Deep groundwater exploration in hard rock terrains is critical in regions where deep aquifers may offer long-term water security amidst an increasing scarcity. However, such exploration is globally challenged by geological complexity and the limitations of traditional investigative techniques. Accurate estimation of hydraulic parameters, particularly permeability (k), is essential for effective groundwater management and future resource planning. Conventional borehole-based methods for measuring k are invasive, costly, time-consuming, and limited to sparse, point-scale observations, making them inadequate for characterizing deep and heterogeneous aquifer systems. Geophysical methods offer a promising non-invasive alternative, enabling broader spatial coverage with reduced surface disturbance. Previous empirical geophysical approaches, such as vertical electrical sounding (VES), are generally restricted to shallow depths (< 200 m), relatively homogeneous geological settings, and one-dimensional interpretations. This study demonstrates, for the first time, the use of controlled-source audio-frequency magnetotellurics (CSAMT) to estimate two- and three-dimensional k distributions to depths exceeding 1 km in crystalline and sedimentary terrains. The method relies on an empirical resistivity-permeability relationship calibrated using 116 core samples from six boreholes (0-200 m). While the specific equation derived in this study is site-specific to the Jinji area and should not be directly transferred elsewhere, the broader methodology, integrating CSAMT resistivity with local borehole calibration, offers a transferable framework for k estimation in other complex geological settings. The results show that CSAMT, when calibrated with borehole data, can reliably capture deep subsurface variability and produce spatially continuous hydrogeological models in hard rock terrains. While CSAMT inversion is inherently ill-posed, the incorporation of ground-truth data significantly enhances model robustness and interpretability. By reducing dependence on extensive drilling, this approach represents a significant advancement in deep groundwater exploration. It provides a scalable methodology for sustainable groundwater resource management, while emphasizing the need for local calibration in any new application.