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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>
<h2>NAME
<a name="NAME"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">grdfft −
Perform mathematical operations on grid files in the
wavenumber (or frequency) domain</p>
<h2>SYNOPSIS
<a name="SYNOPSIS"></a>
</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>
<h2>DESCRIPTION
<a name="DESCRIPTION"></a>
</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><b>−G</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>Specify the name of the output grid file. (See GRID FILE
FORMATS below).</p></td></tr>
</table>
<h2>OPTIONS
<a name="OPTIONS"></a>
</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"><b>−A</b></p></td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em">Take the directional derivative
in the <i>azimuth</i> direction measured in degrees CW from
north.</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−C</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>Upward (for <i>zlevel</i> > 0) or downward (for
<i>zlevel</i> < 0) continue the field <i>zlevel</i>
meters.</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−D</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−E</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−F</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−I</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−L</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>Leave trend alone. By default, a linear trend will be
removed prior to the transform.</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−M</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−N</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−S</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>Multiply each element by <i>scale</i> in the space
domain (after the frequency domain operations). [Default is
1.0].</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−T</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p><b>−V</b></p></td>
<td width="8%"></td>
<td width="78%">
<p>Selects verbose mode, which will send progress reports
to stderr [Default runs "silently"].</p></td></tr>
</table>
<h2>GRID FILE FORMATS
<a name="GRID FILE FORMATS"></a>
</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>
<h2>EXAMPLES
<a name="EXAMPLES"></a>
</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>
<h2>SEE ALSO
<a name="SEE ALSO"></a>
</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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