gravfft(1) GMT gravfft(1)
NAME
gravfft - Compute gravitational attraction of 3-D surfaces in the
wavenumber (or frequency) domain
SYNOPSIS
gravfft ingrid [ ingrid2 ] -Goutfile [ -Cn/wavelength/mean_depth/tbw
] [ -Ddensity|rhogrid ] [ -En_terms ] [ -F[f[+]|g|v|n|e] ] [
-Iw|b|c|t |k ] [ -Nparams ] [ -Q ] [ -Tte/rl/rm/rw[/ri][+m] ] [
-V[level] ] [ -Wwd] [ -Zzm[zl] ] [ -fg ]
Note: No space is allowed between the option flag and the associated
arguments.
DESCRIPTION
gravfft can be used into three main modes. Mode 1: Simply compute the
geopotential due to the surface given in the topo.grd file. Requires a
density contrast (-D) and possibly a different observation level (-W).
It will take the 2-D forward FFT of the grid and use the full Parkeras
method up to the chosen terms. Mode 2: Compute the geopotential
response due to flexure of the topography file. It will take the 2-D
forward FFT of the grid and use the full Parkeras method applied to
the chosen isostatic model. The available models are the aloading from
topa, or elastic plate model, and the aloading from belowa which
accounts for the plateas response to a sub-surface load (appropriate
for hot spot modeling - if you believe them). In both cases, the model
parameters are set with -T and -Z options. Mode 3: compute the admit-
tance or coherence between two grids. The output is the average in the
radial direction. Optionally, the model admittance may also be calcu-
lated. The horizontal dimensions of the grdfiles 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. Given the number of choices this program offers, is difficult
to state what are options and what are required arguments. It depends
on what you are doing; see the examples for further guidance.
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.
-Goutfile
Specify the name of the output grid file or the 1-D spectrum ta-
ble (see -E). (See GRID FILE FORMATS below).
OPTIONAL ARGUMENTS
-Cn/wavelength/mean_depth/tbw
Compute only the theoretical admittance curves of the selected
model and exit. n and wavelength are used to compute (n * wave-
length) the total profile length in meters. mean_depth is the
mean water depth. Append dataflags (one or two) of tbw in any
order. t = use afrom topa model, b = use afrom belowa model.
Optionally specify w to write wavelength instead of frequency.
-Ddensity|rhogrid
Sets density contrast across surface. Used, for example, to com-
pute the gravity attraction of the water layer that can later be
combined with the free-air anomaly to get the Bouguer anomaly.
In this case do not use -T. It also implicitly sets -N+h.
Alternatively, specify a co-registered grid with density con-
trasts if a variable density contrast is required.
-En_terms
Number of terms used in Parker expansion (limit is 10, otherwise
terms depending on n will blow out the program) [Default = 3]
-F[f[+]|g|v|n|e]
Specify desired geopotential field: compute geoid rather than
gravity
f = Free-air anomalies (mGal) [Default]. Append + to add in
the slab implied when removing the mean value from the topog-
raphy. This requires zero topography to mean no mass anom-
aly.
g = Geoid anomalies (m).
v = Vertical Gravity Gradient (VGG; 1 Eotvos = 0.1 mGal/km).
e = East deflections of the vertical (micro-radian).
n = North deflections of the vertical (micro-radian).
-Iw|b|c|t |k
Use ingrd2 and ingrd1 (a grid with topography/bathymetry) to
estimate admittance|coherence and write it to stdout (-G ignored
if set). This grid should contain gravity or geoid for the same
region of ingrd1. Default computes admittance. Output contains 3
or 4 columns. Frequency (wavelength), admittance (coherence) one
sigma error bar and, optionally, a theoretical admittance.
Append dataflags (one to three) from w|b|c|t. w writes wave-
length instead of wavenumber, k selects km for wavelength unit
[m], c computes coherence instead of admittance, b writes a
fourth column with aloading from belowa theoretical admittance,
and t writes a fourth column with aelastic platea theoretical
admittance.
