Table 1 Summary of all input arguments available to customize the behaviour of the TephraFits function

Required

fitType

Fitting strategie(s), required to be entered as the third input argument. Accepts:

String or cell array

 ∙’exponential’: Fit using a single or multiple exponential segments as

of strings

developed by Pyle (1989) and Fierstein and Nathenson (1992)

 ∙’powerlaw’: Power–law fit as developed by Bonadonna and Houghton (2005)

 ∙’Weibull’: Weibull fit as developed by Bonadonna and Costa (2012)

dataType

Type of input data. Accepts:

String

 ∙’isopach’ (default)

  −xData: Square root of isopach area (km)

  −yData: Isopach thickness (cm)

 ∙’isomass’

  −xData: Square root of isomass area (km)

  −yData: Isomass load (kg m ⁻²)

 ∙’isopleth’

  −xData: Square root of isopleth area (km)

  −yData: Clast diameter (cm)

 ∙’transect’

  −xData: Distance from source (km)

  −yData: Deposit thickness (cm)

Fit-specific

Exponential

BIS

Location of the break(s)-in-slope for multiple exponential segments specified as a numeric value for 2 segments or a n−1 vector for n segments. The location specifies the value of xData after which the break-in-slope occurs. If BIS is not specified, only one exponential segment is used.

Double or vector of double

segments

The segments option enables the automatic fitting of exponential segment by minimising residuals. The value should be a 1×2 vector containing the minimum and maximum number of segments to fit.

Double or vector of double

optimize

Defines what parameter to optimize when the segments option is used (optional). Either ’rms’ to minimise the root–mean square error (default) or ’r2’ to maximise the r².

String

Power–law

C

Distal integration limit (km). Used only if fitType contains ’powerlaw’ and if dataType is either ’isopach’ or ’isomass’

Double

T ₀

Ordinate of the most proximal segment of the exponential fits. The ordinate should be expressed as a linear value of yData (i.e. not on a logarithmic scale). It is not necessary to define T₀ when the power–law fit is parsed along the exponential.

Double

Weibull

lambdaRange

Range of λ values entered as a 1×2 vector containing [min,max] used during the optimisation of the Weibull parameters. lambdaRangemust be specified along with nRange. In the specific case of isopachs where the Weibull method is requested along with any other fit type, the function uses the ranges of λ and n defined by Bonadonna and Costa (2013) as a function of the VEI obtained from the other fits.

1×2 vector of double

nRange

Same as lambdaRange

Optional

Probabilistic

runMode

Defines if the probabilistic mode is enabled for the characterization of uncertainties. Accepts:

String

 ∙’single’: A single fit is performed (default)

 ∙’probabilistic’: Multiple runs are performed using Monte Carlo simulations

The following arguments are only used if ’runMode’ is set to ’probabilistic’

nbRuns

Number of runs of the probabilistic mode

Double

xError

Error (in %) on xData. xError can be specified either as a single value, which assumes an equal error for all xData, or as a vector of the same size as xData containing errors on individual points

Double or vector of size of xData

yError

Same as xError for yData

Double or vector of size of yData

CError

Error (in %) on the distal integration limit C. Used only if fitType contains ’powerlaw’ and if dataType is either ’isopach’ or ’isomass’

Double

errorType

Probability density function of the error around the central value used for Monte Carlo simulations. Accepts:

String

 ∙’normal’: Gaussian distribution of errors using user-defined error as 3 sigma of the

distribution (default)

 ∙’uniform’: Uniform distribution of errors using user-defined error as extreme

values

errorBounds

Percentiles used to express the spread of the final values. Should be specified as a 1×2 vector containing [min,max]. By default, using the 5^th and 95^th percentiles

1×2 vector of double

Plotting

Scale

Scale of the y-axis for plotting. Accepts:

String

 ∙’log10’: Log 10 logarithm (default)

 ∙’ln’: Natural logarithm

 ∙’linear’: Linear

maxDistance

Maximum extent of curve extrapolation in distal part for plotting. 1 means 100%, i.e. the distance to the most distal point is doubled (default)

Double

fits2plot

Defines which fits to plot. Parsed as a 1 ×length(fitTypes) boolean vector. For example, if fitType = ’exponential’, ’powerlaw and ’fits2plot’ is [1,0], only the exponential fit will be plotted

Boolean vector of size of fitType

plotType

Plot type. Accepts:

String

 ∙’subplot’: Multiple plots in one figure (default)

 ∙’separate’: Individual figure for each plot

 ∙’none’: No plot