Emanuel Huber
2018-03-06
There is a critical need in hydrogeological modeling for geologically more realistic representation of the subsurface. Indeed, widely-used representations of the subsurface heterogeneity based on smooth basis functions such as cokriging or the pilot-point approach fail at reproducing the connectivity of high permeable geological structures that control subsurface solute transport. To realistically model the connectivity of high permeable structures of coarse, braided river deposits, multiple-point statistics and object-based models are promising alternatives. We therefore propose a new object-based model that, according to a sedimentological model, mimics the dominant processes of floodplain dynamics. Contrarily to existing models, this object-based model possesses the following properties: (1) it is consistent with field observations (outcrops, ground-penetrating radar data, etc.), (2) it allows different sedimentological dynamics to be modeled that result in different subsurface heterogeneity patterns, (3) it is light in memory and computationally fast, and (4) it can be conditioned to geophysical data. In this model, the main sedimentological elements (scour fills with open-framework–bimodal gravel cross-beds, gravel sheet deposits, open-framework and sand lenses) and their internal structures are described by geometrical objects. Several spatial distributions are proposed that allow to simulate the horizontal position of the objects on the floodplain as well as the net rate of sediment deposition. The model is grid-independent and any vertical section can be computed algebraically. Furthermore, model realizations can serve as training images for multiple-point statistics.
Huber E., Huggenberger P., Caers J. (2016) Presentation: A 3D object-based model to simulate highly-heterogeneous, coarse, braided river deposits. AGU 2016 Fall Meeting, San Francisco, California, USA, 12–16 December 2016. DOI: 10.13140/RG.2.2.29333.32489
if(!require("devtools")) install.packages("devtools")
devtools::install_github("emanuelhuber/CBRDM")
library(CBRDM)This is an ongoing project. If you have any questions, don't hesitate to contact me:
Thank you!
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E. Huber, P. Huggenberger (2016) Subsurface flow mixing in coarse, braided river deposits. Hydrology and Earth System Sciences, 20:2035–2046. DOI: 10.5194/hess-20-2035-2016
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Huber E. and Huggenberger P. (2015) Morphological perspective on the sedimentary characteristics of a coarse, braided reach: Tagliamento River (NE Italy) . Geomorphology, 248: 111–124. DOI: 10.1016/j.geomorph.2015.07.015
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Huggenberger, P., Regli, C., 2006. A sedimentological model to characterize braided river deposits for hydrogeological applications. In: Sambrook Smith, G.H., Best, J.L., Bristow, C.S., Petts, G.E. (Eds.), Braided Rivers: Process, Deposits, Ecology and Management. Blackwell Publishing Ltd, Oxford, UK, pp. 51–74. DOI: 10.1002/9781444304374.ch3.
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Beres, M., Huggenberger, P., Green, A.G., Horstmeyer, H., 1999. Using two- and three-dimensional georadar methods to characterize glaciofluvial architecture. Sediment. Geol. 129 (1–2), 1–24. DOI: 10.1016/S0037-0738(99)00053-6.
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Siegenthaler, C., Huggenberger, P., 1993. Pleistocene Rhine gravel: deposits of a braided river system with dominant pool preservation. Geol. Soc. Lond., Spec. Publ. 75, 147–162. DOI: 10.1144/GSL.SP.1993.075.01.09.
This model simulates trough fills with cross-bedding and horizontal layers. The trough fills are approximated by a series of truncated ellipsoids.
We create an instance of the class Trough using the constructor function trough(). The objects properties and positions are drawn from random distribution:
# Trough Fills
TF <- trough(pos = matrix(runif(9, 10,90), nrow=3, ncol=3),
size = cbind(rnorm(3, 40, 5), rnorm(3, 20,2),
rnorm(3, 2, 0.5)),
theta = runif(3,0,3.14),
rH = rep(6, 3))To visualise this trough fills, use the function plotTopView():
plotTopView(TF, border = "blue", col = "grey", asp = 1)
To plot one specific trough fill:
plotTopView(TF, border = "blue", col = "grey", asp = 1)
plotTopView(TF[2], border = "blue", col = "green", asp = 1, add = TRUE)
Add cross-bedding:
para <- list(nF = 10, # nF cross-beds
rpos = 0.75, # 0 <= rpos <=1
phi = 2.2) # orientation angle
TF <- crossBedding(TF, para)
plotTopView(TF, border = "blue", col = "grey", asp = 1)
Different cross-bedding for each trough fills:
para <- list(nF = c(10, 3, 30), # nF cross-beds
rpos = c(0, 0.75, 1), # 0 <= rpos <=1
phi = c(0, -1, 2.2)) # orientation angle
TF <- crossBedding(TF, para)
plotTopView(TF, border = "blue", col = "grey", asp = 1)
The object properties (L = length, rLW= length-width ratio, rLH = length-height ratio, theta = orientation angle, rH = truncation ratio ) are defined by probability distributions (here the uniform probability distribution).
