grdseamount

grdseamount(cmd0::String="", arg1=nothing; kwargs...)

Create synthetic seamounts (Gaussian, parabolic, polynomial, cone or disc; circular or elliptical).

(Warning: Manual translate by Claude. Needs revision)

Description

grdseamount will compute the combined topographic shape of multiple synthetic seamounts given their individual shape parameters. We read from table (or pass a matrix/GMTdataset) a list of seamount locations and sizes and can evaluate either Gaussian, parabolic, conical, polynomial or disc shapes, which may be circular or elliptical, and optionally truncated. Various options are available to modify the result, including an option to add in a background depth or set unmodified nodes to NaN.

The input data must contain lon, lat, radius, height for each seamount. For elliptical features (requires elliptical=true), we expect lon, lat, azimuth, semi-major, semi-minor, height instead. If flat seamount tops is specified (via flattening) with no value appended, then an extra column with flattening is expected. For temporal evolution of topography the time option may be used, in which case the data file must have two additional columns with the start and stop time of seamount construction.

Required Arguments

intable : – Input table (file name, matrix, or GMTdataset) with seamount parameters. For circular seamounts: lon, lat, radius, height. For elliptical seamounts (elliptical=true): lon, lat, azimuth, semi-major, semi-minor, height.
G or outgrid : – outgrid=“filename”
Give the name of the output grid file. If time is set then outgrid must be a filename template.
I or inc or increment or spacing : – inc=x_inc | inc=(x_inc, y_inc) | inc=“xinc[+e|n][/yinc[+e|n]]”
Specify the grid increments or the block sizes. More at spacing
R or region or limits : – limits=(xmin, xmax, ymin, ymax) | limits=(BB=(xmin, xmax, ymin, ymax),) | limits=(LLUR=(xmin, xmax, ymin, ymax),units=“unit”) | …more
Specify the region of interest. More at limits. For perspective view view, optionally add zmin,zmax. This option may be used to indicate the range used for the 3-D axes. You may ask for a larger w/e/s/n region to have more room between the image and the axes.

Optional Arguments

A or mask : – mask=true | mask=“out/in” | mask=(out=val, in=val, scale=val)
Build a mask grid only that may be used to manipulate gridded data sets to exclude or isolate seamount observations; append outside/inside values [1/NaN]. Height and flattening are ignored. Use scale to increase all seamount radii or semi-axes first.
C or shape : – shape=:gaussian | shape=:cone | shape=:disc | shape=:parabola | shape=:polynomial
Select a seamount shape function. Choose among :cone (c), :disc (d), :gaussian (g), :polynomial (o) and :parabola (p) [Default is Gaussian]. All but the disc can be truncated via a flattening parameter set by flattening. The polynomial model has amplitude \(v(u) = (1+u)^3(1-u)^3/(1+u^3)\) where \(u = r / r_0\) is the normalized radius.
D or unit : – unit=:k | unit=:m | unit=:n | unit=:d
Append the Cartesian unit used for horizontal distances in the input file. Not allowed for geographic data, which we automatically convert to km using a flat Earth assumption.
E or elliptical : – elliptical=true
Set elliptical data file format. We expect input records to contain (lon, lat, azimuth, semi-major, semi-minor, height) for each seamount [Default is Circular data format, expecting lon, lat, radius, height].
F or flattening : – flattening=value | flattening=true
Seamounts will be truncated to guyots. Append flattening from 0 (no flattening) up to, but not including, 1. If no argument is given then we expect to find the flattening in the last input column [no truncation]. Ignored if used with shape=:disc.
H or densities : – densities=“H/rho_l/rho_h” | densities=(H=val, rho_l=val, rho_h=val, densify=val, power=val)
Set reference seamount parameters for an ad-hoc variable radial density function with depth. Give the low and high seamount densities in kg/m³ or g/cm³ and the fixed reference height H in meters. Use densify to change the water-pressure-driven flank density increase over the full reference height [0] and power to set the variable density profile exponent [1, linear]. The radial density function is: \[\rho(r,z) = \rho_l + \Delta \rho_f \left (\frac{H-h(r)}{H} \right ) + \Delta \rho_s \left ( \frac{h(r)-z(r)}{H} \right )^p\]
K or density_grid : – density_grid=“filename”
Append the file name for a crossection grid with the predicted densities of the reference model. Uses normalized coordinates (both x and y go from 0 to 1 in increments of 0.005).
L or list_stats : – list_stats=true | list_stats=hn
List area, volume, and mean height for each seamount; no grid will be created. Optionally, append hn for a noise-floor cutoff level below which we ignore area and volume [0].
M or list : – list=“filename” | list=true
Write the times and names of all grids created to the text file. Requires time. If no file is given then we write to standard output. The output listing is suitable as input to grdflexure.
N or normalize : – normalize=value
Normalize the relief grid(s) so the maximum grid height equals value [no normalization].
Q or build_mode : – build_mode=:cumulative | build_mode=:incremental | build_mode=“c/g”
Set build modes. Can only be used with time. The default is build_mode=“c/g”.
- bmode determines how we construct the surface: c for cumulative volume through time or i for the incremental volume added for each time increment.
- fmode determines the volume flux curve: c for constant volume flux or g for Gaussian volume flux [Default] between the start and stop times of each feature.
S or slide : – slide=(azimuth=(…), beta=val, hc=val, heights=(…), power=val, time=(…), u0=val, volume=val)
Set parameters controlling the simulation of sectoral, rotational land slides. Available modifiers:
- azimuth: specifies the azimuthal sector affected by the slide [0/360]
- beta: sets positive power coefficient for the normalized slide volume fraction time-curve [1]
- hc: sets the flank level where the debris deposit begins [h1/2]
- heights: sets the lower and upper heights of the flank source area
- power: activates angular variation in the radial slide profile (power > 2)
- time: sets the time span over which the slide develops (requires time)
- u0: sets normalized radial slide shape parameter > 0 [0.2]
- volume: sets desired fractional volume of the slide (in percent)
T or time : – time=t0 | time=“t0/t1/dt” | time=“t0/t1/dt+l”
Specify t0, t1, and time increment (dt) for a sequence of calculations [Default is one step, with no time dependency]. Default unit is years; append k for kyr and M for Myr. For a logarithmic time scale, append +l and give the number of steps instead of increment. If time is set, then the input seamount table must have two extra columns for the start and stop time.
V or verbose : – verbose=true | verbose=level
Select verbosity level. More at verbose
W or density_output : – density_output=“filename”
Give the name of the vertically averaged density grid file. If time is set then this must be a filename template. Requires densities to define the density model.
Z or level : – level=value | level=NaN
Set the background water depth [0]. As all seamounts have positive relief, you may use a larger negative level to place them under water. Alternatively, use level=NaN to flag unused nodes (not allowed if build_mode=:incremental).
bi or binary_in : – binary_in=??
Select native binary format for primary table input. More at
f or colinfo : – colinfo=??
Specify the data types of input and/or output columns (time or geographical data). More at

