grdflexure(1) GMT grdflexure(1)
NAME
grdflexure - Compute flexural deformation of 3-D surfaces for various
rheologies
SYNOPSIS
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.
DESCRIPTION
grdflexure computes the flexural response to loads using a range of
user-selectable rheologies. User may select from elastic, viscoelas-
tic, or firmoviscous (with one or two viscous layers). Temporal evolu-
tion can also be modeled by providing incremental load grids and speci-
fying a range of model output times.
REQUIRED ARGUMENTS
topogrd
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 syn-
tax) 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.
-Drm/rl[/ri]/rw
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, Youngas
modulus, and Poissonas ratio; see -C to change these values).
-Goutfile
If -T is set then grdfile must be a filename template that con-
tains a floating point format (C syntax). If the filename tem-
plate 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.
OPTIONAL ARGUMENTS
-ANx/Ny/Nxy
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.
-Cppoisson
Change the current value of Poissonas ratio [0.25].
-CyYoung
Change the current value of Youngas modulus [7.0e10 N/m^2].
-Fnu_a[/h_a/nu_m]
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.
-N[a|f|m|r|s|nx/ny][+a|[+d|h|l][+e|n|m][+twidth][+v][+w[suffix]][+z[p]]
Choose or inquire about suitable grid dimensions for FFT and set
optional parameters. Control the FFT dimension:
-Na lets the FFT select dimensions yielding the most accurate
result.
-Nf will force the FFT to use the actual dimensions of the
data.
-Nm lets the FFT select dimensions using the least work mem-
ory.
-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 lin-
ear 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 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.
-Llist Write the names and evaluation times of all grids that were cre-
ated 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].
-Tt0[u][/t1[u]/dt[u]|file]|n][+l]
Specify t0, t1, and time increment (dt) for sequence of calcula-
tions [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. Alterna-
tively, 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 a|)
Select verbosity level [c].
-fg Geographic grids (dimensions of longitude, latitude) will be
converted to meters via a aFlat Eartha approximation using the
current ellipsoid parameters.
-^ or just -
Print a short message about the syntax of the command, then
exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explana-
tion 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 all options, then exits.
GRID FILE FORMATS
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 apackinga of grids, writing out floating point
data as 1- or 2-byte integers. (more a|)
GRID DISTANCE UNITS
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.
CONSIDERATIONS
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.
PLATE FLEXURE NOTES
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 effec-
tive 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.
EXAMPLES
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
REFERENCES
Cathles, L. M., 1975, The viscosity of the earth^<i>as mantle, Princeton
University Press.
Wessel. P., 2001, Global distribution of seamounts inferred from grid-
ded Geosat/ERS-1 altimetry, J. Geophys. Res., 106(B9), 19,431-19,441,
http://dx.doi.org/10.1029/2000JB000083.
Wessel, P., 2016, Regionalaresidual 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.
SEE ALSO
gmt(1), grdfft(1), gravfft(1), grdmath(1), grdproject(1),
grdseamount(1)
COPYRIGHT
2017, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
5.4.2 Jun 24, 2017 grdflexure(1)
gmt5 5.4.2 - Generated Wed Jun 28 18:27:14 CDT 2017