Stratigraphy as a low-pass filter: selective preservation of spatial variability on a Holocene carbonate platform

Walther’s law, a fundamental principle in geoscience, predicts that laterally adjacent depositional environments become preserved as a vertical succession of layers (facies). As an expression of uniformitarianism, this law underpins interpretations of Earth’s history, yet it has not been quantitatively tested. We test this law and examine its limitations by quantifying multidecadal changes in environmental heterogeneity (1945-2019) in the Bahamas and extrapolating them to millennial timescales using forward modelling. Virtual stratigraphic successions predicted by Walther’s law contain substantially greater heterogeneity than observed in sediment cores. This discrepancy arises because small and short-lived environment patches undergo rapid turnover and fail to accumulate sufficient sediment for preservation. Our work establishes a quantitative framework for defining preservation thresholds and demonstrates that stratigraphy functions as a low-pass filter on environmental variability, selectively preserving low spatial- and temporal-frequency environmental signals. These findings fundamentally constrain how environmental change can be reconstructed from the sedimentary record.