# talwani3d¶

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

## Synopsis¶

gmt talwani3d [ modeltable ] [ -A ] [ -Drho ] ] [ -Ff|n[lat]|v ] [ -Goutfile ] [ -Iincrement ] [ -M[h][v] ] [ -Ntrackfile ] [ -Rregion ] [ -Zlevel|obsgrid ] [ -V[level] ] [ -bibinary ] [ -dnodata ] [ -eregexp ] [ -fflags ] [ -iflags ] [ -oflags ] [ -rreg ] [ -x[[-]n] ] [ --PAR=value ]

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 horizontal contours of a 3-D body at different z-levels, with one contour per segment. Each segment header must contain the parameters zlevel rho, which states the z level of the contour and the density of this slice (optionally, 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 desired elevations) or at arbitrary output points specified via -N. Choose between 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. The segment header for each slice will be examined for the pair zlevel rho, i.e., the depth level of the slice and a density contrast in kg/m^3; see -D for overriding this value.
-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 (and registration) have already been initialized; use -I (and -r) 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 a fixed density contrast that overrides any individual slice settings in the model file, in kg/m^3.
-Ff|n|v
Specify desired gravitational field component. Choose between f (free-air anomaly) [Default], n (geoid; optionally append average latitude for normal gravity reference value [Default is mid-grid (or mid-profile if -N)]) 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 distance units used. Append h to indicate that both horizontal distances are in km [m], and append z to indicate vertical distances are in km [m].
-Ntrackfile
Specifies individual (x, y[, z]) 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. If trackfile has 3 columns we take the z value as our observation level; this level may be overridden via -Z.
-V[level] (more …)
Select verbosity level [c].
-Zlevel|obsgrid
Set observation level, either as a constant or variable by giving the name of a grid with observation levels. If the latter is used then this grid determines the output grid region as well [0].
-bi[ncols][t] (more …)
Select native binary format for primary 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.
-fflags
Geographic grids (i.e., dimensions of longitude, latitude) will be converted to km via a “Flat Earth” approximation using the current ellipsoidal 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][,][,t[word]] (more …)
Select input columns and transformations (0 is first column, t is trailing text, append word to read one word only).
-ocols[,…][t[word]] (more …)
Select output columns (0 is first column; t is trailing text, append word to write one word only).
-r[g|p] (more …)
Set 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.
--PAR=value
Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.

## 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 (-jg) using the authalic radius (see PROJ_MEAN_RADIUS). You can use -jf to perform “Flat Earth” calculations (quicker but less accurate) or -je to perform exact geodesic calculations (slower but more accurate; see PROJ_GEODESIC for method used).

## Examples¶

To compute the free-air anomalies on a grid over a 3-D body that has been contoured and saved to body3d.txt, using 1700 kg/m^3 as the fixed density contrast, with horizontal distances in km and vertical distances in meters, try

gmt talwani3d -R-200/200/-200/200 -I2 -Mh -G3dgrav.nc body3d.txt -D1700 -Ff


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

gmt talwani3d -Ncrossing.txt -Mh body3d.txt -D1700 -Fv > vgg_crossing.txt


Finally, the geoid anomaly along the same track in crossing.txt for the same model (at 30S) is written to n_crossing.txt by

gmt talwani3d -Ncrossing.txt -Mh body3d.txt -D1700 -Fn-30 -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.