A high-precision and fast algorithm for three-dimensional magnetic anomalies on undulating terrain

This study addresses the challenge of efficiently and accurately computing three-dimensional undulating surface magnetic field data, which has become increasingly difficult with the development of airborne magnetic survey technologies. To solve this problem, we propose a new computational method that is both efficient and highly precise. This method utilizes a planar three-dimensional fast-forward algorithm to calculate multiple planar magnetic fields at different heights, followed by local continuation combined with trilinear interpolation to achieve an accurate conversion from planar magnetic fields to undulating surface magnetic fields. This enables the completion of three-dimensional high-precision fast forward calculations that can then be applied to the inversion algorithm to calculate the distribution of the three-dimensional magnetization rate. Multiple model examples were tested to verify the accuracy and efficiency of the proposed method.