U.S. DEPARTMENT OF THE INTERIOR 

U.S. GEOLOGICAL SURVEY

DIGITAL GRID OF ISOSTATIC RESIDUAL GRAVITY 

OF NORTH AMERICA: A DIGITAL DATABASE

By 

R.W. Simpson and R.C. Jachens^

Open-File Report 95-238

This report is preliminary and has not been reviewed for conformity with U.S. Geological 

Survey editorial standards or with the North American Stratigraphic Code. Any use of 

trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

1995 

iMenlo Park, CA 94025
DIGITAL GRID OF ISOSTATIC RESIDUAL GRAVITY 

OF NORTH AMERICA

by R.W. Simpson and R.C. Jachens

A digital grid of isostatic residual gravity of North America (figure 1) was prepared using 

an Airy-Heiskanen model of local compensation with the following parameters: density 

of topographic load, 2.67 g/cm^; density contrast across the bottom of root, 0.35 g/cm^; 

depth to bottom of root for elevations at sea level, 30 km. The isostatic correction 

procedure is discussed in detail in Simpson and others (1986). Data gaps in Greenland, 

parts of western Canada, eastern Russia, and Mexico are caused by absence or 

unavailability of Bouguer gravity values.

Although global studies of the Earth's gravity field (e.g. Heiskanen and Vening Meinesz, 

1958; Bowin, 1985) indicate that, on a worldwide scale, isostatic compensation obtains 

to a high degree, no single isostatic model or set of isostatic parameters is likely to 

adequately describe the geometry of compensating masses over an entire continent. 

However, the depth of the compensating masses will tend to smooth out their 

gravitational signal at the Earth's surface, and differences between various isostatic 

models will tend to be smooth and long-wavelength. If one's goal is to enhance the 

gravitational anomalies produced by geologic bodies in the upper crust, then to first 

order, the application of some isostatic correction is more important than the exact details 

of the compensation model used.

It is important to realize that the isostatic residual anomalies appearing on this map, 

especially those with wavelengths of 1000 km or less, do not necessarily imply the 

existence of isostatic imbalance. Simpson and others (1986) pointed out that isostatic 

residual anomalies can exist over density heterogeneities in the middle and upper crust 

even when such heterogeneities are in perfect isostatic equilibrium. Most of the shorter 

wavelength anomalies on this map can be attributed to geologic bodies in the middle or 

upper crust, and most of these bodies, we think, are likely to be nearly in isostatic 

equilibrium. Longer wavelength anomalies on this map may reflect isostatic imbalance 

or possibly density heterogeneities deep within the Earth's mantle or core that are 

effectively decoupled from the shallow isostatic system. The broad isostatic residual 

gravity low centered over Hudson Bay in Canada probably does reflect isostatic 

disequilibrium caused by melting of the great Pleistocene ice sheets. Also, the broad 

gravity highs over the Pacific Ocean south of the Aleutian Islands of Alaska and 

southwest of the west coast of Central America probably reflect dynamic processes 

associated with the subduction of oceanic lithospheric plates. For more information on 

the significance of isostatic residual gravity anomalies and for discussion of some
individual anomalies within the conterminous United States, see Simpson and others 

(1986,1988) and Jachens and others (1989).

Additional processing can be performed on isostatic residual maps to remove, at least to 

first order, the gravitational effects of compensating masses supporting dense bodies 

within the crust. (The isostatic correction has removed the compensating masses 

supporting topographic loads.) This additional processing results in a "decompensative 

gravity anomaly map" as described by Cordell and others (1991). This processing has 

not been applied to the grid described in this report.

The construction of an isostatic residual gravity map requires, in addition to an isostatic 

model, a Bouguer gravity data set to which the isostatic correction is applied and a 

topographic data set to define the geometry of the compensating masses in the model. 

