1GRDFFT(1) GMT GRDFFT(1)
2
6 grdfft - Do mathematical operations on grids in the wavenumber (or fre‐
7 quency) domain
8
10 grdfft ingrid [ ingrid2 ] [ -Goutfile|table ] [ -Aazimuth ] [
11 -Czlevel ] [ -D[scale|g] ] [ -E[r|x|y][+w[k]][+n] ] [
12 -F[r|x|y]params ] [ -I[scale|g] ] [ -Nparams ] [ -Sscale ] [
13 -V[level] ] [ -fg ]
14 Note: No space is allowed between the option flag and the associated
16 arguments.
17
19 grdfft will take the 2-D forward Fast Fourier Transform and perform one
20 or more mathematical operations in the frequency domain before trans‐
21 forming back to the space domain. An option is provided to scale the
22 data before writing the new values to an output file. The horizontal
23 dimensions of the grid are assumed to be in meters. Geographical grids
24 may be used by specifying the -fg option that scales degrees to meters.
25 If you have grids with dimensions in km, you could change this to
26 meters using grdedit or scale the output with grdmath.
27
29 ingrid 2-D binary grid file to be operated on. (See GRID FILE FORMATS
30 below). For cross-spectral operations, also give the second grid
31 file ingrd2.
32 -Goutfile
34 Specify the name of the output grid file or the 1-D spectrum ta‐
35 ble (see -E). (See GRID FILE FORMATS below).
36
38 -Aazimuth
39 Take the directional derivative in the azimuth direction mea‐
40 sured in degrees CW from north.
41 -Czlevel
43 Upward (for zlevel > 0) or downward (for zlevel < 0) continue
44 the field zlevel meters.
45 -D[scale|g]
47 Differentiate the field, i.e., take d(field)/dz. This is equiva‐
48 lent to multiplying by kr in the frequency domain (kr is radial
49 wave number). Append a scale to multiply by (kr * scale)
50 instead. Alternatively, append g to indicate that your data are
51 geoid heights in meters and output should be gravity anomalies
52 in mGal. [Default is no scale].
53 -E[r|x|y][+w[k]][+n]
55 Estimate power spectrum in the radial direction [r]. Place x or
56 y immediately after -E to compute the spectrum in the x or y
57 direction instead. No grid file is created. If one grid is given
58 then f (i.e., frequency or wave number), power[f], and 1 stan‐
59 dard deviation in power[f] are written to the file set by -G
60 [stdout]. If two grids are given we write f and 8 quantities:
61 Xpower[f], Ypower[f], coherent power[f], noise power[f],
62 phase[f], admittance[f], gain[f], coherency[f]. Each quantity
63 is followed by its own 1-std dev error estimate, hence the out‐
64 put is 17 columns wide. Give +w to write wavelength instead of
65 frequency, and if your grid is geographic you may further append
66 k to scale wavelengths from meter [Default] to km. Finally, the
67 spectrum is obtained by summing over several frequencies.
68 Append +n to normalize so that the mean spectral values per fre‐
69 quency are reported instead.
70 -F[r|x|y]params
72 Filter the data. Place x or y immediately after -F to filter x
73 or y direction only; default is isotropic [r]. Choose between a
74 cosine-tapered band-pass, a Gaussian band-pass filter, or a But‐
75 terworth band-pass filter.
76 Cosine-taper:
78 Specify four wavelengths lc/lp/hp/hc in correct units
79 (see -fg) to design a bandpass filter: wavelengths
80 greater than lc or less than hc will be cut, wavelengths
81 greater than lp and less than hp will be passed, and
82 wavelengths in between will be cosine-tapered. E.g.,
83 -F1000000/250000/50000/10000 -fg will bandpass, cutting
84 wavelengths > 1000 km and < 10 km, passing wavelengths
85 between 250 km and 50 km. To make a highpass or lowpass
86 filter, give hyphens (-) for hp/hc or lc/lp. E.g.,
87 -Fx-/-/50/10 will lowpass x, passing wavelengths > 50 and
88 rejecting wavelengths < 10. -Fy1000/250/-/- will highpass
89 y, passing wavelengths < 250 and rejecting wavelengths >
90 1000.
