2009 Dransfield - conforming falcon gravity and the global gravity anomaly

FALCON gravity and the global gravity anomaly

Dransfield 1/20

Conf orming FALCON gravity and the global gravity anomaly

Mark Dransfield1

Submitted 27 May 2009.

ABSTRACT

Gravity derived only from airborne gravity gradient measurements with a normal error distribution

will have an error that increases with wavelength. It is straightforward in principle to use sparsely

sampled regional gravimeter data to provide the long wavelength information, thereby conforming

the derived gravity to the regional gravity. Regional surface or airborne gravimeter data are not

always available and can be difficult and expensive to collect in many of the areas where an airborne

gravity gradiometer survey is flown. However the recent release by the Danish National Space Centre

of the DNSC08 global gravity anomaly data has provided regional gravity data for the entire earth of

adequate quality for this purpose. Studies over three areas, including comparisons with ground,

marine and airborne gravimetry, demonstrate the validity of this approach. Future improvements in

global gravity anomaly data are expected, particularly as the product from the recently launched

GOCE satellite becomes available, and these will lead directly to an improvement in the very wide

bandwidth gravity available after conforming FALCON gravity with the global gravity.

INTRODUCTION

Airborne gravity gradiometry has been in use for ten years (Dransfield 2007). It delivers

measurements of the gravity field from the air at a sensitivity and spatial resolution dramatically

better than airborne gravimetry. At 3 km wavelength and a survey speed of 120 knots, the FALCON

airborne gravity gradiometer (AGG) has a gravity error along a single survey line of about 0.2 mGal

(Boggs and Dransfield 2004); an airborne gravimeter in these circumstances cannot do better than 1.4

mGal (van Kann 2004). At shorter wavelengths this disparity increases rapidly; at longer wavelengths

it decreases slowly.

For many exploration problems only the short wavelengths are of interest but in some cases the long

wavelength gravity is important.

1 Fugro Airborne Surveys Pty Ltd., e-mail: [email protected]


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The rotating gravity gradiometer instrument technology developed by Lockheed Martin is used in

both the FALCON AGG and the full-tensor gradiometer (FTG) (Difrancesco et al. 2009). These are the

only instrument technologies in airborne use today.

The gravity gradient measurements contain error. For fixed-wing FALCON surveys, the error is well

characterised by normally distributed noise with a standard deviation of about 3 Eö in a bandwidth of

0.18 Hz. Its power spectrum is that of band-limited white noise (i.e., independent of frequency across

the bandwidth).

The calculation of gravitational acceleration from measured gravity gradients is an integration and the

integration of the white noise results in an error in the gravitational acceleration that increases with

decreasing frequency. Since measurements are made from an aircraft moving at approximately

constant speed, decreasing frequency corresponds to increasing wavelength.

Analysis of survey data suggests that the error in gravity data derived from a FALCON AGG survey

can be approximately characterised as 0.1 mGal/√λ where λ is the wavelength in kilometres (Boggs

and Dransfield 2004).

In principle, this deficiency at long wavelengths may be addressed by merging the FALCON-derived

gravity with already existing regional gravity data to provide the highest possible sensitivity over the

widest bandwidth. Such a merging of data sets is called ‘conforming’ and many FALCON gravity

data sets have been conformed to available regional data sets. Examples have been published (Rose et

al. 2006).

Many FALCON surveys are collected in areas where there is no existing gravity data from either

marine, ground or airborne gravimetry surveys. Sometimes there are existing gravity data but the

coverage only partially intersects the area of the FALCON survey. A more complete solution is

desirable.

Complete global gravity coverage at long wavelengths is available in the public domain and can be

used for this purpose.

DNSC08 GRAVITY DATA

The global gravity anomaly is defined in Li et al. (2006). Global gravity anomaly data are derived from

many data sets including satellite measurements of sea surface altitudes and direct measurements of

gravity from the ground, the ocean, the air and space. These data may be modeled.


