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 ] [ -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
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 -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
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 measured
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
equivalent 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
-F Filter the data. Place x or y immediately after -F to filter x
or y direction only; default is isotropic. Specify four
wavelengths in correct units (see -M) to design a bandpass
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.,
-F1000000/250000/50000/10000 -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.
-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.
-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 -L.
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 -C800 -V -Gmag_800.grd
To transform geoid heights in m (geoid.grd) on a geographical grid to
free-air gravity anomalies in mGal, do
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
integrate 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
grdfft gravity.grd -D -D -V -Ggrav_2nd_derivative.grd
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
grdfft topo.grd -T20000/2800/3330/1030/2300 -C4000 -S0.022
where 0.022 is the scale needed for the first term in Parker's
expansion for computing gravity from topography (= 2 * PI * G * (rhom
gmt, grdedit, grdmath, grdproject
Man(1) output converted with