-N[a|f|m|r|s|nx/ny][+a|[+d|h|l][+e|n|m][+twidth][+v][+w[suffix]][+z[p]]
Choose or inquire about suitable grid dimensions for FFT and set
optional parameters. Control the FFT dimension:
-Na lets the FFT select dimensions yielding the most accurate
result.
-Nf will force the FFT to use the actual dimensions of the
data.
-Nm lets the FFT select dimensions using the least work mem-
ory.
-Nr lets the FFT select dimensions yielding the most rapid
calculation.
-Ns will present a list of optional dimensions, then exit.
-Nnx/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 lin-
ear 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 +twidth. When +n is in
effect, the tapering is applied instead to the data margins
as no extension is available [0%].
Control messages being reported: +v will report suitable
dimensions during processing.
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.
-Q Writes out a grid with the flexural topography (with z positive
up) whose average depth was set by -Zzm and model parameters by
-T (and output by -G). That is the agravimetric Mohoa. -Q
implicitly sets -N+h
-S Computes predicted gravity or geoid grid due to a subplate load
produced by the current bathymetry and the theoretical model.
The necessary parameters are set within -T and -Z options. The
number of powers in Parker expansion is restricted to 1. See an
example further down.
-Tte/rl/rm/rw[/ri][+m]
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 ri is not provided it defaults to rl. Give average mantle
depth via -Z. If the elastic thickness is > 1e10 it will be
interpreted as the flexural rigidity (by default it is computed
from te and Young modulus). Optionally, append +m to write a
grid with the Mohoas geopotential effect (see -F) from model
selected by -T. If te = 0 then the Airy response is returned.
-T+m implicitly sets -N+h
-Wwd Set water depth (or observation height) relative to topography
[0]. Append k to indicate km.
-Zzm[zl]
Moho [and swell] average compensation depths (in meters positive
dows a the depth). For the aload from topa model you only have
to provide zm, but for the aloading from belowa donat forget zl.
-V[level] (more a|)
Select verbosity level [c].
-fg Geographic grids (dimensions of longitude, latitude) will be
converted to meters via a aFlat Eartha approximation using the
current ellipsoid parameters.
-^ or just -
Print a short message about the syntax of the command, then
exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explana-
tion 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 all options, then exits.
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 apackinga of grids, writing out floating point
data as 1- or 2-byte integers. (more a|)
GRID DISTANCE UNITS
If the grid does not have meter as the horizontal unit, append +uunit
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.
PLATE FLEXURE
The FFT solution to elastic plate flexure requires the infill density
to equal the load density. This is typically only true directly
beneath the load; beyond the load the infill tends to be lower-density
sediments or even water (or air). Wessel [2001] proposed an approxima-
tion that allows for the specification of an infill density different
from the load density while still allowing for an FFT solution. Basi-
cally, the plate flexure is solved for using the infill density as the
effective load density but the amplitudes are adjusted by a factor A =
sqrt ((rm - ri)/(rm - rl)), which is the theoretical difference in
amplitude due to a point load using the two different load densities.
The approximation is very good but breaks down for large loads on weak
plates, a fairy uncommon situation.
EXAMPLES
To compute the effect of the water layer above the bat.grd bathymetry
using 2700 and 1035 for the densities of crust and water and writing
the result on water_g.grd (computing up to the fourth power of bathyme-
try in Parker expansion):
gmt gravfft bat.grd -D1665 -Gwater_g.grd -E4
Now subtract it from your free-air anomaly faa.grd and you will get the
Bouguer anomaly. You may wonder why we are subtracting and not adding.