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Earth gravity models consist of a set of coefficients for a best-fit spherical harmonic expansion of the

gravity anomaly. The earth gravity model EGM2008, released in 2008 and freely available from the US

government National Geospatial Intelligence Agency (NGA), provides terms in the expansion to

degree 2160 or 5 arc-minutes (Pavlis et al. 2008). This is equivalent to a spatial wavelength of 10 arc-

minutes, or about 17 km.

Also in 2008, the Danish National Space Centre released the DNSC08 gravity anomaly data with

complete global coverage (Andersen et al. 2008). The DNSC08 global gravity anomaly field improves

previous gravity anomaly data: over oceans, and particularly in shallow water, by re-tracking and re-

picking the satellite data; in polar regions by use of the latest results over the Arctic (Forsberg and

Skourup 2005); and on land by incorporating the EGM2008.

The DNSC08 gravity anomaly data over the ocean have been shown to have an RMS difference with

marine gravity of 2.78 mGal in the Florida Keys and a comparison with marine gravity along an

800 km long line measured in the Caribbean had an RMS difference of 2.86 mGal and a 0.5 coherence

at 17.5 km and 0.9 coherence at 25 km (Andersen et al. 2008). Generally, one expects the DNSC08

accuracy over oceans to be poorer where the surface of the ocean is disturbed from an equipotential

surface such as in very shallow water and where there are strong currents or tides. However, the error

estimates over ocean are lower than for EGM2008. On land, the DNSC08 gravity relies on EGM2008.

The global RMS errors (including ocean) for EGM2008 are estimated by the NGA at 4.1 mGal but

excluding the oceans, Himalayas and Andes, the RMS error drops to approximately 2.5 mGal. In

mountainous terrain, the error can be tens of mGals. Evaluations have been performed by numerous

groups around the world by comparison with existing survey and gravity data sets (see for example,

Claessens et al. 2009 and Dawod et al. 2009) and their results are consistent with NGA error estimates.

These figures suggest an accuracy and spatial resolution that could often meet the requirements for

conforming FALCON gravity.

The DNSC08 gravity anomaly data form a free-air gravity anomaly field with complete coverage on

the geoid surface and are accurate at long wavelengths. The gravity data from a FALCON AGG

survey are the gravity anomaly data on the survey flight surface and are accurate at short

wavelengths.

The FALCON gravity is collected on a different (higher) surface. A rigorous methodology would

require the continuation of one data set to the height of the other. If the height difference is very small

compared to the shortest wavelength in the DNSC08 gravity data, then the continuation may be

omitted without significant effect.


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For exploration purposes, we prefer terrain-corrected data but the DNSC08 gravity is not terrain

corrected. However, the conforming of terrain-corrected FALCON gravity onto free-air DNSC08

gravity will preserve the terrain corrections at wavelengths below the cross-over wavelength which

must be at least 20 km. This is consistent with current practice in FALCON data processing since

terrain corrections are generally carried out only to a distance of between 10 and 20 km from each

observation point.

For the purposes of this study, I use FALCON gravity without any terrain correction. This is the

equivalent of free-air gravity and so provides a like-for-like comparison with the gravity data from

other sources.

METHODOLOGY - CALCULATION OF CONFORMED GRAVITY

Preliminary comments

In this article I describe results from a proof-of-concept study to demonstrate that regional gravity,

and particularly the DNSC08 global gravity anomaly data, may be used to conform FALCON gravity

data. For this purpose, I developed the following workflow. The key steps are vertical continuation (if

necessary), matched filtering and simple addition.

Good coverage is important. The regional data should extend sufficiently beyond the FALCON

survey area as to avoid edge effects from the filtering stage of processing. The cut-off wavelength for

the filtering must be larger than the sample spacing.

