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<h1 align=center>GRDFFT</h1>
<a href="#NAME">NAME</a><br>
<a href="#SYNOPSIS">SYNOPSIS</a><br>
<a href="#DESCRIPTION">DESCRIPTION</a><br>
<a href="#OPTIONS">OPTIONS</a><br>
<a href="#GRID FILE FORMATS">GRID FILE FORMATS</a><br>
<a href="#EXAMPLES">EXAMPLES</a><br>
<a href="#SEE ALSO">SEE ALSO</a><br>
<hr>
<a name="NAME"></a>
<h2>NAME</h2>
<p style="margin-left:11%; margin-top: 1em">grdfft −
Perform mathematical operations on grid files in the
wavenumber (or frequency) domain</p>
<a name="SYNOPSIS"></a>
<h2>SYNOPSIS</h2>
<p style="margin-left:11%; margin-top: 1em"><b>grdfft</b>
<i>in_grdfile</i> <b>−G</b><i>out_grdfile</i> [
<b>−A</b><i>azimuth</i> ] [
<b>−C</b><i>zlevel</i> ] [
<b>−D</b>[<i>scale</i><b>|g</b>] ] [
<b>−E</b>[<b>x|y</b>][<b>w</b>] ] [
<b>−F</b>[<b>x</b>|<b>y</b>]<i>params</i> ] [
<b>−I</b>[<i>scale</i><b>|g</b>] ] [ <b>−L</b> ]
[ <b>−M</b> ] [ <b>−N</b><i>stuff</i> ] [
<b>−S</b><i>scale</i> ] [
<b>−T</b><i>te/rl/rm/rw/ri</i> ] [ <b>−V</b>
]</p>
<a name="DESCRIPTION"></a>
<h2>DESCRIPTION</h2>
<p style="margin-left:11%; margin-top: 1em"><b>grdfft</b>
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 <b>−M</b> option that scales degrees to
meters. If you have grids with dimensions in km, you could
change this to meters using <b><A HREF="grdedit.html">grdedit</A></b> or scale the
output with <b><A HREF="grdmath.html">grdmath</A></b>. <i><br>
in_grdfile</i></p>
<p style="margin-left:22%;">2-D binary grid file to be
operated on. (See GRID FILE FORMATS below).</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−G</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Specify the name of
the output grid file. (See GRID FILE FORMATS below).</p></td>
</table>
<a name="OPTIONS"></a>
<h2>OPTIONS</h2>
<p style="margin-left:11%; margin-top: 1em">No space
between the option flag and the associated arguments.</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−A</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Take the
directional derivative in the <i>azimuth</i> direction
measured in degrees CW from north.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−C</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Upward (for
<i>zlevel</i> > 0) or downward (for <i>zlevel</i> < 0)
continue the field <i>zlevel</i> meters.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−D</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 * <i>scale</i>)
instead. Alternatively, append <b>g</b> to indicate that
your data are geoid heights in meters and output should be
gravity anomalies in mGal. [Default is no scale].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−E</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Estimate power
spectrum in the radial direction. Place <b>x</b> or <b>y</b>
immediately after <b>−E</b> to compute the spectrum in
the x or y direction instead. No grid file is created; f
(i.e., frequency or wave number), power[f], and 1 standard
deviation in power[f] are written to stdout. Append <b>w</b>
to write wavelength instead of frequency.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−F</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Filter the data.
Place <b>x</b> or <b>y</b> immediately after <b>−F</b>
to filter <i>x</i> or <i>y</i> direction only; default is
isotropic. Choose between a cosine-tapered band-pass, a
Gaussian band-pass filter, or a Butterworth band-pass
filter. Cosine-taper: Specify four wavelengths
<i>lc</i>/<i>lp</i>/<i>hp</i>/<i>hc</i> in correct units
(see <b>−M</b>) to design a bandpass filter:
wavelengths greater than <i>lc</i> or less than <i>hc</i>
will be cut, wavelengths greater than <i>lp</i> and less
than <i>hp</i> will be passed, and wavelengths in between
will be cosine-tapered. E.g., <b>−F</b>
1000000/250000/50000/10000 <b>−M</b> 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 <i>hp</i>/<i>hc</i> or
<i>lc</i>/<i>lp</i>. E.g., <b>−Fx</b>-/-/50/10 will
lowpass <i>x</i>, passing wavelengths > 50 and rejecting
wavelengths < 10. <b>−Fy</b> 1000/250/-/- will
highpass <i>y</i>, passing wavelengths < 250 and
rejecting wavelengths > 1000. Gaussian band-pass: Append
<i>lo</i>/<i>hi</i>, the two wavelengths in correct units
(see <b>−M</b>) 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 <i>hi</i> or <i>lo</i> wavelength, respectively. E.g.,
<b>−F</b>-/30 will lowpass the data using a Gaussian
filter with half-weight at 30, while <b>−F</b> 400/-
will highpass the data. Butterworth band-pass: Append
<i>lo</i>/<i>hi</i>/<i>order</i>, the two wavelengths in
correct units (see <b>−M</b>) and the filter order (an
integer) to design a bandpass filter. At the given
wavelengths the Butterworth filter weights will be 0.5. To
make a highpass or lowpass filter, give a hyphen (-) for the
<i>hi</i> or <i>lo</i> wavelength, respectively. E.g.,
<b>−F</b>-/30/2 will lowpass the data using a
2nd-order Butterworth filter, with half-weight at 30, while
<b>−F</b> 400/-/2 will highpass the data.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−I</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 *
<i>scale</i>) instead. Alternatively, append <b>g</b> to
indicate that your data set is gravity anomalies in mGal and
output should be geoid heights in meters. [Default is no
scale].</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−L</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Leave trend alone.
