Mathematics – Logic
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufm.t51a1512c&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #T51A-1512
Mathematics
Logic
3255 Spectral Analysis (3205, 3280), 8138 Lithospheric Flexure, 8194 Instruments And Techniques
Scientific paper
The estimation of the effective elastic thickness of the lithosphere (T_e) using spectral relationships between gravity and topography has become a controversial topic in recent years. However, one area which has received relatively little attention is the bias in estimates of T_e and the internal loading fraction (F_2) which results from spectral leakage and noise when using the multi-tapered free-air admittance method. In this study, I use grids of synthetic data to assess the magnitude of that bias. I also assess the bias which occurs when T_e within other planets is estimated using the admittance between observed and topographic line-of-sight accelerations of orbiting satellites. I find that leakage can cause the estimated admittance and coherence to be significantly in error, but only if the box in which they are estimated is too small. The definition of `small' depends on the redness of the gravity spectrum. On the Earth, there is minimal error in the estimate of T_e if the admittance between surface gravity and topography is estimated within a box at least 3000-km-wide. When the true T_e is less than 20~km and the true coherence is high, the errors in the estimate of T_e are mostly less than 5~km for all box sizes greater than 1000~km. On the other hand, when the true T_e is greater than 20~km and the box size is 1000~km, the best-fit T_e is likely to be at least 5-10~km less than the true T_e. Even when the true coherence is high, it is not possible to use the free-air admittance to distinguish between real and spurious small fractions of internal loading when the boxes are smaller than 2000~km in size. Furthermore, the trade-off between T_e and F_2 means that even small amounts of leakage can shift the best-fit values of T_e and F_2 by an appreciable amount when the true F_2 is greater than zero. Geological noise in the gravity is caused by subsurface loads, the flexural surface expression of which has been erased by erosion and deposition. I find that noise in the gravity introduces error and uncertainty, but no additional bias, into estimates of the admittance. On the other hand, I find that estimates of T_e made using the popular Bouguer coherence method are biased upwards by geological noise, potentially by more than a factor of three. At the altitude of most satellites (200-400~km), gravity is much redder than it is at ground-level; therefore it is necessary to work with much larger boxes when using line-of-sight accelerations than it is when using surface measurements. These problems limit the usefulness of GRACE range-acceleration data when estimating T_e in regions of the Earth which are poorly- covered by existing gravity surveys.
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