GRDFFT(1) Generic Mapping Tools GRDFFT(1)NAMEgrdfft - Perform mathematical operations on grid files in the wavenum‐
ber (or frequency) domain
SYNOPSISgrdfft in_grdfile -Gout_grdfile [ -Aazimuth ] [ -Czlevel ] [
-D[scale|g] ] [ -E[x|y][w] ] [ -F[x|y]params ] [ -I[scale|g] ] [ -L ] [
-M ] [ -Nstuff ] [ -Sscale ] [ -Tte/rl/rm/rw/ri ] [ -V ]
DESCRIPTIONgrdfft will take the 2-D forward Fast Fourier Transform and perform one
or more mathematical operations in the frequency domain before trans‐
forming 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 -M option that scales degrees to meters.
If you have grids with dimensions in km, you could change this to
meters using grdedit or scale the output with grdmath.
in_grdfile
2-D binary grid file to be operated on. (See GRID FILE FORMATS
below).
-G Specify the name of the output grid file. (See GRID FILE FOR‐
MATS below).
OPTIONS
No space between the option flag and the associated arguments.
-A Take the directional derivative in the azimuth direction mea‐
sured 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 equiv‐
alent 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 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 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. Choose between a
cosine-tapered band-pass, a Gaussian band-pass filter, or a But‐
terworth band-pass filter. Cosine-taper: Specify four wave‐
lengths lc/lp/hp/hc in correct units (see -M) to design a band‐
pass 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., -F 1000000/250000/50000/10000 -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. -Fy
1000/250/-/- will highpass y, passing wavelengths < 250 and
rejecting wavelengths > 1000. Gaussian band-pass: Append lo/hi,
the two wavelengths in correct units (see -M) to design a band‐
pass 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 hi or lo wavelength, respectively. E.g.,
-F-/30 will lowpass the data using a Gaussian filter with half-
weight at 30, while -F 400/- will highpass the data. Butter‐
worth band-pass: Append lo/hi/order, the two wavelengths in cor‐
rect units (see -M) 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 fil‐
ter, give a hyphen (-) for the hi or lo wavelength, respec‐
tively. E.g., -F-/30/2 will lowpass the data using a 2nd-order
Butterworth filter, with half-weight at 30, while -F 400/-/2
will highpass the data.
-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 grid file is a geographi‐
cal 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 grdpro‐
ject.
-N Choose or inquire about suitable grid dimensions for FFT. -Nf
will force the FFT to use the dimensions of the data. -Nq will
inQuire about more suitable dimensions. -Nnx/ny will do FFT on
array size nx/ny (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.
-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 grid file) 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.
-V Selects verbose mode, which will send progress reports to stderr
[Default runs "silently"].
GRID FILE FORMATS
By default GMT writes out grid as single precision floats in a COARDS-
complaint netCDF file format. However, GMT is able to produce grid
files in many other commonly used grid file formats and also facili‐
tates 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 =id[/scale/offset[/nan]], where id is a two-
letter identifier of the grid type and precision, and scale and offset
are optional scale factor and offset to be applied to all grid values,
and nan 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 grdreformat(1)
and Section 4.17 of the GMT Technical Reference and Cookbook for more
information.
When reading a netCDF file that contains multiple grids, GMT will read,
by default, the first 2-dimensional grid that can find in that file. To
coax GMT into reading another multi-dimensional variable in the grid
file, append ?varname to the file name, where varname is the name of
the variable. Note that you may need to escape the special meaning of ?
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
?varname suffix can also be used for output grids to specify a variable
name different from the default: "z". See grdreformat(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.
EXAMPLES
To upward continue the sea-level magnetic anomalies in the file
mag_0.grd to a level 800 m above sealevel:
grdfft mag_0.grd -C 800 -V -G mag_800.grd
To transform geoid heights in m (geoid.grd) on a geographical grid to
free-air gravity anomalies in mGal:
grdfft geoid.grd -Dg -V -G 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 inte‐
grate gravity to get geoid, then take the directional derivative, and
finally scale radians to micro-radians:
grdfft faa.grd -Ig 38 -S 1e6 -V -G 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 differen‐
tiating twice:
grdfft gravity.grd -D -D -V -G grav_2nd_derivative.grd
The first order gravity anomaly (in mGal) due to the compensating sur‐
face 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 -T 20000/2800/3330/1030/2300 -S 0.022 -C 4000 -G
comp_faa.grd
where 0.022 is the scale needed for the first term in Parker's expan‐
sion for computing gravity from topography (= 2 * PI * G * (rhom -
rhol)).
SEE ALSOGMT(1), grdedit(1), grdmath(1), grdproject(1)GMT 4.5.14 1 Nov 2015 GRDFFT(1)
