grdfft(1) GMT grdfft(1)
NAME
grdfft - Do mathematical operations on grids in the wavenumber (or fre-
quency) domain
SYNOPSIS
grdfft ingrid [ ingrid2 ] [ -Goutfile|table ] [ -Aazimuth ] [
-Czlevel ] [ -D[scale|g] ] [ -E[r|x|y][+w[k]][+n] ] [
-F[r|x|y]params ] [ -I[scale|g] ] [ -Nparams ] [ -Sscale ] [
-V[level] ] [ -fg ]
Note: No space is allowed between the option flag and the associated
arguments.
DESCRIPTION
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 grid are assumed to be in meters. Geographical grids
may be used by specifying the -fg 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.
REQUIRED ARGUMENTS
ingrid 2-D binary grid file to be operated on. (See GRID FILE FORMATS
below). For cross-spectral operations, also give the second grid
file ingrd2.
-Goutfile
Specify the name of the output grid file or the 1-D spectrum ta-
ble (see -E). (See GRID FILE FORMATS below).
OPTIONAL ARGUMENTS
-Aazimuth
Take the directional derivative in the azimuth direction mea-
sured in degrees CW from north.
-Czlevel
Upward (for zlevel > 0) or downward (for zlevel < 0) continue
the field zlevel meters.
-D[scale|g]
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[r|x|y][+w[k]][+n]
Estimate power spectrum in the radial direction [r]. Place x or
y immediately after -E to compute the spectrum in the x or y
direction instead. No grid file is created. If one grid is given
then f (i.e., frequency or wave number), power[f], and 1 stan-
dard deviation in power[f] are written to the file set by -G
[stdout]. If two grids are given we write f and 8 quantities:
Xpower[f], Ypower[f], coherent power[f], noise power[f],
phase[f], admittance[f], gain[f], coherency[f]. Each quantity
is followed by its own 1-std dev error estimate, hence the out-
put is 17 columns wide. Give +w to write wavelength instead of
frequency, and if your grid is geographic you may further append
k to scale wavelengths from meter [Default] to km. Finally, the
spectrum is obtained by summing over several frequencies.
Append +n to normalize so that the mean spectral values per fre-
quency are reported instead.
-F[r|x|y]params
Filter the data. Place x or y immediately after -F to filter x
or y direction only; default is isotropic [r]. Choose between a
cosine-tapered band-pass, a Gaussian band-pass filter, or a But-
terworth band-pass filter.
Cosine-taper:
Specify four wavelengths lc/lp/hp/hc in correct units
(see -fg) 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 -fg 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.
Gaussian band-pass:
Append lo/hi, the two wavelengths in correct units (see
-fg) to design a bandpass filter. At the given wave-
lengths 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 low-
pass the data using a Gaussian filter with half-weight at
30, while -F400/- will highpass the data.
Butterworth band-pass:
Append lo/hi/order, the two wavelengths in correct units
(see -fg) and the filter order (an integer) to design a
bandpass filter. At the given cut-off wavelengths the
Butterworth filter weights will be 0.707 (i.e., the power
spectrum will therefore be reduced by 0.5). To make a
highpass or lowpass filter, give a hyphen (-) for the hi
or lo wavelength, respectively. E.g., -F-/30/2 will low-
pass the data using a 2nd-order Butterworth filter, with
half-weight at 30, while -F400/-/2 will highpass the
data.
-Goutfile|table
Filename for output netCDF grid file OR 1-D data table (see -E).
This is optional for -E (spectrum written to stdout) but manda-
tory for all other options that require a grid output.
-I[scale|g]
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].
-N[a|f|m|r|s|nx/ny][+a|[+d|h|l][+e|n|m][+twidth][+v][+w[suffix]][+z[p]]
Choose or inquire about suitable grid dimensions for FFT and set
optional parameters. Control the FFT dimension:
-Na lets the FFT select dimensions yielding the most accurate
result.
-Nf will force the FFT to use the actual dimensions of the
data.
-Nm lets the FFT select dimensions using the least work mem-
ory.
-Nr lets the FFT select dimensions yielding the most rapid
calculation.
-Ns will present a list of optional dimensions, then exit.
-Nnx/ny will do FFT on array size nx/ny (must be >= grid file
size). Default chooses dimensions >= data which optimize
speed and accuracy of FFT. If FFT dimensions > grid file
dimensions, data are extended and tapered to zero.
Control detrending of data: Append modifiers for removing a lin-
ear trend:
+d: Detrend data, i.e. remove best-fitting linear trend
[Default].
