Electromagnetic methods play a critical role in geothermal exploration due to their strong sensitivity to key system components, including heat sources, reservoirs, and caprocks. However, practical three-dimensional controlled-source electromagnetic (CSEM) inversion for geothermal targets remains computationally challenging because of the extremely high model dimensionality and the prohibitive cost of repeatedly solving large-scale linear systems within Gauss–Newton (GN) frameworks. These limitations restrict the application of high-resolution 3D CSEM inversion to real geothermal field data. To address this unresolved problem, we propose an efficient 3D CSEM Gauss–Newton inversion algorithm based on solution space dimension reduction (SSDR). The core novelty of the proposed approach lies in the integration of SSDR with a direct–iterative hybrid solver (DIHS), which reduces the effective degrees of freedom in the inversion model while preserving the accuracy required for forward and adjoint electromagnetic simulations. This strategy significantly improves computational efficiency without sacrificing inversion fidelity, thereby advancing the feasibility of high-resolution 3D CSEM inversion in complex geothermal settings. The accuracy, stability, and efficiency of the proposed algorithm are systematically validated through numerical experiments on layered and geothermal models. Furthermore, the method is applied to the three-dimensional inversion of field-based CSEM data from the Yingshan geothermal area, Hubei Province, China, demonstrating high reliability and practical effectiveness. By jointly interpreting inversion results from both magnetotelluric (MT) and CSEM datasets, the geothermal genesis pattern of the study area is analyzed and a conceptual geothermal genetic model is established. These results provide important technical support for geothermal resource exploration and development, and illustrate how the proposed method advances the state of the art in 3D electromagnetic inversion for geothermal applications.
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