Jonathan Kirby

The effect of ‘noise’ on estimates of the elastic thickness of the continental lithosphere by the coherence method

[1] We model the lithosphere as a uniform elastic plate overlying an inviscid fluid and loaded with both surface and subsurface fractal loads to generate synthetic topography and gravity data. To simulate data having low (topographic) signal to (gravity) noise ratio we use an algebraically larger exponent for the subsurface load in the spectral synthesis fractal algorithm.The gravity power spectrum then decays less rapidly than that of topography, the spectra resembling those for central Australia. We find that the coherence method using multitaper spectral estimation yields significant underestimates of plate thickness for both low and normal signal-to-noise ratio data, unless the data window is larger than several times the true flexural wavelength. We quantify this bias for the parameters used here and apply it as a correction to an effective elastic thickness estimate for central Australia, obtaining a value of 115 ± 25 km. INDEX TERMS: 8110 Tectonophysics: Continental tectonics—general (0905); 8159 Tectonophysics: Rheology—crust and lithosphere; 1236 Geodesy and Gravity: Rheology of the lithosphere and mantle (8160). Citation: Swain, C. J., and J. F. Kirby, The effect of ‘noise’ on estimates of the elastic thickness of the continental lithosphere by the coherence method, Geophys. Res. Lett., 30(11), 1574, doi:10.1029/2003GL017070, 2003.

Improving the spatial resolution of effective elastic thickness estimation with the fan wavelet transform

Abstract We show here a simple technique to improve the spatial resolution of the fan wavelet method for effective elastic thickness ( T e ) estimation that we have previously developed. The technique involves reducing the number of significant oscillations within the Gaussian window of the Morlet wavelet from approximately five to three or fewer (while making an additional correction for its no-longer-zero mean value). Testing with synthetic models and data over South America indicates that the accompanying reduction in wavenumber resolution does not seriously affect the accuracy of the T e estimates. Comparison against the more widely-used multitaper Fourier transform approach shows that the enhanced wavelet method not only improves upon the multitaper methods spatial resolution, but also is computationally much faster and requires the arbitrary variation of only one parameter compared to three for the multitaper method. Finally, we present a modified method to compute the predicted coherence using the multitaper method that, while not improving its spatial resolution, does improve the bias of recovered T e estimates.

Complete spherical Bouguer gravity anomalies over Australia

Complete (or refined) spherical Bouguer gravity anomalies have been computed for all 1 095 065 land gravity observations in the June 2007 release of the Australian national gravity database. The spherical Bouguer shell contribution was computed using the supplied ground elevations of the gravity observations. The spherical terrain corrections, residual to each Bouguer shell, were computed on a 9 arc-second grid (∼250 m by ∼250 m spatial resolution) from a global Newtonian integration using heights from version 2.1 of the GEODATA digital elevation model (DEM) over Australia and the GLOBE and JGP95E global DEMs outside Australia. A constant topographic mass-density of 2670 kg/m3 was used for both the spherical Bouguer shell and spherical terrain correction terms. The difference between the complete spherical and complete planar Bouguer gravity anomaly exhibits an almost constant bias of about −18.7 mGal over areas with moderate elevation changes, thus verifying the planar model as a reasonable approximation in these areas. However, the results suggest that in mountainous areas with large elevation changes, the complete spherical Bouguer gravity anomaly should be selected in preference over the less-rigorous complete planar counterpart.

Comparison of digital elevation models over Australia and external validation using ERS-1 satellite radar altimetry

Digital elevation models (DEMs) are widely relied upon as representations of the Earths topographic morphology. The most widely used global DEMs available are ETOPO5, TerrainBase and JGP95E at a 5‐arc‐minute spatial resolution, and the GTOPO30 and GLOBE (version 1) global DEMs at a 30‐arc‐second spatial resolution. This paper presents the results of intercomparisons of these global DEMs over Australia, and with the GEODATA 9‐arc‐second DEM (version 1) of Australia. These DEMs were also compared to an independently produced, altimeter‐derived orthometric height database. This allows not only a totally independent assessment of the quality of these different DEMs over Australia, but also an insight into the ERS‐1 radar altimeters ability to measure orthometric heights on land. The results of all these comparisons reveal large differences among the DEMs, with the greatest difference between JGP95E and ETOPO5 (mean 49 m, standard deviation ±274 m). The comparison with the altimeter‐derived database shows good agreement with the version 1 GEODATA DEM (mean 2 m, standard deviation ±27 m), thus demonstrating that the altimeter is a viable method for quality assessment of DEMs in lowland regions. A further conclusion is that the representation of the Australian land surface in both the JGP95E and TerrainBase global DEMs is more accurate than the higher resolution GLOBE (version 1) global DEM, even though JGP95E displays a disparity along the 140°E meridian because of the different data sources used in its construction.

