Mathematical aspects of non-steady-state diagenesis

Berner (1971) has solved the differential equation governing the concentration in interstitial water of substances produced or consumed during steady-state diagenesis. We have shown that closed solutions exist for non-steady-state diagenesis as well, and that these solutions are best obtained by means of Green's functions. Non-uniform distribution of decomposable organic matter in sediments is a major cause of non-steady-state diagenesis. However, the effect of such non-uniform distributions on the composition of interstitial water in sediments is pronounced only when the rate of deposition exceeds ca. 200 cm/1000 yr. At slower deposition rates, diffusion is sufficiently rapid to damp out major fluctuations in the concentration of ions such as SO^2?₄, NH⁺₄, PO^3?₄, and HCO^?₃. Concentration profiles of these ions therefore tend to be similar to steady-state profiles even if the concentration of decomposable organic matter is quite heterogeneous.The concentration of SO^2?₄ frequently approaches 0 in marine sediments rich in decomposable organic matter. In such sediments the total quantity of SO^2?₄ reduced during diagenesis is proportional to the concentration of SO^2?₄ in sea water even if the bacterial rate of decomposition of organic matter is nearly independent of the SO^2?₄ concentration in interstitial water. This implies that the rate of SO^2?₄ removal from sea water by reduction to sulfide is roughly proportional to the sulfate concentration in seawater.Solutions for the diagenetic equation exist for reasonable variations of the rate of ionic diffusion in interstitial waters and for changes in the rate of deposition due to compaction.