Bouguer gravity data came from the gridded digital data set used to prepare the Decade of 

North American Geology (DNAG) gravity anomaly map of North America (Committee 

for the Gravity Anomaly Map of North America, 1987). For the offshore areas where 

this grid contains free-air gravity anomalies, Bouguer anomalies were computed using 5- 

minute average elevations from a world topographic data set obtained from the National 

Oceanic and Atmospheric Administration (NOAA) Data Center in Boulder, Colorado, 

USA. The resulting Bouguer gravity grid has a 6-km by 6-km interval based on the 

DNAG transverse Mercator projection. The model Airy-Heiskanen isostatic root, used to 

calculate the isostatic correction, was also defined by the 5-minute average elevations 

obtained from the NOAA Data Center.

The digital grid of isostatic residual gravity of North America has the following 

specifications:

columns 1495

rows 1430

x0 -4480 km

y0 700km

dx 6km

dy 6km

projection DNAG transverse Mercator

central meridian long. 100° W.

base latitude lat. 0°

The grid is stored by rows, beginning at the lower left corner of the map area. xo and yo 

are the projected coordinates of the lower left grid point; dx and dy are the intervals 

between columns and rows, respectively. Grid elements with values greater than 1x10^8
denote locations for which no gravity values were available in the starting grid used to 

prepare the gravity anomaly map of North America.

The grid is available in a binary form called "Branch of Geophysics Standard Grid 

format" as well in a compressed (using the Unix compress command) ascii form. A 

description of the Standard Grid format is given in Appendix A. The uncompressed ascii 

version can be converted to binary Standard Grid form using a Fortran?? program called 

ascii2sg.f which is described in Appendix B. This program could be modified to convert 

the grid to other binary or ascii formats if desired.

To obtain the database by anonymous ftp, contact Robert W. Simpson (telephone 415- 

329-4865; FAX 415-329-5163: E-mail simpson@gold.wr.usgs.gov) or Robert C. Jachens 

(telephone 415-329-5300; E-mailjachens@mojave.wr.usgs.gov).

REFERENCES CITED

Bowin, Carl, 1985, Global gravity maps and the structure of the Earth, in Hinze, W.J. ed., 

The Utility of Regional Gravity and Magnetic Anomaly Maps: Tulsa, Oklahoma, 

USA, Society of Exploration Geophysicists, p. 88-101.

Committee for the Gravity Anomaly Map of North America, 1987, Gravity anomaly map 

of North America: Boulder, Colorado, Geological Society of America, 5 sheets, scale 

1:5,000,000.

Cordell, Lindrith, Zorin, Y.A., and Keller, G.R., 1991, The decompensative gravity 

anomaly and deep structure of the region of the Rio Grande rift: Journal of 

Geophysical Research, v. 96, p. 6557-6568.

Heiskanen, W.A., and Vening Meinesz, F.A., 1958, The earth and its gravity field: New 

York, McGraw-Hill.

Jachens, R.C., Simpson, R.W., Blakely, R.J., and Saltus, R.W., 1989, Isostatic residual 

gravity and crustal geology of the United States, in Pakiser, L.C., and Mooney, W.D., 

eds., Geophysical Framework of the Continental United States: Geological Society of 

America Memoir 172, p. 405-422.

Simpson, R.W., Hildenbrand, T.C., Jachens, R.C., Barnes, D.F., 1988, Geologic 

implications of a new isostatic residual gravity map of North America: Geological 

Society of America, Abstracts with Programs, v. 20, p. A-325.

Simpson, R.W., Jachens, R.C., Blakely, R.J., and Saltus, R.W., 1986, A new isostatic 

residual gravity map of the conterminous United States with a discussion on the 

significance of isostatic residual anomalies: Journal of Geophysical Research, v. 91, 

p. 8348-8372.
APPENDIX A - STANDARD GRID FORMAT

The Branch of Geophysics "standard format" for binary storage of two-dimensional 

arrays consists of two basic parts: (1) a single header record that provides descriptive 

parameters about the two-dimensional array and (2) multiple records containing the 

gridded data.

A. Header record:

The header record contains the following parameters (assuming the x-axis is parallel to 

rows and the y axis is parallel to columns):

ID: 56 ascii characters of identification,

PGM: 8 ascii characters identifying the origin of the data,

NCOL: Number of columns of data (integer),

NROW: Number of rows of data (integer),

NZ: NZ = 1 (integer),

COL1: The x coordinate of the first column (real),

DCOL: The spacing between columns (real),

ROW1: The y coordinate of the first row (real),

DROW: The spacing between rows (real),

IPROJ: The projection code (integer) (12=DNAG),

CMER: The central meridian in degrees (real), and

BLAT: The base latitude in degrees (real).

