NAME

      grdfft - Perform mathematical operations on grdfiles in the frequency
      domain

SYNOPSIS

      grdfft in_grdfile -Gout_grdfile [ -Aazimuth ] [ -Czlevel ] [
      -D[scale|g] ] [ -E[x|y][w] ] [ -F[x|y]lc/lp/hp/hc ] [ -I[scale|g] ] [
      -L ] [ -M ] [ -Sscale ] [ -Tte/rl/rm/rw/ri ] [ -V ]

DESCRIPTION

      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 grdfiles are assumed to be in meters.
      Geographical grids may be used by specifying the -M option that scales
      degrees to meters.  If you have grdfiles with dimensions in km, you
      could change this to meters using grdedit or scale the output with
      grdmath.
           No space between the option flag and the associated arguments.
      Use upper case for the option flags and lower case for modifiers.

      in_grdfile
           2-D binary grd file to be operated on.

      -G   Specify the name of the output grd file.

OPTIONS

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

      -C   Upward (for zlevel > 0) or downward (for zlevel < 0) continue the
           field zlevel meters.

      -D   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].

      -E   Estimate power spectrum in the radial direction.  Place x or y
           immediately after -E to compute the spectrum in the x or y
           direction instead.  No grdfile is created; f (i.e., frequency or
           wave number), power[f], and 1 standard deviation in power[f] are
           written to stdout.  Append w to write wavelength instead of
           frequency.

      -F   Filter the data.  Place x or y immediately after -F to filter x
           or y direction only; default is isotropic.  Specify four
           wavelengths in correct units (see -M) 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 -M 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.

      -I   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].

      -L   Leave trend alone.  By default, a linear trend will be removed
           prior to the transform.

      -M   Map units.  Choose this option if your grdfile is a geographical
           grid and you want to convert degrees into meters.  If the data
           are close to either pole, you should consider projecting the
           grdfile onto a rectangular coordinate system using grdproject.

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

      -T   Compute the isostatic compensation from the topography load
           (input grdfile) on an elastic plate of thickness te.  Also append
           densities for load, mantle, water, and infill in SI units.  If te
           == 0 then the Airy response is returned.  -T implicitly sets -L.

EXAMPLES

      To upward continue the sea-level magnetic anomalies in the file
      mag_0.grd to a level 800 m above sealevel, try

      grdfft mag_0.grd -C800 -V -Gmag_800.grd

      To transform geoid heights in m (geoid.grd) on a geographical grid to
      free-air gravity anomalies in mGal, do

      grdfft geoid.grd -Dg -M -V -Ggrav.grd

      To transform gravity anomalies in mGal (faa.grd) 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:

      grdfft faa.grd -Ig -A38 -S1e6 -V -Gdefl_38.grd

      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:

      grdfft gravity.grd -D -D -V -Ggrav_2nd_derivative.grd

      The first order gravity anomaly (in mGal) due to the compensating
      surface caused by the topography load topo.grd (in m) on a 20 km thick
      elastic plate, assumed to be 4 km beneath the observation level can be
      computed as

      grdfft topo.grd -T20000/2800/3330/1030/2300 -C4000 -S0.022
      -Gcomp_faa.grd

      where 0.022 is the scale needed for the first term in Parker's
      expansion for computing gravity from topography (= 2 * PI * G * (rhom
      - rhol)).

SEE ALSO

      gmt, grdedit, grdmath, grdproject