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Journal ArticleDOI

Requirements for airborne gravity gradient terrain corrections

Mark Dransfield1
01 Dec 2010-Exploration Geophysics (CSIRO PUBLISHING)-Vol. 2010, Iss: 1, pp 1-4
TL;DR: In this article, a combination of mathematical analysis and simulation studies has led to quantification of the requirements: current on-shore, low-level gradiometer surveys require sub-metre accuracy in navigation and in digital terrain model heights; cell sizes in the terrain model should be about one-third of the ground clearance.
Abstract: Accurate terrain corrections are important for all gravity surveying. In airborne surveys, a digital model of the terrain is constructed and terrain corrections are calculated at each airborne measurement point. Airborne gravity gradiometry is of high spatial resolution and is particularly sensitive to nearby topographic variations, placing particular requirements on the terrain corrections. A combination of mathematical analysis and simulation studies has led to quantification of the requirements: current on-shore, low-level gradiometer surveys require sub-metre accuracy in navigation and in digital terrain model heights; cell sizes (and therefore also topographic sampling) in the terrain model should be about one-third of the ground clearance. The choice of terrain correction density depends on the application and it is important that the interpreter of the corrected gravity data has the ability to test the impact of changes in this density. Accurate calculation of the gravity gradient field at the airborne sampling points may be achieved by a wide variety of either spatial or harmonic domain methods. Calculation in the harmonic domain is fast but assumes the data represent a periodic function on a planar surface. Padding methods for periodic extension and piecewise continuation away from a plane both add error and slow the calculation. Spatial domain methods are slower but can be sped up by the use of various approximations. In both cases, a clear understanding of accuracy requirements is essential for making an appropriate tradeoff between accuracy and speed.
Citations
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Journal ArticleDOI
Tianyou Chen1, Mark Dransfield1
TL;DR: In this article, the authors present the results of the HeliFalcon AGG survey conducted in the Aso-Oguni area exploring for geothermal fields, examin the technical challenges presented by the rugged terrains, describe some aspects of the data acquisition and processing, and present the survey results.
Abstract: Since the first Falcon AGG survey in 1999 (van Leuwen et al., 2000), fixed-wing airborne gravity gradiometry (AGG) has proved to be a valuable tool for mining and oil and gas explora¬tion (Dransfield, 2007). The more compact digital Falcon AGG allowed the system to be installed in a helicopter and helicopter AGG surveys began in 2006 (Boggs et al., 2007). Compared with fixed-wing aircraft, the helicopter platform can fly surveys low and slow, offering superior spatial resolution as well as an improved signal-to-noise ratio (Dransfield, 2007). The superior spatial resolution and improved signal-to-noise ratio provided by helicopter AGG enhances its capability to detect smaller targets and better delineate subtler features. Dransfield and Christensen (2013) reported a HeliFalcon performance of 6 Eo RMS at 45 m resolution in vertical gravity gradient, by far the finest spatial resolution of any airborne AGG system. Another advantage afforded by helicopter AGG is its capa¬bility to follow terrains more closely especially in areas of high relief. Christensen and Hodges (2013) compared the vertical grav¬ity gradient from HeliFalcon with the simulated fixed-wing result over the Iron Range survey in the Canadian Rocky Mountains where the terrain variation reaches 1900 m. They showed that in this terrain, a fixed-wing survey would have to fly at ground clearances of more than 1000 m for much of the survey area. This high ground clearance would have greatly suppressed the signal at short wavelengths and degraded the spatial resolution. In this paper, we look at the HeliFalcon AGG survey conducted in the Aso-Oguni area exploring for geothermal fields, examin the technical challenges presented by the rugged terrains, describe some aspects of the data acquisition and processing, and present the survey results.

Cites background from "Requirements for airborne gravity g..."

  • ...In addition, Dransfield (2010) has shown that the sampling of the terrain surface must be at a spacing of about one-third of the ground clearance....

