# slumping model

June 8, 2014
By

(This article was first published on Dan Kelley Blog/R, and kindly contributed to R-bloggers)

# Introduction

I got interested in layered sedimentation from viewing a video and decided it would be interesting to code this into R. More on that in due course, but my first step was to code a syatem with one sediment “type”.

# Procedure

The following code drops sediment particles at x=1, and lets them roll downhill until they reach the bottom or a ledge. It draws numbers at the sedimented particles’ final positions. Since the numbers start at 1, the values are like inverse ages.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 m <- 51 # number of particles n <- 10 # grid width debug <- FALSE # put TRUE for debugging info <- function(...) if (debug) cat(...) pch <- 20 cex <- 4/log2(n) type <- "t" set.seed(1) rollDownhill <- function(X, Z) { info("rollDownhill(", X, ",", Z, ")\n", sep = "") if (Z == 1) return(list(x = X, z = Z)) ## Particles roll down-slope until they hit the bottom... ... or a ledge ## comprising two particles. XX <- X ZZ <- Z while (0 == S[XX + 1, ZZ - 1]) { # move down and to right info(" XX:", XX, " ZZ:", ZZ, "\n") XX <- XX + 1 ZZ <- which(0 == S[XX, ])[1] if (ZZ == 1) break if (XX == n) break } return(list(x = XX, z = ZZ)) } S <- matrix(0, nrow = n, ncol = n) # 'S' means 'space' par(mar = c(3, 3, 1, 1), mgp = c(2, 0.7, 0)) plot(1:n, 1:n, type = "n", xlab = "", ylab = "") xDrop <- 1 # location of drop; everything goes here or to right for (i in 1:m) { # 'p' means partcle while (0 == length(zDrop <- which(0 == S[xDrop, ])[1])) { info("in while line 72\n") xDrop <- xDrop + 1 if (xDrop == n) { message("RHS") break } } info("particle:", i, " ") p <- rollDownhill(xDrop, zDrop) S[p$x, p$z] <- 1 if (type == "p") { points(p$x, p$z, col = "gray", pch = pch, cex = cex) } else { text(p$x, p$z, i, col = "gray") } } 

# Discussion and conclusions

Reading the numbers on the graph as inverse age, one can see an interesting age structure.

Viewed along diagonals, ages increase by 1 time unit with every lateral step away from the source.

Viewed along Z levels, though, the time step is more interesting. You can see this at a glance, by first-differencing the values along z=1, and then at z=2, etc.

I suppose that if something came along and sliced the sediment mound along z levels, we’d see this more interesting pattern of time variation in the lateral.

I wonder if these patterns (or the code) are of interest to geologists?