the use of stokes boundary values problems for the determination of the geoid requires that gravity anomalies (as boundary values) are known on geoid (as boundary). while, the gravity observations are measured on the earth's surface, to obtain boundary data, the surface gravity anomalies does are downward from the terrain onto geoid. for downward continuation (dwc) of surface gravity anoma...

one of the main steps within the geoid computation methodology without applying the stokes formula is downward continuation of the harmonic residual observables from the surface of the earth down to the surface of the reference ellipsoid. this downward continuation is done via the abel-poisson integral and its derivatives. this integral in which the unknowns, i.e. harmonic residual potential va...

the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the disturbing gravity observations are only available on the earth’s surface. downward contin...

in this paper we consider a petrovsky viscoelastic inverse source problem with memory term in the boundary condition. we obtain sufficient conditions on relaxation function and initial data for which the solutions of problem are asymptotically stable when the integral overdetermination tends to zero as time goes to infinity.