Using Fuzzy Logic for the Analysis of Sea-level Indicators with Respect to Glacial-isostatic Adjustment: An Application to the Richmond-Gulf Region, Hudson Bay

An important constraint for the inference of mantle viscosity is the variation of the Holocene relative sea-level (RSL) height (with respect to today) following the last deglaciation. As a measure of this variation, sea-level indicators (SLIs) related to the RSL heights at specific past time epochs are used. For the inversion of the RSL-height change in terms of mantle viscosity, neighbouring SLIs may be grouped into an RSL diagram taken as representative for the region considered. Usually, the nominal height and age of a particular SLI are the only characteristics considered when determining the former RSL height. However, only SLIs based on isolation basins yield a narrow range for this height, whereas SLIs based on fossil samples provide a lower bound (shells), an upper bound (driftwood) or a finite interval (basal peat) for it. To also use fossil samples objectively, we develop a classification scheme of the depositional conditions based on fuzzy logic. After the definition of appropriate membership functions, this method leads to a systematic interpretation of the large number of SLIs available. We apply this method to SLIs from the Richmond-Gulf region, southeastern Hudson Bay, near the former glaciation center of Canada and derive a decay time of 5 ka for the exponential function best fitting the RSL diagram for this region.