@Article{CiCP-10-4,
author = {},
title = {A Fast Local Level Set Method for Inverse Gravimetry},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {4},
pages = {1044--1070},
abstract = {<p style="text-align: justify;">We propose a fast local level set method for the inverse problem of gravimetry.
The theoretical foundation for our approach is based on the following uniqueness
result: if an open set D is star-shaped or x<sub>3</sub>-convex with respect to its center of gravity,
then its exterior potential uniquely determines the open set D. To achieve this
purpose constructively, the first challenge is how to parametrize this open set D as its
boundary may have a variety of possible shapes. To describe those different shapes we
propose to use a level-set function to parametrize the unknown boundary of this open
set. The second challenge is how to deal with the issue of partial data as gravimetric
measurements are only made on a part of a given reference domain Ω. To overcome
this difficulty, we propose a linear numerical continuation approach based on the single
layer representation to find potentials on the boundary of some artificial domain
containing the unknown set D. The third challenge is how to speed up the level set inversion
process. Based on some features of the underlying inverse gravimetry problem
such as the potential density being constant inside the unknown domain, we propose a
novel numerical approach which is able to take advantage of these features so that the
computational speed is accelerated by an order of magnitude. We carry out numerical
experiments for both two- and three-dimensional cases to demonstrate the effectiveness
of the new algorithm.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.100710.021210a},
url = {https://global-sci.com/article/80954/a-fast-local-level-set-method-for-inverse-gravimetry}
}