sandplover.strat.compute_compensation

sandplover.strat.compute_compensation(stratal_surfaces, time_idxs=None, clip_ends=0)

Compute compensation, given stratal surfaces.

This function is an implementation of the compensation statistic [1] [2] that has been widely adapted studies of stratigraphic channelized deposits. The metric is an assessment of the coefficient of variation in accumulation over space, averaged over increasing vertical stratigraphic time [1].

\[\sigma_{ss}(T) = \left( \int_L \left[ \frac{r(T;x)}{\hat{r}(x)} - 1 \right]^2 dL \right)^{1/2}\]

where, \(r(T;x)\) is the local sedimentation rate measured at a specific point x over the time interval T, \(\hat{r}(x)\) is the average sedimentation rate at point x over the entire timeseries, and \(L\) is the length of the stratigraphic sections for computation.

Here, we implement an adaptable and flexible function to help asses compensational stacking. To understand the conceptual meaning of function outputs and how to work with these outputs to assess compensational stacking patterns in stratigraphy, see the example on Compensational Stacking and especially references therein.

This function operates on a two-dimensional array of stratal surfaces. Time is expected to be oriented along the first axis dimension. See the examples below for function use.

Parameters:

  • stratal_surface (ndarray or DataArray) – Array of stratigraphic surfaces, with vaules in the array representing elevations (i.e., stratigraphic height) and any other dimensions representing a spatial coordinate. This array should record along the first dimension each isochron in the stratigraphic record collapsed to that elevation at which the sedimentary surface at all later times occupied a higher stratigraphic height.

  • time_idxs (ndarray, optional) – NOT IMPLEMENTED; only works for all input surfaces. Which time indices of the stratal_surfaces array to use for computation. I.e., specifying indices will subset the stratal_surfaces array for faster computations.

  • clip_ends (int, optional) – How many stratigraphic columns from the edge of the section to ignore from the computation. This can be used to remove columns which have no deposition recorded, or are effected by bouundary conditions and/or wall effects. Can be int or 2-tuple of int, specifying the left and right clip indicies. Default is 0, no clipping.

Returns:

  • sigmas – Compensation calculation for all combinations of pairs in stratal_surfaces.

  • window_lengths – The averaging windows used for each compensation calculation. These values are returned in the same coordinates as input times. For example, if stratal_surfaces is a DataArray then window_lengths records the time intervals between surfaces, and if stratal_surfaces is an ndarray then window_lengths records the number of array indices between surfaces.

Examples