After all the Bouguer anomaly pretends to correct the mass deficiency
presented by the water layer, so we should add because water is less
dense than the rocks below. The answer relies on the way gravity
effects are computed by the Parkeras method and practical aspects of
using the FFT.
gmt grdmath faa.grd water_g.grd SUB = bouguer.grd
Want an MBA anomaly? Well compute the crust mantle contribution and add
it to the sea-bottom anomaly. Assuming a 6 km thick crust of density
2700 and a mantle with 3300 density we could repeat the command used to
compute the water layer anomaly, using 600 (3300 - 2700) as the density
contrast. But we now have a problem because we need to know the mean
Moho depth. That is when the scale/offset that can be appended to the
gridas name comes in hand. Notice that we didnat need to do that before
because mean water depth was computed directly from data (notice also
the negative sign of the offset due to the fact that z is positive up):
gmt gravfft bat.grd=nf/1/-6000 -D600 -Gmoho_g.grd
Now, subtract it from the Bouguer to obtain the MBA anomaly. That is:
gmt grdmath bouguer.grd moho_g.grd SUB = mba.grd
To compute the Moho gravity effect of an elastic plate bat.grd with Te
= 7 km, density of 2700, over a mantle of density 3300, at an average
depth of 9 km
gmt gravfft bat.grd -Gelastic.grd -T7000/2700/3300/1035+m -Z9000
If you add now the sea-bottom and Mohoas effects, you will get the full
gravity response of your isostatic model. We will use here only the
first term in Parker expansion.
gmt gravfft bat.grd -D1665 -Gwater_g.grd -E1
gmt gravfft bat.grd -Gelastic.grd -T7000/2700/3300/1035+m -Z9000 -E1
gmt grdmath water_g.grd elastic.grd ADD = model.grd
The same result can be obtained directly by the next command. However,
PAY ATTENTION to the following. I donat yet know if itas because of a
bug or due to some limitation, but the fact is that the following and
the previous commands only give the same result if -E1 is used. For
higher powers of bathymetry in Parker expansion, only the above example
seams to give the correct result.
gmt gravfft bat.grd -Gmodel.grd -T7000/2700/3300/1035 -Z9000 -E1
And what would be the geoid anomaly produced by a load at 50 km depth,
below a region whose bathymetry is given by bat.grd, a Moho at 9 km
depth and the same densities as before?
gmt gravfft topo.grd -Gswell_geoid.grd -T7000/2700/3300/1035 -Fg -Z9000/50000 -S -E1
To compute the admittance between the topo.grd bathymetry and faa.grd
free-air anomaly grid using the elastic plate model of a crust of 6 km
mean thickness with 10 km effective elastic thickness in a region of 3
km mean water depth:
gmt gravfft topo.grd faa.grd -It -T10000/2700/3300/1035 -Z9000
To compute the admittance between the topo.grd bathymetry and geoid.grd
geoid grid with the aloading from belowa (LFB) model with the same as
above and sub-surface load at 40 km, but assuming now the grids are in
geographic and we want wavelengths instead of frequency:
gmt gravfft topo.grd geoid.grd -Ibw -T10000/2700/3300/1035 -Z9000/40000 -fg
To compute the gravity theoretical admittance of a LFB along a 2000 km
long profile using the same parameters as above
gmt gravfft -C400/5000/3000/b -T10000/2700/3300/1035 -Z9000/40000
REFERENCES
Luis, J.F. and M.C. Neves. 2006, The isostatic compensation of the
Azores Plateau: a 3D admittance and coherence analysis. J. Geothermal
Volc. Res. Volume 156, Issues 1-2, Pages 10-22,
http://dx.doi.org/10.1016/j.jvolgeores.2006.03.010
Parker, R. L., 1972, The rapid calculation of potential anomalies, Geo-
phys. J., 31, 447-455.
Wessel. P., 2001, Global distribution of seamounts inferred from grid-
ded Geosat/ERS-1 altimetry, J. Geophys. Res., 106(B9), 19,431-19,441,
http://dx.doi.org/10.1029/2000JB000083
SEE ALSO
gmt(1), grdfft(1), grdmath(1), grdproject(1)
COPYRIGHT
2017, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
5.4.2 Jun 24, 2017 gravfft(1)
gmt5 5.4.2 - Generated Wed Jun 28 18:08:16 CDT 2017