surface - adjustable tension continuous curvature surface gridding algorithm

surface[xyzfile]-Goutputfile.grd-Ix_inc[m|c][/y_inc[m|c]]-Rwest/east/south/north[r] [-Aaspect_ratio] [-Cconvergence_limit] [-H[nrec] ] [-Lllower] [-Luupper] [-Nmax_iterations] [-Q] [-Ssearch_radius[m] ] [-Ttension_factor[ib] ] [-V[l] ] [-Zover-relax-ation_factor] [-:] [-bi[s][n] ] [-f[i|o]colinfo]

surfacereads randomly-spaced (x,y,z) triples from standard input [orxyzfile] and produces a binary grdfile 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 Lapla- cian 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 topog- raphy 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 grdfile with values, or simply be the mini- mum/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.-Ix_inc[and optionallyy_inc] is the grid spacing. Appendmto indicate minutes orcto indicate seconds.-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 wesn. The two shorthands-Rg-Rdstand for global domain (0/360 or -180/+180 in longitude respectively, with -90/+90 in latitude). For calendar time coordinates you may either give relative time (relative to the selected TIME_EPOCH and in the selected TIME_UNIT; appendtto-JX|x), or 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 as indicated (however, input/output and plotting formats are flexible).

-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 thancon-vergence_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). Number of header records can be changed by editing your .gmtdefaults4 file. If used,GMTdefault is 1 header record. Use-Hiif only input data should have header records [Default will write out header records if the input data have them]. Not used with binary data.-LImpose limits on the output solution.llowersets the lower bound.lowercan be the name of a grdfile with lower bound val- ues, a fixed value,dto set to minimum input value, orufor unconstrained [Default].uuppersets the upper bound and can be the name of a grdfile with upper bound values, a fixed value,dto set to maximum input value, orufor unconstrained [Default].-NNumber of iterations. Iteration will cease whenconver-gence_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 sup- presses 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 sur- face with free edges, i.e. a natural bicubic spline. Use-Tten-sion_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 cur- vature 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 iter- ates the equations exactly, and will always assure stable con- vergence. 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 is double]. Appendnfor the number of columns in the binary file(s). [Default is 3 input columns].-fSpecial formatting of input and output columns (time or geo- graphical data) Specifyi(nput) oro(utput) [Default is both input and output]. Give one or more columns (or column ranges) separated by commas. AppendT(Absolute calendar time),t(time relative to chosen TIME_EPOCH),x(longitude),y(latitude),g(geographic coordinate), orf(floating point) to each column or column range item.

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

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 parameter D_FORMAT in your .gmtdefaults4 file prior to runningblockm*, or choose binary input and/or output using single or double precision storage.

blockmean(l),blockmedian(l),blockmode(l),gmt(l),nearneighbor(l),triangulate(l)

Smith, W. H. F, and P. Wessel, 1990, Gridding with continuous curvature splines in tension,Geophysics, 55, 293-305. GMT4.0 1 Oct 2004 SURFACE(l)

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