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>Return to Research
Multi-scale analysis of geophysical fields such as gravity, topography, and crustal deformation
My Ph.D. thesis (at MIT, under the supervision of Sean Solomon and Brad Hager) focused on the development and application of a multi-resolution (wavelet-like) perspective on the analysis of geodynamics problems. This particular effort developed a crude approach (analogous to a Gabor Transform, but with a frequency dependent window) for analyzing data on a sphere. More specifically, our approach focused on the case when the original data is provided as spherical harmonic coefficients. The challenge was to maintain some sense of spectral or scale-dependent information, while being able to discriminate processes affecting different regions. My bias is that it is key to stay in the spherical domain and not suffer all the pitfalls of projecting data into a local Cartesian space. Any adopted approach should not violate any sense of conservation of original information. The approach we developed included a Nyquist condition for dealing with truncated spherical harmonic data. We applied these spatio-spectral localization techniques to studies of topographic compensation on Venus (2, 3), Mars (14), and Earth (4).
More recently, we have begun to adopt a multi-resolution perspective in other aspects of our work. We are looking at wavelet-based temporal filtering of continuous GPS data as well as a multi-scale estimation of the surface strain field as constrained by GPS.
(Top) Free-air gravity in an oblique Mercator projection. (Middle) Gravity profiles along the great circle path shown above. (Bottom) RMS amplitude spectrogram of the free air gravity. The spectrogram is estimated using the full two-dimensional gravity field. We associate the spatially and spectrally concentrated signal at degrees 5-9 centered on Hudson Bay to be the result of incomplete post-glacial rebound. For more details, see ref 4.This multi-scale strain estimation is of interest since most approaches tend to mix the scales over which strain is estimated, thereby leading to results that can be difficult to interpret. At the same time, we want to estimate strain at the smallest scale allowable by local data distribution. A multi-scale strain estimator may also form the basis of an efficient “event” detector in regions with dense GPS networks such as in Japan, Taiwan, and the U.S.. 14 Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution, McGovern P. J., S. C. Solomon, D. E. Smith,M. T. Zuber, M. Simons, M. A. Wieczorek, R. J. Phillips, G. A. Neumann, O. Aharonson, and J. W. Head, J. Geophys. Res., 107 (E12), 5136, doi: 10, 1029/2002JE001854, 2002,; Correction, J. Geophys. Res.,109, E07007, doi:10.1029/2004JE002286, July 2004, [PDF]
4 Localization of the gravity field and the signature of glacial rebound, M. Simons and B. H. Hager, Nature, 390, 500-504, 1997. [PDF]
3 Localization of gravity and topography: Constraints on the tectonics and mantle dynamics of Venus, M. Simons, S. C. Solomon, and B. H. Hager, Geophys. J. Int., 131, 24-44, 1997.2 Global variations in the geoid/topography admittance of Venus, M. Simons, B. H. Hager, and S. C. Solomon, Science, 264, 798-803, 1994. [PDF]
Mark Simons' Paper Collection: Entire paper including figures are all made available online (within the bounds of copyright restrictions).