The vertical position of the layers is defined by a Poisson process with parameter ag (the rate of sediment deposition = mean thickness of sediment deposited per event).
The horizontal distribution of trough fills on each layers is defined by a Strauss process with parameters bet (beta), gam (gamma) and d interaction distance (the function rStrauss in the spatstat R-package). Warning: a bad parameter choice may lead to extremely long computations.
The cross-bedding parameters are also defined according probability distribution. Note that here nF defines the cross-bed thickness (I will change that next time).
para <- list("L" = list(type = "runif", min = 40, max = 70),
"rLW" = list(type = "runif", min = 3, max = 4),
"rLH" = list(type = "runif", min = 45, max = 66),
"theta" = list(type = "runif", min = -20 * pi / 180,
max = 20 * pi / 180),
"rH" = 2,
"vpp" = list(type = "poisson",
lambda = 0.05),
"hpp" = list(type = "strauss",
bet = 1e-2,
gam = 0.2,
d = 100,
fd = c(5, 1),
nit = 5000, n0 = 3),
"nF" = list(type = "rint", min = 2, max = 5),
"rpos" = list(type = "runif", min = 0.65, max = 1),
"phi" = list(type = "runif", min = -1.5, max = 1.5)
)Now we define the simulation box:
modbox <- list("x" = c(0,200),
"y" = c(0,100),
"z" = c(0,10)
)And run the simulation:
mod <- sim(modbox, hmodel = "strauss", para) # takes some times...Top view (the layers are "transparent") and show the vertical section lines:
plotTopView(mod, border = "red", col = "grey", asp = 1)
lv <- c(1, 0, -50)
lh <- c(0, 1, -50)
l <- c(1, 2, -250)
RConics::addLine(lv, col = "blue", lwd = 3)
RConics::addLine(lh, col = "black", lwd = 4)
RConics::addLine(l, col = "green", lwd = 4)
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Vertical section along the line
lv:smod <- section(mod, lv) plotSection(smod, border = "red", col = "grey", asp = 2, ylim = c(0, 10), xlim = c(0,100), ylab = "z (m)", xlab = "x (m)") title("Vertical section along 'lv' (blue line)")
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Vertical section along the line
lh:smod <- section(mod, lh) plotSection(smod, border = "red", col = "grey", asp = 2, ylim = c(0, 10), xlim = c(-50, 150), ylab = "z (m)", xlab = "y (m)") title("Vertical section along 'lh' (black line)")
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Vertical section along the line
l:smod <- section(mod, l) plotSection(smod, border = "red", col = "grey", asp = 2, ylim = c(0, 10), xlim = c(-20, 170), ylab = "z (m)", xlab = "x' (m)") title("Vertical section along 'l' (green line)")
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Define the pixelisation box (
x,y,z) as well as the pixel resolution (dx,dy,dz).mbox <- list(x = modbox$x, y = modbox$y, z = modbox$z, dx = 1, dy = 1, dz = 0.1)
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Pixelise
PIX <- pixelise(mod, mbox)
The function
pixelise()maps the object on the grid and attributes unique identifier (integer) to the pixels belonging to the same object. The layers have negative values while the throughs have positive values.library(plot3D) # horizontal section plot3D::image2D(PIX$XYZ[,, 50], x = PIX$x, y = PIX$y, asp = 1)
