8/01/13
This version is more completely described in the following reference.

Sandwell, D. T., E. Garcia, K. Soofi, P. Wessel, M. Chandler, and W. H. F. Smith, Towards 1 mGal Global 
Marine Gravity from CryoSat-2, Envisat, and Jason-1, The Leading Edge, August, 2013

http://topex.ucsd.edu/sandwell/publications/144.pdf

10/05/12

The improvements in this gravity model V20.1 are the addition of Jason-1 altimetry data using two years from two interleved repeat intervals as well as 120 days from the new geodetic mission orbit.  In addition 24 months of CryoSat data were used and more repeat cycles of Envisat data were added to help fill gaps in the polar regions. (filter is 0.5 gain at 16 km wavelength).

01/14/12

The improvements in this gravity model V19.1 are related to the use of 16 months of CryoSat altimetry data (LRN, SAR, and SIN).  In addition 12 months Envisat data from the new 30-day repeat ground track were used. The vertical gravity gradient file is now the total vertical vravity gradient and the units are 0.1 Eotvos unit so they can be treated just like the gravity data in GMT.

12/5/08

The improvements in V18.1 are described in the following publication 
which is in press at JGR.

Sandwell, D. T., and W. H. F. Smith, Global marine gravity from retracked Geosat and ERS-1 
altimetry: Ridge Segmentation versus spreading rate, J. Geophys. Res., in press, October, 2008
http://topex.ucsd.edu/sandwell/publications/122.pdf

ABSTRACT
Three approaches are used to reduce the error in the satellite-derived marine gravity anomalies.   
First, we have retracked the raw waveforms from the ERS-1 and Geosat/GM missions resulting in 
improvements in range precision of 40% and 27%, respectively.   Second, we have used the 
recently-published EGM2008 global gravity model as a reference field to provide a seamless 
gravity transition from land to ocean.  Third we have used a biharmonic spline interpolation 
method to construct residual vertical deflection grids. Comparisons between shipboard gravity 
and the global gravity grid show errors ranging from 2.0 mGal in the Gulf of Mexico to 4.0 mGal 
in areas with rugged seafloor topography.  The largest errors of up to 20 mGal occur on the 
crests of narrow large seamounts.  The global spreading ridges are well resolved and show 
variations in ridge axis morphology and segmentation with spreading rate.  For rates less 
than about 60 mm/yr the typical ridge segment is 50-80 km long while it increases dramatically 
at higher rates (100-1000 km).  This transition, spreading rate of 60 mm/yr also marks the 
transition from axial valley to axial high.  We speculate that a single mechanism controls 
both transitions; candidates include both lithospheric and asthenospheric processes.

3/19/07

Version 16.1 gravity is similar to V15.1 except that the
gravity field runs to a higher latitude.

param   V15.1     V16.1
___________________________
nlon     21600    21600
nlat     12672    17280
rlt0   -72.006  -80.738
rltf    72.006   80.738
___________________________
The projection is the same spherical Mercator used in all of our
other gravity grids.

Some additional parameters for this model:
 - low-pass filter has a 0.5 gain  at a wavelength of 14 km.
 - the tension in the bi-harmonic spline fit is 0.25
 - there is one spline knot for every other grid cell.  V15
   had a spline knot for every third grid cell.

The file curv.img.15.1 is a file of vertical gravity gradient
derived from the curvature of the ocean surface.  The units
of this file are 0.05 Eotovos units.  Note that the EGM96
gravity model was not added back to the grid so the long wavelengths
(> 200 km are absent).

5/1/05

Version 15.1 gravity is a major improvement over V11.1 and all previous
versions.

