The complexity of geochemical patterns in surficial media makes it necessary to consider the uncertainty when identifying geochemical anomalies in geochemical prospecting. In this contribution, the type of uncertainty related to spatial modelling of geochemical element distribution based on a limited number of observations is considered. A hybrid method combining the integrated nested Laplace approximation (INLA) and the stochastic partial differential equation (SPDE), commonly termed “INLA + SPDE”, is employed to simulate the spatial distribution of a geochemical variable. The local singularity analysis (LSA) is then performed on each realization simulated by INLA + SPDE. Based on the ensemble of local singularity exponent maps, geochemical anomalies can be evaluated by considering both the intensity and uncertainty of local singularity. A case study of processing 1:50, 000 stream sediment samples collected from the Fanshan district, Fujian province of China, further illustrates and validates the procedure, and enhance the knowledge of hydrothermal mineralization-related geochemical patterns in this region. The findings indicate that (1) INLA + SPDE offers a viable alternative to existing methods for simulating spatial distribution of geochemical element distributions, with advantages in quantifying uncertainties of model responses as well as model parameters, computational efficiency due to INLA, etc.; (2) it is an effective way to combine INLA + SPDE and LSA to facilitate identifying geochemical anomalies by considering both the intensity and uncertainty of geochemical patterns. The delineated geochemical anomalies based on the mean of local singularity exponents should be paid attention in further geochemical exploration, but those associated with high uncertainty should be taken care of and further verified by other evidences. The workflow that combines INLA + SPDE and LSA can also be used to obtain information from other types of geoscientific data, and can hence enrich the toolbox for further mineral exploration.

地表介质中地球化学模式的复杂性使得在地球化学勘探中识别地球化学异常时必须考虑不确定性。在此贡献中，考虑了基于有限数量的观测值的与地球化学元素分布的空间建模有关的不确定性类型。采用混合嵌套积分拉普拉斯近似（INLA）和随机偏微分方程（SPDE）的混合方法（通常称为“ INLA + SPDE”）来模拟地球化学变量的空间分布。然后，对通过INLA + SPDE模拟的每个实现执行局部奇异性分析（LSA）。基于局部奇异性指数图的整体，可以通过考虑局部奇异性的强度和不确定性来评估地球化学异常。以处理来自福建省繁山地区的1:50，000河流沉积物样本为例，进一步说明并验证了该程序，并增强了该地区与热液成矿有关的地球化学模式的知识。研究结果表明：（1）INLA + SPDE为模拟地球化学元素分布空间分布的现有方法提供了可行的替代方法，具有在量化模型响应以及模型参数，INLA引起的计算效率等不确定性方面的优势；（2）是结合考虑地球化学模式的强度和不确定性，将INLA + SPDE和LSA结合在一起以帮助识别地球化学异常的有效方法。在进一步的地球化学勘探中，应注意基于局部奇异指数平均值的划定地球化学异常，但应注意那些与高不确定性有关的异常，并由其他证据进一步验证。结合了INLA + SPDE和LSA的工作流也可以用于从其他类型的地球科学数据中获取信息，从而可以丰富工具箱以进行进一步的矿物勘探。