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- .. index:: ! grdfft
- .. include:: module_core_purpose.rst_
- ******
- grdfft
- ******
- |grdfft_purpose|
- Synopsis
- --------
- .. include:: common_SYN_OPTs.rst_
- **gmt grdfft** *ingrid* [ *ingrid2* ]
- [ |-G|\ *outfile*\|\ *table* ]
- [ |-A|\ *azimuth* ]
- [ |-C|\ *zlevel* ]
- [ |-D|\ [*scale*\|\ **g**] ]
- [ |-E|\ [**r**\|\ **x**\|\ **y**][**+w**\ [**k**]][**+n**] ]
- [ |-F|\ [**r**\|\ **x**\|\ **y**]\ *params* ]
- [ |-I|\ [*scale*\|\ **g**] ]
- [ |-N|\ *params* ]
- [ |-S|\ *scale* ]
- [ |SYN_OPT-V| ]
- [ |SYN_OPT-f| ]
- [ |SYN_OPT--| ]
- |No-spaces|
- Description
- -----------
- **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 grid are assumed to be in meters. Geographical grids
- may be used by specifying the |SYN_OPT-f| option that scales degrees to
- meters. If you have grids with dimensions in km, you could change this
- to meters using :doc:`grdedit` or scale the output with :doc:`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*.
- **-G**\ *outfile*
- Specify the name of the output grid file or the 1-D spectrum table
- (see **-E**). (See GRID FILE FORMATS below).
- Optional Arguments
- ------------------
- .. _-A:
- **-A**\ *azimuth*
- Take the directional derivative in the *azimuth* direction measured
- in degrees CW from north.
- .. _-C:
- **-C**\ *zlevel*
- Upward (for *zlevel* > 0) or downward (for *zlevel* < 0) continue
- the field *zlevel* meters.
- .. _-D:
- **-D**\ [*scale*\|\ **g**]
- 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:
- **-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 standard 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 output 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 frequency are reported instead.
- .. _-F:
- **-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 Butterworth band-pass filter.
- Cosine-taper:
- Specify four wavelengths *lc*/*lp*/*hp*/*hc* in correct units (see |SYN_OPT-f|)
- 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., **-F**\ 1000000/250000/50000/10000 |SYN_OPT-f|
- 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. **-Fy**\ 1000/250/-/- will highpass *y*,
- passing wavelengths < 250 and rejecting wavelengths > 1000.
- Gaussian band-pass:
- Append *lo*/*hi*, the two wavelengths in correct units
- (see |SYN_OPT-f|) to design a bandpass filter. At the given wavelengths
- 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 lowpass the data using a
- Gaussian filter with half-weight at 30, while **-F**\ 400/- will
- highpass the data.
- Butterworth band-pass:
- Append *lo*/*hi*/*order*,
- the two wavelengths in correct units (see |SYN_OPT-f|) 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 lowpass the data
- using a 2nd-order Butterworth filter, with half-weight at 30, while
- **-F**\ 400/-/2 will highpass the data.
- .. _-G:
- **-G**\ *outfile*\|\ *table*
- Filename for output netCDF grid file OR 1-D data table (see **-E**).
- This is optional for -E (spectrum written to stdout) but mandatory for
- all other options that require a grid output.
- .. _-I:
- **-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].
- .. include:: explain_fft.rst_
- .. _-S:
- **-S**\ *scale*
- Multiply each element by *scale* in the space domain (after the
- frequency domain operations). [Default is 1.0].
- .. _-V:
- .. |Add_-V| unicode:: 0x20 .. just an invisible code
- .. include:: explain_-V.rst_
- |SYN_OPT-f|
- Geographic grids (dimensions of longitude, latitude) will be converted to
- meters via a "Flat Earth" approximation using the current ellipsoid parameters.
- .. include:: explain_help.rst_
- .. include:: explain_grd_inout_short.rst_
- Grid Distance Units
- -------------------
- If the grid does not have meter as the horizontal unit, append **+u**\ *unit* to the input file name to convert from the
- specified unit to meter. If your grid is geographic, convert distances to meters by supplying |SYN_OPT-f| 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 |SYN_OPT-f|. If the data are close to either pole, you should
- consider projecting the grid file onto a rectangular coordinate system
- using :doc:`grdproject`
- Normalization of Spectrum
- -------------------------
- By default, the power spectrum returned by **-E** simply sums the contributions
- 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 proportional to *q*. Appending **n** will instead compute the mean power
- per output frequency and in this case the white noise process will have a
- white radial spectrum as well.
- Examples
- --------
- .. include:: explain_example.rst_
- To obtain the normalized radial spectrum from the remote data grid @white_noise.nc,
- after removing the mean, let us try::
- gmt grdfft @white_noise.nc -Er+n -N+a > spectrum.txt
- 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
- integrate 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
- differentiating 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 reflection,
- 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
- --------
- :doc:`gmt`, :doc:`grdedit`,
- :doc:`grdfilter`,
- :doc:`grdmath`,
- :doc:`grdproject`,
- :doc:`gravfft <supplements/potential/gravfft>`
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