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grdflexure - Compute flexural deformation of 3-D surfaces for various rheologies


grdflexure topogrd rm/rl[/ri]/rw Te[u] outgrid [ Nx/Ny/Nxy ] [ ppoisson ] [ yYoung ] [
nu_a[/h_a/nu_m] ] [ list ] [ [f|q|s|nx/ny][+a|d|h|l][+e|n|m][+twidth][+w[suffix]][+z[p]] [
beta ] [ -Tt0[u][/t1[u]/dt[u]|n][+l] ] [ [level] ] [ wd] [ zm] [ -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.


2-D binary grid file with the topography of the load (in meters); See GRID FILE
FORMATS below. If -T is used, topogrd may be a filename template with a floating
point format (C syntax) and a different load file name will be set and loaded for
each time step. The load times thus coincide with the times given via -T (but not
all times need to have a corresponding file). Alternatively, give topogrd as
=*flist*, where flist is an ASCII table with one topogrd filename and load time per
record. These load times can be different from the evaluation times given via -T.
For load time format, see -T.

Sets density for mantle, load, infill (optional, otherwise it is assumed to equal
the load density), and water or air. If ri differs from rl then an approximate
solution will be found. If ri is not given then it defaults to rl.

-ETe Sets the elastic plate thickness (in meter); append k for km. If the elastic
thickness exceeds 1e10 it will be interpreted as a flexural rigidity D (by default
D is computed from Te, Young's modulus, and Poisson's ratio; see -C to change these

If -T is set then grdfile must be a filename template that contains a floating
point format (C syntax). If the filename template also contains either %s (for
unit name) or %c (for unit letter) then we use the corresponding time (in units
specified in -T) to generate the individual file names, otherwise we use time in
years with no unit.


Specify in-plane compressional or extensional forces in the x- and y-directions, as
well as any shear force [no in-plane forces]. Compression is indicated by negative
values, while extensional forces are specified using positive values.

Change the current value of Poisson's ratio [0.25].

Change the current value of Young's modulus [7.0e10 N/m^2].

Specify a firmoviscous model in conjunction with an elastic plate thickness
specified via -E. Just give one viscosity (nu_a) for an elastic plate over a
viscous half-space, or also append the thickness of the asthenosphere (h_a) and the
lower mantle viscosity (nu_m), with the first viscosity now being that of the
asthenosphere. Give viscosities in Pa*s. If used, give the thickness of the
asthenosphere in meter; append k for km.

Choose or inquire about suitable grid dimensions for FFT and set optional
parameters. Control the FFT dimension:
-Nf will force the FFT to use the actual dimensions of the data.

-Nq will inQuire about more suitable dimensions, report those, then continue.

-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:
+d: Detrend data, i.e. remove best-fitting linear trend [Default].

+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:
+e extends the grid by imposing edge-point symmetry [Default],

+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 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

-Llist Write the names and evaluation times of all grids that were created to the text
file list. Requires -T.

-Mtm Specify a viscoelastic model in conjunction with an elastic plate thickness
specified via -E. Append the Maxwell time tm for the viscoelastic model (in ).

-Sbeta Specify a starved moat fraction in the 0-1 range, where 1 means the moat is fully
filled with material of density ri while 0 means it is only filled with material of
density rw (i.e., just water) [1].

Specify t0, t1, and time increment (dt) for sequence of calculations [Default is
one step, with no time dependency]. For a single specific time, just give start
time t0. The unit is years; append k for kyr and M for Myr. For a logarithmic time
scale, append +l and specify n steps instead of dt. Alternatively, give a file
with the desired times in the first column (these times may have individual units
appended, otherwise we assume year). We then write a separate model grid file for
each given time step.

-Wwd Set reference depth to the undeformed flexed surface in m [0]. Append k to
indicate km.

-Zzm Specify reference depth to flexed surface (e.g., Moho) in m; append k for km. Must
be positive. [0].

-V[level] (more ...)
Select verbosity level [c].

-fg Geographic grids (dimensions of longitude, latitude) will be converted to meters
via a "Flat Earth" approximation using the current ellipsoid parameters.

-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows
use just -).

-+ or just +
Print an extensive usage (help) message, including the explanation of any
module-specific option (but not the GMT common options), then exits.

-? or no arguments
Print a complete usage (help) message, including the explanation of options, then

Print GMT version and exit.

Print full path to GMT share directory and exit.


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. To specify the precision, scale and offset, the user should
add the suffix =id[/scale/offset[/nan]], where id is a two-letter identifier of the grid
type and precision, and scale and offset are optional scale factor and offset to be
applied to all grid values, and nan is the value used to indicate missing data. In case
the two characters id is not provided, as in =/scale than a id=nf is assumed. When
reading grids, the format is generally automatically recognized. If not, the same suffix
can be added to input grid file names. See grdconvert and Section grid-file-format of the
GMT Technical Reference and Cookbook for more information.

When reading a netCDF file that contains multiple grids, GMT will read, by default, the
first 2-dimensional grid that can find in that file. To coax GMT into reading another
multi-dimensional variable in the grid file, append ?varname to the file name, where
varname is the name of the variable. Note that you may need to escape the special meaning
of ? in your shell program by putting a backslash in front of it, or by placing the
filename and suffix between quotes or double quotes. The ?varname suffix can also be used
for output grids to specify a variable name different from the default: "z". See
grdconvert and Sections modifiers-for-CF and grid-file-format of the GMT Technical
Reference and Cookbook for more information, particularly on how to read splices of 3-,
4-, or 5-dimensional grids.


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] 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,

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