分进化算法的地球物理线性反演

地球物理反问题线性化处理之后, 各种反演算法归结为对病态线性方程组的求解. 为了快速准确地计算出地球物理参数, 本文提出了一种全新的基于LSQR算法的混合差分进化算法(Hybrid Differential Evolution Algorithm, HDE). 该算法利用LSQR算法给出DE算法的初始种群, 提高DE算法的计算速度和稳定性. 在不同噪声水平下, 对四种正则化方法Tikhonov、TSVD、LSQR和HDE的反演结果进行详细比较. 理论模型和实际数据反演的结果都表明: 改进的HDE算法应用于地球物理反问题的求解是成功的: 反演结果与原设定模型具有较高的相关性, 在稳定性和准确性上较常规的反演算法都具有一定的优势; 而且不需要给定正则化参数, 具有更强的实用性.

Geophysical linear inversion based on hybrid differential evolution algorithm

After linearization of various geophysical inverse problems, all kinds of inversion algorithms are reduced to solve ill-conditioned linear systems. In order to estimate geophysical parameters rapidly and accurately, a new hybrid differential evolution (HDE) algorithm based on LSQR is proposed. Using LSQR to give the initial population, the computation speed and stability of original DE algorithm are improved greatly. Under different noise conditions, we make a detailed comparison among the inversion results computed by four kinds of regularization methods such as Tikhonov, TSVD, LSQR and HDE algorithm. The inversion results of theoretical models and the actual data show that the improved HDE algorithm for solving geophysical inverse problems is successful as they have high relevance with original models without regularization parameters; furthermore the new algorithm has more advantages in stability, accuracy and practicality than conventional ones.