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Recommended Standards and Format for the

North American Gravity Database

by

Standards /Format Working Group,North American Gravity Database Committee

September 2003

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Outline

Executive SummaryIntroductionRole and Procedures of the Standards/Format Working GroupRecommendations

1. Data and Metadata Formats2. Datums

a. Horizontalb. Verticalc. Observed Gravity

3. Gravity Correctionsa. Theoretical (Ellipsoid) Gravityb. Height Correctionc. Bouguer Correctiond. Indirect Effect (Correction)e. Terrain (Bathymetry) Effectf. Atmospheric Effectg. Isostatic Compensation Effect

4. Gravity Anomaliesa. Free-Air Gravity Anomalyb. Complete Bouguer Gravity Anomalyc. Isostatic Gravity Anomalyd. Gravity Anomalies for Geodesy

5. Updating the Standards and Format of the DatabaseWorking GroupReferences

Executive Summary

Recognizing the need for improved regional gravity databases, aninternational effort by governmental agencies, universities, professionalorganizations, and private industry is underway to update the publiclyavailable North American Gravity Database. The current database thatwas released roughly two decades ago needs revision to improve itsoverall quality, coverage, observation density, and versatility.Considerable data have been made available in the intervening periodand improvements are possible in the calculation of gravity anomaliesby taking advantage of available terrain and geodetic models and high-

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speed data processing procedures and facilities. Data will be madeavailable in a web-based system as part of the U.S. GeoinformaticsProgram and through other governmental agencies. TheGeoinformatics Program is a fully integrated data system that hassoftware for accessing and processing the data, including mapping,profiling, modeling, and filtering and provides useful tutorials.

The database will have a comprehensive menu making it usefulfor those with differing scientific interests and backgrounds. The userwill be able to select desired corrections to the gravity data, units,datums, and type of gravity anomaly and retrieve information on thepredicted errors in the data. The default gravity anomalies (inmilligals) of the database based on internationally accepted datums andconstants will be useful for geological studies and most geophysicalinvestigations. In contrast to the current U.S. gravity database thepreferred (default) vertical datum for the gravity correctioncalculations is the Earth’s ellipsoid rather than the geoid (sea level),although users of the database may select an option that uses the geoidas the vertical datum. The difference in the gravity anomalies calculatedusing the ellipsoid vertical datum rather than the geoid will benegligible to most users. Database fields and formats will accommodatethe increasingly available high-resolution, airborne, satellite, marine,and gradient gravity data and will be modified appropriately asadditional data are obtained and improvements are made in dataprocessing. The database will be continually updated as additional dataare obtained and improvements are made in data processing.

A consensus viewpoint on the recommendations for standards andformats of the North American Gravity Database reached by aninternational Working Group are specified in this report. Theserecommendations follow internationally accepted procedures.Differences remain among the Group pertaining to details of theprocedures and emphasis; accordingly, alternatives to the consensus ordefault views are presented. The major differences pertain to thedivergence in views regarding nomenclature and methods of calculatinganomalies between geophysicists and geodesists. The majority of theusers of the database are anticipated to be geophysicists or thoseinterested in using the data for geological purposes. Thus, precedent isgiven to the geophysical view, but alternatives are provided in thedatabase to make it useful to geodesy as well. These recommendationsmay be useful in designing national gravity databases.

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IntroductionRecognizing the need for improved regional gravity databases, an

international effort by governmental agencies, universities, professionalorganizations, and private industry is underway to update the publiclyavailable North American Gravity Database. The current database consistingof both land and marine data that was released roughly two decades agoneeds revision to improve its overall quality, coverage, observation density,and versatility. Considerable data have been made available in theintervening period and improvements are possible in the calculation ofgravity anomalies by taking advantage of available terrain and geodeticmodels, geodetic datums, and high-speed data processing procedures andfacilities.

The revision process was initiated during a meeting of the NorthAmerican Gravity Database Committee at the 2002 Fall AGU Meetingbuilding upon current efforts in substantially improving the digital gravitydatabase of the United States. Plans and progress in the U.S. program arereported by Keller et al. (2002) and Hildenbrand et al. (2002a) and in U.S.Geological Survey Open-File Report 02-463 (Hildenbrand et al., 2002b).The Open-File Report is available at http://geopubs.wr.usgs.gov/open-file/of02-463. These publications explain the importance of the revisedgravity databases and the operational plan for implementing the U.S.database.