In the examples here, I have conformed un-terrain corrected FALCON gravity with free-air regional

gravity. The method applies equally to fully terrain corrected FALCON gravity because the terrain

corrections are only necessary to distances of between 10 and 20 km, depending on the magnitude of

the topography.

Workflow

The regional and FALCON gravity data are processed separately until ready for summation.

An area of regional gravity extending to well beyond the FALCON survey boundary in all directions

is selected. The data grid is projected onto the same coordinates as the FALCON data (usually a

universal transverse mercator projection). If necessary, the data are then upward or downward

continued to the mean survey altitude of the FALCON survey.

The summation of the two datasets assumes that the data are collected on the same surface. In

practice, this continuation step may often be omitted. The continuation operator is exponential


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(Blakely p317) so vertical continuation of low-pass filtered gravity data has negligible effect if the cut-

off wavenumber of the filter corresponds to a wavelength much larger than the continuation distance.

For a height difference of ∆h and a cut-off wavelength l, the error due to omitting the continuation

step must be less than:

1 exp∆

− −∆ ≈

h

l

h

l (1.1)

for ∆h<<l.

For example, for a height difference of 100 m and a cut-off wavelength of 30 km, omission of the

continuation will produce an error less than 0.3%.

The regional data are then filtered with a low-pass cosine squared filter parametrised by a pair of

wavelengths (λ0, λ1). This step is described in more detail below in Appendix 1. The resulting grid is

interpolated to the same grid spacing as the FALCON grid and cropped to the same areal extent.

The FALCON gravity data are gridded to a sample spacing usually between one-third and one-

quarter of the line spacing. They are high-pass filtered with the cosine-squared filter complementary

to the one used for the regional data as described in Appendix 1. The two grids are added to produce

the final conformed gravity grid.

All filtering and downward continuation described here was performed using the magmap 2D

Fourier processing package in Geosoft’s OASIS montaj.

STUDY AREA 1 – VREDEFORT, SOUTH AFRICA

The Vredefort structure, approximately 100 km south-west of Johannesburg, South Africa, comprises a

40 km wide core consisting of Archean granitoid gneisses surrounded in the northern half by a 120 km

wide semi-circular collar of steeply dipping Late Archean to Early Proterozoic volcanic and

sedimentary rocks. The southern half of the structure is covered by younger sediments and volcanics

(Karoo Supergroup) of the Witwatersrand Basin. The structure is generally accepted as being the

erosional remnant of a complex impact crater (Ameglio 2005). Its proximity to Johannesburg and its

well-known and clear expression in the gravity field make it a useful test site for airborne gravity

systems. I had access to ground gravimetry and airborne GT-1A gravimetry as well as the DNSC08

gravity and the gravity from a FALCON AGG survey.

FALCON AGG Survey

In February 2007, Fugro Airborne Surveys flew a FALCON AGG survey over the Vredefort Dome

area in the Republic of South Africa. The survey comprised two blocks and the results from the


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eastern block have been used in this study. The eastern block was flown north-south with a line

spacing of 1 km, and with 2 east-west tie-lines spaced at 40 km, over an area 60 km north-south by

40 km east-west (Figure 1a) and covering most of the Vredefort Dome structure. The ground clearance

was nominally 80 m flown in a drape over the terrain, corresponding to ellipsoidal heights of between

1430 and 1740 m. Summer conditions meant moderate to high turbulence at this survey height and the

mean difference noise (Boggs and Dransfield 2004) for the FALCON differential curvature gradients

was 3.6 Eö. Productivity was typical for these conditions with the 4800 line-km for both eastern and

western blocks completed in 3 weeks.

Figure 1. FALCON flight path (a) and shaded pseudocolour image (b) of the FALCON gravity filtered

with a 1 km low-pass filter over the Vredefort Dome study area, South Africa.

