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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
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