1GRDFLEXURE(1) GMT GRDFLEXURE(1)
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6 grdflexure - Compute flexural deformation of 3-D surfaces for various
7 rheologies
8
10 grdflexure topogrd -Drm/rl[/ri]/rw -ETe[u] -Goutgrid [ -ANx/Ny/Nxy
11 ] [ -Cppoisson ] [ -CyYoung ] [ -Fnu_a[/h_a/nu_m] ] [ -Llist ] [
12 -N[f|q|s|nx/ny][+a|d|h|l][+e|n|m][+twidth][+w[suffix]][+z[p]] [ -Sbeta
13 ] [ -Tt0[u][/t1[u]/dt[u]|file] |n][+l] ] [ -V[level] ] [ -Wwd] [
14 -Zzm] [ -fg ]
15 Note: No space is allowed between the option flag and the associated
17 arguments.
18
20 grdflexure computes the flexural response to loads using a range of
21 user-selectable rheologies. User may select from elastic, viscoelas‐
22 tic, or firmoviscous (with one or two viscous layers). Temporal evolu‐
23 tion can also be modeled by providing incremental load grids and speci‐
24 fying a range of model output times.
25
27 topogrd
28 2-D binary grid file with the topography of the load (in
29 meters); See GRID FILE FORMATS below. If -T is used, topogrd
30 may be a filename template with a floating point format (C syn‐
31 tax) and a different load file name will be set and loaded for
32 each time step. The load times thus coincide with the times
33 given via -T (but not all times need to have a corresponding
34 file). Alternatively, give topogrd as =flist, where flist is an
35 ASCII table with one topogrd filename and load time per record.
36 These load times can be different from the evaluation times
37 given via -T. For load time format, see -T.
38 -Drm/rl[/ri]/rw
40 Sets density for mantle, load, infill (optional, otherwise it is
41 assumed to equal the load density), and water or air. If ri
42 differs from rl then an approximate solution will be found. If
43 ri is not given then it defaults to rl.
44 -ETe Sets the elastic plate thickness (in meter); append k for km.
46 If the elastic thickness exceeds 1e10 it will be interpreted as
47 a flexural rigidity D (by default D is computed from Te, Young's
48 modulus, and Poisson's ratio; see -C to change these values).
49 -Goutfile
51 If -T is set then grdfile must be a filename template that con‐
52 tains a floating point format (C syntax). If the filename tem‐
53 plate also contains either %s (for unit name) or %c (for unit
54 letter) then we use the corresponding time (in units specified
55 in -T) to generate the individual file names, otherwise we use
56 time in years with no unit.
57
59 -ANx/Ny/Nxy
60 Specify in-plane compressional or extensional forces in the x-
61 and y-directions, as well as any shear force [no in-plane
62 forces]. Compression is indicated by negative values, while
63 extensional forces are specified using positive values.
64 -Cppoisson
66 Change the current value of Poisson's ratio [0.25].
67 -CyYoung
69 Change the current value of Young's modulus [7.0e10 N/m^2].
70 -Fnu_a[/h_a/nu_m]
72 Specify a firmoviscous model in conjunction with an elastic
73 plate thickness specified via -E. Just give one viscosity
74 (nu_a) for an elastic plate over a viscous half-space, or also
75 append the thickness of the asthenosphere (h_a) and the lower
76 mantle viscosity (nu_m), with the first viscosity now being that
77 of the asthenosphere. Give viscosities in Pa*s. If used, give
78 the thickness of the asthenosphere in meter; append k for km.
79 -N[a|f|m|r|s|nx/ny][+a|[+d|h|l][+e|n|m][+twidth][+v][+w[suffix]][+z[p]]
81 Choose or inquire about suitable grid dimensions for FFT and set
82 optional parameters. Control the FFT dimension:
83 -Na lets the FFT select dimensions yielding the most accurate
84 result.
85 -Nf will force the FFT to use the actual dimensions of the
87 data.
88 -Nm lets the FFT select dimensions using the least work mem‐
90 ory.
91 -Nr lets the FFT select dimensions yielding the most rapid
93 calculation.
94 -Ns will present a list of optional dimensions, then exit.
96 -Nnx/ny will do FFT on array size nx/ny (must be >= grid file
98 size). Default chooses dimensions >= data which optimize
99 speed and accuracy of FFT. If FFT dimensions > grid file
100 dimensions, data are extended and tapered to zero.
101 Control detrending of data: Append modifiers for removing a lin‐
103 ear trend:
104 +d: Detrend data, i.e. remove best-fitting linear trend
105 [Default].
106 +a: Only remove mean value.
108 +h: Only remove mid value, i.e. 0.5 * (max + min).
110 +l: Leave data alone.
112 Control extension and tapering of data: Use modifiers to control
114 how the extension and tapering are to be performed:
115 +e extends the grid by imposing edge-point symmetry
116 [Default],
117 +m extends the grid by imposing edge mirror symmetry
119 +n turns off data extension.
121 Tapering is performed from the data edge to the FFT grid edge
123 [100%]. Change this percentage via +twidth. When +n is in
124 effect, the tapering is applied instead to the data margins
125 as no extension is available [0%].
126 Control messages being reported: +v will report suitable
128 dimensions during processing.