The long-term goal of the U.S. and North American gravity databaserevisions is “…to facilitate the creation of an open and flexible data systempopulated and maintained by user members of the Earth Sciencecommunity.” Gravity data contributed to the North American GravityDatabase (NAGDB) by agencies, universities, companies, and individualswill be processed in a uniform manner from the principal facts of the gravityobservations. These data will be made available in a web-based data systemas part of the U.S. Geoinformatics Program and through other governmentalagencies. The Geoinformatics Program is a fully integrated data system thathas software for accessing and processing the data, including mapping,profiling, modeling, and filtering.

The database will provide a comprehensive menu making it useful forthose with differing scientific interests and backgrounds. The user will beable to select desired corrections to the gravity data, units used, datumsemployed, and type of gravity anomaly and retrieve information on thepredicted errors in the data. The default gravity anomalies (in milligals) ofthe database based on internationally accepted datums and constants will be

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useful for geological studies and most geophysical investigations. In contrastto the current U.S. gravity database the preferred (default) vertical datum forthe gravity correction calculations is the ellipsoid rather than the geoid (sealevel), although users of the database may select an option that uses thegeoid as the vertical datum. The difference in the gravity anomaliescalculated using the ellipsoid vertical datum rather than the geoid will benegligible to most users. Database fields and formats will accommodate theincreasingly available high-resolution, airborne, satellite, marine, andgradient gravity data.

This web-based system, including data, analysis and processingsupport, and useful tutorials will be available to gravity experts, bothgeophysicists and geodesists, as well as to the growing body of non-specialists interested in gravity data. Plans call for upgrading the NorthAmerican Gravity Database as additional data are obtained andimprovements are made in data processing.

Role and Procedures of the Standards/Format Working GroupAn important objective of the revision of the North American Gravity

Database is to improve and standardize the methodology and formulae usedin preparing and presenting the principal facts of the observations andcorrection of these data into gravity anomalies. The Standards/FormatWorking Group, consisting of representatives of the involved NorthAmerican countries and the various constituencies using and developing thedatabase, was established to make recommendations for achieving this goalbuilding on internationally accepted protocols, formulae, and parameters.Each nation may choose standards and formats to comply with their nationalinterests, procedures, and standards, but the mission of the Working Groupis to reach a consensus on recommendations for the standards and formats tobe used in preparing the North American Gravity Database for public web-based distribution. These recommendations may prove useful in designinggravity databases for individual nations.

In considering the standards and formats to be used in the NAGDBthe Working Group used as a starting point the operational plan of the U.S.Gravity Database as specified in Open-File 02-463. The decisions regardingthe U.S. database were developed from presentations and discussions at anAugust 2002 workshop and subsequent communications among the gravitydata community. Members of the Standards/Format Working Group for theNAGDB were solicited for their views together with supporting material onprocedures, formats, formulae, and parameters. These recommendationswere sent to appropriate focus group leader who had the responsibility of

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organizing suggestions on a specific component of the problem, e.g.,datums, anomalies, and terrain and bathymetry effects.

A consensus viewpoint on the recommendations, as specified in thisreport, was developed from this input. However, differences remain amongthe Group pertaining to details of the procedures and emphasis. Whereverpossible alternatives are presented to the consensus or default views. Themajor differences pertain to the divergence in views regarding nomenclatureand methods of calculating anomalies between geophysicists and geodesists(Hackney and Featherstone, 2003; Li, 2003). The majority of the users of thedatabase are anticipated to be geophysicists or those interested in using thedata for geological purposes. Thus, precedent is given to the geophysicalview, but alternatives are provided in the database to make it as useful aspossible to geodesy. The collateral information provided with the NAGDBneeds to emphasize this and provide specific and clear definition ofnomenclature and procedures used in preparing and presenting the databaseand options for use of the data in geodesy.

A Steering Committee of representatives of interested governmentalunits and the Co-Chairmen of the North American Gravity DatabaseCommittee, Tom Hildenbrand and Randy Keller, guided the overall effort ofthe Working Group. The members of the Working Group, SteeringCommittee, and the focus group leaders are listed at the end of this report.

RecommendationsA basic premise of the recommendations of the Working Group, as

explained in the U.S.G.S. Open-File Report 02-463 is that procedures andformats should be based on internationally accepted standards andmethodologies that are referenced in the geophysical literature andapplicable to the entire North American continent. The emphasis is onmaking the dataset of broad use to the geophysics community. However,international standards and formats do differ depending on the proposed useof the data and accuracy requirements. Procedures also may vary dependingon available computational power, software, and collateral data. As a resultthere is no single universal accepted standard or format. The recentdiscussion of standardization and errors in Bouguer gravity correctionsbetween LaFahr (1991a; 1991b; and 1998) and Talwani (1998) is evidencethat differences in procedures remain a matter of scientific debate.

