Accurate interpretation of magnetic anomalies relies heavily on reduction- to- the- pole (RTP), component conversion, and tensor transformation. However, these processes often encounter instability issues in low- latitude regions, particularly near the magnetic equator. This study introduces a novel approach based on the equivalent source method to address this challenge. Our method performs RTP, component conversion, and tensor transformation of magnetic anomalies over curved surfaces in low- latitude regions. The proposed method leverages the physical relationship between the potential field and its source, employs parallel computation for the kernel function matrix, and establishes a system of linear equations. To enhance stability, we incorporate regularized sensitivity matrix weighting constraints into the objective function. The conjugate gradient method is then used to solve the objective function minimization problem, yielding the equivalent source physical property distribution. These results are subsequently substituted into relevant formulae to reconstruct or convert magnetic anomaly components and tensors, producing stable and highly accurate RTP, component, and tensor transformation results for any surface. Synthetic model tests demonstrate that this method achieves high computational accuracy for surface- observed magnetic anomalies in low- latitude regions, as well as its robustness against noise. Practical application to magnetic anomaly data from the Magur Islands study area, located at the boundary of the Caroline Plate and the Pacific Plate, has yielded highly satisfactory results.