Journal of Conference Abstracts

Isotropic Spherical Wavelets and the Relaxation Spectrum of Postglacial Rebound

Ming Fang (fang@chandler.mit.edu) & Bradford Hager (brad@chandler.mit.edu)

¹Department of Earth Atmospheric & Planetary Sciences, Massachusetts Institute of Technology, Cambridge MA, 02139, U.S.A.

For three decades the relaxation spectrum estimated by McConnell (1968) using uplift data along Fennoscandian shorelines has stood out as the only available relaxation time vs. wavenumber spectrum for postglacial rebound. A noticeable feature of McConnell's spectrum is the nearly constant long wavelength asymptote, from wavenumbers corresponding to degree 25 down to the long-wavelength truncation corresponding to degree 5. The former Fennoscandian ice load was confined to a region approximately 1000 km in radius. It was questioned even by McConnell himself (1968) whether such a spatially localized signal could indeed correctly reveal the signature of the long wavelength modes of relaxation. The importance of having a correct relaxation spectrum is demonstrated by the recent argument about which viscosity models best fit McConnell's spectrum (see Peltier, 1998).

since the former ice loads were scattered over the Earth's surface at discrete locations, postglacial rebound provides a typical spatial-frequency localization problem (e.g., Simons and Hager, 1997). In this paper, we utilize isotropic spherical wavelets to explore the spatial-frequency character of relaxation signals for the Laurentide ice sheet, centered near Hudson Bay, and the Fennoscandian ice sheet. We find that that the characteristic relaxation time for the Fennoscandian ice sheet as a whole is at harmonic degree 16. Therefore, McConnell's spectrum is not reliable, at least below degree 16. For the larger Laurentide ice sheet, the characteristic relaxation time is at degree 9, as noted by Simons & Hager (1997). Our conclusion is further supported by the success of explaining the so-called decay times, introduced by Mitrovica (1996). These decay times were calculated by fitting relative sea level curves using fixed ice and viscosity models with relaxation times up to degree 246. We are able to fit the decay times qualitatively with only single degrees using a simple viscosity model: Degree 9 for the Laurentide ice sheet and degree 16 for the Fennoscandian ice sheet, respectively.

As applications of our result, we first modify McConnell's spectrum in the wavelength band between degree 9 and degree 16. This new spectrum clearly suggests that the true spectrum is not constant at long wavelengths. Then, we examine Peltier's (1998) argument by using the modified relaxation spectrum. Our results show that none of the viscosity models compared by Peltier (1998) fit the new spectrum through the entire wavelength band. Mitrovica & Forte's (1997) model fits the spectrum better than Peltier's (1998) models VM2 and VM3 at lower degrees, and the reverse is true at higher degrees. By analyzing a bundle of "realistic" viscosity models, we propose a new model which fits the modified spectrum throughout the wavelength band. A test of sensitivity of relaxation times to the viscosity structure is presented.