A fundamental goal of the methodologies is a standardized procedurethat provides the observed and theoretical (or predicted) gravity values and,thus, the gravity anomalies at observation sites to an accuracy of the order ofa few hundredths of a milligal. This accuracy serves most geologic,

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geophysical, and geodetic purposes and is compatible with those obtainablein observations and corrections. However, increasing interest in data to ahigher accuracy for engineering, environmental, and subsurface reservoirstudies indicate that it is advisable to provide formats for gravity datarepositories that will accept and maintain data to a higher precision than ahundredth of a milligal.

The long-term goal for gravity anomaly calculations is to provideprocedures for specifying the theoretical (or predicted) gravity at anobservation site that account for the Earth’s sphericity, terrain, andbathymetry in a single correction based on local, regional, and global digitalelevation models using appropriate earth-material densities. Thesecalculations may be based on radial elements of a spherical Earth correctedfor the appropriate ellipticity. Limitations in current procedures andauxiliary data do not permit achievement of this long-term goal. Clearly,movement toward this goal will be an incremental process with the standardsand formats for a North American Gravity Database subject to change. As aresult they should be reviewed and evaluated on a regular basis.

Rather than suggest an unrealistic goal that cannot be reached in thenear term, the Working Group recommends the acceptance of severalcurrently used assumptions and approximations in the computation of theobserved and theoretical gravity values and anomalies. The resulting gravitydata for North America will serve most purposes. The goal is to achieve anaccuracy approaching a few hundredths of a milligal in the current database,but it is understood that this accuracy will not be reached for all gravityobservations and calculations of theoretical gravity at observation sites andanomalies. Many observations, corrections, and anomalies will have anaccuracy approaching a tenth of a milligal.

For the most part the recommendations of the Working Group followclosely those made for the U.S. Gravity Database as explained in U.S.G.S.Open-File Report 02-463, but there are notable differences particularly withregard to geodetic datums and resulting modifications in the correctionprocedure. The overall recommendations specified below include those ofthe U.S. Gravity Database where appropriate and modifications plusdocumentation with appropriate references. Alternative approaches are notedwhere there is significant support for them in the community. Specificrecommendations are presented in bold type.

1. Data and Metadata FormatsASCII format should be used for principal facts andmetadata. Separate formats will be needed for land and

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marine data. The fields should include not only theprincipal facts (location, station height, observedgravity, and terrain correction) together with anestimate of their errors, but collateral data such as thesource of the data, date of acquisition, date ofsubmission to the NAGDB, observational procedures,instrumentation, type of gravity observation, referencedatums used (e.g., the datum used to calculate theellipsoid height), density used in Bouguer and terraincorrections, related height data such as water depth formarine and lake observations, depth to undergroundobservations, and height above ground surface forairborne surveys, reference (base) gravity station, etc.The standard format of the International Association ofGeodesy’s Bureau Gravimetrique International shouldbe used wherever possible with additions, deletions,and modifications as recommended for the NAGDB.

Users of the database should be provided with a menufrom which they can request specified fields and units.Gravity values should be available in milligals and theSI unit of acceleration, m/s2. Longitude should beavailable in either a +360o field or in West longitudedegrees. The vertical position of the gravity observationshould be available in meters and feet and withreference to the ellipsoid (height) and to the geoid(elevation). The default (preferred) unit for gravity ismilligal and meter for vertical distance referenced tothe ellipsoid.

Fields should be provided in the format formeasurements of the vertical gradient of gravity inEötvös units and the estimated accuracy of themeasurement. It will be desirable to include fields fortensor gravity measurements, when these observationsare available to the database.

Geographical coordinates should be in decimal degreesto 7 places, heights (elevations) in meters to 3 places,and gravity observations and anomalies in milligals to 4

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places. Digits beyond the accuracy of the data shouldnot be given, i.e., they should be blank filled, not zerofilled. If error estimates are unavailable these errorfields should be blank. The source of the data should beprovided in a field that is keyed to a collateral data setproviding metadata on standards, references,procedures, errors, etc.

Components of terrain and isostatic correctionsdetermined by different procedures or to differentaccuracies should be listed independently. The errors ofeach component should be estimated and theprocedures used in the calculation of the componentshould be specified.

Most data sets will not justify the accuracy of theprescribed data format, but the additional digits inthe data fields will allow retention of the accuracy ofincreasingly available high-resolution gravity datathat may reach these limits.

Gravity values included in this format are observedgravity, gravity corrections, and anomalies.

Metadata that give information on data sources andtheir attributes as currently residing in databases suchas those of the U.S. National Imagery and MappingAgency should be retained because of theirimportance in appraising the data set. Similarinformation should be solicited from all data setscontributed to the NAGDB and placed in theappropriate fields.