By default, a linear trend will be removed prior to the
transform.</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−M</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Map units. Choose
this option if your grid file 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 grid file
onto a rectangular coordinate system using
<b><A HREF="grdproject.html">grdproject</A></b>.</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−N</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Choose or inquire
about suitable grid dimensions for FFT. <b>−Nf</b>
will force the FFT to use the dimensions of the data.
<b>−Nq</b> will inQuire about more suitable
dimensions. <b>−N</b><i>nx/ny</i> will do FFT on array
size <i>nx/ny</i> (Must be >= grid file size). Default
chooses dimensions >= data which optimize speed, accuracy
of FFT. If FFT dimensions > grid file dimensions, data
are extended and tapered to zero.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−S</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Multiply each
element by <i>scale</i> in the space domain (after the
frequency domain operations). [Default is 1.0].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−T</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Compute the
isostatic compensation from the topography load (input grid
file) on an elastic plate of thickness <i>te</i>. Also
append densities for load, mantle, water, and infill in SI
units. If <i>te</i> == 0 then the Airy response is returned.
<b>−T</b> implicitly sets <b>−L</b>.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−V</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects verbose
mode, which will send progress reports to stderr [Default
runs "silently"].</p></td>
</table>
<a name="GRID FILE FORMATS"></a>
<h2>GRID FILE FORMATS</h2>
<p style="margin-left:11%; margin-top: 1em">By default
<b><A HREF="GMT.html">GMT</A></b> writes out grid as single precision floats in a
COARDS-complaint netCDF file format. However, <b><A HREF="GMT.html">GMT</A></b> 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 2- or 4-byte integers. To specify the precision,
scale and offset, the user should add the suffix
<b>=</b><i>id</i>[<b>/</b><i>scale</i><b>/</b><i>offset</i>[<b>/</b><i>nan</i>]],
where <i>id</i> is a two-letter identifier of the grid type
and precision, and <i>scale</i> and <i>offset</i> are
optional scale factor and offset to be applied to all grid
values, and <i>nan</i> is the value used to indicate missing
data. When reading grids, the format is generally
automatically recognized. If not, the same suffix can be
added to input grid file names. See <b><A HREF="grdreformat.html">grdreformat</A></b>(1)
and Section 4.17 of the GMT Technical Reference and Cookbook
for more information.</p>
<p style="margin-left:11%; margin-top: 1em">When reading a
netCDF file that contains multiple grids, <b><A HREF="GMT.html">GMT</A></b> will
read, by default, the first 2-dimensional grid that can find
in that file. To coax <b><A HREF="GMT.html">GMT</A></b> into reading another
multi-dimensional variable in the grid file, append
<b>?</b><i>varname</i> to the file name, where
<i>varname</i> is the name of the variable. Note that you
may need to escape the special meaning of <b>?</b> in your
shell program by putting a backslash in front of it, or by
placing the filename and suffix between quotes or double
quotes. The <b>?</b><i>varname</i> suffix can also be used
for output grids to specify a variable name different from
the default: "z". See <b><A HREF="grdreformat.html">grdreformat</A></b>(1) and
Section 4.18 of the GMT Technical Reference and Cookbook for
more information, particularly on how to read splices of 3-,
4-, or 5-dimensional grids.</p>
<a name="EXAMPLES"></a>
<h2>EXAMPLES</h2>
<p style="margin-left:11%; margin-top: 1em">To upward
continue the sea-level magnetic anomalies in the file
mag_0.grd to a level 800 m above sealevel:</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdfft</b>
mag_0.grd <b>−C</b> 800 <b>−V −G</b>
mag_800.grd</p>
<p style="margin-left:11%; margin-top: 1em">To transform
geoid heights in m (geoid.grd) on a geographical grid to
free-air gravity anomalies in mGal:</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdfft</b>
geoid.grd <b>−Dg −V −G</b> grav.grd</p>
<p style="margin-left:11%; margin-top: 1em">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:</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdfft</b>
faa.grd <b>−Ig</b> 38 <b>−S</b> 1e6 <b>−V
−G</b> defl_38.grd</p>
<p style="margin-left:11%; margin-top: 1em">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:</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdfft</b>
gravity.grd <b>−D −D −V −G</b>
grav_2nd_derivative.grd</p>
<p style="margin-left:11%; margin-top: 1em">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</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdfft</b>
topo.grd <b>−T</b> 20000/2800/3330/1030/2300
<b>−S</b> 0.022 <b>−C</b> 4000 <b>−G</b>
comp_faa.grd</p>
<p style="margin-left:11%; margin-top: 1em">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)).</p>
<a name="SEE ALSO"></a>
<h2>SEE ALSO</h2>
<p style="margin-left:11%; margin-top: 1em"><i><A HREF="GMT.html">GMT</A></i>(1),
<i><A HREF="grdedit.html">grdedit</A></i>(1), <i><A HREF="grdmath.html">grdmath</A></i>(1),
<i><A HREF="grdproject.html">grdproject</A></i>(1)</p>
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