A new efficient random search algorithm is introduced for solving inversion problems in geophysical studies. The proposed algorithm is inherently a stochastic optimization method which is built on the concept of gradient descending and Lévy flights. Therefore, the algorithm is referred to as the Lévy gradient descent (L-GD). In which, the Lévy flights is a special class of random walk which consists of many short steps along with a few large steps. Such movements are observed in a varying range of fields, including animals’ foraging patterns, fluid dynamics, transport of light and so on. Meanwhile, the Lévy flights typically shows much higher speed in searching for sparsely located targets compared to the well-known Brownian walks, which make them preferable to drive random search algorithms. As shown in the paper, besides optimal solutions of the inverse problems, the L-GD algorithm could also produce estimations on the error distributions of the resultant model parameters. Following a detailed introduction of the methodology, parameter settings of the algorithm are discussed in length through statistical experiments. Subsequently, the proposed algorithm is evaluated using numeric tests and shows attracting properties of the global convergence and significant higher searching efficiency compared to commonly adopted stochastic optimization techniques in geophysical inversions. Moreover, the L-GD algorithm is applied to the inversions of gravity and seismic travel time data and has achieved the same accuracy as gradient-based optimization methods. Meanwhile, though error estimations generated by L-GD algorithm are essentially qualitative, they could still provide valuable information to help evaluating the resultant model parameters, which is of great importance for practical geophysical inversions.

提出了一种新的有效的随机搜索算法，用于解决地球物理研究中的反演问题。所提出的算法本质上是一种基于梯度下降和Lévy飞行概念的随机优化方法。因此，该算法称为Lévy梯度下降（L-GD）。其中，Lévy航班是一类特殊的随机行走，包括许多短步和几步大步。在各种领域都可以观察到这种运动，包括动物的觅食方式，流体动力学，光的传输等。同时，与众所周知的布朗步行相比，Lévy航班在寻找稀疏目标时通常表现出更高的速度，这使其更适合驱动随机搜索算法。如本文所示，除了反问题的最佳解，L-GD算法还可以对所得模型参数的误差分布进行估计。在详细介绍了该方法之后，将通过统计实验详细讨论算法的参数设置。随后，使用数值测试对提出的算法进行了评估，与地球物理反演中常用的随机优化技术相比，该算法显示出全局收敛的吸引性质和显着更高的搜索效率。此外，L-GD算法被应用于重力和地震历时数据的反演，并获得了与基于梯度的优化方法相同的精度。同时，尽管L-GD算法生成的误差估计本质上是定性的，