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**PROGRAM:**

**NAME**

grdfft - Do mathematical operations on grids in the wavenumber (or frequency) domain

**SYNOPSIS**

**grdfft**

__ingrid__[

__ingrid2__]

__outfile__[

__azimuth__] [

__zlevel__] [ [

__scale__|

**g**] ] [ [

**r**|

**x**|

**y**][

**w**[

**k**]] ] [

[

**r**|

**x**|

**y**]

__params__] [ [

__scale__|

**g**] ] [

[

**f**|

**q**|

**s**|

__nx/ny__][

**+a**|

**d**|

**h**|

**l**][

**+e**|

**n**|

**m**][

**+t**

__width__][

**+w**[

__suffix__]][

**+z**[

**p**]] ] [

__scale__] [ [

__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 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

**-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__.

**-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**

__azimuth__

Take the directional derivative in the

__azimuth__direction measured in degrees CW

from north.

**-C**

__zlevel__

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 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[r|x|y][w[k]]**

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. Append

**w**to write wavelength instead of frequency. If your grid is

geographic you may further append

**k**to scale wavelengths from meter [Default] to

km.

**-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

**-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.,

**-F**1000000/250000/50000/10000

**-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.

**-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

**-fg**) 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

**-fg**) and the

filter order (an integer) to design a bandpass filter. At the given

wavelengths the Butterworth 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**-/30/2 will lowpass the data using a 2nd-order

Butterworth filter, with half-weight at 30, while

**-F**400/-/2 will highpass

the data.

**-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[f|q|s|**

__nx/ny__

**][+a|[+d|h|l][+e|n|m][+t**

__width__

**][+w[**

__suffix__

**]][+z[p]]**

Choose or inquire about suitable grid dimensions for FFT and set optional

parameters. Control the FFT dimension:

**-Nf**will force the FFT to use the actual dimensions of the data.

**-Nq**will inQuire about more suitable dimensions, report those, then continue.

**-Ns**will present a list of optional dimensions, then exit.

**-N**

__nx/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 linear 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

**+t**

__width__. When

**+n**is in effect, the tapering is applied

instead to the data margins as no extension is available [0%].

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__.

**-S**

__scale__

Multiply each element by

__scale__in the space domain (after the frequency domain

operations). [Default is 1.0].

**-V[**

__level__

**]**

**(more**

**...)**

Select verbosity level [c].

**-fg**Geographic grids (dimensions of longitude, latitude) will be converted to meters

via a "Flat Earth" approximation using the current ellipsoid parameters.

**-^**

**or**

**just**

**-**

Print a short message about the syntax of the command, then exits (NOTE: on Windows

use just

**-**).

**-+**

**or**

**just**

**+**

Print an extensive usage (help) message, including the explanation 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 options, then

exits.

**--version**

Print GMT version and exit.

**--show-datadir**

Print full path to GMT share directory and exit.

**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 "packing" of grids, writing out floating point

data as 1- or 2-byte integers. To specify the precision, scale and offset, the user should

add the suffix

**=**

__id__[

**/**

__scale__

**/**

__offset__[

**/**

__nan__]], where

__id__is a two-letter identifier of the grid

type and precision, and

__scale__and

__offset__are optional scale factor and offset to be

applied to all grid values, and

__nan__is the value used to indicate missing data. In case

the two characters

__id__is not provided, as in

**=/**

__scale__than a

__id__

**=**

__nf__is assumed. When

reading grids, the format is generally automatically recognized. If not, the same suffix

can be added to input grid file names. See

**grdconvert**and Section grid-file-format of the

GMT Technical Reference and Cookbook for more information.

When reading a netCDF file that contains multiple grids, GMT will read, by default, the

first 2-dimensional grid that can find in that file. To coax GMT into reading another

multi-dimensional variable in the grid file, append

**?**

__varname__to the file name, where

__varname__is the name of the variable. Note that you may need to escape the special meaning

of

**?**in your shell program by putting a backslash in front of it, or by placing the

filename and suffix between quotes or double quotes. The

**?**

__varname__suffix can also be used

for output grids to specify a variable name different from the default: "z". See

**grdconvert**and Sections modifiers-for-CF and grid-file-format of the GMT Technical

Reference and Cookbook for more information, particularly on how to read splices of 3-,

4-, or 5-dimensional grids.

**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

**-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**

**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 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 -Ewk -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.

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