A method for terrain correction of potential field geophysical survey data measured above an examined medium having density and/or magnetization is described, using potential field data including but not limited to gravity and/or magnetic total field and/or vector and/or tensor data. The potential field sensors may measure the gravity and/or magnetic total field and/or vector and/or tensor data at least one receiving position with respect to the examined medium. The terrain of the examined medium may be described by a spatially variable analytic function of the material properties of the examined medium. The terrain response for at least one component of the measured potential field in at least one receiver location (potential field data) may be calculated using special form of surface integral over the terrain based on 3D analog of the Cauchy-type integrals. This surface integration ensures accurate representation of the terrain response.