## 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