Here is an evaluation of this model in relation to previous models
based on the rms difference (mGal) between the satellite gravity and three
shipboard gravity profiles.

ship            V7.2    V8.1    V9.1    V11.1   V15.1
_____________________________________________________
conrad 2802     4.42    4.17    4.00    3.33    2.63
conrad 2912     5.85    5.66    5.44    5.15    3.99
ewing 921       4.07    3.64    3.56    4.03    2.85
_____________________________________________________
More extensive evaluations including a blind analysis by
Marcia Maia at IFREMER can be found at:
ftp://topex.ucsd.edu/pub/sandwell/grav_eval

Specific improvements:
1) All ERS-1 geodetic mission data were retracked to improve the along-
track slope precision from 8.23 microradians to 4.01 microradian.
The along-track resolution of repeat profiles also improves from
43 km to 32 km.  A more complete discussion of the retracking methods
as well as results are provided in [Sandwell and Smith, GJI, 2004]
http://topex.ucsd.edu/sandwell/publications/105.pdf

2) The second major improvement is that all Geosat Geodetic Mission
data were retracked using the same basic algorithm.  These data will
be available at the NOAA Laboratory for satellite Altimetry.  Please
contact John Lillibridge John.Lillibridge@noaa.gov

3) We applied a correction for amplitude and phase shift in Geosat and
Topex data (not retracked) caused by the onboard alpha/beta tracker. The phase 
shift is 1.67 km along-track.  This shift caused some blurring of E-W oriented
gravity anomalies. 

4) Errors due to mesoscale variability and tides were removed from all along-
track slope profiles. This was accomplished by low-pass filtering the difference
between the profiles and the V11.1 grid using a filter with a 0.5 amplitude
gain at 120 km wavelength.  This smoothed difference, which absorbs the mesoscale
variability and tide error, was then removed from each profile. 

5) A major difference in this version is that residual along-track slopes
were gridded using biharmonic splines in tension. The primary references are:

Sandwell, D. T., Biharmonic Spline Interpolation of GEOS-3 and SEASAT Altimeter
Data, Geophys. Res. Lett., 14, 139-142, 1987

Wessel, P., and D. Bercovici, Interpolation with Splines in Tension: A
Green's Function Approach, Mathematical Geology, V. 30, no. 1,, p.77-93, 1998

The final conversion from north and east vertical deflection to gravity has a
wavelength of 16 km.

1/24/04

Version 11.1 is a major improvement over V10.2 because
it includes re-tracked ERS-1 data.  Retracking reduces
the noise level by 40%.

V11.1  -  low pass cutoff wavelength 14.4km

10/14/02
 
Version 10.2 is just like version 9.2 but a different
low-pass filtered was used.

V9.1  -  low pass cutoff wavelength 14.4km
V10.1 -  low pass cutoff wavelength 17.1km

06/04/99

Version 9.1 recalculated from filtered north and east grids.
Result is the same but the hit map was added in a different
way.  Gravity values were forced to be even using nint and then 1 was
added if this pixel was hit.

01/06/99

Version 9.1 is similar to version 8.1.  The main change
is that the along-track data were low-lass filtered with a 0.5 gain at
12 km wavelength.  Version 8.1 used a 10 km wavelength.  The 2-D filter
applied later in the processing still has a 0.5 gain at 18 km so the
additional along-track filter has little effect on the final resolution
of the grid.

Here is a simple evaluation of the grid based on the
rms difference (mGal) between the satellite gravity and three
shipboard gravity profiles.

ship		V7.2	V8.1	V9.1
_____________________________________
conrad 2802	4.42	4.17	4.00
conrad 2912	5.85	5.66	5.44
ewing 921	4.07	3.64	3.56
_____________________________________


12/20/98

Version 8.1 is based on completely new gridding software for computing 
marine gravity anomaly from along-track sea surface slope profiles 
[Sandwell & Smith, JGR v102, #B5, 10,03910,054, 1997].  More efficient 
numerical code enables us to grid the data at a finer 1 minute resolution. 
Other improvements include:
- increased short wavelength resolution is achieved through less 
filtering of the vertical deflection grids (0.5 gain at 18 km instead of 
24 km);
- better matching of gravity anomalies across coastlines is achieved by 
using EGM96 to degree 360, as opposed to JGM3 to degree 70;
- a new iteration scheme enforces a consistency check such that the 
components of vertical deflection have zero curl;
- finally, a global approach to the two-dimensional FFT coupled with a 
higher degree reference model enables us to construct geoid height in 
addition to gravity anomaly.