91 Gaussian band-pass:
93 Append lo/hi, the two wavelengths in correct units (see
94 -fg) to design a bandpass filter. At the given wave‐
95 lengths the Gaussian filter weights will be 0.5. To make
96 a highpass or lowpass filter, give a hyphen (-) for the
97 hi or lo wavelength, respectively. E.g., -F-/30 will low‐
98 pass the data using a Gaussian filter with half-weight at
99 30, while -F400/- will highpass the data.
100 Butterworth band-pass:
102 Append lo/hi/order, the two wavelengths in correct units
103 (see -fg) and the filter order (an integer) to design a
104 bandpass filter. At the given cut-off wavelengths the
105 Butterworth filter weights will be 0.707 (i.e., the power
106 spectrum will therefore be reduced by 0.5). To make a
107 highpass or lowpass filter, give a hyphen (-) for the hi
108 or lo wavelength, respectively. E.g., -F-/30/2 will low‐
109 pass the data using a 2nd-order Butterworth filter, with
110 half-weight at 30, while -F400/-/2 will highpass the
111 data.
112 -Goutfile|table
114 Filename for output netCDF grid file OR 1-D data table (see -E).
115 This is optional for -E (spectrum written to stdout) but manda‐
116 tory for all other options that require a grid output.
117 -I[scale|g]
119 Integrate the field, i.e., compute integral_over_z (field * dz).
120 This is equivalent to divide by kr in the frequency domain (kr
121 is radial wave number). Append a scale to divide by (kr * scale)
122 instead. Alternatively, append g to indicate that your data set
123 is gravity anomalies in mGal and output should be geoid heights
124 in meters. [Default is no scale].
125 -N[a|f|m|r|s|nx/ny][+a|[+d|h|l][+e|n|m][+twidth][+v][+w[suffix]][+z[p]]
127 Choose or inquire about suitable grid dimensions for FFT and set
128 optional parameters. Control the FFT dimension:
129 -Na lets the FFT select dimensions yielding the most accurate
130 result.
131 -Nf will force the FFT to use the actual dimensions of the
133 data.
134 -Nm lets the FFT select dimensions using the least work mem‐
136 ory.
137 -Nr lets the FFT select dimensions yielding the most rapid
139 calculation.
140 -Ns will present a list of optional dimensions, then exit.
142 -Nnx/ny will do FFT on array size nx/ny (must be >= grid file
144 size). Default chooses dimensions >= data which optimize
145 speed and accuracy of FFT. If FFT dimensions > grid file
146 dimensions, data are extended and tapered to zero.
147 Control detrending of data: Append modifiers for removing a lin‐
149 ear trend:
150 +d: Detrend data, i.e. remove best-fitting linear trend
151 [Default].
152 +a: Only remove mean value.
154 +h: Only remove mid value, i.e. 0.5 * (max + min).
156 +l: Leave data alone.
158 Control extension and tapering of data: Use modifiers to control
160 how the extension and tapering are to be performed:
161 +e extends the grid by imposing edge-point symmetry
162 [Default],
163 +m extends the grid by imposing edge mirror symmetry
165 +n turns off data extension.
167 Tapering is performed from the data edge to the FFT grid edge
169 [100%]. Change this percentage via +twidth. When +n is in
170 effect, the tapering is applied instead to the data margins
171 as no extension is available [0%].
172 Control messages being reported: +v will report suitable
174 dimensions during processing.
175 Control writing of temporary results: For detailed investigation
177 you can write the intermediate grid being passed to the forward
178 FFT; this is likely to have been detrended, extended by
179 point-symmetry along all edges, and tapered. Append +w[suffix]
180 from which output file name(s) will be created (i.e.,
181 ingrid_prefix.ext) [tapered], where ext is your file extension.