# vertical section at x = 50.5 plot3D::image2D(PIX$XYZ[which(PIX$x == 50.5),,], x = PIX$y, y = PIX$z, asp = 2)
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Set the facies identifier to the pixels:
- 0 = layers
- 1 = bimodal gravel (trough)
- 2 = open-framework gravel
FAC <- setProp(PIX$XYZ, type = c("facies")) # horizontal section plot3D::image2D(FAC[,, 50], x = PIX$x, y = PIX$y, asp = 1)
# vertical section at x = 50.5 plot3D::image2D(FAC[which(PIX$x == 50.5),,], x = PIX$y, y = PIX$z, asp = 2)
The hydraulic properties of the facies are given by the data
faciesProp:data(faciesProp) faciesProp # the facies hydraulic properties
## $gp ## p Kmean Klogsd Kvani de ## 0.2010 0.0015 0.5000 6.0000 12.1000 ## ## $bm ## p Kmean Klogsd Kvani de ## 0.2500 0.0015 0.1000 1.0000 9.2000 ## ## $ow ## p Kmean Klogsd Kvani de ## 0.35 0.10 0.10 1.00 26.90 -
set hydraulic conductivity
HK <- setProp(PIX$XYZ, type = c("K"), fprop = faciesProp) # horizontal section plot3D::image2D(HK[,, 50], x = PIX$x, y = PIX$y, asp = 1)
# vertical section at x = 50.5 plot3D::image2D(HK[which(PIX$x == 50.5),,], x = PIX$y, y = PIX$z, asp = 2)
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vertical anisotropy of the hydraulic conductivity
VANI <- setProp(PIX$XYZ, type = c("Kvani"), fprop = faciesProp) # horizontal section plot3D::image2D(VANI[,, 50], x = PIX$x, y = PIX$y, asp = 1)
# vertical section at x = 50.5 plot3D::image2D(VANI[which(PIX$x == 50.5),,], x = PIX$y, y = PIX$z, asp = 2)
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porosity
PORO <- setProp(PIX$XYZ, type = c("p"), fprop = faciesProp) # horizontal section plot3D::image2D(PORO[,, 50], x = PIX$x, y = PIX$y, asp = 1)
# vertical section at x = 50.5 plot3D::image2D(PORO[which(PIX$x == 50.5),,], x = PIX$y, y = PIX$z, asp = 2)
rnxyz <- dim(PIX$XYZ)
nx <- rnxyz[1]
ny <- rnxyz[2]
nz <- rnxyz[3]
# x-side: x x z (200 x 100) at y = 0
vx <- (PIX$x)
vy <- rep(0, nz)
vz <- matrix(rep(PIX$z, each = nx), ncol = nz,
nrow = nx, byrow = FALSE)
M1 <- plot3D::mesh(vx, vy)
plot3D::surf3D(M1$x, M1$y, vz, colvar = (HK[,1,]),
col = plot3D::jet2.col(201),
bty = "f", cex = 0.01, pch = 20, clim = range(HK),
clab = "hydraulic conductivity (m/s)", ticktype = "detailed",
theta = 40 , expand = 5, scale = FALSE, resfac = 0, clog = TRUE,
xlim = modbox$x, ylim = modbox$y,
zlim = modbox$z, #extent3D(gwMod)[5:6],
xlab = "x", ylab = "y", shade = TRUE, ltheta = -125, lphi = 45,
colkey = list(plot = TRUE, width = 0.5, length = 0.5,
cex.axis = 0.8, side = 1),
col.axis = "black", col.panel = "white", col.grid = "grey",
lwd.panel = 1, lwd.grid = 2, box = TRUE)
# y-side: y x z (100 x 100) at x =
vx <- rep(max(PIX$x), ny)
vy <- PIX$y
vz <- matrix(rep(PIX$z, ny), ncol = nz,
nrow = ny, byrow = TRUE)
M1 <- plot3D::mesh(vy, vx)
plot3D::surf3D(M1$y, M1$x, vz, colvar = HK[nx,,],
col = plot3D::jet2.col(201), add = TRUE, expand = 5, scale = FALSE,
resfac = 0, clog = TRUE, clim = range(HK),
colkey = list(plot = FALSE))
# z-side: x x y (200 x 100) at z = 10
vx <- rev(PIX$x)
vy <- PIX$y
vz <- matrix(rep(rep(max(PIX$z), nz), each = ny),
ncol = ny, nrow = nx, byrow = TRUE)
M1 <- plot3D::mesh(vx, vy)
plot3D::surf3D(M1$x, M1$y, vz, colvar = (HK[,,nz]),
col = plot3D::jet2.col(201), add = TRUE, expand = 5, scale = FALSE,
resfac = 0, clog = TRUE, clim = range(HK),
colkey = list(plot = FALSE))