Error estimates should be solicited for stationlocations, heights, observed gravity, terrain andisostatic corrections, and gravity anomalies of allnew data provided to the NAGDB.

The date of acquisition of the gravity observations aswell as the date the data are placed in the NAGDBshould be provided. The latter will permit users tointerrogate the database for data contributed since theuser’s last update.

The preferred (default) observed gravity and gravityanomalies are based on the recommended datums,

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constants, and procedures in this report, but it isunderstood that some users may wish to have gravityvalues based on other standards. This is particularlytrue when merging the new data with existing datasets based on other standards. Wherever possiblethese needs should be met by providing gravity datausing alternative datums, constants, and proceduresspecified by the user.

Web links should be provided to availabledescriptions of North American gravity benchmarks(base stations).

The format for satellite-derived gravity observationsshould follow standardized procedures used by theU.S. National Imagery and Mapping Agency.

2. Datumsa. Horizontal

The International Terrestrial Reference Frame(WGS84) should be used for the horizontal datumwith provision made for optimal conversion to otherhorizontal datums, e.g., NAD83, NAD27.

The International Terrestrial Reference Frame(ITRF) is internationally accepted and agrees withthe WGS84 reference frame to the one-centimeterlevel. However, it should be noted that platemotion causes annual movements that may exceedthis precision. Precise WGS84 coordinates agreewith ITRF coordinates at the ten-centimeter levelbecause WGS84 is a realization of the ITRF usingbroadcast satellite ephemeris precise to tencentimeters.

WGS84 has been subject to change. Its thirdversion (National Imagery and Mapping Agency,2000) is slightly different from the first version ofWGS84 and GRS80. GRS80 has not changed sinceits inception. Although we recommend WGS84 asthe vertical and horizontal datums and GRS80 asthe reference ellipsoid for theoretical gravity, thetwo different datums produce no significantrelative gravity differences. The gravity difference

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between the latest (third) version of WGS84 andGRS80 (or the first version of WGS84) is less than0.5 microgal for ellipsoid height up to 3000 mworldwide after removing an absolute level of0.1433 mGal. The gravity difference is mainlycaused by the GM difference (0.582) betweenWGS84 (3896004.418) and GRS (3896005). Toavoid confusion among datums of WGS84, werecommend the use of the ITRF datum.

ITRF is the coordinate system for satellite radar-derived gravity data sets over the oceans.

Software is readily available for converting fromone horizontal coordinate system to another.

b. VerticalEllipsoidal height relative to the ITRF (WGS84)datum should be used as the default verticaldistance with optimal conversion provided toother vertical datums, e.g., NGVD29, CVGD28,and NAVD88. Additionally, orthometric height(elevation) relative to appropriate national geoid(sea level) should be provided. As a result twoheights should be given for each station: theellipsoid height relative to the ellipsoid and theelevation relative to the accepted geoid for theregion.

No one vertical datum is appropriate for allregions. To achieve consistency therecommendation is to use ellipsoidal heightrelative to the same ITRF (WGS84) datumsuggested for the horizontal (latitude, longitude)coordinates.

The geoid models GEOID99 in the U.S. andHTv2.0 in Canada, as well as the transformationVERTCON in the U.S., provide software forconversion from one datum to another.

The recommended use of ITRF (WGS84) iscontrary to the suggestion to use the NGVD29datum for the U.S. Gravity Database (Hildenbrandet al., 2002b).

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Despite the common usage of NGVD29 in gravitystudies, NAVD88 is preferable to it because thenewer datum removes distortions found inNGVD29.

Canada can only produce elevations relative toCGVD28, i.e., mean sea level, which is consistentwith NGVD29 and Mexico is covered byNAVD88, but not by NGVD29 or CGVD 28.

A more accurate vertical datum and geoid isimminent from new global gravity data observedduring the Grace satellite mission. Accordingly,conversion of NGVD29 gravity-related heights toNAVD88 should be postponed until the GRACE-derived datums are available.

An ellipsoid-based vertical datum is advantageousbecause gravity observation positioning is nowcommonly obtained by GPS that provides theheight relative to the ellipsoid. Another advantageof the use of ellipsoid-referenced heights is that the‘indirect effect’ of gravity can be eliminated in thecalculation of gravity anomalies. This isparticularly beneficial to the geophysical use ofgravity (Li and Götze, 2001).

Use of the ellipsoidal height relative to the ITRF(WGS84) datum rather than the height relative tothe geoid will produce only very long-wavelengthBouguer and isostatic gravity anomaly differenceswith amplitudes of less than roughly 10 mGal. Asa result the effect of using the ellipsoidal heightwill be negligible on geological studies and mostgeophysical investigations.

c. Observed GravityObserved gravity should be referenced to IGSN71 without the Honkasalo term for tidaldeformation.

