{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T09:37:34Z","timestamp":1791452254176,"version":"4.3.3"},"reference-count":53,"publisher":"Society of Exploration Geophysicists","issue":"1","content-domain":{"domain":["library.seg.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2015,1,1]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>We have developed a local level-set method for inverting 3D gravity-gradient data. To alleviate the inherent nonuniqueness of the inverse gradiometry problem, we assumed that a homogeneous density contrast distribution with the value of the density contrast specified a priori was supported on an unknown bounded domain D so that we may convert the original inverse problem into a domain inverse problem. Because the unknown domain D may take a variety of shapes, we parametrized the domain D by a level-set function implicitly so that the domain inverse problem was reduced to a nonlinear optimization problem for the level-set function. Because the convergence of the level-set algorithm relied heavily on initializing the level-set function to enclose the gravity center of a source body, we applied a weighted L1-regularization method to locate such a gravity center so that the level-set function can be properly initialized. To rapidly compute the gradient of the nonlinear functional arising in the level-set formulation, we made use of the fact that the Laplacian kernel in the gravity force relation decayed rapidly off the diagonal so that matrix-vector multiplications for evaluating the gradient can be accelerated significantly. We conducted extensive numerical experiments to test the performance and effectiveness of the new method.<\/jats:p>","DOI":"10.1190\/geo2014-0188.1","type":"journal-article","created":{"date-parts":[[2015,1,2]],"date-time":"2015-01-02T02:13:36Z","timestamp":1420164816000},"page":"G35-G51","update-policy":"https:\/\/doi.org\/10.1190\/crossmark-policy","source":"Crossref","is-referenced-by-count":35,"title":["A local level-set method for 3D inversion of gravity-gradient data"],"prefix":"10.1190","volume":"80","author":[{"given":"Wangtao","family":"Lu","sequence":"first","affiliation":[{"name":"Michigan State University 1 , Department of Mathematics, East Lansing, Michigan, . E-mail: wangtaol@math.msu.edu ; qian@math.msu.edu .","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianliang","family":"Qian","sequence":"additional","affiliation":[{"name":"Michigan State University 1 , Department of Mathematics, East Lansing, Michigan, . 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