Provided by: gmt-common_5.4.5+dfsg-1_all bug


       grdfft - Do mathematical operations on grids in the wavenumber (or frequency) domain


       grdfft ingrid [ ingrid2 ] [  -Goutfile|table ] [  -Aazimuth ] [  -Czlevel ] [  -D[scale|g]
       ] [  -E[r|x|y][+w[k]][+n] ] [  -F[r|x|y]params ] [  -I[scale|g] ] [  -Nparams ] [  -Sscale
       ] [  -V[level] ] [ -fg ]

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


       grdfft  will  take  the  2-D  forward  Fast  Fourier  Transform  and  perform  one or more
       mathematical operations in the frequency domain before  transforming  back  to  the  space
       domain. An option is provided to scale the data before writing the new values to an output
       file. The horizontal dimensions of the grid 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.


       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.

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


              Take  the  directional  derivative  in the azimuth direction measured in degrees CW
              from north.

              Upward (for zlevel > 0) or downward (for zlevel <  0)  continue  the  field  zlevel

              Differentiate  the field, i.e., take d(field)/dz. This is equivalent to multiplying
              by kr in the frequency domain (kr  is  radial  wave  number).  Append  a  scale  to
              multiply  by  (kr  * scale) instead.  Alternatively, append g to indicate that your
              data are geoid heights in meters and output should be gravity  anomalies  in  mGal.
              [Default is no scale].

              Estimate power spectrum in the radial direction [r]. Place x or y immediately after
              -E to compute the spectrum in the x  or  y  direction  instead.  No  grid  file  is
              created.  If  one  grid is given then f (i.e., frequency or wave number), power[f],
              and 1 standard deviation in power[f] are written to the file set by -G [stdout]. If
              two  grids  are  given  we write f and 8 quantities: Xpower[f], Ypower[f], coherent
              power[f], noise power[f], phase[f],  admittance[f],  gain[f],  coherency[f].   Each
              quantity  is  followed  by its own 1-std dev error estimate, hence the output is 17
              columns wide.  Give +w to write wavelength instead of frequency, and if  your  grid
              is geographic you may further append k to scale wavelengths from meter [Default] to
              km.  Finally, the spectrum is obtained by summing over several frequencies.  Append
              +n  to  normalize  so  that  the  mean  spectral  values per frequency are reported

              Filter the data. Place x or y immediately after -F to filter x or y direction only;
              default  is  isotropic  [r].  Choose between a cosine-tapered band-pass, a Gaussian
              band-pass filter, or a Butterworth band-pass filter.

                     Specify four wavelengths lc/lp/hp/hc in correct units (see -fg) to design  a
                     bandpass  filter:  wavelengths  greater than lc or less than hc will be cut,
                     wavelengths greater than lp and less than hp will be passed, and wavelengths
                     in  between  will  be cosine-tapered. E.g., -F1000000/250000/50000/10000 -fg
                     will  bandpass,  cutting  wavelengths  >  1000  km  and  <  10  km,  passing
                     wavelengths  between 250 km and 50 km. To make a highpass or lowpass filter,
                     give hyphens (-) for hp/hc or lc/lp.  E.g.,  -Fx-/-/50/10  will  lowpass  x,
                     passing  wavelengths  >  50  and rejecting wavelengths < 10. -Fy1000/250/-/-
                     will highpass y, passing wavelengths < 250 and rejecting wavelengths > 1000.

              Gaussian band-pass:
                     Append lo/hi, the two wavelengths in correct units (see  -fg)  to  design  a
                     bandpass  filter.  At the given wavelengths the Gaussian filter weights will
                     be 0.5. To make a highpass or lowpass filter, give a hyphen (-) for  the  hi
                     or  lo  wavelength, respectively. E.g., -F-/30 will lowpass the data using a
                     Gaussian filter with half-weight at 30,  while  -F400/-  will  highpass  the

              Butterworth band-pass:
                     Append  lo/hi/order,  the two wavelengths in correct units (see -fg) and the
                     filter order (an integer) to design a bandpass filter. At the given  cut-off
                     wavelengths  the  Butterworth  filter weights will be 0.707 (i.e., the power
                     spectrum will therefore be reduced by 0.5). To make a  highpass  or  lowpass
                     filter,  give  a hyphen (-) for the hi or lo wavelength, respectively. E.g.,
                     -F-/30/2 will lowpass the data using a 2nd-order  Butterworth  filter,  with
                     half-weight at 30, while -F400/-/2 will highpass the data.

              Filename  for output netCDF grid file OR 1-D data table (see -E).  This is optional
              for -E (spectrum written to stdout)  but  mandatory  for  all  other  options  that
              require a grid output.

              Integrate  the  field,  i.e.,  compute  integral_over_z  (field  *  dz).   This  is
              equivalent to divide by kr in the frequency domain  (kr  is  radial  wave  number).
              Append  a  scale  to  divide  by  (kr  * scale) instead. Alternatively, append g to
              indicate that your data set is gravity anomalies in mGal and output should be geoid
              heights in meters. [Default is no scale].

              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 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:
                 +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

              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

              Multiply each element by scale in the space  domain  (after  the  frequency  domain
              operations). [Default is 1.0].

       -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
              just use -).

       -+ 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  all  options,
              then exits.


       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


       By  default,  the  power  spectrum  returned  by  -E  simply  sums  the contributions from
       frequencies that are part of the output frequency.  For x- or y-spectra this means summing
       the  power  across  the  other frequency dimension, while for the radial spectrum it means
       summing up power within each annulus of width delta_q, the radial frequency  (q)  spacing.
       A  consequence  of  this summing is that the radial spectrum of a white noise process will
       give a linear radial power spectrum that is proportional to q.  Appending n  will  instead
       compute  the mean power per output frequency and in this case the white noise process will
       have a white radial spectrum as well.


       To upward continue the sea-level magnetic anomalies in the file to a level 800  m
       above sealevel:

              gmt grdfft -C800 -V

       To  transform  geoid  heights  in  m ( on a geographical grid to free-air gravity
       anomalies in mGal:

              gmt grdfft -Dg -V

       To transform gravity anomalies in  mGal  (  to  deflections  of  the  vertical  (in
       micro-radians)  in  the  038 direction, we must first integrate gravity to get geoid, then
       take the directional derivative, and finally scale radians to micro-radians:

              gmt grdfft -Ig -A38 -S1e6 -V

       Second vertical derivatives of gravity anomalies are  related  to  the  curvature  of  the
       field. We can compute these as mGal/m^2 by differentiating twice:

              gmt grdfft -D -D -V

       To  compute  cross-spectral  estimates for co-registered bathymetry and gravity grids, and
       report result as functions of wavelengths in km, try

              gmt grdfft gravity.grd -E+wk -fg -V > cross_spectra.txt

       To examine the pre-FFT grid after detrending, point-symmetry reflection, and tapering  has
       been  applied,  as well as saving the real and imaginary components of the raw spectrum of
       the data in, try

              gmt grdfft -N+w+z -fg -V

       You can now make plots of the data in,, and


       gmt, grdedit, grdfilter, grdmath, grdproject, gravfft


       2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe