GRDFFT(1)

NAME
grdfft - Perform mathematical operations on grid files in the wavenumber (or frequency) domain

SYNOPSIS
grdfft in_grdfile -Gout_grdfile [ -Aazimuth ] [ -Czlevel ] [ -D[scale|g] ] [ -E[x|y][w] ] [ -F[x|y]params ] [ -I[scale|g] ] [ -L ] [ -M ] [ -Nstuff ] [ -Sscale ] [ -Tte/rl/rm/rw/ri ] [ -V ]

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 -M 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.

in_grdfile
    2-D binary grid file to be operated on. (See GRID FILE FORMATS below).

-G  Specify the name of the output grid file. (See GRID FILE FORMATS below).

OPTIONS
No space between the option flag and the associated arguments.

-A  Take the directional derivative in the azimuth direction measured in degrees CW from north.

-C  Upward (for zlevel > 0) or downward (for zlevel < 0) continue the field zlevel meters.

-D  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  Estimate power spectrum in the radial direction. Place x or y immediately after -E to compute the spectrum in the x or y direction instead. No grid file is created; f (i.e., frequency or wave number), power[f], and 1 standard deviation in power[f] are written to stdout. Append w to write wavelength instead of frequency.

-F  Filter the data. Place x or y immediately after -F to filter x or y direction only; default is isotropic. 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 -M) 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 -M 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 -M) 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 -M) 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  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].

-L  Leave trend alone. By default, a linear trend will be removed prior to the transform.

-M  Map units. Choose this option if your grid file is a geographical grid and you want to convert degrees into meters. If the data are close to either pole, you should consider projecting the grid file onto a rectangular coordinate system using grdproject.

-N  Choose or inquire about suitable grid dimensions for FFT. -Nf will force the FFT to use the dimensions of the data. -Nq will inQuire about more suitable dimensions. -Nnx/ny will do FFT on array size nx/ny (Must be >= grid file size). Default chooses dimensions >= data which optimize speed, accuracy of FFT. If FFT dimensions > grid file dimensions, data are extended and tapered to zero.

-S  Multiply each element by scale in the space domain (after the frequency domain operations). [Default is 1.0].

-T  Compute the isostatic compensation from the topography load (input grid file) on an elastic plate of thickness te. Also append densities for load, mantle, water, and infill in SI units. If te == 0 then the Airy response is returned. -T implicitly sets -L.

-V  Selects verbose mode, which will send progress reports to stderr [Default runs "silently"].

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 2- or 4-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. When reading grids, the format is generally automatically recognized. If not, the same suffix can be added to input grid file names. See grdreformat(1) and Section 4.17 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 grdreformat(1) and Section 4.18 of the GMT Technical Reference and Cookbook for more information, particularly on how to read splices of 3-, 4-, or 5-dimensional grids.

EXAMPLES
To upward continue the sea-level magnetic anomalies in the file mag_0.grd to a level 800 m above sealevel:

grdfft mag_0.grd -C 800 -V -G mag_800.grd

To transform geoid heights in m (geoid.grd) on a geographical grid to free-air gravity anomalies in mGal:

grdfft geoid.grd -Dg -V -G grav.grd

To transform gravity anomalies in mGal (faa.grd) 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:

grdfft faa.grd -Ig 38 -S 1e6 -V -G defl_38.grd

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:

grdfft gravity.grd -D -D -V -G grav_2nd_derivative.grd

The first order gravity anomaly (in mGal) due to the compensating surface caused by the topography load topo.grd (in m) on a 20 km thick elastic plate, assumed to be 4 km beneath the observation level can be computed as

grdfft topo.grd -T 20000/2800/3330/1030/2300 -S 0.022 -C 4000 -G comp_faa.grd

where 0.022 is the scale needed for the first term in Parker's expansion for computing gravity from topography (= 2 * PI * G * (rhom - rhol)).

SEE ALSO
GMT(1), grdedit(1), grdmath(1), grdproject(1)