Provided by: gmt_4.5.11-1build1_amd64

**NAME**

surface - adjustable tension continuous curvature surface gridding algorithm

**SYNOPSIS**

surface[xyzfile]-Goutputfile.grd-Ixinc[unit][=|+][/yinc[unit][=|+]]-Rwest/east/south/north[r] [-Aaspect_ratio] [-Cconvergence_limit] [-H[i][nrec] ] [-Lllower] [-Luupper] [-Nmax_iterations] [-Q] [-Ssearch_radius[m] ] [-Ttension_factor[i|b] ] [-V[l] ] [-Zover-relaxation_factor] [-:[i|o] ] [-bi[s|S|d|D[ncol]|c[var1/...]] ] [-fcolinfo]

**DESCRIPTION**

surfacereads randomly-spaced (x,y,z) triples from standard input [orxyzfile] and produces a binary grid file of gridded values z(x,y) by solving: (1 - T) * L (L (z)) + T * L (z) = 0 where T is a tension factor between 0 and 1, and L indicates the Laplacian operator. T = 0 gives the "minimum curvature" solution which is equivalent to SuperMISP and the ISM packages. Minimum curvature can cause undesired oscillations and false local maxima or minima (See Smith and Wessel, 1990), and you may wish to use T > 0 to suppress these effects. Experience suggests T ~ 0.25 usually looks good for potential field data and T should be larger (T ~ 0.35) for steep topography data. T = 1 gives a harmonic surface (no maxima or minima are possible except at control data points). It is recommended that the user pre-process the data withblockmean,blockmedian, orblockmodeto avoid spatial aliasing and eliminate redundant data. You may impose lower and/or upper bounds on the solution. These may be entered in the form of a fixed value, a grid with values, or simply be the minimum/maximum input data values.xyzfile3 column ASCII file [or binary, see-b] holding (x,y,z) data values. If no file is specified,surfacewill read from standard input.-GOutput file name. Output is a binary 2-D.grdfile. Note that the smallest grid dimension must be at least 4.-Ix_inc[and optionallyy_inc] is the grid spacing. Optionally, append a suffix modifier.Geographical(degrees)coordinates: Appendmto indicate arc minutes orcto indicate arc seconds. If one of the unitse,k,i, ornis appended instead, the increment is assumed to be given in meter, km, miles, or nautical miles, respectively, and will be converted to the equivalent degrees longitude at the middle latitude of the region (the conversion depends onELLIPSOID). If /y_incis given but set to 0 it will be reset equal tox_inc; otherwise it will be converted to degrees latitude.Allcoordinates: If=is appended then the corresponding maxx(east) ory(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 thenumberofnodesdesired by appending+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 Appendix B for details. Note: if-Rgrdfileis used then grid spacing has already been initialized; use-Ito override the values.-Rxmin,xmax,ymin, andymaxspecify the Region of interest. For geographic regions, these limits correspond towest,east,south,andnorthand you may specify them in decimal degrees or in [+-]dd:mm[:ss.xxx][W|E|S|N] format. Appendrif lower left and upper right map coordinates are given instead of w/e/s/n. The two shorthands-Rgand-Rdstand for global domain (0/360 and -180/+180 in longitude respectively, with -90/+90 in latitude). Alternatively, specify the name of an existing grid file and the-Rsettings (and grid spacing, if applicable) are copied from the grid. For calendar time coordinates you may either give (a) relative time (relative to the selectedTIME_EPOCHand in the selectedTIME_UNIT; appendtto-JX|x), or (b) absolute time of the form [date]T[clock] (appendTto-JX|x). At least one ofdateandclockmust be present; theTis always required. Thedatestring must be of the form [-]yyyy[-mm[-dd]] (Gregorian calendar) or yyyy[-Www[-d]] (ISO week calendar), while theclockstring must be of the form hh:mm:ss[.xxx]. The use of delimiters and their type and positions must be exactly as indicated (however, input, output and plot formats are customizable; seegmtdefaults).