129 Control writing of temporary results: For detailed investigation
131 you can write the intermediate grid being passed to the forward
132 FFT; this is likely to have been detrended, extended by
133 point-symmetry along all edges, and tapered. Append +w[suffix]
134 from which output file name(s) will be created (i.e.,
135 ingrid_prefix.ext) [tapered], where ext is your file extension.
136 Finally, you may save the complex grid produced by the forward
137 FFT by appending +z. By default we write the real and imaginary
138 components to ingrid_real.ext and ingrid_imag.ext. Append p to
139 save instead the polar form of magnitude and phase to files
140 ingrid_mag.ext and ingrid_phase.ext.
141 -Llist Write the names and evaluation times of all grids that were cre‐
143 ated to the text file list. Requires -T.
144 -Mtm Specify a viscoelastic model in conjunction with an elastic
146 plate thickness specified via -E. Append the Maxwell time tm
147 for the viscoelastic model (in ).
148 -Sbeta Specify a starved moat fraction in the 0-1 range, where 1 means
150 the moat is fully filled with material of density ri while 0
151 means it is only filled with material of density rw (i.e., just
152 water) [1].
153 -Tt0[u][/t1[u]/dt[u]|file]|n][+l]
155 Specify t0, t1, and time increment (dt) for sequence of calcula‐
156 tions [Default is one step, with no time dependency]. For a
157 single specific time, just give start time t0. The unit is
158 years; append k for kyr and M for Myr. For a logarithmic time
159 scale, append +l and specify n steps instead of dt. Alterna‐
160 tively, give a file with the desired times in the first column
161 (these times may have individual units appended, otherwise we
162 assume year). We then write a separate model grid file for each
163 given time step.
164 -Wwd Set reference depth to the undeformed flexed surface in m [0].
166 Append k to indicate km.
167 -Zzm Specify reference depth to flexed surface (e.g., Moho) in m;
169 append k for km. Must be positive. [0].
170 -V[level] (more ...)
172 Select verbosity level [c].
173 -fg Geographic grids (dimensions of longitude, latitude) will be
175 converted to meters via a "Flat Earth" approximation using the
176 current ellipsoid parameters.
177 -^ or just -
179 Print a short message about the syntax of the command, then
180 exits (NOTE: on Windows just use -).
181 -+ or just +
183 Print an extensive usage (help) message, including the explana‐
184 tion of any module-specific option (but not the GMT common
185 options), then exits.
186 -? or no arguments
188 Print a complete usage (help) message, including the explanation
189 of all options, then exits.
190
192 By default GMT writes out grid as single precision floats in a
193 COARDS-complaint netCDF file format. However, GMT is able to produce
194 grid files in many other commonly used grid file formats and also
195 facilitates so called "packing" of grids, writing out floating point
196 data as 1- or 2-byte integers. (more ...)
197
199 If the grid does not have meter as the horizontal unit, append +uunit
200 to the input file name to convert from the specified unit to meter. If
201 your grid is geographic, convert distances to meters by supplying -fg
202 instead.
203
205 netCDF COARDS grids will automatically be recognized as geographic. For
206 other grids geographical grids were you want to convert degrees into
207 meters, select -fg. If the data are close to either pole, you should
208 consider projecting the grid file onto a rectangular coordinate system
209 using grdproject.
210
212 The FFT solution to plate flexure requires the infill density to equal
213 the load density. This is typically only true directly beneath the
214 load; beyond the load the infill tends to be lower-density sediments or
215 even water (or air). Wessel [2001, 2016] proposed an approximation
216 that allows for the specification of an infill density different from
217 the load density while still allowing for an FFT solution. Basically,
218 the plate flexure is solved for using the infill density as the effec‐
219 tive load density but the amplitudes are adjusted by the factor A =
220 sqrt ((rm - ri)/(rm - rl)), which is the theoretical difference in
221 amplitude due to a point load using the two different load densities.
222 The approximation is very good but breaks down for large loads on weak
223 plates, a fairy uncommon situation.
224
226 To compute elastic plate flexure from the load topo.nc, for a 10 km
227 thick plate with typical densities, try
228 gmt grdflexure topo.nc -Gflex.nc -E10k -D2700/3300/1035
230 To compute the firmoviscous response to a series of incremental loads
232 given by file name and load time in the table l.lis at the single time
233 1 Ma using the specified rheological values, try
234 gmt grdflexure -T1M =l.lis -D3300/2800/2800/1000 -E5k -Gflx/smt_fv_%03.1f_%s.nc -F2e20 -Nf+a
236
238 Cathles, L. M., 1975, The viscosity of the earth's mantle, Princeton
239 University Press.
240 Wessel. P., 2001, Global distribution of seamounts inferred from grid‐
242 ded Geosat/ERS-1 altimetry, J. Geophys. Res., 106(B9), 19,431-19,441,
243 http://dx.doi.org/10.1029/2000JB000083.
244 Wessel, P., 2016, Regional–residual separation of bathymetry and
246 revised estimates of Hawaii plume flux, Geophys. J. Int., 204(2),
247 932-947, http://dx.doi.org/10.1093/gji/ggv472.
248
250 gmt, grdfft, gravfft grdmath, grdproject, grdseamount
251
253 2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
2545.4.5 Feb 24, 2019 GRDFLEXURE(1)