Joint inversion of self-potential and active-source electrical data constrained by a Gaussian mixture model prior for detecting water-bearing anomalies in tunnels

Water-bearing fractured zones, dissolution fractures and infilled low resistivity bodies ahead of tunnel faces generally produce low resistivity anomalies and self-potential (SP) volumetric source strength responses. However, the restricted observation space in tunnels and the limited sensitivity of a single physical field make it difficult for single-field inversion to jointly constrain anomaly location, extent and multi-property relationships. This study proposes a Gaussian mixture model (GMM)-constrained joint inversion method for tunnel SP and active-source electrical data. Resistivity and SP volumetric source strength are parameterized on a common discretized grid. A GMM prior is introduced to describe the statistical classes of different geological units in the multi-property parameter space, and a joint objective function is constructed by integrating active-source electrical data fitting, SP data fitting, multi-property class constraints and spatial regularization. The inverse problem is solved through class probability updating and Gauss-Newton iterations. Numerical experiments show that the method identifies water-bearing anomalies at different distances and scales and recovers their locations, main extents and multi-property responses. Application to the Qinhe No. 2 Tunnel further shows that the interpreted water-bearing structures agree with water-rich fractured zones and local water inflow revealed by subsequent excavation. These results demonstrate that the proposed method provides a feasible approach for refined identification of water-bearing anomalies in tunnels using multi-property statistical prior constraints.