**OPTIONS**

-AAspect ratio. If desired, grid anisotropy can be added to the equations. Enteraspect_ratio, where dy = dx /aspect_ratiorelates the grid dimensions. [Default = 1 assumes isotropic grid.]-CConvergence limit. Iteration is assumed to have converged when the maximum absolute change in any grid value is less thanconvergence_limit. (Units same as data z units). [Default is scaled to 0.1 percent of typical gradient in input data.]-HInput file(s) has header record(s). If used, the default number of header records isN_HEADER_RECS. Use-Hiif only input data should have header records [Default will write out header records if the input data have them]. Blank lines and lines starting with # are always skipped. Not used with binary data.-LImpose limits on the output solution.llowersets the lower bound.lowercan be the name of a grid file with lower bound values, a fixed value,dto set to minimum input value, orufor unconstrained [Default].uuppersets the upper bound and can be the name of a grid file with upper bound values, a fixed value,dto set to maximum input value, orufor unconstrained [Default].-NNumber of iterations. Iteration will cease whenconvergence_limitis reached or when number of iterations reachesmax_iterations. [Default is 250.]-QSuggest grid dimensions which have a highly composite greatest common factor. This allows surface to use several intermediate steps in the solution, yielding faster run times and better results. The sizes suggested by-Qcan be achieved by altering-Rand/or-I. You can recover the-Rand-Iyou want later by usinggrdsampleorgrdcuton the output ofsurface.-SSearch radius. Entersearch_radiusin same units as x,y data; appendmto indicate minutes. This is used to initialize the grid before the first iteration; it is not worth the time unless the grid lattice is prime and cannot have regional stages. [Default = 0.0 and no search is made.]-TTension factor[s]. These must be between 0 and 1. Tension may be used in the interior solution (above equation, where it suppresses spurious oscillations) and in the boundary conditions (where it tends to flatten the solution approaching the edges). Using zero for both values results in a minimum curvature surface with free edges, i.e., a natural bicubic spline. Use-Ttension_factorito set interior tension, and-Ttension_factorbto set boundary tension. If you do not appendiorb, both will be set to the same value. [Default = 0 for both gives minimum curvature solution.]-VSelects verbose mode, which will send progress reports to stderr [Default runs "silently"].-Vlwill report the convergence after each iteration;-Vwill report only after each regional grid is converged.-ZOver-relaxation factor. This parameter is used to accelerate the convergence; it is a number between 1 and 2. A value of 1 iterates the equations exactly, and will always assure stable convergence. Larger values overestimate the incremental changes during convergence, and will reach a solution more rapidly but may become unstable. If you use a large value for this factor, it is a good idea to monitor each iteration with the-Vloption. [Default = 1.4 converges quickly and is almost always stable.]-:Toggles between (longitude,latitude) and (latitude,longitude) input and/or output. [Default is (longitude,latitude)]. Appendito select input only oroto select output only. [Default affects both].-biSelects binary input. Appendsfor single precision [Default isd(double)]. UppercaseSorDwill force byte-swapping. Optionally, appendncol, the number of columns in your binary input file if it exceeds the columns needed by the program. Or appendcif the input file is netCDF. Optionally, appendvar1/var2/...to specify the variables to be read. [Default is 3 input columns].-fSpecial formatting of input and/or output columns (time or geographical data). Specifyioroto make this apply only to input or output [Default applies to both]. Give one or more columns (or column ranges) separated by commas. AppendT(absolute calendar time),t(relative time in chosenTIME_UNITsinceTIME_EPOCH),x(longitude),y(latitude), orf(floating point) to each column or column range item. Shorthand-f[i|o]gmeans-f[i|o]0x,1y(geographic coordinates).

**GRID** **VALUES** **PRECISION**

Regardless of the precision of the input data, GMT programs that create grid files will internally hold the grids in 4-byte floating point arrays. This is done to conserve memory and furthermore most if not all real data can be stored using 4-byte floating point values. Data with higher precision (i.e., double precision values) will lose that precision once GMT operates on the grid or writes out new grids. To limit loss of precision when processing data you should always consider normalizing the data prior to processing.

**EXAMPLES**

To grid 5 by 5 minute gravity block means from the ASCII data in hawaii_5x5.xyg, using atension_factor= 0.25, aconvergence_limit= 0.1 milligal, writing the result to a file called hawaii_grd.grd, and monitoring each iteration, try:surfacehawaii_5x5.xyg-R198/208/18/25-I5m-Ghawaii_grd.grd-T0.25-C0.1-Vl

**BUGS**

surfacewill complain when more than one data point is found for any node and suggest that you runblockmean,blockmedian, orblockmodefirst. If you did runblockm*and still get this message it usually means that your grid spacing is so small that you need more decimals in the output format used byblockm*. You may specify more decimal places by editing the parameterD_FORMATin your .gmtdefaults4 file prior to runningblockm*, or choose binary input and/or output using single or double precision storage. Note that only gridline registration is possible withsurface. If you need a pixel- registered grid you can resample a gridline registered grid usinggrdsample-T.

**SEE** **ALSO**

blockmean(1),blockmedian(1),blockmode(1),GMT(1),nearneighbor(1),triangulate(1)

**REFERENCES**

Smith, W. H. F, and P. Wessel, 1990, Gridding with continuous curvature splines in tension,Geophysics, 55, 293-305.