The measured modulated differential curvature gradients were processed by the usual multi-step

FALCON AGG processing procedures. After the initial reduction of error due to the residual effects of

aircraft motion, the data were demodulated and low-pass filtered with a 6th order Butterworth low

pass filter at a 0.18 Hz cut-off frequency. The demodulated data were corrected for the self-gradient

effects of the aircraft and tie-line levelled. These differential curvature gravity gradient data were

transformed in the wavenumber domain into the free-air gravity data used for this study (Figure 1b).

A parallel stream of data processing also produced terrain-corrected data and thence the full gravity

gradient tensor as well as terrain-corrected gravity but these data are not described in this study.

A minimum length scale of 40 km means that the choice of cross-over wavelengths can be determined

on the basis of sample spacing and sensitivities.

a b


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GT-1A Airborne Gravimetry Survey

The airborne gravimetry survey, flown in March 2004, has been previously reported by Ameglio

(2005). It was flown with a GT-1A gravimeter and, like the FALCON AGG survey, in two blocks,

eastern and western. The GT-1A eastern block covers very nearly the same area as the FALCON AGG

eastern block. It was flown at constant barometric altitude of 450 m AGL (approximately 2100 m

above the GRS80 ellipsoid) with a 2 km line-spacing (tie-line spacing 22 km). The traverse line

orientation was north-south (Figure 2a).

Figure 2. GT-1A flight path (a) and shaded pseudocolour image of the airborne GT-1A gravity low-pass

filtered with a 107 second (approximately 7 km) cut-off over the Vredefort Dome study area, South

Africa.

Ameglio (2005) describes the data processing:

“Gravity data are sampled at ~18 Hz, sub-sampled to 2 Hz and integrated with dual

frequency DGPS data to remove effects of vertical aircraft acceleration and Eötvös effect.

Final gravity is reduced using a non-stationary adaptive Kalman filter using: raw gravity;

aircraft vertical velocity (DGPS phase information); and platform misalignment errors.”

The gravity data were filtered at 107 seconds, equivalent to 7.05 km at the mean survey speed of

70 m/sec (Figure 2b).

Ground Gravimetry

The free-air ground gravity data are of varying sample spacing (Figure 3a) and made available by the

South African Council for Geoscience. There are a number of isolated circular gravity anomalies

a b


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visible in the shaded image of these data (Figure 3b) that are due to a single measurement and are not

visible in the FALCON gravity. These may be erroneous data but their impact on the gridded data

appears limited in extent to a few kilometres. After the filtering in the conforming process, the impact

on the final conformed data will be very small.

Figure 3. Ground gravity sample locations (a) and a shaded pseudocolour image of the gridded ground

gravity (b) over the Vredefort Dome study area, South Africa. Sample spacings vary from a few hundred

metres (densest area near bottom left of the map) to about 10 kilometres. The image has a number of

very small circular features predominantly in the north and east suggestive of aliasing of erroneous data.

The largest sample spacing is about 10 km suggesting both cross-over filter wavelengths should be

about or greater than 20 km.

Conformed Results

The DNSC08 gravity data over the Vredefort study area are shown as a shaded pseudo-colour image

in Figure 4a. As expected, these data have no information at short wavelength. The long wavelength

features are clearly present.

The FALCON gravity data were conformed to each of the ground gravity, airborne GT-1A gravity and

DNSC08 gravity (see Figure 4 b, c and d). In all cases, the conforming wavelengths are 30 and 40 km.

The ground and GT-1A gravimetry could be expected to support shorter wavelengths but the

DNSC08 data over land is unlikely to do so. The purpose of performing the conforming to several

different sets of gravity data is to allow comparison and so I have chosen to apply the same filter

parameters in all three cases.

a b


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Figure 4. (a) DNSC08 gravity over Vredefort Dome study area, South Africa; (b) FALCON gravity

conformed to DNSC08 gravity; (c) FALCON gravity conformed to ground gravity and (d) FALCON

gravity conformed to GT1A gravity.

