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gravfft(1)                            GMT                           gravfft(1)




NAME

       gravfft  -  Compute  gravitational  attraction  of  3-D surfaces in the
       wavenumber (or frequency) domain


SYNOPSIS

       gravfft ingrid [ ingrid2 ]  -Goutfile [   -Cn/wavelength/mean_depth/tbw
       ]  [   -Ddensity|rhogrid  ]  [   -En_terms  ]  [   -F[f[+]|g|v|n|e] ] [
       -Iw|b|c|t |k ] [  -Nparams ] [  -Q  ]  [   -Tte/rl/rm/rw[/ri][+m]  ]  [
       -V[level] ] [  -Wwd] [  -Zzm[zl] ] [ -fg ]

       Note:  No  space  is allowed between the option flag and the associated
       arguments.


DESCRIPTION

       gravfft can be used into three main modes. Mode 1: Simply  compute  the
       geopotential due to the surface given in the topo.grd file.  Requires a
       density contrast (-D) and possibly a different observation level  (-W).
       It  will take the 2-D forward FFT of the grid and use the full Parkeras
       method up to the  chosen  terms.   Mode  2:  Compute  the  geopotential
       response  due  to  flexure of the topography file. It will take the 2-D
       forward FFT of the grid and use the  full Parkeras  method  applied  to
       the chosen isostatic model.  The available models are the aloading from
       topa, or elastic plate  model,  and  the  aloading  from  belowa  which
       accounts  for  the  plateas response to a sub-surface load (appropriate
       for hot spot modeling - if you believe them). In both cases, the  model
       parameters  are  set with -T and -Z options. Mode 3: compute the admit-
       tance or coherence between two grids. The output is the average in  the
       radial  direction.  Optionally, the model admittance may also be calcu-
       lated. The horizontal dimensions of the grdfiles are assumed to  be  in
       meters.  Geographical  grids  may  be used by specifying the -fg option
       that scales degrees to meters. If you have grids with dimensions in km,
       you  could change this to meters using grdedit or scale the output with
       grdmath.  Given the number of choices this program offers, is difficult
       to  state  what are options and what are required arguments. It depends
       on what you are doing; see the examples for further guidance.


REQUIRED ARGUMENTS

       ingrid 2-D binary grid file to be operated on. (See GRID  FILE  FORMATS
              below).   For  cross-spectral  operations,  also give the second
              grid file ingrd2.

       -Goutfile
              Specify the name of the output grid file or the 1-D spectrum ta-
              ble (see -E). (See GRID FILE FORMATS below).


OPTIONAL ARGUMENTS

       -Cn/wavelength/mean_depth/tbw
              Compute  only  the theoretical admittance curves of the selected
              model and exit. n and wavelength are used to compute (n *  wave-
              length)  the  total  profile length in meters. mean_depth is the
              mean water depth. Append dataflags (one or two) of  tbw  in  any
              order.  t  =  use  afrom topa model, b = use afrom belowa model.
              Optionally specify w to write wavelength instead of frequency.

       -Ddensity|rhogrid
              Sets density contrast across surface. Used, for example, to com-
              pute the gravity attraction of the water layer that can later be
              combined with the free-air anomaly to get the  Bouguer  anomaly.
              In  this  case  do  not  use  -T.  It also implicitly sets -N+h.
              Alternatively, specify a co-registered grid  with  density  con-
              trasts if a variable density contrast is required.

       -En_terms
              Number of terms used in Parker expansion (limit is 10, otherwise
              terms depending on n will blow out the program) [Default = 3]

       -F[f[+]|g|v|n|e]
              Specify desired geopotential field: compute  geoid  rather  than
              gravity
                 f  = Free-air anomalies (mGal) [Default].  Append + to add in
                 the slab implied when removing the mean value from the topog-
                 raphy.   This  requires zero topography to mean no mass anom-
                 aly.

                 g = Geoid anomalies (m).

                 v = Vertical Gravity Gradient (VGG; 1 Eotvos = 0.1  mGal/km).

                 e = East deflections of the vertical (micro-radian).

                 n = North deflections of the vertical (micro-radian).

       -Iw|b|c|t |k
              Use  ingrd2  and  ingrd1  (a grid with topography/bathymetry) to
              estimate admittance|coherence and write it to stdout (-G ignored
              if  set). This grid should contain gravity or geoid for the same
              region of ingrd1. Default computes admittance. Output contains 3
              or 4 columns. Frequency (wavelength), admittance (coherence) one
              sigma error  bar  and,  optionally,  a  theoretical  admittance.
              Append  dataflags  (one  to three) from w|b|c|t.  w writes wave-
              length instead of wavenumber, k selects km for  wavelength  unit
              [m],  c  computes  coherence  instead  of admittance, b writes a
              fourth column with aloading from belowa theoretical  admittance,
              and  t  writes  a fourth column with aelastic platea theoretical
              admittance.

       -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.

       -Q     Writes out a grid with the flexural topography (with z  positive
              up)  whose average depth was set by -Zzm and model parameters by
              -T (and output by  -G).  That  is  the  agravimetric  Mohoa.  -Q
              implicitly sets -N+h

       -S     Computes  predicted gravity or geoid grid due to a subplate load
              produced by the current bathymetry and  the  theoretical  model.
              The  necessary  parameters are set within -T and -Z options. The
              number of powers in Parker expansion is restricted to 1.  See an
              example further down.

