The development of a structural-parametric approach to constructing analytical approximations is considered. Within the framework of the new method, which includes modified S-approximations and determination of the integral curves of the vector field, a method is proposed for finding the analytic continuation of the field in the case of profile (route) geophysical measurements. The results of a mathematical experiment using real data on an anomalous gravitational field from data of marine areal gravimetric and airborne gravimetric route surveys are presented. It is shown that the proposed analysis algorithm is promising for finding analytic continuations of geopotential fields within a certain neighborhood of the measurement profile when a sufficient volume of areal data is lacking.