Gradient and smoothness regularization operators for geophysical inversion on unstructured meshes

Geophysical Journal International

Volumn 195, Issue 1, 2013, Pages 330-341

  Lelièvre, Peter G ^a   Farquharson, Colin G ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Gravity anomalies and Earth structure; Inverse theory; Magnetic anomalies: modelling and interpretation

Indexed keywords

GEOLOGICAL INFORMATION; GRAVITY ANOMALIES AND EARTH STRUCTURES; INVERSE THEORY; LINEAR SYSTEM OF EQUATIONS; MAGNETIC ANOMALIES: MODELLING AND INTERPRETATIONS; REGULARIZATION SCHEMES; STRUCTURAL INFORMATION; STRUCTURAL ORIENTATIONS;

GEOPHYSICS; INVERSE PROBLEMS; LINEAR SYSTEMS;

STRUCTURAL GEOLOGY;

DATA INTERPRETATION; GRADIENT ANALYSIS; GRAVITY ANOMALY; INVERSE ANALYSIS; MAGNETIC ANOMALY; NUMERICAL MODEL; PARAMETERIZATION; SMOOTHING; SPATIAL ANALYSIS;

EID: 84885706974     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1093/gji/ggt255     Document Type: Article

References (52)

1. Bodin, T., Sambridge, M., Rawlinson, N. & Arroucau, P., 2012. Transdimensional tomography with unknown data noise, Geophys. J. Int., 189, 1536-1556.
2. Bosch, M. & McGaughey, J., 2001. Joint inversion of gravity and magnetic data under lithologic constraints, Leading Edge, 20, 877-881.
3. Boschi, L. & Dziewonski, A.M., 1999. High- and low-resolution images of the earth's mantle: implications of different approaches to tomographic modeling, J. geophys. Res., 104(B11), 25 567-25 594.
4. Burgess, D.A. & Giles, M.B., 1997. Renumbering unstructured grids to improve the performance of codes on hierarhical memory machines, Adv. Eng. Softw., 28, 189-201.
5. Davis, K. & Li, Y., 2011. Fast solution of geophysical inversion using adaptive mesh, space-filling curves and wavelet compression, Geophys. J. Int., 185, 157-166.
6. Doetsch, J., Linde, N., Pessognelli, M., Green, A.G. & Günther, T., 2012. Constraining 3-D electrical resistance tomography with GPR reflection data for improved aquifer characterization, J. appl. Geophys., 78, 68-76.
7. Farquharson, C.G., 2008. Constructing piecewise-constant models in multidimensional minimum-structure inversions, Geophysics, 73(1), K1-K9.
8. Farquharson, C.G. & Oldenburg, D.W., 1998. Non-linear inversions using generalmeasures of data misfit and model structure, Geophys. J. Int., 134, 213-227.
9. Farquharson, C.G., Ash, M.R. & Miller, H.G., 2008. Geologically constrained gravity inversion for the Voisey's Bay ovoid deposit, Leading Edge, 27(1), 64-69.
10. Fregoso, E. & Gallardo, L.A., 2009. Cross-gradients joint 3D inversion with applications to gravity and magnetic data, Geophysics, 74(4), L31-L42.
11. Gallardo, L.A. & Meju, M.A., 2004. Joint two-dimensional DC resistivity and seismic travel time inversion with cross-gradients constraints, J. geophys. Res., 109, B03311, doi:10.1029/2003JB002716.
12. Greaves, D.M. & Borthwick, A.G.L., 1999. Hierarchical tree-based finite element mesh generation, Int. J. Numer. Methods Eng., 45, 447-471.
13. Günther, T., Rücker, C. & Spitzer, K., 2006. Three-dimensional modelling and inversion of DC resistivity data incorporating topography-II. Inversion, Geophys. J. Int., 166, 506-517.
14. Haber, E., Heldmann, S.&Ascher, U., 2007. Adaptive finite volume method for distributed non-smooth parameter identification, Inverse Probl., 23, 1659-1676.
15. Hermann, V., Käser, M. & Castro, C.E., 2011. Non-conforming hybrid meshes for efficient 2-D wave propagation using the Discontinuous Galerkin Method, Geophys. J. Int., 184, 746-758.
16. Krotkiewski, M. & Dabrowski, M., 2011. High-performance unstructured 3D modeling on modern clusters with thousands of cpus, in European Geosciences Union General Assembly, Vienna, Austria, Vol. 13, p. 6798.
17. Lelièvre, P.G.&Oldenburg,D.W., 2009.Acomprehensive study of including structural orientation information in geophysical inversions, Geophys. J. Int., 178, 623-637.
18. Lelièvre, P.G., Farquharson, C.G. & Hurich, C.A., 2011a. Computing firstarrival seismic traveltimes on unstructured 3D tetrahedral grids using the fast marching method, Geophys. J. Int., 184(2), 885-896.
19. Lelièvre, P.G., Farquharson, C.G. & Hurich, C.A., 2011b. Inversion of firstarrival seismic traveltimes without rays, implemented on unstructured grids, Geophys. J. Int., 185(2), 749-763.
20. Li,Y.&Oldenburg,D.W., 1996. 3-D inversion of magnetic data, Geophysics, 61(2), 394-408.
21. Li, Y. & Oldenburg, D.W., 2000. Joint inversion of surface and threecomponent borehole magnetic data, Geophysics, 65(2), 540-552.
22. Li, Y. & Oldenburg, D.W., 2003. Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method, Geophys. J. Int., 152, 251-265.
23. Nolet, G. & Montelli, R., 2005. Optimal parameterization of tomographic models, Geophys. J. Int., 161, 365-372.
