Recent Developments in Inverse Problems - Abstract

Kontak, Max

New results on the numerical solution of the nonlinear inverse gravimetric problem

It is well-known, that the gravitational potential $V_mathcalE,rho$ of a body $mathcalEsubseteqmathbbR^3$, e.,g the Earth, with mass density $rho$ is given by [ V_mathcalE,rho = gamma int_mathcalE fracrho(x) x-cdot, mathrmdx, ] where $gamma$ denotes the gravitational constant. For a fixed set $mathcalE$, the operator $T_mathcalE: rho mapsto V_mathcalE,rho$ is linear and the emphlinear inverse gravimetric problem is known to be ill-posed, violating all three of Hadamard's conditions. Uniqueness of a solution can be guaranteed, i.,e. by assuming $Deltarho=0$, which is not reasonable from the geoscientific perspective. On the other hand, considering a fixed function $rho$ and assuming, that $mathcalE$ is star-shaped with respect to the origin, i.,e. $mathcalE(sigma) = rxi: 0leq r