Slide Simulation

The simulation of land slides via slide is not a physical model (apart from preserving mass). Instead, we approximate the shapes of rotational landslides via simple geometric shapes and functions. The radial slide height is modeled as:

\[h_s(r) = h_s(u) = h_1 + (h_2 - h_1)q(u) = h_1 + (h_2 - h_1) u_0 \left (\frac{1 + u_0}{u + u_0} - 1\right ),\]

where \(u = (r - r_2)/(r_1 - r_2)\) is the normalized horizontal distance of the rupture surface.

By default, the radial slide profile is fixed regardless of where in the slide sector we look. However, angular variation can be added via the function:

\[s(\alpha) = s(\gamma) = 1 - \lvert \gamma \rvert ^p,\]

where \(\gamma = 2 (\alpha - \alpha_1)/(\alpha_2 - \alpha_1) - 1\) and p is the power exponent.

The normalized volume rate distribution over time is simulated by:

\[\psi(t) = \psi(\tau) = \tau^\beta = \left (\frac{t - t_0}{t_1 - t_0} \right )^\beta,\]

where \(\tau\) is the normalized time during a slide event and \(\beta\) is set via beta [1].

Notes

Because the Gaussian curve only drops to 1.11% of its peak amplitude at the base radius (3 sigma) of a seamount, we actually evaluate Gaussian curves all the way to 4 sigma so that the amplitude drops to 0.034% of peak height before we jump to zero. This prevents the otherwise very noticeable step at the base of the seamount.