Observed gravity should be tied to theInternational Gravity Standardization Net 1971(IGSN71) (Morelli et al., 1974).

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The IGSN71 values include the Honkasalo (1964)correction for tidal deformation. This correctionshould be removed (Moritz, 1980), i.e., no tidalcorrection should be included in IGSN71. Morelliet al. (1974) give the Honkasalo term as

2sin31(0371.0 −=g ϕ) mGal,where ϕ is the latitude. The correction varies from+0.04 at the equator to –0.07 mGal at the poles.

Standard procedures for reducing gravitymeasurements to observed gravity should bespecified in the tutorial explanatory materialaccompanying the NAGDB. The use of IUGGrecommended procedures is encouraged for tidalcorrections, meter ‘drift’, local atmosphericeffects, calibration of gravimeters, and ties togravity benchmarks.

3. Gravity Correctionsa. Theoretical (Ellipsoid) Gravity

Theoretical gravity on the GRS80 ellipsoidshould be determined using the Somiglianaclosed-form equation. The theoretical gravity accounting for the mass,

shape, and rotation of the Earth is the gravity onthe best-fitting ellipsoidal surface of the Earth.The latest ellipsoid recommended by theInternational Union of Geodesy and Geophysics(IUGG) is the GRS80 (Moritz, 1980).Conversion to more modern ellipsoids has anegligible effect on the theoretical gravity (in therange of thousandths of a milligal). However, thisequation should be updated when recommendedby the IUGG.

The Somigliana closed-form formula to calculatethe theoretical gravity, ϕg at latitude ϕ, is

φ

ϕϕ

22

2

sin1

sin1

e

kgg e

−

+= .

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where the GRS80 reference ellipsoid has thefollowing values:

67715.978032=eg mGal k = 0.001931851353

e2 = 0.00669438002290. Corrections made in older reference systems can

be easily adjusted to the GRS80 system.Alternatively, corrections can be made topreviously accepted reference systems whenrequested by the database user.

b. Height CorrectionThe height correction should be calculatedusing the second-order approximationformula of Heiskanen and Moritz (1969) forthe change in theoretical gravity based on theGRS80 ellipsoid with height relative to theellipsoid. Historically, this height correction is called the

‘free-air’ correction and associated with theelevation (or orthometric height) above the geoid(sea level) and not the ellipsoid height.

Heiskanen and Moritz (1969, p. 79) give thesecond-order approximation formula for thiscorrection to the theoretical gravity for a heighth in meters relative to the ellipsoid as:

2sin)253(1[

2mfmf

a

gg eh +−+++−=

2

23]

a

hgh

e+ϕ

where the GRS80 ellipsoid has the followingparameter values:

a = semimajor axis = 6,378.137 km b = semiminor axis = 6,356.7523141 km

f = flattening = 0.003352810681

eg = 978,032.67715 mGal

GMbam /22ω= = 0.00344978600308 ω = angular velocity = 7,292,115 x 10-11

radians s-1

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GM = geocentric gravitational constant =3,986,005 x 108 m3s-2.

For the GRS80 ellipsoid the second-orderformula is

282 102125.7)sin0004398.03087691.0( hhgh−×+−−= ϕ

where the ellipsoid height h is in meters and hg isin milligals.

c. Bouguer CorrectionThe closed-form formula for the gravity effectof a spherical cap (LaFehr, 1991) of radius166.7 km based on a spherical Earth with aradius of 6371 km, height relative to theellipsoid, and a density of 2,670 kg/m3 shouldbe used in calculating the Bouguercorrection.

The Bouguer correction accounts for thegravitational attraction of a layer of the Earthwith a thickness equal to the difference inheight between the station and the verticaldatum; in this case, the ellipsoid.

This correction, BCg , has traditionally been

calculated assuming the Earth between thestation and the vertical datum is an infinitehorizontal slab, that is hGg

BCσπ2= where G =

gravitational constant = 6.673 +/- 0.01 x 10-11

m3kg-1s-2 (Mohr and Taylor, 2001) [Note: Thisis the most recently accepted value for G anddiffers from the value provided in GRS80], σis the density of the horizontal slab in kg/m3,and h is the height of the station in metersrelative to the ellipsoid in the procedurerecommended in this report rather than usingthe elevation H in meters above/below thegeoid or sea level. In this formulation thecorrection is given in units of m/s2 that isconverted to milligals by multiplying by 105.To avoid the effect of the curvature of theEarth, the closed-form formula of LaFehr

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(1991) for a spherical cap of radius 166.7 km isrecommended. According to LaFehr (1991, p.1181) the selection of the radius of 166.7 kmfor the spherical cap minimizes “…thedifferences between the effect of the cap andthat of an infinite horizontal slab for asignificant range of elevations.”

