GRDFLEXURE(1gmt) | GMT | GRDFLEXURE(1gmt) |
grdflexure - Compute flexural deformation of 3-D surfaces for various rheologies
grdflexure topogrd -Drm/rl[/ri]/rw -ETe[u] -Goutgrid [ -ANx/Ny/Nxy ] [ -Cppoisson ] [ -CyYoung ] [ -Fnu_a[/h_a/nu_m] ] [ -Llist ] [ -N[f|q|s|nx/ny][+a|d|h|l][+e|n|m][+twidth][+w[suffix]][+z[p]] [ -Sbeta ] [ -Tt0[u][/t1[u]/dt[u]|file] |n][+l] ] [ -V[level] ] [ -Wwd] [ -Zzm] [ -fg ]
Note: No space is allowed between the option flag and the associated arguments.
grdflexure computes the flexural response to loads using a range of user-selectable rheologies. User may select from elastic, viscoelastic, or firmoviscous (with one or two viscous layers). Temporal evolution can also be modeled by providing incremental load grids and specifying a range of model output times.
-Nf will force the FFT to use the actual dimensions of the data.
-Nm lets the FFT select dimensions using the least work memory.
-Nr lets the FFT select dimensions yielding the most rapid calculation.
-Ns will present a list of optional dimensions, then exit.
-Nnx/ny will do FFT on array size nx/ny (must be >= grid file size). Default chooses dimensions >= data which optimize speed and accuracy of FFT. If FFT dimensions > grid file dimensions, data are extended and tapered to zero.
Control detrending of data: Append modifiers for removing a linear trend:
+a: Only remove mean value.
+h: Only remove mid value, i.e. 0.5 * (max + min).
+l: Leave data alone.
Control extension and tapering of data: Use modifiers to control how the extension and tapering are to be performed:
+m extends the grid by imposing edge mirror symmetry
+n turns off data extension.
Tapering is performed from the data edge to the FFT grid edge [100%]. Change this percentage via +twidth. When +n is in effect, the tapering is applied instead to the data margins as no extension is available [0%].
Control messages being reported: +v will report suitable dimensions during processing.
Control writing of temporary results: For detailed investigation you can write the intermediate grid being passed to the forward FFT; this is likely to have been detrended, extended by point-symmetry along all edges, and tapered. Append +w[suffix] from which output file name(s) will be created (i.e., ingrid_prefix.ext) [tapered], where ext is your file extension. Finally, you may save the complex grid produced by the forward FFT by appending +z. By default we write the real and imaginary components to ingrid_real.ext and ingrid_imag.ext. Append p to save instead the polar form of magnitude and phase to files ingrid_mag.ext and ingrid_phase.ext.
By default GMT writes out grid as single precision floats in a COARDS-complaint netCDF file format. However, GMT is able to produce grid files in many other commonly used grid file formats and also facilitates so called "packing" of grids, writing out floating point data as 1- or 2-byte integers. (more ...)
If the grid does not have meter as the horizontal unit, append +uunit to the input file name to convert from the specified unit to meter. If your grid is geographic, convert distances to meters by supplying -fg instead.
netCDF COARDS grids will automatically be recognized as geographic. For other grids geographical grids were you want to convert degrees into meters, select -fg. If the data are close to either pole, you should consider projecting the grid file onto a rectangular coordinate system using grdproject.
The FFT solution to plate flexure requires the infill density to equal the load density. This is typically only true directly beneath the load; beyond the load the infill tends to be lower-density sediments or even water (or air). Wessel [2001, 2016] proposed an approximation that allows for the specification of an infill density different from the load density while still allowing for an FFT solution. Basically, the plate flexure is solved for using the infill density as the effective load density but the amplitudes are adjusted by the factor A = sqrt ((rm - ri)/(rm - rl)), which is the theoretical difference in amplitude due to a point load using the two different load densities. The approximation is very good but breaks down for large loads on weak plates, a fairy uncommon situation.
To compute elastic plate flexure from the load topo.nc, for a 10 km thick plate with typical densities, try
gmt grdflexure topo.nc -Gflex.nc -E10k -D2700/3300/1035
To compute the firmoviscous response to a series of incremental loads given by file name and load time in the table l.lis at the single time 1 Ma using the specified rheological values, try
gmt grdflexure -T1M =l.lis -D3300/2800/2800/1000 -E5k -Gflx/smt_fv_%03.1f_%s.nc -F2e20 -Nf+a
Cathles, L. M., 1975, The viscosity of the earth's mantle, Princeton University Press.
Wessel. P., 2001, Global distribution of seamounts inferred from gridded Geosat/ERS-1 altimetry, J. Geophys. Res., 106(B9), 19,431-19,441, http://dx.doi.org/10.1029/2000JB000083.
Wessel, P., 2016, Regional–residual separation of bathymetry and revised estimates of Hawaii plume flux, Geophys. J. Int., 204(2), 932-947, http://dx.doi.org/10.1093/gji/ggv472.
gmt, grdfft, gravfft grdmath, grdproject, grdseamount
2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
May 21, 2019 | 5.4.5 |