# talwani3d¶

talwani3d - Compute geopotential anomalies over 3-D bodies by the method of Talwani

## Synopsis¶

talwani3d [ modeltable ] [ -A ] [ -Drho ] ] [ -Ff|n|v ] [ -Goutfile ] [ -Iincrement ] [ -M[h][v] ] [ -Ntrackfile ] [ -Rregion ] [ -Zlevel|obsgrid ] [ -V[level] ] [ -bibinary ] [ -dnodata ] [ -eregexp ] [ -fg ] [ -iflags ] [ -oflags ] [ -r ] [ -x[[-]n] ]

Note: No space is allowed between the option flag and the associated arguments.

## Description¶

talwani3d will read the multi-segment modeltable from file or standard input. This file contains contours of a 3-D body at different z-levels, with one contour per segment. The segment header must contain the parameters zlevel rho, which states the z contour level and the density of this slice (individual slice densities may be overridden by a fixed density contrast given via -D). We can compute anomalies on an equidistant grid (by specifying a new grid with -R and -I or provide an observation grid with elevations) or at arbitrary output points specified via -N. Chose from free-air anomalies, vertical gravity gradient anomalies, or geoid anomalies. Options are available to control axes units and direction.

## Required Arguments¶

modeltable
The file describing the horizontal contours of the bodies. Contours will be automatically closed if not already closed, and repeated vertices will be eliminated.
-Ixinc[unit][+e|n][/yinc[unit][+e|n]]
x_inc [and optionally y_inc] is the grid spacing. Optionally, append a suffix modifier. Geographical (degrees) coordinates: Append m to indicate arc minutes or s to indicate arc seconds. If one of the units e, f, k, M, n or u is appended instead, the increment is assumed to be given in meter, foot, km, Mile, nautical mile or US survey foot, respectively, and will be converted to the equivalent degrees longitude at the middle latitude of the region (the conversion depends on PROJ_ELLIPSOID). If y_inc is given but set to 0 it will be reset equal to x_inc; otherwise it will be converted to degrees latitude. All coordinates: If +e is appended then the corresponding max x (east) or y (north) may be slightly adjusted to fit exactly the given increment [by default the increment may be adjusted slightly to fit the given domain]. Finally, instead of giving an increment you may specify the number of nodes desired by appending +n to the supplied integer argument; the increment is then recalculated from the number of nodes and the domain. The resulting increment value depends on whether you have selected a gridline-registered or pixel-registered grid; see GMT File Formats for details. Note: if -Rgrdfile is used then the grid spacing has already been initialized; use -I to override the values.
-Rxmin/xmax/ymin/ymax[+r][+uunit] (more …)
Specify the region of interest.

## Optional Arguments¶

-A
The z-axis should be positive upwards [Default is down].
-Dunit
Sets fixed density contrast that overrides any setting in model file, in kg/m^3.
-Ff|n|v
Specify desired gravitational field component. Choose between f (free-air anomaly) [Default], n (geoid) or v (vertical gravity gradient).
-Goutfile
Specify the name of the output data (for grids, see GRID FILE FORMATS below). Required when an equidistant grid is implied for output. If -N is used then output is written to stdout unless G specifies an output file.
-M[h][v]
Sets units used. Append h to indicate horizontal distances are in km [m], and append z to indicate vertical distances are in km [m].
-Ntrackfile
Specifies locations where we wish to compute the predicted value. When this option is used there are no grids and the output data records are written to stdout.
-V[level] (more …)
Select verbosity level [c].
-Zlevel|obsgrid
Set observation level either as a constant or give the name of a grid with observation levels. If the latter is used the the grid determines the output grid region [0].
-bi[ncols][t] (more …)
Select native binary input. [Default is 2 input columns].
-d[i|o]nodata (more …)
Replace input columns that equal nodata with NaN and do the reverse on output.
-e[~]”pattern” | -e[~]/regexp/[i] (more …)
Only accept data records that match the given pattern.
-fg
Geographic grids (dimensions of longitude, latitude) will be converted to km via a “Flat Earth” approximation using the current ellipsoid parameters.
-h[i|o][n][+c][+d][+rremark][+rtitle] (more …)
Skip or produce header record(s). Not used with binary data.
-icols[+l][+sscale][+ooffset][,] (more …)
Select input columns and transformations (0 is first column).
-ocols[,…] (more …)
Select output columns (0 is first column).
-r (more …)
Set pixel node registration [gridline].
-x[[-]n] (more …)
Limit number of cores used in multi-threaded algorithms (OpenMP required).
-:[i|o] (more …)
Swap 1st and 2nd column on input and/or output.
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option (but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.

## Units¶

For map distance unit, append unit d for arc degree, m for arc minute, and s for arc second, or e for meter [Default], f for foot, k for km, M for statute mile, n for nautical mile, and u for US survey foot. By default we compute such distances using a spherical approximation with great circles. Prepend - to a distance (or the unit is no distance is given) to perform “Flat Earth” calculations (quicker but less accurate) or prepend + to perform exact geodesic calculations (slower but more accurate).

## Examples¶

To compute the free-air anomalies on a grid over a 3-D body that has been contoured and saved to body.txt, using 1.7 g/cm^3 as the density contrast, try

gmt talwani3d -R-200/200/-200/200 -I2 -G3dgrav.nc body.txt -D1700 -Fg


To obtain the vertical gravity gradient anomaly along the track in crossing.txt for the same model, try

gmt talwani3d -Ncrossing.txt body.txt -D1700 -Fv > vgg_crossing.txt


Finally, the geoid anomaly along the same track in crossing.txt for the same model is written to n_crossing.txt by

gmt talwani3d -Ncrossing.txt body.txt -D1700 -Fn -Gn_crossing.txt


## References¶

Kim, S.-S., and P. Wessel, 2016, New analytic solutions for modeling vertical gravity gradient anomalies, Geochem. Geophys. Geosyst., 17, http://dx.doi.org/10.1002/2016GC006263.

Talwani, M., and M. Ewing, 1960, Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape, Geophysics, 25, 203-225.