182 Finally, you may save the complex grid produced by the forward
183 FFT by appending +z. By default we write the real and imaginary
184 components to ingrid_real.ext and ingrid_imag.ext. Append p to
185 save instead the polar form of magnitude and phase to files
186 ingrid_mag.ext and ingrid_phase.ext.
187 -Sscale
189 Multiply each element by scale in the space domain (after the
190 frequency domain operations). [Default is 1.0].
191 -V[level] (more ...)
193 Select verbosity level [c].
194 -fg Geographic grids (dimensions of longitude, latitude) will be
196 converted to meters via a "Flat Earth" approximation using the
197 current ellipsoid parameters.
198 -^ or just -
200 Print a short message about the syntax of the command, then
201 exits (NOTE: on Windows just use -).
202 -+ or just +
204 Print an extensive usage (help) message, including the explana‐
205 tion of any module-specific option (but not the GMT common
206 options), then exits.
207 -? or no arguments
209 Print a complete usage (help) message, including the explanation
210 of all options, then exits.
211
213 By default GMT writes out grid as single precision floats in a
214 COARDS-complaint netCDF file format. However, GMT is able to produce
215 grid files in many other commonly used grid file formats and also
216 facilitates so called "packing" of grids, writing out floating point
217 data as 1- or 2-byte integers. (more ...)
218
220 If the grid does not have meter as the horizontal unit, append +uunit
221 to the input file name to convert from the specified unit to meter. If
222 your grid is geographic, convert distances to meters by supplying -fg
223 instead.
224
226 netCDF COARDS grids will automatically be recognized as geographic. For
227 other grids geographical grids were you want to convert degrees into
228 meters, select -fg. If the data are close to either pole, you should
229 consider projecting the grid file onto a rectangular coordinate system
230 using grdproject
231
233 By default, the power spectrum returned by -E simply sums the contribu‐
234 tions from frequencies that are part of the output frequency. For x-
235 or y-spectra this means summing the power across the other frequency
236 dimension, while for the radial spectrum it means summing up power
237 within each annulus of width delta_q, the radial frequency (q) spacing.
238 A consequence of this summing is that the radial spectrum of a white
239 noise process will give a linear radial power spectrum that is propor‐
240 tional to q. Appending n will instead compute the mean power per out‐
241 put frequency and in this case the white noise process will have a
242 white radial spectrum as well.
243
245 To upward continue the sea-level magnetic anomalies in the file
246 mag_0.nc to a level 800 m above sealevel:
247 gmt grdfft mag_0.nc -C800 -V -Gmag_800.nc
249 To transform geoid heights in m (geoid.nc) on a geographical grid to
251 free-air gravity anomalies in mGal:
252 gmt grdfft geoid.nc -Dg -V -Ggrav.nc
254 To transform gravity anomalies in mGal (faa.nc) to deflections of the
256 vertical (in micro-radians) in the 038 direction, we must first inte‐
257 grate gravity to get geoid, then take the directional derivative, and
258 finally scale radians to micro-radians:
259 gmt grdfft faa.nc -Ig -A38 -S1e6 -V -Gdefl_38.nc
261 Second vertical derivatives of gravity anomalies are related to the
263 curvature of the field. We can compute these as mGal/m^2 by differenti‐
264 ating twice:
265 gmt grdfft gravity.nc -D -D -V -Ggrav_2nd_derivative.nc
267 To compute cross-spectral estimates for co-registered bathymetry and
269 gravity grids, and report result as functions of wavelengths in km, try
270 gmt grdfft bathymetry.nc gravity.grd -E+wk -fg -V > cross_spectra.txt
272 To examine the pre-FFT grid after detrending, point-symmetry reflec‐
274 tion, and tapering has been applied, as well as saving the real and
275 imaginary components of the raw spectrum of the data in topo.nc, try
276 gmt grdfft topo.nc -N+w+z -fg -V
278 You can now make plots of the data in topo_taper.nc, topo_real.nc, and
280 topo_imag.nc.
281
283 gmt, grdedit, grdfilter, grdmath, grdproject, gravfft
284
286 2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
2875.4.5 Feb 24, 2019 GRDFFT(1)