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<HTML>
<HEAD>
<TITLE>grdfft</TITLE>
</HEAD>
<BODY>
<H1>grdfft</H1>
<HR>
<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
grdfft - Perform mathematical operations on grdfiles in
the frequency domain
</PRE>
<H2>SYNOPSIS</H2><PRE>
<B>grdfft</B> <I>in</I><B>_</B><I>grdfile</I> <B>-G</B><I>out</I><B>_</B><I>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>[<I>x|y</I>]<I>lc/lp/hp/hc</I> ] [
<B>-I</B>[<I>scale</I><B>|g</B>] ] [ <B>-L</B> ] [ <B>-M</B> ] [ <B>-S</B><I>scale</I> ] [ <B>-T</B><I>te/rl/rm/rw/ri</I>
] [ <B>-V</B> ]
</PRE>
<H2>DESCRIPTION</H2><PRE>
<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 grdfiles 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 grdfiles 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>.
No space between the option flag and the associ
ated arguments. Use upper case for the option flags and
lower case for modifiers.
<I>in</I><B>_</B><I>grdfile</I>
2-D binary grd file to be operated on.
<B>-G</B> Specify the name of the output grd file.
</PRE>
<H2>OPTIONS</H2><PRE>
<B>-A</B> Take the directional derivative in the <I>azimuth</I>
direction measured in degrees CW from north.
<B>-C</B> Upward (for <I>zlevel</I> > 0) or downward (for <I>zlevel</I> <
0) continue the field <I>zlevel</I> meters.
<B>-D</B> Differentiate the field, i.e., take d(field)/dz.
This is equivalent to multiplying by kr in the fre
quency domain (kr is radial wave number). Append a
scale to multiply by (kr * <I>scale</I>) instead. Alterna
tively, append <B>g</B> to indicate that your data are
geoid heights in meters and output should be grav
ity anomalies in mGal. [Default is no scale].
<B>-E</B> 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 grd
file is created; f (i.e., frequency or wave num
ber), power[f], and 1 standard deviation in
power[f] are written to stdout. Append <B>w</B> to write
wavelength instead of frequency.
to filter x or y direction only; default is
isotropic. Specify four wavelengths in correct
units (see <B>-M</B>) to design a bandpass filter; wave
lengths 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>-F</B>x-/-/50/10
will lowpass X, passing wavelengths > 50 and
rejecting wavelengths < 10. <B>-F</B>y1000/250/-/- will
highpass Y, passing wavelengths < 250 and rejecting
wavelengths > 1000.
<B>-I</B> 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].
<B>-L</B> Leave trend alone. By default, a linear trend will
be removed prior to the transform.
<B>-M</B> 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 <B><A HREF="grdproject.html">grdproject</A></B>.
<B>-S</B> Multiply each element by <I>scale</I> in the space domain
(after the frequency domain operations). [Default
is 1.0].
<B>-T</B> Compute the isostatic compensation from the topog
raphy load (input grdfile) on an elastic plate of
thickness <I>te</I>. Also append densities for load, man
tle, 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>.
<B>-V</B> Selects verbose mode, which will send progress
reports to stderr [Default runs "silently"].
</PRE>
<H2>EXAMPLES</H2><PRE>
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 <B>-C</B>800 <B>-V</B> <B>-G</B>mag_800.grd
ical grid to free-air gravity anomalies in mGal, do
grdfft geoid.grd <B>-Dg</B> <B>-M</B> <B>-V</B> <B>-G</B>grav.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 <B>-Ig</B> <B>-A</B>38 <B>-S</B>1e6 <B>-V</B> <B>-G</B>defl_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 <B>-D</B> <B>-D</B> <B>-V</B> <B>-G</B>grav_2nd_derivative.grd
The first order gravity anomaly (in mGal) due to the com
pensating 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 <B>-T</B>20000/2800/3330/1030/2300 <B>-C</B>4000 <B>-S</B>0.022
<B>-G</B>comp_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)).
</PRE>
<H2>SEE ALSO</H2><PRE>
<I>gmt</I>(l), <I><A HREF="grdedit.html">grdedit</A></I>(l), <I><A HREF="grdmath.html">grdmath</A></I>(l), <I><A HREF="grdproject.html">grdproject</A></I>(l)
</PRE>
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