NAME
surface - adjustable tension continuous curvature surface gridding
algorithm
SYNOPSIS
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 ]
DESCRIPTION
surface reads randomly-spaced (x,y,z) triples from standard input [or
xyzfile] 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 with blockmean, blockmedian, or blockmode to
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.
xyzfile
3 column ASCII file [or binary, see -b] holding (x,y,z) data
values. If no file is specified, surface will read from standard
input.
-G Output file name. Output is a binary 2-D .grd file.
-I x_inc [and optionally y_inc] is the grid spacing. Append m to
indicate minutes or c to indicate seconds.
-R xmin, xmax, ymin, and ymax specify the Region of interest. For
geographic regions, these limits correspond to west, east,
south, and north and you may specify them in decimal degrees or
in [+-]dd:mm[:ss.xxx][W|E|S|N] format. Append r if lower left
and upper right map coordinates are given instead of wesn. The
two shorthands -Rg -Rd stand 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; append t to -JX|x), or absolute time of the form
[date]T[clock] (append T to -JX|x). At least one of date and
clock must be present; the T is always required. The date string
must be of the form [-]yyyy[-mm[-dd]] (Gregorian calendar) or
yyyy[-Www[-d]] (ISO week calendar), while the clock string 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).
OPTIONS
-A Aspect ratio. If desired, grid anisotropy can be added to the
equations. Enter aspect_ratio, where dy = dx / aspect_ratio
relates the grid dimensions. [Default = 1 assumes isotropic
grid.]
-C Convergence limit. Iteration is assumed to have converged when
the maximum absolute change in any grid value is less than con-
vergence_limit. (Units same as data z units). [Default is scaled
to 0.1 percent of typical gradient in input data.]
-H Input file(s) has Header record(s). Number of header records can
be changed by editing your .gmtdefaults4 file. If used, GMT
default is 1 header record. Use -Hi if only input data should
have header records [Default will write out header records if
the input data have them]. Not used with binary data.
-L Impose limits on the output solution. llower sets the lower
bound. lower can be the name of a grdfile with lower bound val-
ues, a fixed value, d to set to minimum input value, or u for
unconstrained [Default]. uupper sets the upper bound and can be
the name of a grdfile with upper bound values, a fixed value, d
to set to maximum input value, or u for unconstrained [Default].
-N Number of iterations. Iteration will cease when conver-
gence_limit is reached or when number of iterations reaches
max_iterations. [Default is 250.]
-Q Suggest 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 -Q can be achieved by altering
-R and/or -I. You can recover the -R and -I you want later by
using grdsample or grdcut on the output of surface.
-S Search radius. Enter search_radius in same units as x,y data;
append m to 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.]
-T Tension 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_factori to set interior tension, and -Ttension_factorb to
set boundary tension. If you do not append i or b, both will be
set to the same value. [Default = 0 for both gives minimum cur-
vature solution.]
-V Selects verbose mode, which will send progress reports to stderr
[Default runs "silently"]. -Vl will report the convergence
after each iteration; -V will report only after each regional
grid is converged.
-Z Over-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 -Vl option.
[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)]. Append
i to select input only or o to select output only. [Default
affects both].
-bi Selects binary input. Append s for single precision [Default is
double]. Append n for the number of columns in the binary
file(s).
[Default is 3 input columns].
-f Special formatting of input and output columns (time or geo-
graphical data) Specify i(nput) or o(utput) [Default is both
input and output]. Give one or more columns (or column ranges)
separated by commas. Append T (Absolute calendar time), t (time
relative to chosen TIME_EPOCH), x (longitude), y (latitude), g
(geographic coordinate), or f (floating point) to each column or
column range item.
EXAMPLES
To grid 5 by 5 minute gravity block means from the ASCII data in
hawaii_5x5.xyg, using a tension_factor = 0.25, a convergence_limit =
0.1 milligal, writing the result to a file called hawaii_grd.grd, and
monitoring each iteration, try:
surface hawaii_5x5.xyg -R198/208/18/25 -I5m -Ghawaii_grd.grd -T0.25
-C0.1 -VL
BUGS
surface will complain when more than one data point is found for any
node and suggest that you run blockmean, blockmedian, or blockmode
first. If you did run blockm* 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 by blockm*. You may specify more decimal places
by editing the parameter D_FORMAT in your .gmtdefaults4 file prior to
running blockm*, or choose binary input and/or output using single or
double precision storage.
SEE ALSO
blockmean(l), blockmedian(l), blockmode(l), gmt(l), nearneighbor(l),
triangulate(l)
REFERENCES
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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