modifiedBchron

This package provides a version of the Bchron R package, with features added to improve usability with deep time geochronology data (e.g., Argon-Argon, Uranium-Lead). If you use this package please cite Trayler et al.¹ for the deep time additions and Haslett & Parnell² for the underlying Bchron model framework.

Introduction

Bchron is a bayesian age-depth model implemented in R. Since it was originally designed for radiocarbon analyses It lacks some features that are desirable to those working with U-Pb or ⁴⁰Ar/³⁹Ar geochronology data. In this package we have made several modifications including

• We allow individual dates to be grouped to form complex probability density functions, reproducing the practice in both U-Pb and ⁴⁰Ar/³⁹Ar geochronology of convolving many single crystal or spot analyses into a single age distribution.
• We have added an adaptive Markov Chain Monte Carlo Algorithm³ to ensure efficient exploration off parameter space, independent of the scale of the data (e.g., 1 Ma vs 1,000 ka, vs 1,000,000 a)
• We have removed automated outlier rejection. We instead recommend pre-screening data using established criteria based on the physical mechanisms of crystal growth and open system behavior in volcanic rocks.

Installation

modifiedBchron can be installed using the devtools R package.

# copy this code into R
# install.packages('devtools')
devtools::install_github('robintrayler/modifiedBchron')

If this installation fails, you may also need to install Rtools on Windows or on macOS you may need to install command line tools.

# install command line tools on macOS
# copy this code into macOS Terminal (not R!)
xcode-select --install

Once modifiedBchron is installed it can be loaded as an R package by adding library(modifiedBchron) to the beginning of an R script.

Usage

Data Inputs

modifiedBchron requires several inputs, shown in the table below.

• ids: These are the sample names. Samples with the same ids will be combined into a single summed probability distribution.
• ages: these are the radiometric ages for each sample. In this example, each age is a single zircon grain TIMS age.
• ageSds: The analytical uncertainty for each ages expressed as 1 standard deviation for gaussian distributions, or as a half-range for uniform distributions.
• positions: The stratigraphic position of each sample in units above base of the section. The positions for samples within an ids group must all match exactly. If you are working with depths then you can simply make your measurements negative (e.g., 200 meters below core-top becomes -200 "above" base).
• positionThicknesses: The stratigraphic uncertainty of each positions expressed as a half thickness. For example a volcanic as that is 2 meters thick at 100 meters above base would have a positions of 100 and a positionThicknesss of 1. The thicknesses for each ids group must match exactly.
• distType: The statistical distribution to use for each sample. Defaults to Gaussian (G). Uniform distributions (U) are also supported.

ids	age	ageSds	position	thickness	distType
CV13	17.634	0.016	48.25	3.125	G
CV13	17.629	0.025	48.25	3.125	G
CV13	17.603	0.029	48.25	3.125	G
CV13	17.599	0.019	48.25	3.125	G
CV13	17.592	0.020	48.25	3.125	G
C5DnB	17.530	0.005	75.93	1.000	U
CO	17.119	0.113	84.50	2.500	G
CO	17.119	0.113	84.50	2.500	G
CO	17.180	0.133	84.50	2.500	G
CO	17.240	0.103	84.50	2.500	G
CO	17.351	0.104	84.50	2.500	G
CO	17.401	0.123	84.50	2.500	G
CO	17.431	0.113	84.50	2.500	G
CO	17.492	0.123	84.50	2.500	G
CO	17.613	0.133	84.50	2.500	G
C5DnT	17.240	0.005	91.10	1.000	U
KARG-15-09	17.028	0.032	151.50	1.800	G
KARG-15-09	16.997	0.023	151.50	1.800	G
KARG-15-01	16.854	0.012	161.00	0.000	G
KARG-15-01	16.850	0.014	161.00	0.000	G
KARG-15-01	16.849	0.016	161.00	0.000	G
KARG-15-01	16.846	0.021	161.00	0.000	G
KARG-15-01	16.836	0.015	161.00	0.000	G
Toba Blanca	16.883	0.018	175.00	0.000	G
Toba Blanca	16.859	0.038	175.00	0.000	G
Toba Blanca	16.823	0.030	175.00	0.000	G
CV-10	16.877	0.029	179.00	0.000	G
CV-10	16.833	0.025	179.00	0.000	G
CV-10	16.760	0.034	179.00	0.000	G
CV-10	16.751	0.057	179.00	0.000	G
CO3	16.397	0.088	193.50	1.500	G
CO3	16.468	0.098	193.50	1.500	G
CO3	16.601	0.086	193.50	1.500	G
CO3	16.644	0.081	193.50	1.500	G
CO3	16.656	0.083	193.50	1.500	G
CO3	16.667	0.113	193.50	1.500	G
CO3	16.678	0.079	193.50	1.500	G
CO3	16.685	0.082	193.50	1.500	G

Example

The core function of modifiedBchron is ageModel(). ageModel() takes the data shows in the table above and outputs a bayesian age model.

# load the package
library(modifiedBChron) 

# load the example data (csv of table above)
df <- read.csv(file = './data/example_data.csv')

# run the age model
age_model <- ageModel(ages = df$age,
                  ageSds = df$ageSds,
                  positions = df$position,
                  ids = df$ids,
                  positionThicknesses = df$thickness,
                  distTypes = df$distType,
                  predictPositions = seq(48.25, 193.50, by = 1),
                  MC = 10000,  # how many iterations 
                  burn = 2000) # how many iterations to discard
)

You can view the plot the output of the age model using the modelPlot() function.

modelPlot(model = age_model, 
          scale = 8) # changes the height of the probability distributions

You can predict the age of new stratigraphic positions using the agePredict() function. The newPositions and newPositionThicknesses follow the same general rules as positions and positionThicknesses in ageModel().

age_predictions <- agePredict(model = age_model, 
           newPositions = c(57, 120, 150),
           newPositionThicknesses = c(1, 3, 0.5))

Finally you can add age_predictions to a plot using modelPlot().

modelPlot(model, 
          agePredictOutput = age_predictions,
          scale = 8, 
          ylim = c(45, 250))

Footnotes

1. Trayler, R.B., Schmitz, M.D., Cuitiño, J.I., Kohn, M.J., Bargo, M.S., Kay, R.F., Strömberg, C.A.E., and Vizcaíno, S.F., 2020, An Improved Approach To Age-Depth Modeling In Deep Time: Implications For The Santa Cruz Formation, Argentina: Geological Society of America Bulletin, v. 132, p. 233–244. ↩

2. Haslett, J., and Parnell, A.C., 2008, A Simple Monotone Process With Application To Radiocarbon-Dated Depth Chronologies: Applied Statistics, v. 57, p. 399–418, doi:doi: 10.1111/j.1467-9876.2008.00623.x. ↩

3. Haario, H., Saksman, E., and Tamminen, J., 1999, Adaptive proposal distribution for random walk Metropolis algorithm: Computational Statistics, v. 14, p. 375–396. ↩