# (49) Analysis of the Atlantic seafloor depth/age relationship

In this example we show an example of data analysis using grids of seafloor depth and age for a region in the south Atlantic. We use module grdsample to convert the age grid to the same pixel registration used by the depth grid. Dumping separate x,y,z triplets with grd2xyz lets us paste the output back via gmtconvert to make binary tables of age,depth,depth. Here, depth is repeated in order to use blockmode for modal depth estimation and xyz2grd for mapping the data density. We image the density of (age,depth) points, overlay the modal depths and their robust uncertainty bars, and compute and plot two models for the expected depths as a function of age (see legend). Note we place most of the legend twice to achieve the thin-on-thick pen effect in the legend.

    #!/usr/bin/env bash
    #               GMT EXAMPLE 49
    #
    # Purpose:      Illustrate data analysis using the seafloor depth/age relationship
    # GMT modules:  blockmode, gmtmath, grdcontour, grdimage, grdsample, makecpt,
    #		basemap, legend, colorbar, plot, xyz2grd
    #

    gmt begin ex49
    	# Convert coarser age grid to pixel registration to match bathymetry grid
    	gmt grdsample @age_gridline.nc -T -Gage_pixel.nc
    	# Image depths with color-coded age contours
    	gmt makecpt -Cabyss -T-7000/0 -H > z.cpt
    	gmt makecpt -Chot -T0/100/10 -H > t.cpt
    	gmt grdimage @depth_pixel.nc -JM15c -Cz.cpt -B -BWSne --FORMAT_GEO_MAP=dddF
    	gmt plot -W1p @ridge_49.txt
    	gmt grdcontour age_pixel.nc -A+f14p -Ct.cpt -Wa0.1p+c -GL30W/22S/5E/13S
    	gmt colorbar -Cz.cpt -DjTR+w5c/0.4c+h+o0.75c/0.4c -Baf+u" km" -W0.001 -F+p1p+gbeige
    	# Obtain depth, age pairs by dumping grids and pasting results
    	gmt grd2xyz age_pixel.nc -bof > age.bin
    	gmt grd2xyz @depth_pixel.nc -bof > depth.bin
    	gmt convert -A age.bin depth.bin -bi3f -o2,5,5 -bo3f > depth-age.bin
    	# Create and map density grid of (age,depth) distribution
    	gmt xyz2grd -R0/100/-6500/0 -I0.25/25 -r depth-age.bin -bi3f -An -Gdensity.nc
    	# WHy do we need the -R below? otherwise it fails to work
    	gmt grdimage density.nc -R0/100/-6500/0 -JX15c/10c -Q -Y12c -Ct.cpt
    	# Obtain modal depths every ~5 Myr
    	gmt blockmode -R0/100/-10000/0 -I5/10000 -r -E depth-age.bin -bi3f -o0,2,3 > modal.txt
    	# Compute Parsons & Sclater [1977] depth-age curve
    	# depth(t) =   350 * sqrt(t) + 2500, t < 70 Myr
    	#	   =  6400 - 3200 exp (-t/62.8), t > 70 Myr
    	gmt math -T0/100/0.1 T SQRT 350 MUL 2500 ADD T 70 LE MUL 6400 T 62.8 DIV NEG EXP 3200 MUL SUB T 70 GT MUL ADD NEG = ps.txt
    	gmt plot ps.txt -W4p,green
    	gmt plot ps.txt -W1p
    	# Compute Stein & Stein [1992] depth-age curve
    	# depth(t) =  365 * sqrt(t) + 2600,  t < 20 Myr
    	#	   = 5651 - 2473 * exp (-0.0278*t), t > 20 Myr
    	gmt math -T0/100/0.1 T SQRT 365 MUL 2600 ADD T 20 LE MUL 5651 T -0.0278 MUL EXP 2473 MUL SUB T 20 GT MUL ADD NEG = ss.txt
    	# Plot curves and place the legend
    	gmt plot ss.txt -W4p,white
    	gmt plot ss.txt -W1p
    	gmt plot -Ss0.4c -Gblue modal.txt -Ey+p1p,blue
    	gmt plot -Ss0.1c -Gwhite modal.txt
    	gmt basemap -R0/100/0/6.5 -JX15c/-10c -Bxaf+u" Myr" -Byaf+u" km" -BWsNe
    	gmt legend -DjRT+w6.5c+o0.25c -F+p1p+gbeige+s <<- EOF
    	S 0.5c - 0.9c - 4p,green 1c Parsons & Sclater (1977)
    	S 0.5c - 0.9c - 4p,white 1c Stein & Stein (1992)
    	S 0.5c s 0.4c blue - 1c Modal depth estimates
    	EOF
    	gmt legend -DjRT+w6.5c+o0.25c <<- EOF
    	S 0.5c - 0.9c - 1p 0.75c
    	S 0.5c - 0.9c - 1p 0.75c
    	S 0.5c s 0.1c white - 0.75c
    	EOF
    	rm -f age_pixel.nc age.bin depth.bin depth-age.bin density.nc modal.txt ps.txt ss.txt z.cpt t.cpt
    gmt end show

Seafloor depth vs. age in the south Atlantic.