Continuous wavelet-like filter for a spherical surface and its application to localized admittance function on Mars

Physics of the Earth and Planetary Interiors

Volumn 135, Issue 1, 2003, Pages 1-16

  Kido, Motoyuki ^a   Yuen, David A ^b   Vincent, Alain P ^c  

^a JAPAN AGENCY FOR MARINE EARTH SCIENCE AND TECHNOLOGY   (Japan)

^b UNIVERSITY OF MINNESOTA   (United States)

^c UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Admittance; Bandpass filter; Martian gravity data; Wavelet

Indexed keywords

GRAVITY; MARS; TRANSFORM; WAVELET;

EID: 0037440439     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0031-9201(02)00176-0     Document Type: Article

References (56)

1. Antoine, J.-P., Jacques, L., Vandergheynst, P., in press. Wavelets on the sphere: implementation and approximation. Appl. Comput. Harmonic Anal.
2. Arkani-Hamed, J., 2000. Strength of Martian lithosphere beneath large volcanoes. J. Geophys. Res. 105, 26713-26732.
3. Barnett, D.M., Nimmo, F., 2002. Strength of faults on Mars from MOLA topography. Icarus 157 (1), 24-42.
4. Bergeron, S.Y., Vincent, A.P., Yuen, D.A., Tranchant, B.J.S., Tchong, C., 1999. Viewing seismic velocity anomalies with 3D continuous Gaussian wavelets. Geophys. Res. Lett. 26, 2311- 2314.
5. Bergeron, S.Y., Yuen, D.A., Vincent, A.P., 2000. Capabilities of 3D wavelet transforms to detect plume-like structures from seismic tomography. Geophys. Res. Lett. 27, 3433-3436.
6. Chiao, L.-Y., Kuo, B.Y., 2001. Multiscale seismic tomography. Geophys. J. Int. 145, 517-527.
7. Daugman, J.G., 1985. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. J. Opt. Soc. Am. A 2, 1160-1169.
8. Folland, G.B., 1989. Harmonic Analysis in Phase Space. Princeton University Press, Princeton, p. 288.
9. Forsyth, D.W., 1985. Subsurface loading and estimates of the flexural rigidity of continental lithosphere. J. Geophys. Res. 90, 12623-12632.
10. Freeden, W., Schreiner, M., 1995. Non-orthogonal expansions on the sphere. Math. Meth. Appl. Sci. 18, 83-120.
11. Freeden, W., Windheuser, U., 1996. Spherical wavelet transform and its discretization. Adv. Comput. Math. 5, 51-94.
12. Freeden, W., Windheuser, U., 1998. Combined spherical harmonic and wavelet expansion-a future concept in Earth's gravitational determination. Appl. Comput. Harmonic Anal. 4, 1-37.
13. Frey, H.V., Roark, J.H., Shockey, K.M., Frey, E.L., Sakimoto, S.E.H., 2002. Ancient lowlands on Mars. Geophys. Res. Lett. 29 No.10:10.1029/2001GL013832.
14. Gabor, D., 1946. Theory of Communication. J. IEEE (London) 93 III No. 26, 429-457.
15. Gibert, D., Hohlschneider, M., Le Mouel, J.-L., 1998. Wavelet analysis of the Chandler Wobble. J. Geophys. Res. 103, 27069- 27089.
16. Goldreich, P., Toomre, A., 1969. Some remarks on polar wandering. J. Geophys. Res. 74, 2555-2567.
17. Guyodo, Y., Gaillot, P., Channell, J.E.T., 2000. Wavelet analysis of relative geomagnetic paleointensity at ODP Site 983. Earth Planet. Sci. Lett. 184, 109-123.
18. Hartmann, W.K., 1993. Moons and Planets. Wordsworth, Belmont, CA, 510 pp.
19. Kaula, W.M., 1968. An Introduction to Planetary Physics. The Terrestrial Planets. John Wiley, NY.
20. Kumar, P., Foufoula-Georgiou, E., 1997. Wavelet analysis for geophysical applications. Rev. Geophys. 35, 385-412.