The results show better short wavelength gravity resolution, especially 
at the crests of seamounts.  However, the noise level increases in 
proportion to the change in resolution.  Agreement with ship gravity 
measurements reduces the rms misfit to a typical value of 4.2 mGal from 
4.5 mGal.

This version includes the following data:
all ERS-1 GM data (two 176-day cycles Ocean Product)
all Geosat/GM data
stack of 62 repeat cycles of Geosat/ERM
stack of 42 repeat cycles of ERS 35-day repeat
stack of 120 repeat cycles of TOPEX 10-day repeat

Please try our web site.
http://topex.ucsd.edu/mar_grav.html

Version 8.1 gravity file also encodes the locations of the altimeter
measurements in the lowest bit.  Anomalies are stored as milligal times 10,
rounded to the nearest even value.  Even numbers signify no altimeter 
measurement in that cell while odd numbers (10*milligal +1)
signify the cell contains a measurement.  The programs img2xyz and img2grd
have been modified to use this information and thus require more options.

The files in this directory contain global marine gravity anomalies
gridded on a Mercator projection  The grid was derived 
from the following data sources:

Geosat/ERM - Average of 62 Geosat Exact Repeat Mission profiles.

Geosat/GM  - Recently declassified Geosat Geodetic mission data for
             for all ocean areas.  The original Geosat/GM GDR's can be 
             obtained on CD-ROM from:

             National Oceanographic Data Center
             User Services Branch
             NOAA/NESDIS E/OC21
             1825 Connecticut Ave., NW
             Washington, DC 20235

             Tel. 202-606-4549
             Internet: services@nodc2.nodc.noaa.gov

ERS        - ERS OPR GDR's from the first 42 repeat cycles
             of the 35-day repeat orbit were averaged to
             improve their accuracy and resolution.


ERS-1/GM   - ERS-1 OPR GDR's from the entire geodetic mission

TOPEX      - TOPEX GDR's from the first 120 repeat cycles of the mission.

The gridded data are stored in an integer*2 format without any 
header or record information. 

grav.8.1.img       A 12672 by 21600 grid of 2-byte integers = 547,430,400 bytes.
                   Byte order is big_endian.
                   The gravity anomaly units are 0.1 milligal. An even
                   value signifies the cell does not have an altimeter
                   measurement while an odd value signifies that it does.
                   The Mercator projected image spans longitudes from 0 E to
                   360 E and latitudes from 72.006 N to -72.006 N.
                   A spherical earth is used for the Mercator projection.
                   The center of the upper left grid cell (i.e. the first
                   integer in the file) is located at 72.0009 N, .00833333 E.
                   Longtiudes increase with a 1/30 degree spacing.  The
                   The center of the last integer in the file is located 
                   at -72.0009 N, 359.933 E.

The files can be accessed either with the program img2xyg or the GMT program
img2grd.  In addition, it can be used with image processing programs such
ER-Mapper or GIPS.

img2xyg          - A Fortran/C program to extract a sub area from the global
                   gravity grid and write an ascii file of longitude, latitude,
                   gravity anomaly values.  This file can be gridded using
                   any standard gridding program such as the GMT programs
                   xyz2grd or surface. Either all of the grid cells can be
                   output or just those cells that contain an altimeter
                   measurement.

interp_ship      - A Fortran/C program to interpolate the gravity field along
                   a random ship track.

img2mercgrd      - GMT users can make a .grd file of a sub region with either of these
img2latlongrd      two programs.  These programs should be obtained from the GMT3.0
                   supplements tar file.

grav.8.1.img.ers - A header for ER-Mapper with the proper projection information.

gips_grav.head   - A GIPS header to attach to the front of world_grav.img.new.
                   (GIPS is an image processing package written by Peter Ford
                    at MIT.  It is primarily used for Planetary applications.)


6/3/96

Version 7.2 is described in the following reference:

Sandwell, D. T. and W. H. F. Smith, Marine Gravity from Geosat and ERS-1 Altimetry, 
J. Geophys. Res., 102, 10039-10054, 1997.
http://topex.ucsd.edu/sandwell/publications/71.pdf
