1 resultado para mathematical content
em Publishing Network for Geoscientific
Resumo:
Sediment cores collected from the Eastern Equatorial Pacific Ocean display a clear positive second-order relationship between wet bulk density (WBD) and carbonate content. This has long interested the paleoceanography community because detailed Gamma Ray Attenuation Porosity Evaluator (GRAPE) measurements, which approximate WBD, might be used to determine records of carbonate content at very high temporal resolution. Although general causes for the relationship are known, they have not been presented and discussed systematically on the basis of first principles. In this study, we measure the mass and carbonate content of 50 sediment samples with known WBD from Site U1338, before and after rinsing with de-ionized water; we also determine the mass related proportion of coarse (> 63 µm) material. Samples exhibit clear relationships between WBD, carbonate content, mass loss upon rinsing, and grain size. We develop a series of mathematical expressions to describe these relationships, and solve them numerically. As noted by previous workers, the second-order relationship between WBD and carbonate content results from the mixing of biogenic carbonate and biogenic silica, which have different grain densities and different porosities. However, at high carbonate content, a wide range in WBD occurs because samples with greater amounts of coarse carbonate have higher porosity. Moreover compaction impacts carbonate particles more than biogenic silica particles. As such, a single two-component equation cannot be used to determine carbonate content accurately across depth intervals where both the porosity and type of carbonate vary. Instead, the WBD-carbonate relationship is described by an infinite series of curves, each which represents mixing of multiple sediment components with different densities and porosities. Dissolved ions also precipitate from pore space during sample drying, which adds mass to the sediment. Without rinsing samples, simple empirical relationships between WBD and carbonate content are further skewed by salt dilution.