This page gives an overview of the fundamental principles of sediment mixing used by the Particle-Size Toolbox.

Sediment transport is an inherently non-linear process and often consists of selective erosion and deposition. The example shown in the figure below is an analogy of a fluvial environment, where mixing between two particle-size distributions takes place over a distance.

Plots G and H show how using a log-ratio transformation converts spatial changes into quasi-linear functions. Plot H shows how log-ratio particle-size distributions can be broken down into their principal components. These transformations are used to model changes in sediment texture in 3D space by the Particle-Size Toolbox.

Plot C illustrates how mixing two sediments is a non-linear process, or rather it is a linear process in log-ratio space. The boomerang-shaped curve is characteristic of what happens when two particle-size distributions are mixed. This same process happens when irregularly-spaced borehole data are converted into regularly spaced borehole data (runpst - 6. Regularize borehole data)

A series of plots showing the gradual mixing of two particle-size distributions: (A) The original distribution a (black) and the added distribution b (red). (B) The percentage-frequency distributions that result from the gradual mixing of a and b. (C) The mixing process summarized as a trend line in a ternary diagram. Note how the trend it describes a boomerang shaped curve. This is very typical of sediments in natural environments. (D) The components of the ternary diagram (C) plotted against distance. (E) Changes in the first four moments of the mixed distribution plotted against distance (mean, standard deviation, skewness and kurtosis (given as colour)). (F) Interdependency between distribution moments expressed in 4D space. (G) The clr-transformed components from the ternary diagram (C) plotted against distance. Note how the non-linear trends in (D) are now much more linear. (H) The principal component scores (eigenvalues) of log-ratio -transformed particle-size distributions. The slope of the first principal component quantifies the rate of mixing between the two particle-size distributions a and b. All other principal components scores are zero.

A series of plots showing the gradual mixing of two particle-size distributions: (A) The original distribution

a(black) and the added distributionb(red). (B) The percentage-frequency distributions that result from the gradual mixing ofaandb. (C) The mixing process summarized as a trend line in a ternary diagram. Note how the trend it describes a boomerang shaped curve. This is very typical of sediments in natural environments. (D) The components of the ternary diagram (C) plotted against distance. (E) Changes in the first four moments of the mixed distribution plotted against distance (mean, standard deviation, skewness and kurtosis (given as colour)). (F) Interdependency between distribution moments expressed in 4D space. (G) The clr-transformed components from the ternary diagram (C) plotted against distance. Note how the non-linear trends in (D) are now much more linear. (H) The principal component scores (eigenvalues) of log-ratio -transformed particle-size distributions. The slope of the first principal component quantifies the rate of mixing between the two particle-size distributionsaandb. All other principal components scores are zero.