The height difference to the ground gravity is approximately 80 m. Upward continuation was not

performed and the maximum error from this omission can be estimated (using equation (1.1)) as 0.3%

using 0.08 km as the height difference and 30 km as the minimum wavelength. The amplitude range

of the gravity field is 90 mGal, so the error due to omitting upward continuation is less than

0.25 mGal.

a b

c d


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For conforming the FALCON gravity to the GT-1A gravity, the height difference is about 600 m,

leading to a maximum error of 1.8 mGal. This is significant and so the GT-1A gravity data were

downward continued by 600 m before filtering.

There is a still larger height difference of approximately 1.5 km between the DNSC08 and the

FALCON gravity. Continuation is clearly required here because the error of omission could be as

large as 5% or 4.5 mGal. The DNSC08 gravity were upward continued by 1.5 km before filtering.

Figure 5. (a) The difference between using DNSC08 and ground gravity over the Vredefort Dome study

area, South Africa. The RMS of the difference is 1.7 mGal. (b) Difference between FALCON gravity

data conformed with GT1A and ground gravity. The RMS of the difference is 1.5 mGal.

Each gravimetry grid was low-pass filtered with the cosine-square filter. The FALCON gravity grid

was high-pass filtered with the equivalent filter and added separately to each filtered gravimetry grid

to produce the results shown in Figure 4 (b, c and d). All are imaged with a linear colour scale over the

same range of values and using the same colour mapping table. All are shaded the same. A visual

inspection suggests that the results are very similar although subtle differences can be seen.

Figure 5 (a and b) image the difference between the conformed results using DNSC08 and ground

gravity and between the conformed results using GT-1A and ground gravity respectively. These

figures show that the difference is at wavelengths greater than 40 km as expected since the data are

post-filter. The RMS difference between GT-1A and ground gravity is 1.5 mGal and that between

DNSC08 and ground gravity is 1.7 mGal. The GT-1A gravity are not referenced to a base station,

hence the offset of about 17 mGal between the GT1A free-air gravity and the other data sets.

a b


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Comparing any of these results with the original FALCON gravity (Figure 1b) shows that there were

no significant deficiencies in the FALCON gravity at long wavelength.

STUDY AREA 2 – GIPPSLAND BASIN, AUSTRALIA

The Gippsland Basin is an important source of oil and gas for Australia and about 14 significant fields

have been discovered there since the first gas discovery in 1964. The fields are within the mature,

sand-rich siliciclastics of the Latrobe Group deposited during sea-floor spreading between the Late

Cretaceous and Early Eocene.

FALCON AGG Survey

The FALCON AGG survey in the Bass Strait has been reported by Rose et al. (2006) whom I follow

here. In July 2002, Fugro Airborne Surveys flew a FALCON survey over a 35 km by 40 km area of the

Gippsland Basin in Bass Strait. The survey was flown east-west with a line spacing of 300 m, and with

north-south tie-lines spaced at 5 km (Figure 6a). Nominal surface clearance was 175 m. Productivity

was typical for these conditions with the 5000 line-km completed in 13 days, including 5 days lost to

poor weather.

Figure 6. (a) FALCON survey flight path and (b) shaded pseudocolour image of FALCON gravity (after

Rose et al. 2006) over the Gippsland Basin study area, Australia.

The aims of the survey were to compare the FALCON gravity data with marine gravimetry being

collected at about the same time, and to see what geological information was contained in the gravity

data over an area where the geology is well understood. This study led to the initial work on

recovering long wavelength gravity for FALCON AGG surveys.

a b


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The resultant gravity image (Figure 6b) is dominated by major basin and basement faulting with the

gravity highs predominantly explained by uplift. The basement is at depths of 6000 to 8000 metres.

Shallow faults are also visible in the sun-shaded data, appearing as sharp linear features.