24. Okabe, M., 1979. Analytic expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies, Geophysics, 44(4), 730-741.
25. Oliker, L., Li, X., Heber, G. & Biswas, R., 2000. Ordering unstructured meshes for sparse matrix computations on leading parallel systems, in Proceedings of the 7th International Workshop on Solving Irregularly Structured Problems in Parallel, Cancun, Mexico.
26. Owen, S.J., 1998. A survey of unstructured mesh generation technology, in International Meshing Roundtable, Dearborn, MI, pp. 239-267.
27. Peter, D. et al., 2011. Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes, Geophys. J. Int., 186, 721-739.
28. Piggott, M.D., Gorman, G.J., Pain, C.C., Allison, P.A., Candy, A.S., Martin, B.T. & Wells, M.R., 2008. A new computational framework for multiscale ocean modelling based on adapting unstructured meshes, Int. J. Numer. Methods Fluids, 56, 1003-1015.
29. Rüger, A. & Hale, D., 2006. Meshing for velocity modeling and ray tracing in complex velocity fields, Geophysics, 71(1), U1-U11.
30. Sambridge, M. & Faletič, R., 2003. Adaptive whole Earth tomography, Geochem. Geophys. Geosyst., 4(3), 1022, doi:10.1029/2001GC000213.
31. Sambridge, M. & Gudmundsson, O., 1998. Tomographic systems of equations with irregular cells, J. geophys. Res., 103(B1), 773-781.
32. Sambridge, M. & Rawlinson, N., 2005. Seismic tomography with irregular meshes, in Seismic Earth: Array Analysis of Broadband Seismograms, Vol. 157 of Geophysical Monography Series, pp. 49-65, eds Levander, A. & Nolet, G., American Geophysical Union.
33. Samet, H., 1984. The quadree and related hierarchical data structures, Comput. Surv., 16(2), 187-260.
34. Schaefer, J.F., Boschi, L. & Kissling, E., 2011. Adaptively parametrized surface wave tomography: methodology and a new model of the european upper mantle, Geophys. J. Int., 186, 1431-1453.
35. Schmid, D.W., Dabrowski, M. & Krotkiewski, M., 2008. Evolution of large amplitude 3d fold patterns: a FEM study, Phys. Earth planet. Inter., 171, 400-408.
36. Sethian, J.A., 1996. A fast marching level set method for monotonically advancing fronts, Proc. Natl. Acad. Sci. USA, 93, 1591-1595.
37. Sethian, J.A. & Vladimirsky, A., 2000. Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes, Proc. Natl. Acad. Sci. USA, 97(11), 5699-5703.
38. Shewchuk, J.R., 1996. Triangle: engineering a 2D quality mesh generator and delaunay triangulator, in Applied Computational Geometry: Towards Geometric Engineering,Vol. 1148 of Lecture Notes in Computer Science, pp. 203-222, eds Lin, M.C. & Manocha, D., Springer.
39. Shewchuk, J.R., 2002. Delaunay refinement algorithms for triangular mesh generation, Comput. Geom., Theory Appl., 22(1-3), 21-74.
40. Shewchuk, J.R., 2003. Triangle: a two-dimensional quality mesh generator and delaunay triangulator. Available at: http://www.cs.cmu.edu/ {ogonek}quake/triangle.html. Last accessed April 2013.
41. Si, H., Fuhrmann, J. & Gärtner, K., 2010. Boundary conforming Delaunay mesh generation, Comput. Math. Math. Phys., 50(1), 38-53.
42. Si, H., 2007. Tetgen: a quality tetrahedral mesh generator and a 3d delaunay triangulator. Available at: http://tetgen.berlios.de. Last accessed April 2013.
43. Si, H., 2008a. Three dimensional boundary conforming Delaunay mesh generation, PhD thesis, Technische Universität Berlin.
44. Si, H., 2008b. Adaptive tetrahedral mesh generation by constrained Delaunay refinement, Int. J. Numer. Methods Eng., 75(7), 856-880.
45. Si, H., 2010. Constrained Delaunay tetrahedral mesh generation and refinement, Finite Elem. Anal. Des., 46(1-2), 33-46.
46. Spakman, W. & Bijwaard, H., 2001. Optimization of cell parameterizations for tomographic inverse problems, Pure appl. Geophys., 158, 1401-1423.
47. Stenerud, V.R., Lie, K. & Kippe, V., 2009. Generalized travel-time inversion on unstructured grids, J. Petrol. Sci. Eng., 65, 175-187.
48. Tikhotsky, S. & Achauer, U., 2008. Inversion of controlled-source seismic tomography and gravity data with the self-adaptive wavelet parametrization of velocities and interfaces, Geophys. J. Int., 172, 619-630.
49. Williams, N.C., 2008. Geologically-constrained UBC-GIF gravity and magnetic inversions with examples from the Agnew-Wiluna greenstone belt,Western Australia, PhD thesis, University of British Columbia.
50. Wilson, C., 2009. Modelling multiple-material flows on adaptive unstructured meshes, PhD thesis, Imperial College London.
51. Wycisk, P.,Hubert, T., Gossel,W.&Neumann, C., 2009. High-resolution 3D spatial modelling of complex geological structures for an environmental risk assessment of abundant mining and industrial megasites, Comput. Geosci., 35, 165-182.
52. Zhou, M., Sahni, O., Shephard,M.S., Carothers, C.D. & Jansen, K.E., 2010. Adjacency-based data reordering algorithm for acceleration of finite element computations, Sci. Program., 18, 107-123.