Parameters COL1, DCOL, ROW1, and DROW should have consistent units (e.g., km).

B. Data records:

Each data record contains one dummy value followed by one row of the grid. Hence, 

the total record length is NCOL+1 words. Note that the first element of the array is the 

lower, left-hand corner of the grid; rows are entered one at a time from bottom to top.

The following Fortran code would read a standard grid:

DIMENSION GRID(500,500) 

CHARACTER ID*56,PGM*8

OPEN(10,FILE='JUNK.GRD', 

& STATUS='OLD',FORM='UNFORMATTED')

READ(10)ID,PGM,NCOL,NROW,NZ,COL1,DCOL,ROWl,DROW, 

& IPROJ,CMER,BLAT 

DO 100 J=1,NROW

READ(10) DUMMY,(GRID(I,J),1=1,NCOL) 

100 CONTINUE

CLOSE(10)
APPENDIX B - PROGRAM ascii2sg.f FOR CONVERTING ASCII FORM.

The format for the ascii version of the data grid can be inferred from the following listing 

for program ascii2sg.f:

cccccccccccccccccccccccccccccccccccccccccccccccccccc 

c ascii2sg.f

c Converts a grid file from ascii to 

c binary Standard Grid format.

character*80 infile, outfile 

character id*56,pgm*8 

dimension row(5000) 

integer iunit,ounit 

parameter (iunit=21, ounit=22)

c Open ascii input version:

print *, ' Ascii Infile: ' 

read '(a)', infile

open (iunit, file=infile, form='formatted 1 , 

& status='old')

c Open binary output version:

print *, ' Binary Outfile: ' 

read '(a)', outfile

open (ounit, file=outfile, form='unformatted 1 , 

& status='new')

c Read ascii version header information. 

read(iunit,1001) id,pgm

1001 format(a56,a8)

read(iunit,1002) ncol,nrow,nz

1002 format(6x,i8,8x,i8,6x,i8)

read(iunit,1003) xo,dx,yo,dy

1003 format(4(5x,e!4.8))

read(iunit,1004) iprj,cm,bl

1004 format(12x,i4,6x,el4.8,6x,el4.8) 

read(iunit,1005) rot,xcen,ycen

1005 format(6x,e!4.8,7x,e!4.8,7x,e!4.8)

c Write binary header.

write(ounit) id,pgm,ncol,nrow,nz,xo,dx,yo,dy, 

& iprj,cm,bl,rot,xcen,ycen

c Read ascii grid row by row and write to binary, 

do 50 j=l,nrow

call rdrowasc (iunit,ncol,row) 

call wrrowbin (ounit,ncol,row) 

50 continue

close(ounit) 

close(iunit) 

stop ' '
end

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc 

subroutine rdrowbin (iunit,ncol,zrow) 

dimension zrow(ncol) 

read(iunit) dum,zrow 

return 

end

subroutine wrrowbin (iunit,ncol,zrow)

dimension zrow(ncol)

dum=0.

write(iunit) dum,zrow

return

end

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc 

subroutine rdrowasc(iunit,ncol,zrow) 

dimension zrow(ncol) 

read(iunit,1001) dum 

read(iunit,1001) zrow 

1001 format(5el5.8) 

return 

end

subroutine wrrowasc(iunit,ncol,zrow) 

dimension zrow(ncol) 

dum= 0.

write(iunit,1001) dum 

write(iunit,1001) zrow 

1001 format(5e!5.8) 

return 

end

FIGURE CAPTION

Figure 1. Map of isostatic residual gravity of North America based on an Airy-Heiskanen 

model of local compensation with parameters: density of topographic load 2.67 g/cm^; 

density contrast across bottom of root, 0.35 g/cm^; depth to bottom of root for elevations 

at sea level, 30 km.
Isostatic Residual Gravity

A80'

50-

tomGal

1000 2000 3000 4000 5000 KM

70

60

50

403020

10

0

-10-20-30-40-50-60-70-80

(Figure 1