21. Lemoine, F.G., Smith, D.E., Rowlands, D.D., Zuber, M.T., Neumann, G.A., Chinn, D.S., Pavlis, D.E., 2001. An improved solution of the gravity field of Mars (GMM2B) from Mars Global Surveyor. J. Geophys. Res. 106, 23359-23376.
22. Lesur, V., Gubbins, D., 1999. Evaluation of fast spherical transforms for geophysical applications. Geophys. J. Int. 139, 547-555.
23. Li, T.-H.,1999. Multiscale representation and analysis of spherical data by spherical wavelets. SIAM J. Sci. Comput. 21, 924-953.
24. Malamud, B.D., Turcotte, D.L., 2001. Wavelet analyses of Mars polar topography. J. Geophys. Res. 106, 17498-17504.
25. Mallat, S., 1998. A Wavelet Tour of Signal Processing. Academic Press, Boston.
26. Matyska, C., Yuen, D.A., Breuer, D., Spohn, T., 1998. Symmetries of volcanic distributions on Mars and Earth and their mantle plume dynamics. J. Geophys. Res. 103, 28587-28597.
27. McGill, G.E., Dimitriou, A.M., 1990. Origin of the Martian global dichotomy by crustal thinning in the late Noachian or early Hesperian. J. Geophys. Res. 95, 12595-12605.
28. McGovern, P.J., Solomon, S.C., Smith, D.E., Zuber, M.T., Neumann, G.A., Head, J.W., 2000. Localized gravity/topography admittance on Mars. Lunar Planet. Sci. 31: abstract 1792.pdf.
29. McKenzie, D., Fairhead, D., 1997. Estimates of the effective elastic thickness of the continental lithosphere from Bouguer and free air gravity anomalies. J. Geophys. Res. 102, 27523-27552.
30. McKenzie, D., Barnett, D.N., Yuan, D.-N., 2002. The relationship between Martian gravity and topography. Earth Planet. Sci. Lett. 195, 1-16.
31. McNutt, M.K., Parker, R.L., 1978. Isostasy in Australia and the evolution of the compensation mechanism. Science 199, 773- 775.
32. Mohlenkamp, M.J., 1999. A fast transform for spherical harmonics. J. Fourier Anal. Appl. 5, 159-184.
33. Moreau, F., Gibert, D., Hohlschneider, M., Saraaco, G., 1999. Identification of sources of potential fields with the continuous wavelet transform: Basic theory. J. Geophys. Res. 104, 5003- 5013.
34. Narcowich, F.J., Ward, J.D., 1996. Nonstationary wavelets on the m-sphere for scattered data. Appl. Comput. Harmonic Anal. 3, 324-336.
35. Piromallo, C., Vincent, A.P., Yuen, D.A., Morelli, A., 2001. Dynamics of the transition zone under Europe inferred from wavelet cross-spectra of seismic tomography. Phys. Earth Planet. Inter. 125, 125-139.
36. Ricard, Y., Fleitout, L., Froidevaux, C., 1984. Geoid heights and lithospheric stresses for a dynamic Earth. Annal. Geophys. 2, 267-286.
37. Simons, F.J., Zuber, M.T., Korenaga, J., 2000. Isostatic response of the Australian lithosphere: estimation of effective elastic thickness and anisotropy using multitaper spectral analysis. J. Geophys. Res. 105, 19163-19184.
38. Simons, M., Solomon, S.C., Hager, B.H., 1997. Localization of gravity and topography: constraints on the tectonics and mantle dynamics of Venus. Geophys. J. Int. 131, 24-44.
39. Smith, D.E., Sjogren, W.L., Tyler, G.L., Balmino, G., Lemoine, F.G., Konopliv, A.S., 1999a. The gravity field of Mars: Results from Mars Global Surveyor. Science 286, 94-97.