Marine Gravimetry

The survey details for the Northern Fields marine gravity data are described in Rose et al. (2006) and I

merely summarise key points here. The data were acquired and processed by Fugro Gravity and

Magnetic Services, as part of a WesternGeco 3D seismic survey between October 2001 and July 2002,

for Esso Australia Pty. Ltd.. The line spacing was 350 m with tie-lines typically greater than 15 km

apart (Figure 7a). The data were low-pass filtered at a cut-off wavelength of about 560 m. The line

spacing and filter length are very similar to those used for the FALCON data. There is some risk that

the sparse tie-lines have not allowed for adequate control of drift.

Figure 7. Marine gravity survey ship tracks within the study area (a) and (b) shaded pseudocolour image

of the Northern Fields marine gravity (after Rose et al. 2006) over the Gippsland Basin study area,

Australia.

The shaded image of the marine gravity (Figure 7b) is significantly smoother than the FALCON

gravity but with the same major features. A significant difference is the clear general trend from high

gravity values in the east to low in the west; this very long wavelength information is not present in

the FALCON gravity.

Conformed Results

The DNSC08 gravity data (shaded image shown in Figure 8a) represent the major features visible in

the marine and FALCON gravity, although clearly with much less resolution. The gravity high in the

a b


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north-west is of higher amplitude than in the marine gravity and the shape of the high in the east

appears significantly different.

Figure 8. (a) DNSC08 gravity for the Gippsland Basin study area, Australia; (b) FALCON gravity

conformed to DNSC08 gravity; (c) FALCON gravity conformed to marine gravity and (d) The difference

between FALCON gravity conformed to DNSC08 and to marine gravity. The RMS difference is 1.1 mGal.

The quality of marine gravimetry would suggest the use of relatively short filter wavelengths, perhaps

in the 10-20 km range. However, the visible shortcomings of the DNSC08 gravity led me to choose the

wavelengths (30, 40) km for the cosine squared filter.

Upward continuation was not performed and the maximum error from this omission can be estimated

in the same way as for the Vredefort study area. The height difference is 0.15 km, the smaller cut-off

wavelength is 30 km and the amplitude range of the gravity field is 25 mGal, so the error due to

omitting upward continuation is less than 0.13 mGal and its omission is not significant.

a b

c d


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The results of conforming the FALCON gravity to the DNSC08 gravity (Figure 8b) and to the marine

gravity (Figure 8c) are presented as shaded images. Visually, the images are very similar although

differences are observable, for example over the gravity high in the north-west mentioned earlier.

Naturally, the differences between the two results are at wavelengths longer than 40 km. The RMS of

the difference is 1.1 mGal (Figure 8d).

STUDY AREA 3 – WEST AFRICA

This last example is from an area over an Aptian salt basin of West Africa. Numerous oil fields have

been discovered below these salt deposits including, for example, the Etame Field (Gill and Cameron,

2002). The region’s geological history is characterised by phases of Cretaceous rifting and subsidence

followed by the formation of the Aptian evaporites (Petters 1991). In our example area, the evaporites

are shallow and complex and may be readily located by FALCON AGG high resolution gravity. The

filled rift zones tend to be oriented approximately north-south and, together with basement structure,

provide gravity signal at longer wavelengths.

FALCON AGG Survey

In late 2007, Fugro Airborne Surveys flew a FALCON AGG and aeromagnetic survey in west Africa.

The block was flown north-south with a line spacing of 400 m, and with east-west tie-lines spaced at

4000 m. The ground clearance was nominally 80 m draped over the terrain. The mean difference noise

(Boggs and Dransfield 2004) for the FALCON curvature gradients was 3.4 Eö. The survey area was

approximately 30 km by 80 km and all of the data were used in the workflow to develop the

conformed data but only a portion of the data are presented. The location of the data is withheld at the

request of the client and all the maps are displayed with transformed coordinates. The FALCON

gravity over the study area are shown in the shaded image of Figure 9a. The salt domes give a clear

isolated gravity low and the salt walls show as long sinuous gravity lows. This signal is superimposed

on a general trend from high gravity in the west to low in the east.