+a: Only remove mean value.
+h: Only remove mid value, i.e. 0.5 * (max + min).
+l: Leave data alone.
Control extension and tapering of data: Use modifiers to control
how the extension and tapering are to be performed:
+e extends the grid by imposing edge-point symmetry
[Default],
+m extends the grid by imposing edge mirror symmetry
+n turns off data extension.
Tapering is performed from the data edge to the FFT grid edge
[100%]. Change this percentage via +twidth. When +n is in
effect, the tapering is applied instead to the data margins
as no extension is available [0%].
Control messages being reported: +v will report suitable
dimensions during processing.
Control writing of temporary results: For detailed investigation
you can write the intermediate grid being passed to the forward
FFT; this is likely to have been detrended, extended by
point-symmetry along all edges, and tapered. Append +w[suffix]
from which output file name(s) will be created (i.e.,
ingrid_prefix.ext) [tapered], where ext is your file extension.
Finally, you may save the complex grid produced by the forward
FFT by appending +z. By default we write the real and imaginary
components to ingrid_real.ext and ingrid_imag.ext. Append p to
save instead the polar form of magnitude and phase to files
ingrid_mag.ext and ingrid_phase.ext.
-Sscale
Multiply each element by scale in the space domain (after the
frequency domain operations). [Default is 1.0].
-V[level] (more a|)
Select verbosity level [c].
-fg Geographic grids (dimensions of longitude, latitude) will be
converted to meters via a aFlat Eartha approximation using the
current ellipsoid parameters.
-^ or just -
Print a short message about the syntax of the command, then
exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explana-
tion of any module-specific option (but not the GMT common
options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation
of all options, then exits.
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
facilitates so called apackinga of grids, writing out floating point
data as 1- or 2-byte integers. (more a|)
GRID DISTANCE UNITS
If the grid does not have meter as the horizontal unit, append +uunit
to the input file name to convert from the specified unit to meter. If
your grid is geographic, convert distances to meters by supplying -fg
instead.
CONSIDERATIONS
netCDF COARDS grids will automatically be recognized as geographic. For
other grids geographical grids were you want to convert degrees into
meters, select -fg. If the data are close to either pole, you should
consider projecting the grid file onto a rectangular coordinate system
using grdproject
NORMALIZATION OF SPECTRUM
By default, the power spectrum returned by -E simply sums the contribu-
tions from frequencies that are part of the output frequency. For x-
or y-spectra this means summing the power across the other frequency
dimension, while for the radial spectrum it means summing up power
within each annulus of width delta_q, the radial frequency (q) spacing.
A consequence of this summing is that the radial spectrum of a white
noise process will give a linear radial power spectrum that is propor-
tional to q. Appending n will instead compute the mean power per out-
put frequency and in this case the white noise process will have a
white radial spectrum as well.
EXAMPLES
To upward continue the sea-level magnetic anomalies in the file
mag_0.nc to a level 800 m above sealevel:
gmt grdfft mag_0.nc -C800 -V -Gmag_800.nc
To transform geoid heights in m (geoid.nc) on a geographical grid to
free-air gravity anomalies in mGal:
gmt grdfft geoid.nc -Dg -V -Ggrav.nc
To transform gravity anomalies in mGal (faa.nc) 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:
gmt grdfft faa.nc -Ig -A38 -S1e6 -V -Gdefl_38.nc
Second vertical derivatives of gravity anomalies are related to the
curvature of the field. We can compute these as mGal/m^2 by differenti-
ating twice:
gmt grdfft gravity.nc -D -D -V -Ggrav_2nd_derivative.nc
To compute cross-spectral estimates for co-registered bathymetry and
gravity grids, and report result as functions of wavelengths in km, try
gmt grdfft bathymetry.nc gravity.grd -E+wk -fg -V > cross_spectra.txt
To examine the pre-FFT grid after detrending, point-symmetry reflec-
tion, and tapering has been applied, as well as saving the real and
imaginary components of the raw spectrum of the data in topo.nc, try
gmt grdfft topo.nc -N+w+z -fg -V
You can now make plots of the data in topo_taper.nc, topo_real.nc, and
topo_imag.nc.
SEE ALSO
gmt(1), grdedit(1), grdfilter(1), grdmath(1), grdproject(1), gravfft(1)
COPYRIGHT
2017, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
5.4.2 Jun 24, 2017 grdfft(1)
gmt5 5.4.2 - Generated Wed Jun 28 18:25:25 CDT 2017