The choice of a density of 2,670 kg/m3 forsolid-earth material above/below the ellipsoid isbased upon an approximation to the averagedensity of the Earth relative to the ellipsoid(Chapin, 1996; Hinze, 2003). In the future theaverage density of the earth material relative tothe ellipsoid over the North American continentmay be mapped using deterministic methods.These density data could be incorporated intothe Bouguer and terrain corrections as analternative in calculating Bouguer and isostaticanomalies in future revisions of the NAGDB.

In the case of marine observations of gravitythe density of sea water is assumed as 1,027kg/m3, for fresh-water observations of gravitythe density of fresh water is 1,000 kg/m3, andfor observations of gravity on glaciers, thedensity of ice is 917 kg/m3.

d. Indirect Effect (Correction)The geophysical indirect effect correction isunnecessary if the default vertical datumrecommended for the NAGDB (the ellipsoidheight relative to the International TerrestrialReference Frame) is used in calculating theheight and Bouguer corrections. Nonethelessthis correction should be provided for eachstation for the user employing the geoid asthe vertical datum.

The ‘geophysical’ indirect effect, which isapplicable to all anomalies, is the gravitationaleffect produced by use of the elevation(orthometric height) relative to sea level (the

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geoid) rather than the height relative to theellipsoid in height-related gravity corrections.The adjective ‘geophysical’ is used todifferentiate it from the indirect effect ingeodetic studies. The difference betweenellipsoid height and elevation is the geoidheight that attains maximum values of the orderof +/-100 m. The indirect effect due to the useof elevation in the height and simple Bouguer(that assumes a horizontal layer) corrections hasthe same sign as the geoid height. Thegravitational effect of this correction for landobservations is 0.1967N mGal/m [(0.3086-2_G{2670})N] where N is the geoid height inmeters assuming a density of 2,670 kg/m3 forthe layer between the ellipsoid and the geoid. Asimilar correction (0.2656N mGal/m) is neededfor marine gravity observations assuming adensity of 1,027 kg/m3 for sea water (Chapmanand Bodine, 1979).

The indirect effect is spatially slowly varyingbecause of the low horizontal gradient of thegeoid. The amplitude of the geoid height forwavelengths shorter than 10 km is usuallysmaller than 10 cm, and the amplitude forwavelengths shorter than 100 km isconsiderably smaller than 1 m.

The use of a vertical datum which is theellipsoid height relative to the ITRF (WGS84)eliminates the need for consideration of thegeophysical indirect effect. Ellipsoid height isgiven directly by modern positioningtechnologies, such as GPS. Thus, the traditionalelevation or orthometric height is a derivedquantity from the ellipsoidal height. Forexample, the conversion of the ellipsoidalheight relative to the WGS84 ellipsoid toelevations can be accomplished usingGEOID99 for the U.S. (see

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http://www.ngs.noaa.gov/PUBS Lib/gislis96.html).

Despite the lack of need for this correction inthe preferred procedure it is recommended thatit be calculated for each station and be madeavailable to the user from the fields menu of thedatabase.

e. Terrain (Bathymetry) EffectA 3-part terrain effect procedure based ondistance from the station should beemployed as height data permits, using adensity for solid earth material of 2,670kg/m3, 1,000 kg/m3 for fresh water, 1,027kg/m3 for ocean water, and 917 kg/m3 forice:

1. Utilize near-station topographicinformation collected in the field,either by instrumentation or visualestimation, to a distance of about 100m from the station, to calculateterrain effects using the gravitationalattraction of a form of segmentedrings centered on the station (e.g.,Hammer’s (1939) method).

2. Use local high-resolution heightdata to calculate terrain effects to adistance of 895 m using a form ofsegmented rings centered on thestation (e.g., Hammer’s [1939]method).

3. Employ digital terrain model datato compute terrain effects from 895 mto 166.7 km based on vertical prismscentered on topographic grids usingPlouff’s (1966) algorithm on 15-sec,1-min, and 3-min topographic gridsand accounting for the Earth’scurvature beyond 14 km.

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The data collector is responsible for obtainingthe heights and terrain corrections of Parts 1.and 2. The selection of the outer distance ofPart 2. is consistent with the resolution of the15-sec terrain grid (≈450 m).

The terrain correction to 895 m can beapproximated with Plouff’s (1966) programusing the 15-sec terrain grid, but it should bestored separately from the corrections of Parts 1and 3. and users advised of its potential error.

