The fictitious compress recovery approach is introduced, which could be applied to the establishment of the Runge-Krarup theorem, the determination of the Bjerhammar's fictitious gravity anomaly, the solution of the "downward continuation" problem of the gravity field, the confirmation of the convergence of the spherical harmonic expansion series of the Earth's potential field, and the gravity field determination in three cases: gravitational potential case, gravitation case, and gravitational gradient case. Several tests using simulation experiments show that the fictitious compress recovery approach shows promise in physical geodesy applications.
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