# man grdfft () - Perform mathematical operations on grdfiles in the frequency domain

## NAME

grdfft - Perform mathematical operations on grdfiles in the frequency domain

## SYNOPSIS

**grdfft** *in_grdfile* **-G***out_grdfile* [ **-A***azimuth* ]
[ **-C***zlevel* ] [ **-D**[*scale***|g**] ] [ **-E**[**x|y**][**w**] ]
[ **-F**[*x|y*]*lc/lp/hp/hc* ] [ **-I**[*scale***|g**] ] [ **-L** ] [ **-M** ]
[ **-N***stuff* ] [ **-S***scale* ] [ **-T***te/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 grdfiles are assumed to be in meters. Geographical grids
may be used by specifying the **-M** option that scales degrees to meters. If you
have grdfiles with dimensions in km, you could change this to meters using **grdedit**
or scale the output with **grdmath**.

No space between the option flag and the associated arguments. Use upper case for the
option flags and lower case for modifiers.

*in_grdfile*- 2-D binary grd file to be operated on.
**-G**- Specify the name of the output grd file.

## OPTIONS

**-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 grdfile 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. Specify four wavelengths 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.,**-F**x-/-/50/10 will lowpass X, passing wavelengths > 50 and rejecting wavelengths < 10.**-F**y1000/250/-/- will highpass Y, passing wavelengths < 250 and rejecting wavelengths > 1000. **-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 grdfile 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 grdfile 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.****-N***nx/ny*will do FFT on array size*nx/ny*(Must be >= grdfile size). Default chooses dimensions >= data which optimize speed, accuracy of FFT. If FFT dimensions > grdfile 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 grdfile) 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"].

## EXAMPLES

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

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,
do

grdfft geoid.grd **-Dg -M** **-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 -A**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)).