A Wavelet-Based Assessment of Topographic-Isostatic Reductions for GOCE Gravity Gradients

Abstract

Gravity gradient measurements from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE) contain significant high- and mid-frequency signal components, which are primarily caused by the attraction of the Earth’s topographic and isostatic masses. In order to mitigate the resulting numerical instability of a harmonic downward continuation, the observed gradients can be smoothed with respect to topographic-isostatic effects using a remove–compute–restore technique. For this reason, topographic-isostatic reductions are calculated by forward modeling that employs the advanced Rock–Water–Ice methodology. The basis of this approach is a three-layer decomposition of the topography with variable density values and a modified Airy–Heiskanen isostatic concept incorporating a depth model of the Mohorovičić discontinuity. Moreover, tesseroid bodies are utilized for mass discretization and arranged on an ellipsoidal reference surface. To evaluate the degree of smoothing via topographic-isostatic reduction of GOCE gravity gradients, a wavelet-based assessment is presented in this paper and compared with statistical inferences in the space domain. Using the Morlet wavelet, continuous wavelet transforms are applied to measured GOCE gravity gradients before and after reducing topographic-isostatic signals. By analyzing a representative data set in the Himalayan region, an employment of the reductions leads to significantly smoothed gradients. In addition, smoothing effects that are invisible in the space domain can be detected in wavelet scalograms, making a wavelet-based spectral analysis a powerful tool.

Appendix

For the band-pass filter in Eq. (30), the filter coefficients used

$$ c_{|k|} = \left\{\begin{array}{ll} 2\Updelta t \left(f_h - f_{l} \right) \quad & k = 0 \\ \left.\frac{\sin{2\pi f \Updelta t}}{\pi k}\right|_{f_{l}}^{f_h} \frac{\sin{\pi k / N}}{\pi k / N} \quad & k = 1,\ldots,N-1 \\ -\frac{1}{2} {\sum \limits _{j=-N+1}^{N-1}} c_{|j|} \quad & k = N \end{array}\right. $$

are adapted from Hamming (1998, p. 127ff.) The sampling period is denoted by $\Updelta t, \,f_{l}$ and f _h are the lower and upper cutoff frequencies, respectively, and N is the filter length. In this study, these parameters have been set to $\Updelta t=1\hbox{s},\, f_{l}= 5 \,\hbox{mHz}, \,f_{h}= 100 \hbox{ mHz}$, and N = 1,000.