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-relaxation_factor] [-:] [-bi[s][n] ]

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 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 grdfile 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.-Ix_inc[and optionallyy_inc] is the grid spacing. Appendmto indicate minutes orcto indicate seconds.-Rwest,east,south, andnorthspecify the Region of interest. To specify boundaries in degrees and minutes [and seconds], use the dd:mm[:ss] format. Appendrif lower left and upper right map coordinates are given instead of wesn.

-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). Number of header records can be changed by editing your .gmtdefaults file. If used,GMTdefault is 1 header record. 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 values, 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 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 using grdsample or grdcut on the output of surface.-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/output. [Default is (longitude,latitude)].-biSelects binary input. Appendsfor single precision [Default is double]. Appendnfor the number of columns in the binary file(s). [Default is 3 input columns].

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 calledhawaii_grd.grd, and monitoring each iteration, try: surface hawaii_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 .gmtdefaults file prior to runningblockm*, or choose binary input and/or output using single or double precision storage.

blockmean, blockmedian, blockmode, gmt, nearneighbor, triangulate

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

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