Like other geophysical inversions, gravity and magnetic inversions can produce severe ambiguous solutions. Therefore, special constraints must be introduced in the process of inversion so as to obtain a unique and stable interpretation. In3Dcase, the situation is worse in that the solution is more ambiguous and the combination of constraints is more difficult. The application of nonlinear inversion makes the interpretation more stable and the introduction of constraints easier than previous linear methods. In addition, the difficulties caused by nonlinear methods, such as the high dimensional searching and the low computation speed, can be tackled and well solved by special pertinent skills. After improvement the application of 3Dinversion will surely be more practical than before.
［1］ Backus G E,Gilbert F. Numerical application of a formalism for geophysical inverse problems［J］. Geophys J Roy Astr Soc, 1967,13:247-276.
［2］ Backus G E,Gilbert F. The resolving power of gross earth data［J］. GeophysJ Roy AstrSoc, 1968,16:169-205.
［3］ Parker R L. Best bounds on density and depth from gavity data［J］.Geophysics, 1974,39:644-649.
［4］ Parker R L. The theory of ideal bodies for gravity interpreta tion［J］. Geophys J Roy Astr Soc, 1975,42:315-334.
［5］ Huestis S P, Parker R L. Bounding the thickness of oceanic magnetized layer［J］. J Geophys Res, 1977,82:5293-5303.
［6］ Ander M E, Huestis S P. Gravity ideal bodies［J］. Geophysics, 1987,52: 1265- 1278.
［7］ Hoed A E,Kennard R W. Ridge regression: Biased estimation for nonorthogonal problems［J］. Technometrics, 1970,12: 55 -67.
［8］ Lanczos C. Linear differential operators［R］ . D Van Nostrand Co,1961.
［9］ Medeiros W E,Silva J B C,Loures L G C L. Symmetric and di rectionally smooth gravity inversion［A］. 62nd Annual Interna tional Meeting［C］. Tulsa:SEG, 1992,529-532.
［10］ Li Y,Oldenburg D W. 3-D inversion of magnetic data［J］. Geophysics, 1996,61:394-408.
［11］ Silva J B C,Medeiros W E,Barbosa V C F. Potential field inver sion: Choosing the appropriate technique to solve a geological problem［J］. Geophysics, 2001,66: 511 - 520.
［12］ Li Y,Oldenburg D W. 3-D inversion of gravity data［J］. Geophysics, 1998,63:109-119.
［13］ Pilkington M. 3-D magnetic imaging using conjugate gradients［J］. Geophysics, 1997,62:1132- 1142.
［14］ Guillen A, Menichetti V. Gravity and magnetic inversion with minimization of a specific functional ［J］. Geophysics, 1984,49,1354-1364.
［15］ Mottl J,Mottlova L. Solution of the inverse gravimetric prob lem with the aid of integer linear programming［J］. Geoexploration, 1972,10: 53 - 62.
［16］ Barbosa V C F,Silva J B C. Generalized compact gravity inver sion［J］. Geophysics, 1994,59:57-68.
［17］ Barbosa V C F,Silva J B C,Medeiros W E. Gravity inversion of basement relief using approximate equality constraints onde pths［J］. Geophysics, 1997,62:1745- 1757.
［18］ Barbosa V C F,Silva J B C,Medeiros W E. Stable inversion of gravity anomalies of sedimentary basins with nonsmooth base ment reliefs and arbitrary density contrast variations［J］. Geo-physics, 1999,64: 754- 764.
［19］ Barbosa V C F,Silva J B C,Medeiros W E. Gravity inversion of a discontinuous relief stabilized by weighted smoothness con sraints on depths［J］. Geophysics, 1997,62: 1429- 1438.
［20］ Bear G W, Al-Shukri H J, Rudman A J. Linear inversion of gravity data for 3-D density distributions［J］. Geophysics, 1995,60:1354-1364.
［21］ Silva J B C. Mapping and depth ordering of residual gravity sources［J］. Geophysics, 1993,58:1408- 1416.
［22］ Braile L W, Keller G R, Peeples W J. Inversion of gravity dar af or two-dimensional density distributions［J］. J Geophys Res, 1974,79,2017-2021.
［23］ Camacho A G, Montesinos F G, Vieira R. Gravity inversion by means of growing bodies［J］. Geophysics,2000,65:95-101.
［24］ Chavez R E,Garland G D. Linear inversion of gravity data using the spectral expansion method［J］. Geophysics, 1985,50:820-824.
［25］ Cordell L. Potential-field sounding using Eulers homogeneity equations and Zidarov bubbling［J］. Geophysics, 1994,59:902-908.
［26］ Fedi M,Rapolla A. 3-D inversion of gravity and magnetic data with depth resolution［J］. Geophysics, 1999,64: 452- 460.
［27］ Last B J,Kubik K. Compact gravity inversion［J］. Geophysics, 1983,48:713-721.
［28］ Leao J W D,Silva J B C. Discrete linear transformations of po tential-field data［J］. Geophysics, 1989, 54, 497- 507.
［29］ Leao J W D, Menezes P T L, Beltrao J F,et al. Gravity inver sion of basement relief constrainted by the knowledged of depth at isolated points［J］. Geophysics, 1996,61: 1702- 1714.
［30］ Lee T, Biehler S. Inversion modeling of gravity with prismatic mass bodies［J］. Geophysics, 1991,56: 1365- 1376.
［31］ Medeiros W E,Silva J B C. Geophysical inversion using approx ing equality constraints ［J ］ . Geophysics, 1996, 61:1678 -1688.
［32］ ene R M. 1986, Gravity inversion using open, reject, and"shape to the anomaly" fill criteria［J］. Geophysics, 1986, 51:988-994.
［33］ Rechardson R M, MacInnes S C. The inversion of gravity data into three-dimensional polyhedral models［J］. J Geophys Res,1989,94:7555-7562.
［34］ Safon C, Vasseur G,Cuer M. Some applications of linear pro gramming to the inverse gravity problem ［J］. Geophysics,1977,42:1215-1229.
［35］ Silva J B C, Hohmann,G W. Nonlinear magnetic inversion u sing a random search method［J］. Geophysics,1983,48: 1645-1658.
［36］ Silva J B C, Hohmann G W. Airborne magnetic susceptibility mapping［J］. Expl Geophys, 1984,15: 1 - 13.
［37］ Vigneresse J L. Damped and constrained least-squares method with application to gravity interpretation［J］. J Geophys, 1978,45:17-28.
［38］ Zidarov D,Zhelev Z. On obtaining a family of bodied with iden tical exterior fields-method of bubbling ［D］. Geophys Prosp,1970,18:14-33.