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Figure 9. (a) FALCON gravity over the West Africa study area. The complex pattern of occasional salt

domes and pervasive, sinuous salt walls is very clear. (b) DNSC08 gravity over the same area. The long

wavelength, near-linear, trend is to the west-south-west in contrast to the FALCON gravity where it is

westerly.

Conformed Results

The DNSC08 gravity over this study area are presented as a shaded image in Figure 9b. As expected,

the short wavelength features due to the Aptian salt are not visible. The general trend of the gravity

low is approximately north-north-west, significantly differently to the northerly trend in the FALCON

gravity. The north-north-west trend direction is consistent with the known effects of the geology in

this area.

Conforming of the FALCON gravity onto the DNSC08 gravity was performed three times using the

filter wavelength pairs (20, 30), (30, 40) and (40, 50) km and the results are shown in Figure 10 (a, c, e).

Upward continuation was not performed and the maximum error from this omission can be estimated

from equation (1.1) as 0.4% from the 0.08 km height difference and 20 km minimum wavelength. The

amplitude range of the gravity field is 160 mGal, so the error due to omitting upward continuation is

less than 0.64 mGal.

It is difficult to see differences between the three conformed results, so I have also presented the

differences between the (20, 30) and (30, 40) km case (Figure 10b) and between the (40, 50) and

(30, 40) km case (Figure 10d).

The broad gravity low running to the north-north-west on the east is a trough with the gravity values

increasing again further to the east. The magnitude of the low increases as the FALCON gravity data

are less filtered. This is because the trough is about 20 – 30 km wide, so that it is strongly reduced in

magnitude when using the (20, 30) km filter, somewhat reduced by the (30, 40) km filter and hardly

affected by the (40, 50) km filter. The DNSC08 gravity data are generally unaffected by all of these

a b


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filters because they contain no information at these wavelengths. Therefore, the (40, 50) km filter is the

best in this circumstance.

Figure 10 (a) FALCON gravity conformed to DNSC08 gravity using filter wavelengths of 20 and 30 km

over the West Africa study area. (b) The difference between FALCON gravity conformed to DNSC08

using filter wavelengths (20,30) km and (30,40) km. The RMS is 2.6 mGal. (c) FALCON gravity

conformed to DNSC08 gravity using filter wavelengths of 30 and 40 km. (d) The difference between

FALCON gravity conformed to DNSC08 using filter wavelengths (40,50) km and (30,40) km. The RMS

is 5.0 mGal. (e) FALCON gravity conformed to DNSC08 gravity using filter wavelengths of 40 and

50 km.

The long wavelength trend direction in the conformed gravity have been changed away from the east-

west direction of the unconformed FALCON gravity into a direction approximately west-south-west.

The conformed results thus provide the best of both worlds: clearly mapping the shallow salt features

against the background of the major basement rift.

a b

c d

e


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DISCUSSION

In these examples, the available local gravimetry always suffered from inadequate coverage for our

purposes. The marine gravimetry at Bass Strait and the GT-1A gravimetry at Vredefort did not cover

the entire area of the respective FALCON surveys; the ground gravimetry at Vredefort had gaps

causing aliasing of the grid. For our examples, I trimmed the area of study to an intersection area to

allow me to make comparisons but this is not appropriate for commercial surveys. The DNSC08

gravity data are available everywhere. There are no gaps in coverage and this is its advantage. In the

fortunate situation of having several data sets, the practical approach would be to first merge the local

gravimetry into the DNSC08 to get the best previously available gravimetry over the area, and then

conform the FALCON gravity into the merged gravity to add the high resolution gravity information.

Figure 11. Applications of gravity in geophysics mapped by wavelength and gravity amplitude. Noise

levels are shown for airborne gravimetry (blue), FALCON AGG (purple) and the prediction for GOCE. It

is clear that the sum of FALCON and GOCE covers nearly the entire set of applications. The figure is

derived from Drinkwater et al. (2007).

