Image processing to extract sequential profiles with high spatial resolution from the 2D map of deformed laminated patterns

Abstract

A method of image processing is presented to extract a sequential profile from a map showing folded pattern of laminations with boudinage, overlapping noise and deficits in order to obtain reliable data for sequential analysis of sedimentary rocks on their cross-section. The raw map data is a digital photograph of any striped pattern of such rocks represented by 2D distribution of density of a certain quantity. The image processing consists of several steps. First, we derive the distribution of local slopes (strike) of laminations by means of statistical analysis of the first and the second spatial derivatives of the density map. Filtering of the local slopes leads to the elimination of noise amplified by differential operations. Secondly, a set of curved isochronous lines is determined by integrating the local slopes to trace smoothly the local strikes of laminae. Thirdly, the original folded pattern of laminations is converted to an “unfolded image” with straight laminations by using the isochronous lines. Finally, a set of a reliable 1D sequential profile of density and its uncertainty profile are derived by computing the mean and variance of density along each of the isochronous lines on the unfolded pattern of laminations. The computer code is tested successfully on the synthetic map data and applied to a set of abundance maps of major elements in Archean banded iron formation to characterize the striped pattern. High resolution is achieved objectively to recognize even thin and faint seams in the laminations. The computer code, lamination tracer, is expected to be useful for the analysis of other types of laminated pattern in various fields such as dendrochronology and sequence stratigraphy to decode the environmental variations in the geologic past.