It is understood that use of elevations(orthometric heights) for both heights of gravitystations and heights in digital terrain models interrain corrections, rather than heights relativeto the ellipsoid, will result in errors due to theindirect effect. The resulting errors arenegligible for most geophysical purposes, butfor consistency in procedures and to eliminatethese errors the ellipsoid height should be usedin terrain corrections as soon as practical. Thechange from digital elevation models to digitalheight models in the calculation of terraineffects should be implemented in futurerevisions of the North American GravityDatabase.

Long-term modifications to these proceduresshould extend the terrain and bathymetry to 500km and beyond using 2- and 5-min elevationand bathymetry grids and an elliptical Earth.Eventually a global correction should becomputed and made available in the NAGDB.Moreover, terrain corrections of improvedaccuracy especially in the inner zones willbecome possible as the higher-resolution digitalterrain models become available.

In the long-term, bathymetry corrections arenecessary taking into account the density of seaand fresh water as appropriate.

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Improved estimates of the densities of earthmaterials should be used in future revisions ofthe NAGDB.

Solid-earth material density should be modifiedwhen densities are available for grid points ofdigital terrain models.

f. Atmospheric EffectThe gravitational effect of the mass of theatmosphere should be determined bylinear interpolation with respect toelevation above sea level using the tablegiven in Moritz (1980). The mass of the atmosphere is included in the

theoretical gravity given by IGF80. The mass ofthe atmosphere decreases with increasingelevation of a station, thus, decreasing theatmospheric gravity effect.

The correction for the change in gravity due tothe mass of the atmosphere is added to theobserved gravity.

An alternative analytical approach for theatmospheric effect should be incorporated intofuture revisions of the NAGDB.

Correction of the observed gravity for localatmospheric mass variations is at the discretionof the data collector. Use of this correctionshould be noted in the NAGDB’s metadata ofthe contributed survey.

g. Isostatic Compensation EffectThe isostatic compensation effect shouldbe calculated with a modified version ofJachens and Roberts (1981) method thatassumes local compensation. The isostaticcorrection for varying depth to ahypothetical crust-mantle boundarycaused by differential topographic orbathymetric loads above or below theellipsoid should be based on a crust-

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mantle boundary density difference of __ =300 kg/m3 and a crustal thickness of 30 kmfor sea level surface elevation. Topographyis modeled assuming a continental crustaldensity of 2,670 kg/m3 using 3-minelements of topography to 166.7 km plusinterpolated values to 180o from Karki et al.(1961). The inverse correlation between regional

elevations and Bouguer gravity anomalies isinterpreted to reflect the gravimetric response totopographic loads by variations of the densityof the crust/lithosphere or a change in thethickness of the crust/lithosphere. To removethese subsurface regional effects the response totopographic loads is calculated by making thesimplifying assumption that the crust varies inthickness accordingly.

The isostatic compensation effect is computedin a manner similar to the terrain model usingthe Airy-Heiskanen model. In the near term thiswill be done using a modified version ofJachens and Roberts (1981) method. However,in the long-term consideration should be givento performing these calculations using a methodin the space domain consistent with theprocedures for calculating the terrain andbathymetry with appropriate global digitalterrain models and taking into account theellipticity of the Earth. It is important to extendthe calculation of the effect of isostaticcompensation to the entire Earth.

It is understood that use of (orthometric)elevations in isostatic corrections rather thanheights relative to the ellipsoid will result inerrors due to the indirect effect, as is the casefor terrain corrections. The resulting errors arenegligible for most geophysical purposes, butfor consistency in procedures and to eliminatethese errors the ellipsoid height should be used

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in isostatic corrections as soon as practical. Thechange from digital elevation models to digitalheight models in the calculation of isostaticeffects should be implemented in futurerevisions of the North American GravityDatabase.

The interpolated values from Karki et al. (1961)need to be replaced by an analytical form infuture revisions of the NAGDB.

The crust-mantle density differential is basedon the average density of the lower 10 km ofthe average global continental crust and thedensity of the uppermost mantle. The density ofthe 10 km layer at the base of the crust isassumed to consist of 50% mafic granulite and50% mafic garnet granulite that results in anaverage density of 3,040 kg/m3 (Christensenand Mooney, 1995; Figure 18). The uppermostmantle is assumed to consist primarily ofperidotite and has a compressional seismicwave velocity of 8.1 km/s. The correspondingdensity is 3,340 kg/m3 (Christensen andMooney, 1995; Figure 16).