40. Smith, D.E., Neumann, G., Ford, P, Arvidson, R.E., Guinness, E.A., Lavney, S.S., 1999b. Mars Global Surveyor Laser Altimeter Initial Experiment Gridded Data Record: NASA Planetary Data System, MGS-M-MOLA-5-IEGDR-L3-V1.0.
41. Smith, D.E., Zuber, M.T., Solomon, S.C., Phillips, R.J., Head, J.W., Garvin, J.B., Banerdt, W.B., Muhleman, D.O., Pettengill, G.H., Neumann, G.A., Lemoine, F.G., Abshire, J.B., Aharonson, O., Brown, C.D., Hauck, S.A., Ivanov, A.B., McGovern, P.J., Zwally, H.J., Duxbury, T.C., 1999c. The global topography of Mars and implications for surface evolution. Science 284, 1495-1503.
42. Smith, D., Neumann, G., Simpson, R., 2000. Mars Global Surveyor Laser Altimeter Initial Experiment Gridded Data Record: NASA Planetary Data System, MGS-M-MOLA-5-IEGDR-L3-V1.0.
43. Smith, D.E., Zuber, M.T., Frey, H.V., Garvin, J.B., Head, J.W., Muhleman, D.O., Pettengill, G.H., Phillips, R.J., Solomon, S.C., Zwally, H.J., Banerdt, W.B., Duxbury, T.C., Golombek, M.P., Lemoine, F.G., Neumann, G.A., Rowlands, D.D., Aharonson, O., Ford, P.G., Ivanov, A.B., McGovern, P.J., Abshire, J.B., Afzal, R.S., Sun, X., 2001. Mars Orbiter Laser Altimeter (MOLA): experiment summary after the first year of global mapping of Mars. J. Geophys. Res. 106, 23689-23722.
44. Solomon, S.C., 2002. An older face for Mars. Nature 418, 27-28.
45. Stacey, F.D., 1992. Physics of the Earth, Third ed. Brookfield Press, Brisbane, 427 pp.
46. Stuhne, G.R., Peltier, W.R., 1999. New icosahedral grid-point discretizations of the shallow water equations on the sphere. J. Comput. Phys. 148, 23-58.
47. Thomas, F.G., Allemand, P., 1993. Quantitative analysis of extensional tectonics of Tharsis bulge, Mars: Geodynamic implications. J. Geophys. Res. 98, 13097-13108.
48. Turcotte, D.L., Shcherbakov, R., Malamud, B.D., Kucinskas, A.B., in press. In the Martian crust also the Martian elastic lithosphere? J. Geophys. Res.
49. Vecsey, L., Matyska, C., 2001. Wavelet spectra and chaos in thermal convection modelling. Geophys. Res. Lett. 28, 395- 398.
50. Wieczorek, M.A., Phillips, R.J., 1998. Potential anomalies on a sphere: applications to the thickness of the lunar crust. J. Geophys. Res. 103, 1715-1724.
51. Yuan, D.-N., Sjogren, W.L., Konopliv, A.S., Kucinskas, A.B., 2001. Gravity field of Mars: a 75th degree and order model. J. Geophys. Res. 106, 23377-23401.
52. Yuen, D.A., Vincent, A.P., Kido, M., Vecsey, L., 2002. Geophysical applications of multidimensional filtering using wavelets. Pure Appl. Geophys. 159, 2285-2309.
53. Zhong, S., Zuber, M.T., 2001. Degree-1 mantle convection and the crustal dichotomy on Mars. Earth Planet. Sci. Lett. 189, 75- 84.
54. Zuber, M.T., Smith, D.E., Solomon, S.C., Muhleman, D.O., Head, J.W., Garvin, J.B., Abshire, J.B., Bufton, J.L., 1992. The Mars Observer Laser Altimeter investigation. J. Geophys. Res. 97, 7781-7798.
55. Zuber, M.T., Solomon, S.C., Phillips, R.J., Smith, D.E., Tyler, G.L., Aharonson, O., Balmino, G., Banerdt, W.B., Head, J.W., McGovern, C.L., Neumann, G.A., Rowlands, D.D., Zhong, S., 2000. Internal structure and early thermal evolution of Mars from Mars Global Surveyor topography and gravity. Science 287, 1788-1793.
56. Zuber, M.T., 2001. The crust and mantle of Mars. Nature 412, 220-227.