A Stochastic Gauss–Newton Framework with Full-Data Line Search for Efficient 3D Magnetotelluric Inversion

3D magnetotelluric (MT) inversion based on the Gauss–Newton (GN) framework plays an important role in deep mineral exploration by imaging subsurface electrical conductivity structures. However, large-scale 3D MT inversion remains computationally expensive due to the high cost of sensitivity-matrix construction. To address this challenge, we develop a stochastic Gauss–Newton (SGN) framework that reduces computational cost through random data subsampling while preserving the practical convergence behavior of GN inversion. In the proposed framework, only a randomly selected subset of data is used to approximate the GN search direction. By exploiting a key property of MT forward modelling, namely that responses at all receivers are obtained simultaneously for each frequency, the line search is performed using the full dataset, ensuring stable convergence of the inversion process. The SGN framework is validated using both a synthetic multiblock model and a field dataset from the Akebasitao area in Xinjiang, China. The recovered models remain highly consistent with those obtained using conventional full-data Gauss–Newton inversion across a wide range of sampling ratios. For the synthetic example, reducing the sampling ratio from 100% to 10% decreases peak memory consumption from approximately 433 GB to 242 GB and reduces runtime from 86.8 h to 23.9 h while maintaining comparable inversion quality. Similar computational savings are achieved for the field-data inversion. The field application successfully recovers the major conductive structures along the margins of the intrusion that are associated with hydrothermal alteration and fluid activity, highlighting the capability of SGN to delineate geologically meaningful targets relevant to deep mineral exploration. These results demonstrate that SGN provides an efficient and scalable approach for large-scale 3D MT inversion.