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Journal ArticleDOI
TL;DR: In this article , the horizontal gravity-gradient stack-moving window correlation (HGGS-MWC) method was proposed for density evaluation of the surface layer without a prior density assumption.
Abstract: The author proposes a new approach for analysing datasets of the differential curvature of a gravity-gradient tensor for density evaluation of the surface layer without a prior density assumption. The method, called the horizontal gravity-gradient stack–moving window correlation (HGGS-MWC) method, is based on a successive MWCs between the acquired data and the data of differential curvature responses of the surface layer calculated based on a digital elevation model. For improving the correlation, a HGGS processing method was devised and patented. It is applied to both datasets before the MWC processing. A point-source differential curvature response has the characteristic of forming a peculiar and symmetrical shape of a quadrant and distributing peaks and troughs over an underlying anomalous mass. These peaks and troughs are near or far away from their centre depending on the depth of the anomalous mass. This enables one to design a filter to enhance the responses of the surface layer. In addition, the HGGS processing affects both the contraction of the gravitational response and the attenuation of responses from deeper subsurface layers. The HGGS-MWC method leads to the production of values of the mass surface roughness ratio (MSR) in the wavenumber domain that are inherent to the measuring plane of surveys and determines the phase relation between the mass of the surface layer and the surface roughness. The MSR is a good indicator of whether a mass surplus or deficit relative to the regional average mass exists under a convex surface layer. Application to the observed datasets was performed in the area where serious landslides were triggered by the 2008 Iwate-Miyagi inland earthquake. Based on a flight height of 150 m, the mass variations of the surface layer, which is down to 300 m below the surface, are properly evaluated by analysing the wavelengths in the data mainly within the range of 270–650 m and perceivably up to 1,650 m. The specific areas can be delineated where low-density deposits, such as possible volcanic ashes and pumices associated with high water content, sit on high mountains with steep slopes. The information is useful for disaster prevention by playing a role in selecting potential areas for conducting further precise surveys. Regional density variations whose wavelengths are longer than 1,650 m remain unsolved and are an issue for future studies. With the issue solved, the results for the density distribution of the surface layer obtained by the HGGS-MWC method will serve for terrain corrections of the vertical gravity-gradient data and gravity data as well.
References
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Journal ArticleDOI
TL;DR: In this paper, it is shown how a series of Fourier transforms can be used to calculate the magnetic or gravitational anomaly caused by an uneven, non-uniform layer of material.
Abstract: Summary It is shown how a series of Fourier transforms can be used to calculate the magnetic or gravitational anomaly caused by an uneven, non-uniform layer of material. Modern methods for finding Fourier transforms numerically are very fast and make this approach attractive in situations where large quantities of observations are available.

1,365 citations

Journal ArticleDOI
TL;DR: In this article, the Fast Fourier Transform (FFT) is used for terrain reduction of land gravity data and satellite altimetry geoid data, and the results are evaluated against a conventional integration program: the accuracy of FFT-computed terrain corrections in actual gravity stations showed anr.m.s.
Abstract: The widespread availability of detailed gridded topographic and bathymetric data for many areas of the earth has resulted in a need for efficient terrain effect computation techniques, especially for applications in gravity field modelling. Compared to conventional integration techniques, Fourier transform methods provide extremely efficient computations due to the speed of the Fast Fourier Transform (FFT. The Fourier techniques rely on linearization and series expansions of the basically unlinear terrain effect integrals, typically involving transformation of the heights/depths and their squares. TheFFT methods will especially be suited for terrain reduction of land gravity data and satellite altimetry geoid data. In the paper the basic formulas will be outlined, and special emphasis will be put on the practial implementation, where a special coarse/detailed grid pair formulation must be used in order to minimize the unavoidable edge effects ofFFT, and the special properties ofFFT are utilized to limit the actual number of data transformations needed. Actual results are presented for gravity and geoid terrain effects in test areas of the USA, Greenland and the North Atlantic. The results are evaluated against a conventional integration program: thus, e.g., in an area of East Greenland (with terrain corrections up to10 mgal), the accuracy ofFFT-computed terrain corrections in actual gravity stations showed anr.m.s. error of0.25 mgal, using height data from a detailed photogrammetric digital terrain model. Similarly, isostatic ocean geoid effects in the Faeroe Islands region were found to be computed withr.m.s. errors around0.03 m

145 citations


Additional excerpts

  • ...Macnae and Chen (1997) studied simulations at very low altitudes; Jekeli and Zhu (2006) compare several algorithms for calculating terrain corrections from a digital terrain model (DTM); Kass and Li (2008) examine practical considerations concerned with the use of the Parker (1972) method in gravity gradiometry and Dransfield and Zeng (2009) provide guidelines for the requirements on navigation and DTM accuracy....

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  • ...Forsberg (1985) uses a convolution approach....

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Journal ArticleDOI
TL;DR: In this article, an iterative fast Fourier procedure is derived for referring to a horizontal plane potential field data measured over a topographic surface, and the convergence of the procedure is studied and it is found that results are satisfactory when the plane is close to the topography, either above, below or intersecting the measurement surface.

64 citations

DOI
01 Jan 1994

43 citations

Journal ArticleDOI
Mark Dransfield1, Yi Zeng2
TL;DR: In this paper, it was shown that terrain-correction errors from elevation errors in the digital elevation model (DEM) are linear in the elevation error but follow an inverse power law in the ground clearance of the aircraft.
Abstract: Terrain corrections for airborne gravity gradiometry data are calculated from a digital elevation model (DEM) grid. The relative proximity of the terrain to the gravity gradiometer and the relative magnitude of the density contrast often result in a terrain correction that is larger than the geologic signal of interest in resource exploration. Residual errors in the terrain correction can lead to errors in data interpretation. Such errors may emerge from a DEM that is too coarsely sampled, errors in the density assumed in the calculations, elevation errors in the DEM, or navigation errors in the aircraft position. Simple mathematical terrains lead to the heuristic proposition that terrain-correction errors from elevation errors in the DEM are linear in the elevation error but follow an inverse power law in the ground clearance of the aircraft. Simulations of the effect of elevation error on terrain-correction error over four measured DEMs support this proposition. This power-law relation may be used in selecting an optimum survey flying height over a known terrain, given a desired terrain-correction error.

39 citations