Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods

We develop new efficient algorithms for a class of inverse problems gravimetry to recover an anomalous volume mass distribution (measure) in the sense that we design fast local level-set methods simultaneously reconstruct both unknown domain and varying density measure from modulus gravity force rather than itself. The equivalent-source principle gravitational potential forces us consider only measures form \begin{document}$ \mu = f\,\chi_{D} $\end{document}, where id="M2">\begin{document}$ f $\end{document} is function id="M3">\begin{document}$ D inside closed set id="M4">\begin{document}$ \bf{R}^n $\end{document}. Accordingly, various constraints are imposed upon so well-posedness theories can be developed corresponding problems, such as problem, domain-density problem. Starting uniqueness theorems derive gradient misfit functional enforce directional-independence constraint further introduce labeling into method geometrical domain; consequently, able given force. Our built localizing evolution around narrow band near zero accelerating numerical modeling by novel low-rank matrix multiplication. Numerical results demonstrate crucial solving problem will impactful on prospecting. To best our knowledge, inversion algorithm first since it based conditional theory