Examples

To compute the shape of a circular Gaussian seamount located at 1W, 2S on a 1 arc minute grid for a basal radius of 30 km and a height of 4500 meters:

using GMT
G = grdseamount([1 2 30 4500], region=(-1.5, -0.5, -2.5, -1.5), inc="1m"")
imshow(G)

To compute the shape of an elliptical conic seamount located at 200,400 on a 1x1 Cartesian grid for basal semi-major axis of 35, semi-minor axis of 20, azimuth of 29, height of 3700 m, and flattening of 0.15:

using GMT
G = grdseamount([200 400 29 35 20 3700], region=(150,250,350,450), inc=1, elliptical=true,
                flattening=0.15, shape=:cone, outgrid="ell_smt.nc")
grdview(G, shade=true, Jz="2c", view=(195,20))

To compute incremental loads from two elliptical, truncated Gaussian seamounts being constructed from 3 Ma to 2 Ma and 2.8 Ma to 1.9 Ma using a constant volumetric production rate, outputting an incremental grid every 0.1 Myr:

using GMT
# lon lat azimuth semi-major semi-minor height tstart tend
data = [0 0 -20 120 60 5000 3.0 2.0;
        50 80 -40 110 50 4000 2.8 1.9]
grdseamount(data, region="-1024/1022/-1122/924+uk", inc=2000, outgrid="smt_%3.1f_%s.nc",
            time="3M/1.9M/0.1M", build_mode="i/c", unit=:k, elliptical=true,
            flattening=0.2, shape=:gaussian, list="files.txt")

Precompiling
 
packages...


   1146.6 ms
  ✓ 
Xorg_xtrans_jll

   1142.8 ms  ✓ Xorg_libXau_jll

   1317.7 ms  ✓ LASzip_jll

   1258.9 ms  ✓ Xorg_libXdmcp_jll

   1436.8 ms  ✓ 
MicrosoftMPI_jll

   1697.0 ms  ✓ MPIPreferences

   1576.6 ms  ✓ snappy_jll

   1616.8 ms  ✓ JpegTurbo_jll

   1598.9 ms
  ✓ XZ_jll

   1530.8 ms  ✓ brotli_jll

   1590.1 ms  ✓ Qhull_jll

    819.1 ms  ✓ Libmount_jll

    989.5 ms  ✓ 
Kerberos_krb5_jll

   1143.5 ms  ✓ Xorg_libpciaccess_jll

   1199.4 ms  ✓ LLVMOpenMP_jll

   1239.4 ms
  ✓ Zstd_jll

   1332.3 ms  ✓ PCRE_jll

   1461.6 ms  ✓ GEOS_jll

   1404.4 ms  ✓ FFTW_jll

   1451.8 ms  ✓ Lz4_jll

   1387.8 ms  ✓ 
libaec_jll

   1404.7 ms
  ✓ ICU_jll

    812.8 ms  ✓ OpenBLAS32_jll

    962.0 ms  ✓ Giflib_jll

    966.5 ms  ✓ LERC_jll

   1588.1 ms  ✓ SQLite_jll

   1478.7 ms  ✓ Xorg_libxcb_jll

   1514.2 ms
  ✓ LAPACK32_jll


   1504.8 ms  ✓ XML2_jll

   1470.3 ms
  ✓ MPItrampoline_jll

   1456.5 ms  ✓ muparser_jll

   1694.5 ms  ✓ libzip_jll

   1725.7 ms  ✓ Ghostscript_jll

   1109.5 ms  ✓ Blosc_jll

   2139.2 ms  ✓ boost_jll

   1217.6 ms
  ✓ HDF4_jll

    557.2 ms  ✓ Xorg_libX11_jll

    747.5 ms  ✓ Libtiff_jll

   1182.6 ms  ✓ Hwloc_jll

    582.5 ms  ✓ Xorg_libXext_jll

    948.0 ms  ✓ LittleCMS_jll

   1986.3 ms  ✓ LibPQ_jll


   1494.6 ms  ✓ PROJ_jll

   1257.1 ms  ✓ OpenMPI_jll

   1250.4 ms  ✓ MPICH_jll


    988.0 ms  ✓ Libglvnd_jll

   2447.3 ms  ✓ Thrift_jll

    917.4 ms  ✓ OpenJpeg_jll

   1253.0 ms  ✓ libgeotiff_jll

    892.5 ms  ✓ libwebp_jll

   1216.4 ms  ✓ HDF5_jll

   1280.5 ms  ✓ Arrow_jll

    720.3 ms  ✓ Leptonica_jll

   1645.8 ms  ✓ NetCDF_jll

   3103.6 ms  ✓ GDAL_jll

   3607.1 ms  ✓ GMT_jll

  57165.2 ms  ✓ GMT

  57 dependencies successfully precompiled in 82 seconds. 24 already precompiled.

Source Code

This function has multiple methods:

grdseamount(cmd0::String; kw...) - grdseamount.jl:6
grdseamount(arg1; kw...) - grdseamount.jl:7

Reference

Smith, J. R. and Wessel, P., 2000, Isostatic consequences of giant landslides on the Hawaiian Ridge, Pure Appl. Geophys., 157, 1097-1114.