1GRDFFT(1) Generic Mapping Tools GRDFFT(1)
2
6 grdfft - Perform mathematical operations on grid files in the wavenum‐
7 ber (or frequency) domain
8
10 grdfft in_grdfile -Gout_grdfile [ -Aazimuth ] [ -Czlevel ] [
11 -D[scale|g] ] [ -E[x|y][w] ] [ -F[x|y]params ] [ -I[scale|g] ] [ -L ] [
12 -M ] [ -Nstuff ] [ -Sscale ] [ -Tte/rl/rm/rw/ri ] [ -V ]
13
15 grdfft will take the 2-D forward Fast Fourier Transform and perform one
16 or more mathematical operations in the frequency domain before trans‐
17 forming back to the space domain. An option is provided to scale the
18 data before writing the new values to an output file. The horizontal
19 dimensions of the grid are assumed to be in meters. Geographical grids
20 may be used by specifying the -M option that scales degrees to meters.
21 If you have grids with dimensions in km, you could change this to
22 meters using grdedit or scale the output with grdmath.
23 in_grdfile
25 2-D binary grid file to be operated on. (See GRID FILE FORMATS
26 below).
27 -G Specify the name of the output grid file. (See GRID FILE FOR‐
29 MATS below).
30
32 No space between the option flag and the associated arguments.
33 -A Take the directional derivative in the azimuth direction mea‐
35 sured in degrees CW from north.
36 -C Upward (for zlevel > 0) or downward (for zlevel < 0) continue
38 the field zlevel meters.
39 -D Differentiate the field, i.e., take d(field)/dz. This is equiv‐
41 alent to multiplying by kr in the frequency domain (kr is radial
42 wave number). Append a scale to multiply by (kr * scale)
43 instead. Alternatively, append g to indicate that your data are
44 geoid heights in meters and output should be gravity anomalies
45 in mGal. [Default is no scale].
46 -E Estimate power spectrum in the radial direction. Place x or y
48 immediately after -E to compute the spectrum in the x or y
49 direction instead. No grid file is created; f (i.e., frequency
50 or wave number), power[f], and 1 standard deviation in power[f]
51 are written to stdout. Append w to write wavelength instead of
52 frequency.
53 -F Filter the data. Place x or y immediately after -F to filter x
55 or y direction only; default is isotropic. Choose between a
56 cosine-tapered band-pass, a Gaussian band-pass filter, or a But‐
57 terworth band-pass filter. Cosine-taper: Specify four wave‐
58 lengths lc/lp/hp/hc in correct units (see -M) to design a band‐
59 pass filter: wavelengths greater than lc or less than hc will be
60 cut, wavelengths greater than lp and less than hp will be
61 passed, and wavelengths in between will be cosine-tapered.
62 E.g., -F1000000/250000/50000/10000 -M will bandpass, cutting
63 wavelengths > 1000 km and < 10 km, passing wavelengths between
64 250 km and 50 km. To make a highpass or lowpass filter, give
65 hyphens (-) for hp/hc or lc/lp. E.g., -Fx-/-/50/10 will lowpass
66 x, passing wavelengths > 50 and rejecting wavelengths < 10.
67 -Fy1000/250/-/- will highpass y, passing wavelengths < 250 and
68 rejecting wavelengths > 1000. Gaussian band-pass: Append lo/hi,
69 the two wavelengths in correct units (see -M) to design a band‐
70 pass filter. At the given wavelengths the Gaussian filter
71 weights will be 0.5. To make a highpass or lowpass filter, give
72 a hyphen (-) for the hi or lo wavelength, respectively. E.g.,
73 -F-/30 will lowpass the data using a Gaussian filter with half-
74 weight at 30, while -F400/- will highpass the data. Butterworth
75 band-pass: Append lo/hi/order, the two wavelengths in correct
76 units (see -M) and the filter order (an integer) to design a
77 bandpass filter. At the given wavelengths the Butterworth fil‐
78 ter weights will be 0.5. To make a highpass or lowpass filter,
79 give a hyphen (-) for the hi or lo wavelength, respectively.
80 E.g., -F-/30/2 will lowpass the data using a 2nd-order Butter‐
81 worth filter, with half-weight at 30, while -F400/-/2 will high‐
82 pass the data.
83 -I Integrate the field, i.e., compute integral_over_z (field * dz).
85 This is equivalent to divide by kr in the frequency domain (kr
86 is radial wave number). Append a scale to divide by (kr *
87 scale) instead. Alternatively, append g to indicate that your
88 data set is gravity anomalies in mGal and output should be geoid
89 heights in meters. [Default is no scale].
