Аннотация:A general approach to the construction of differential boundary conditions for vector fields satisfying the Helmholtz equation is proposed on the basis of the field expansion in multipole series and the application of annihilating operators to them. The resulting differential constraints can be used as boundary conditions
in solving external boundary value problems. Examples of their application to the solution of forward geoelectric problems in three-dimensionally inhomogeneous media are examined. Their use at a finite distance from
the source of an anomaly is shown to yield more accurate results than those obtained under the assumption that
the anomalous field at this distance vanishes. Another effect of their application is a substantial decrease in the
dimensions of the modeling domain and therefore in the time required to solve the forward problem. The “safe”
distance for using the Dirichlet-type boundary conditions is estimated