This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance of the random source from the correlation boundary measurement of the wave field. Compared with existing multi-frequency iterative approaches, our method is non-iterative and requires data at only a single frequency. As a result, the computational cost is significantly reduced. Furthermore, rigorous error analysis is conducted for the proposed method, which gives a quantitative error estimate. Numerical examples are presented to demonstrate effectiveness of the proposed method. Moreover, this method can to be directly applied to stochastic Maxwell equations.

翻译：本文研究了三维弹性波的随机源反问题，其中假设源项由加性白噪声驱动。提出了一种新的计算方法，用于根据波场的相关边界测量数据重构随机源的方差。与现有的多频率迭代方法相比，该方法无需迭代且仅需单一频率的数据，从而显著降低了计算成本。此外，对该方法进行了严格的误差分析，给出了定量的误差估计。数值算例验证了所提方法的有效性。该方法还可直接应用于随机麦克斯韦方程组。