90 -L Leave trend alone. By default, a linear trend will be removed
92 prior to the transform.
93 -M Map units. Choose this option if your grid file is a geographi‐
95 cal grid and you want to convert degrees into meters. If the
96 data are close to either pole, you should consider projecting
97 the grid file onto a rectangular coordinate system using grdpro‐
98 ject.
99 -N Choose or inquire about suitable grid dimensions for FFT. -Nf
101 will force the FFT to use the dimensions of the data. -Nq will
102 inQuire about more suitable dimensions. -Nnx/ny will do FFT on
103 array size nx/ny (Must be >= grid file size). Default chooses
104 dimensions >= data which optimize speed, accuracy of FFT. If
105 FFT dimensions > grid file dimensions, data are extended and
106 tapered to zero.
107 -S Multiply each element by scale in the space domain (after the
109 frequency domain operations). [Default is 1.0].
110 -T Compute the isostatic compensation from the topography load
112 (input grid file) on an elastic plate of thickness te. Also
113 append densities for load, mantle, water, and infill in SI
114 units. If te == 0 then the Airy response is returned. -T
115 implicitly sets -L.
116 -V Selects verbose mode, which will send progress reports to stderr
118 [Default runs "silently"].
119
121 By default GMT writes out grid as single precision floats in a COARDS-
122 complaint netCDF file format. However, GMT is able to produce grid
123 files in many other commonly used grid file formats and also facili‐
124 tates so called "packing" of grids, writing out floating point data as
125 2- or 4-byte integers. To specify the precision, scale and offset, the
126 user should add the suffix =id[/scale/offset[/nan]], where id is a two-
127 letter identifier of the grid type and precision, and scale and offset
128 are optional scale factor and offset to be applied to all grid values,
129 and nan is the value used to indicate missing data. When reading
130 grids, the format is generally automatically recognized. If not, the
131 same suffix can be added to input grid file names. See grdreformat(1)
132 and Section 4.17 of the GMT Technical Reference and Cookbook for more
133 information.
134 When reading a netCDF file that contains multiple grids, GMT will read,
136 by default, the first 2-dimensional grid that can find in that file. To
137 coax GMT into reading another multi-dimensional variable in the grid
138 file, append ?varname to the file name, where varname is the name of
139 the variable. Note that you may need to escape the special meaning of ?
140 in your shell program by putting a backslash in front of it, or by
141 placing the filename and suffix between quotes or double quotes. The
142 ?varname suffix can also be used for output grids to specify a variable
143 name different from the default: "z". See grdreformat(1) and Section
144 4.18 of the GMT Technical Reference and Cookbook for more information,
145 particularly on how to read splices of 3-, 4-, or 5-dimensional grids.
146
148 To upward continue the sea-level magnetic anomalies in the file
149 mag_0.grd to a level 800 m above sealevel:
150 grdfft mag_0.grd -C800 -V -Gmag_800.grd
152 To transform geoid heights in m (geoid.grd) on a geographical grid to
154 free-air gravity anomalies in mGal:
155 grdfft geoid.grd -Dg -V -Ggrav.grd
157 To transform gravity anomalies in mGal (faa.grd) to deflections of the
159 vertical (in micro-radians) in the 038 direction, we must first inte‐
160 grate gravity to get geoid, then take the directional derivative, and
161 finally scale radians to micro-radians:
162 grdfft faa.grd -Ig38 -S1e6 -V -Gdefl_38.grd
164 Second vertical derivatives of gravity anomalies are related to the
166 curvature of the field. We can compute these as mGal/m^2 by differen‐
167 tiating twice:
168 grdfft gravity.grd -D -D -V -Ggrav_2nd_derivative.grd
170 The first order gravity anomaly (in mGal) due to the compensating sur‐
172 face caused by the topography load topo.grd (in m) on a 20 km thick
173 elastic plate, assumed to be 4 km beneath the observation level can be
174 computed as
175 grdfft topo.grd -T20000/2800/3330/1030/2300 -S0.022 -C4000
177 -Gcomp_faa.grd
178 where 0.022 is the scale needed for the first term in Parker's expan‐
180 sion for computing gravity from topography (= 2 * PI * G * (rhom -
181 rhol)).
182
184 GMT(1), grdedit(1), grdmath(1), grdproject(1)
185GMT 4.5.6 10 Mar 2011 GRDFFT(1)