       -Tte/rl/rm/rw[/ri][+m]
              Compute  the  isostatic  compensation  from  the topography load
              (input grid file) on an elastic  plate  of  thickness  te.  Also
              append densities for load, mantle, water and infill in SI units.
              If ri is not provided it defaults to rl.   Give  average  mantle
              depth  via  -Z.  If  the  elastic thickness is > 1e10 it will be
              interpreted as the flexural rigidity (by default it is  computed
              from  te  and  Young  modulus). Optionally, append +m to write a
              grid with the Mohoas geopotential effect  (see  -F)  from  model
              selected  by  -T.  If te = 0 then the Airy response is returned.
              -T+m implicitly sets -N+h

       -Wwd   Set water depth (or observation height) relative  to  topography
              [0].  Append k to indicate km.

       -Zzm[zl]
              Moho [and swell] average compensation depths (in meters positive
              dows a the depth). For the aload from topa model you  only  have
              to provide zm, but for the aloading from belowa donat forget zl.

       -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

       The  FFT  solution to elastic 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 approxima-
       tion  that  allows for the specification of an infill density different
       from the load density while still allowing for an FFT  solution.  Basi-
       cally,  the plate flexure is solved for using the infill density as the
       effective load density but the amplitudes are adjusted by a 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 the effect of the water layer above the  bat.grd  bathymetry
       using  2700  and  1035 for the densities of crust and water and writing
       the result on water_g.grd (computing up to the fourth power of bathyme-
       try in Parker expansion):

              gmt gravfft bat.grd -D1665 -Gwater_g.grd -E4

       Now subtract it from your free-air anomaly faa.grd and you will get the
       Bouguer anomaly. You may wonder why we are subtracting and not  adding.
       After  all  the Bouguer anomaly pretends to correct the mass deficiency
       presented by the water layer, so we should add because  water  is  less
       dense  than  the  rocks  below.  The  answer  relies on the way gravity
       effects are computed by the Parkeras method and  practical  aspects  of
       using the FFT.

              gmt grdmath faa.grd water_g.grd SUB = bouguer.grd

       Want an MBA anomaly? Well compute the crust mantle contribution and add
       it to the sea-bottom anomaly. Assuming a 6 km thick  crust  of  density
       2700 and a mantle with 3300 density we could repeat the command used to
       compute the water layer anomaly, using 600 (3300 - 2700) as the density
       contrast.  But  we  now have a problem because we need to know the mean
       Moho depth. That is when the scale/offset that can be appended  to  the
       gridas name comes in hand. Notice that we didnat need to do that before
       because mean water depth was computed directly from data  (notice  also
       the negative sign of the offset due to the fact that z is positive up):

              gmt gravfft bat.grd=nf/1/-6000 -D600 -Gmoho_g.grd

       Now, subtract it from the Bouguer to obtain the MBA anomaly. That is:

              gmt grdmath bouguer.grd moho_g.grd SUB = mba.grd

       To compute the Moho gravity effect of an elastic plate bat.grd with  Te
       =  7  km, density of 2700, over a mantle of density 3300, at an average
       depth of 9 km

              gmt gravfft bat.grd -Gelastic.grd -T7000/2700/3300/1035+m -Z9000

       If you add now the sea-bottom and Mohoas effects, you will get the full
       gravity  response  of  your  isostatic model. We will use here only the
       first term in Parker expansion.

              gmt gravfft bat.grd -D1665 -Gwater_g.grd -E1
              gmt gravfft bat.grd -Gelastic.grd -T7000/2700/3300/1035+m -Z9000 -E1
              gmt grdmath water_g.grd elastic.grd ADD = model.grd

       The same result can be obtained directly by the next command.  However,
       PAY  ATTENTION  to the following. I donat yet know if itas because of a
       bug or due to some limitation, but the fact is that the  following  and
       the  previous  commands  only give the same result if -E1 is used.  For
       higher powers of bathymetry in Parker expansion, only the above example
       seams to give the correct result.

              gmt gravfft bat.grd -Gmodel.grd -T7000/2700/3300/1035 -Z9000 -E1

       And  what would be the geoid anomaly produced by a load at 50 km depth,
       below a region whose bathymetry is given by bat.grd, a  Moho  at  9  km
       depth and the same densities as before?

              gmt gravfft topo.grd -Gswell_geoid.grd -T7000/2700/3300/1035 -Fg -Z9000/50000 -S -E1

       To  compute  the admittance between the topo.grd bathymetry and faa.grd
       free-air anomaly grid using the elastic plate model of a crust of 6  km
       mean  thickness with 10 km effective elastic thickness in a region of 3
       km mean water depth:

              gmt gravfft topo.grd faa.grd -It -T10000/2700/3300/1035 -Z9000

       To compute the admittance between the topo.grd bathymetry and geoid.grd
       geoid  grid  with the aloading from belowa (LFB) model with the same as
       above and sub-surface load at 40 km, but assuming now the grids are  in
       geographic and we want wavelengths instead of frequency:

              gmt gravfft topo.grd geoid.grd -Ibw -T10000/2700/3300/1035 -Z9000/40000 -fg

       To  compute the gravity theoretical admittance of a LFB along a 2000 km
       long profile using the same parameters as above

              gmt gravfft -C400/5000/3000/b -T10000/2700/3300/1035 -Z9000/40000


REFERENCES

       Luis, J.F. and M.C. Neves. 2006,  The  isostatic  compensation  of  the
       Azores  Plateau:  a 3D admittance and coherence analysis. J. Geothermal
       Volc.    Res.    Volume    156,    Issues     1-2,     Pages     10-22,
       http://dx.doi.org/10.1016/j.jvolgeores.2006.03.010

       Parker, R. L., 1972, The rapid calculation of potential anomalies, Geo-
       phys. J., 31, 447-455.

       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


SEE ALSO

       gmt(1), grdfft(1), grdmath(1), grdproject(1)


COPYRIGHT

       2017, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe



5.4.2                            Jun 24, 2017                       gravfft(1)

gmt5 5.4.2 - Generated Wed Jun 28 18:08:16 CDT 2017
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