Experiments with two different approaches to gridding terrestrial gravity anomalies and their effect on regional geoid computation

Abstract This paper compares the gridding of two types of terrestrial gravity anomaly prior to the computation of regional gravimetric geoid models over Australia. The aim is to investigate the effects of high-frequency components (by way of the terrain correction) on the resulting grid of mean gravity anomalies, and hence the geoid. The gravity anomaly types investigated comprise simple Bouguer anomalies and refined Bouguer anomalies, both computed using a constant topographic mass density. Irrespective of which anomaly type is used for gridding, the relevant additional correction terms are applied to yield an approximation of the mean Helmert anomaly. Regional gravimetric geoid models are then computed over Australia and compared with one another and with GPS-levelling points on the Australian Height Datum. This shows that the application of terrain corrections before or after gravity gridding has only a relatively small effect on the computed geoid in Australia.

THe NZGEOID09 model of New Zealand

Abstract The NZGeoid09 gravimetric quasigeoid model of New Zealand was computed through FFT-based Stokesian integration with a deterministically modified kernel and an iterative computation approach that accounts for offsets among New Zealands 13 different local vertical datums (LVDs). NZGeoid09 is an improvement over the previous NZGeoid05 due to use of the EGM2008 and DNSC08GRA models, and due to improvements to the data processing strategy. The integration parameters of degree of kernel modification L=40 and cap radius ψ0=2.5° were determined empirically through a comparison with 1422 GPS/levelling observations, after the LVD offsets had been removed. The precision of NZGeoid09 was assessed using the same GPS/levelling dataset, yielding an overall standard deviation of 6.2 cm. NZGeoid09 performs better than NZGeoid05 and marginally better than EGM2008, but few data are available in the Southern Alps of New Zealand to give a better evaluation.

Localised Gross-error Detection in the Australian Land Gravity Database

We have used two complementary, data-driven gross-error detection methods to clean the 2004 release of Geoscience Australia’s (GA’s) land gravity database. The first uses the DEM- 9S (version 2) Australian digital elevation model to help verify the gravity observation elevations stored in the database. The second method uses locally interpolated complete/refined Bouguer gravity anomalies, under the assumption that these are smooth and suitable for interpolation, to crosscheck each gravity observation against those surrounding. Together, these methods only identified a total of 237 points (0.021%) in the database that were suspected to be in gross error (differences greater than 250 m and 35 mGal, respectively), of which only nine were identified by both methods. These points will be removed before the computation of the new Australian geoid model, and also supplied to GA for its evaluation. The small number of points identified is a very positive result, in that it shows that the Australian gravity database appears relatively gross-error-free, which bodes well for all previous studies that have relied upon it. However, it is important to point out that this evaluation is inevitably localised and thus only verifies the high- frequency gravity anomaly signal content. Subsequent studies using dedicated satellite gravimetry will be used to identify long- wavelength errors.

New high-resolution grid of gravimetric terrain corrections over Australia

A 9 arc‐second grid of gravimetric terrain corrections has been computed over Australia using ver.2 of the GEODATA 9 arc‐second digital elevation model (DEM) and the fast Fourier transform technique. This supersedes the 27 arc‐second grid previously reported in this journal, computed from ver.1 GEODATA DEM. The improved resolution is possible because of the removal of errors in ver.1 DEM.

Regional geoid-model-based vertical datums – some Australian perspectives

Abstract This article summarises some considerations surrounding a geoid-model-based vertical datum that have to be thought through before its implementation and adoption. Our examples are based on many Australian and some South-East Asian experiences, but these probably also apply elsewhere. The key considerations comprise data quality and availability, politics, and difficulties that users may encounter when adopting quite a different approach to height determination. We advocate some form of new vertical datum to replace the Australian Height Datum, but the exact type (whether using levelling or geoid, or some combination of both) still needs to be decided. We are not specifically opposed to the adoption of a geoid model as the vertical datum, but it is possibly more challenging than appears initially, and may even deter some users that are already well served by levelling-based vertical datums.

The Quest for a New Australian Gravimetric Geoid

This paper outlines some of the tasks required to compute a new generation of Australian gravimetric geoid. These comprise: the preparation of terrestrial gravity and terrain data; the use of appropriate geodetic datums during gravity data reduction; the selection of the best fitting global geopotential model; the application of a digital terrain model to compute gravimetric terrain corrections and their associated indirect effect on the geoid; and, the gridding of gravity anomalies prior to geoid computation. Comparisons of a preliminary Australian gravimetric geoid solution with geometrical control, provided by Global Positioning System (GPS) measurements in conjunction with optical levelling on the Australian Height Datum, illustrate some of the improvements made to date.