The recent availability of the DNSC08 global gravity anomaly data means that global gravity data is

now readily available at a sensitivity and spatial resolution to be useful for constraining the long

wavelengths in FALCON AGG surveys. The Vredefort and Gippsland studies show RMS differences

with ground, marine and airborne gravimetry of 1.1 to 2.6 mGal. This is consistent with my

experience with other data sets. Where better quality gravity data are available, these should be

preferred over the DNSC08 gravity.


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The GOCE mission should deliver a further significant improvement in both sensitivity and resolution

(Drinkwater et al. 2006) to global gravity anomaly data (Figure 11).

CONCLUSIONS

I have demonstrated that the DNSC08 gravity can be used successfully to provide improved long

wavelength information for gravity data derived from FALCON AGG surveys. Occasionally, better

regional gravimetry will be available, either from data collected on the ground, in the air or at sea. In

all cases, the longer wavelengths from the data may be used to conform the FALCON gravity data and

provide the most accurate possible gravity information over the widest possible bandwidth.

ACKNOWLEDGEMENTS

I thank Fugro Airborne Surveys for permission to publish and in particular to show the results from

their GT-1A and FALCON AGG surveys over Vredefort, Xiong Li and Ole Andersen for helping me

understand global gravity from the geodesist’s perspective, VAALCO and David Cameron for

permission to show the West Africa FALCON AGG data, Stephen Saul for assistance with the

Gippsland Basin data and Alan Reid, Duncan Cowan and Gordon Cooper for their very useful input.

FALCON is a registered trade mark of Fugro.

REFERENCES

Ameglio L. 2005. New Fugro airborne gravity system – Survey test over the Vredeford structure

(South Africa). 67th EAGE Conference and Exhibition, Madrid, Spain, Extended Abstracts.

Andersen O. B., Knudsen P., Berry P. A. M., Kenyon S. and N. Pavlis 2008. The DNSC07 high

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APPENDIX 1. CROSS-OVER FILTERING

I use the radially symmetric cosine squared filter for both high and low pass filtering because it

behaves reasonably well and the sum has unity gain everywhere so that the amplitude of the gravity

is preserved in the final conformed result. The low-pass filter is:

( )

0

2 0

0 1

1 0

1

1 for

cos for 2

0 for

π

<

−= ≤ ≤

−

>

k k

k kL k k k k

k k

k k

(1.2)

Similarly, the high-pass filter is:

( )

0

2 1

0 1

0 1

1

0 for

cos for 2

1 for

π

<

−= ≤ ≤

−

>

k k

k kL k k k k

k k

k k

(1.3)

Selecting values for k0 and k1 must be done for each data set and there are some obvious guidelines to

assist in this selection. The crossover filter wavenumbers ought to be chosen so that maximum

accuracy is retained across the widest possible bandwidth. I find it convenient to give the values as

wavelengths rather than wavenumbers in these guidelines:

� When conforming FALCON gravity to any regional gravity, the cross-over wavelengths

should be larger than twice the regional gravity sample spacing.

� When conforming FALCON gravity to airborne gravimeter data, I prefer that the cross-over

wavenumbers are about 20 km (based on Boggs and Dransfield 2004).

� When conforming FALCON gravity to DNSC08 gravity, the cross-over wavelengths should

be greater than 20 km because the DNSC08 has only 0.5 coherence at 18 km. I generally prefer

to use wavelengths of more than 30 km.

� I prefer that the filter wavelengths are not significantly larger than the length of the FALCON

survey area. If there are large gravity anomalies just outside the FALCON survey area then it

is likely that FALCON gravity information at longer wavelengths may be less reliable.

2009 Dransfield - conforming falcon gravity and the global gravity anomaly

Science

gravity error

derived gravity

gravity field

abstract gravity

regional gravity data

long wavelength gravity

measured gravity gradients

conf orming falcon gravity