grdfft - Perform mathematical operations on grdfiles in the frequency
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 ] [ -Nstuff ] [ -Sscale ] [ -Tte/rl/rm/rw/ri ] [ -V ]
grdfft 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 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.
2-D binary grd file to be operated on.
-G Specify the name of the output grd file.
-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 equiva-
lent 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 fre-
-F Filter the data. Place x or y immediately after -F to filter x
or y direction only; default is isotropic. Specify four wave-
lengths in correct units (see -M) to design a bandpass filter:
wavelengths greater than lc or less than hc will be cut, wave-
lengths 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 wave-
lengths > 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, pass-
ing 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.
-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 >= grdfile size). Default chooses
dimensions >= data which optimize speed, accuracy of FFT. If
FFT dimensions > grdfile 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 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
-V Selects verbose mode, which will send progress reports to stderr
[Default runs "silently"].
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 -C800 -V -Gmag_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 -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 inte-
grate 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 differenti-
grdfft gravity.grd -D -D -V -Ggrav_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
grdfft topo.grd -T20000/2800/3330/1030/2300 -S0.022 -C4000
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 -
gmt(l), grdedit(l), grdmath(l), grdproject(l)
GMT4.0 1 Oct 2004 GRDFFT(l)
Man(1) output converted with