On the use of heterogeneous noisy data in spectral gravity field modeling methods
- 138 Downloads
Can data errors be propagated into the results?
Can heterogeneous data be used?
Is error propagation possible with heterogeneous data?
The answer to the above questions is yes and is illustrated for the case of two input data sets and one output.
Firstly, a solution is obtained in the frequency domain using the theory of a two-input, single-output system. The assumption here is that both the input signals and their errors are stochastic variables with known PSDs. The solution depends on the ratios of the error PSD and the signal PSD, i.e., the noise-to-signal ratios of the two inputs. It is shown that, when the two inputs are partially correlated, this solution is equivalent to stepwise collocation.
Secondly, a solution is derived in the frequency domain by a least-squares adjustment of the spectra of the input data. The assumption is that only the input errors are stochastic variables with known power spectral density functions (PSDs). It is shown that the solution depends on the ratio of the noise PSDs.
In both cases, there exists the non-trivial problem of estimating the input noise PSDs, given that we only have available the error variances of the data. An effective but non-rigorous way of overcoming this problem in practice is to approximate the noise PSDs by simple stationary models.
KeywordsPower Spectral Density Gravity Field Stochastic Variable Heterogeneous Data Spectral Density Function
Unable to display preview. Download preview PDF.
- Barzaghi, R., Fermi, A., Tarantola, S. and F. Sansò. 1993. Spectral techniques in inverse Stokes and overdetermined problems.Surveys in Geophysics, Vol. 14, No. 4–5.Google Scholar
- Bendat, J.S. and A.G. Piersol. 1980.Engineering applications of correlation and spectral analysis, John Wiley and Sons, New York.Google Scholar
- Bendat, J.S. and A.G. Piersol. 1986.Random data: Analysis and measurement procedures, Second edition, John Wiley and Sons, New York.Google Scholar
- Bottoni, G.P. and R. Barzaghi. 1993. Fast collocation.Bulletin Géodésique, Vol. 67, No. 2, pp. 119–126.Google Scholar
- Bracewell, R.N. 1986.The Fourier Transform and its Applications, Second edition, revised. McGraw-Hill, New-York.Google Scholar
- Li, J. and M.G. Sideris. 1995. Marine gravity and geoid determination by optimal combination of satellite altimetry and shipborne gravimetry data. Paper presented at theXXI IUGG General Assembly, July 2–14, Boulder, Colorado. Also submitted to theJournal of Geodesy. Google Scholar
- Li, Y.C. 1993. Optimized spectral geoid determination. UCGE Report No. 20050, Department of Geomatics Engineering, The University of Calgary, Calgary, Alberta.Google Scholar
- Li, Y.C. and M.G. Sideris. 1994. Minimization and estimation of geoid undulation errors.Bulletin Géodésique, Vol. 68, pp. 201–219.Google Scholar
- Moritz, H. 1980.Advanced physical geodesy. H. Wichmann Verlag, Karlsruhe, Germany.Google Scholar
- Sansò, F. and G. Sona. 1995. The theory of optimal linear estimation for continuous fields of measurements.Manuscripta Geodaetica (in print).Google Scholar
- Sansò, F. and M.G. Sideris. 1995. On the similarities and differences between systems theory and least-squares collocation in physical geodesy. Paper presented at theXXI IUGG General Assembly, July 2–14, Boulder, Colorado. Also submitted to theJournal of Geodesy. Google Scholar
- Schwarz, K.P., Sideris, M.G. and R. Forsberg. 1990. The use of FFT techniques in physical geodesy,Geophysical Journal International, Vol. 100, pp. 485–514.Google Scholar
- Sideris, M.G. 1987. On the application of spectral techniques to the gravimetric problem. InProc. of the XIX IUGG General Assembly, Tome II, Vancouver, B.C., August 9–22, pp. 428–442.Google Scholar
- Wang, Y.M. 1993. On the optimal combination of geopotential coefficient model with terrestrial gravity data for FFT geoid computations.Manuscripta Geodaetica, Vol. 18, No. 6, pp. 406–416.Google Scholar
- Wu, L. and M.G. Sideris. 1995. Using Multiple Input-Single Output System Relationships in Post Processing of Airborne Gravity Vector Data. InProc. of IAG Symposium G4: Airborne Gravity Field Determination, XXI IUGG General Assembly, July 2–14, Boulder, Colorado.Google Scholar