The average global continental crustal thicknessweighted for crustal type is roughly 40 km(Christensen and Mooney, 1995; Figure 18).Based on the average continental elevation of 1km and assuming isostasy, the sea level crustalthickness is approximately 30 km. Both thecrust-mantle density contrast and the crustalthickness will vary not only from continental tooceanic crust, but also withgeologic/tectonic/petrophysical conditions.However, isostatic effects obtained fromdifferent crustal models vary by only a smallpercentage of their overall effect (e.g.,Simpson, Jachens, Blakely, and Saltus, 1986).

In the long term consideration should be givento improving the computational techniquesemployed in computing the isostatic

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compensation effect and the associatedparameters.

4. Gravity Anomaliesa. Free-Air Gravity Anomaly

Calculate the Free-Air Gravity Anomaly bydetermining the difference between theobserved gravity and the theoretical(predicted) gravity at the station takinginto account the theoretical gravity on theGRS80 ellipsoid, the height of the stationabove the ellipsoid and the atmosphericeffect.

b. Complete Bouguer Gravity AnomalyCalculate the Bouguer Gravity Anomaly bydetermining the difference between theobserved gravity and the theoretical(predicted) gravity at the station taking intoaccount the theoretical gravity on theGRS80 ellipsoid, the height of the stationabove the ellipsoid, the Bouguer andterrain effects, and the atmospheric effect.

Users should have the option of selectingthe solid-earth material density used in thecalculation of the Bouguer correction andterrain effects for the Bouguer GravityAnomaly. This also applies to the IsostaticGravity Anomaly.

In the future it may be possible to request avariable density for the Bouguer correctionand terrain effects based on estimates of thedensity of solid-earth materials over theNorth American continent. This also appliesto Isostatic Gravity Anomaly.

c. Isostatic Gravity AnomalyCalculate the Isostatic Gravity Anomaly bydetermining the difference between theobserved gravity and the theoretical

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(predicted) gravity at the station taking intoaccount the theoretical gravity on theGRS80 ellipsoid, the height of the stationabove the ellipsoid, the Bouguer andterrain effects, the atmospheric effect, andthe isostatic compensation effect.

d. Gravity Anomalies for GeodesyPrecedent is given to ‘geophysical’ gravityanomalies in the North American GravityDatabase. However, consideration ofgeodetic gravity anomalies is facilitated bythe availability of both height relative tothe ellipsoid and elevation relative to theregionally accepted geoid in 2.b., the useof both elevation and height in thecalculation of the terrain (3.e.) and theisostatic compensation effect (3.g.), andthe geophysical indirect effect (3.d.) foreach station.

5. Updating the Standards and Format of the NorthAmerican Gravity Database

The preferred standards and formatsrecommended above are a useful starting pointin preparing a NAGDB. They are achievable inthe near term building upon existing softwareand procedures and will provide very usefulgravity anomaly data for a wide range ofgeoscientists. However, as explained in theabove recommendations, improvements arepossible in these standards and formats thatwill serve the interests of the community ofusers. We suggest that the standards andformat of the database be monitored formodifications that can be made to improve itsaccuracy, effectiveness, and efficiency usingthe suggestions provided herein as a startingpoint. For example, we anticipate that theGRACE satellite mission will lead to definition of

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an improved global geoid that will improve theNAGDB. Potential contributors of gravity data tothe NAGDB should be alerted to the desiredmetadata including error estimates that aredesired for the database.

Working Group

Steering Committee:Tom Hildenbrand (tom@usgs.gov), Bill Hinze (chr.)(bima@ixpres.com) Randy Keller (keller@geo.utep.edu),Andre Mainville (mainville@nrcan.gc.ca), Jaime Urrutia-Fucugauchi (juf@tonatiuh.igeofcu.unam.mx), Mike Webring(mwebring@usgs.gov).

Working Group Membership:Steering Committee members plusCarlos Aiken (aiken@utdallas.edu)John Brozena (john.brozena@nrl.navy.mil)Bernard Coakely (Bernard.Coakley@gi.alaska.edu)David Dater (David.T.Dater@noaa.gov)Guy Flanagan (gflanag@ppco.com)Rene Forsberg (rf@kms.dk)Jim Kellogg (Kellogg@sc.edu)Bob Kucks (kucks@usgs.gov)Xiong Li (xli@fugro.com)Bob Morin (morin@usgs.gov)Mark Pilkington (mpilking@nrcan.gc.ca)Donald Plouff (plouff@mojave.wr.usgs.gov)Tiku Ravat (ravat@geo.siu.edu)Dan Roman (dan.roman@noaa.gov)Dan Winester (Daniel.Winester@noaa.gov)

Focus Group leaders:

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Datums – Andre MainvilleGravity Corrections exclusive of terrain effects – Xiong LiTerrain including bathymetry effects – Mike WebringGravity Anomalies – Carlos AikenFormat – Guy Flanagan

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