A mathematical model has been constructed that enables calculation of the level of atmospheric O2 over the past 570 my from rates of burial and weathering of organic carbon (C) and pyrite sulfur (S). Burial rates as a function of time are calculated from an assumed constant worldwide clastic sedimentation rate and the relative abundance, and C and S contents, of the three rock types: marine sandstones and shales, coal basin sediments, and other non-marine clastics (red beds, arkoses). By our model, values of O2 versus time, using a constant total sedimentation rate, agree with those for variable sedimentation derived from present-day rock abundances and estimates of erosional losses since deposition. This agreement is the result of our reliance on the idea that any increase in total worldwide sediment burial, with consequently faster burial of C and S and greater O2 production, must be accompanied by a corresponding increase in erosion and increased exposure of C and S on the continents to O2 consumption via weathering. It is the redistribution of sediment between the three different rock types, and not total sedimentation rate, that is important in O2 control. To add stability to the system, negative feedback against excessive O2 fluctuation was provided in the modeling by the geologically reasonable assignment of higher weathering rates to younger rocks, resulting in rapid recycling of C and S. We did not use direct O2 negative feedback on either weathering of C and S or burial of C because weathering rates are assumed to be limited by uplift and erosion, and the burial rate of C limited by the rate of sediment deposition. The latter assumption is the result of modern sediment studies which show that marine organic matter burial occurs mainly in oxygenated shallow water and is limited by the rate of supply of nutrients to the oceans by rivers. Results of the modeling indicate that atmospheric O2 probably has varied appreciably over Phanerozoic time. During the Late Carboniferous and Permian periods O2 was higher than previously because of the rise of vascular land plants and the widespread burial of organic matter in vast coal swamps. A large decrease in O2 during the Late Permian was due probably to the drying-up of the coal swamps and deposition of a large proportion of total sediment in C and S-free continental red beds. Sensitivity study shows that major parameters affecting results are the mean C concentration in coal basins and the relative sizes of the reservoirs of young (rapidly recycled) versus old rocks. Less sensitivity was found for changes over time in total land area undergoing weathering and the use of direct O2 negative feedback on marine carbon burial. Good agreement for rates of C burial calculated via our model and via independent models, which are based on the use of stable carbon isotopes, indicates that the dominant factor that has brought about changes in atmospheric O2 level (and the isotopic composition of dissolved inorganic carbon in seawater) over Phanerozoic time is sedimentation and not weathering or higher temperature phenomena such as basalt-seawater reaction.

中文翻译：

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显生宙大气氧的新模型

已经构建了一个数学模型，可以根据有机碳 (C) 和黄铁矿硫 (S) 的掩埋和风化率计算过去 570 年的大气 O2 水平。作为时间函数的埋藏速率是根据假定恒定的全球碎屑沉积速率和三种岩石类型的相对丰度和 C 和 S 含量计算得出的：海相砂岩和页岩、煤盆地沉积物和其他非海相碎屑（红床，arkoses）。根据我们的模型，使用恒定总沉降速率的 O2 随时间变化的值与根据当今岩石丰度得出的可变沉降值和自沉积以来侵蚀损失的估计值一致。该协议是我们依赖于全球沉积物掩埋总量的任何增加，随着 C 和 S 的更快掩埋和 O2 产量的增加，必须伴随着相应的侵蚀增加和大陆上 C 和 S 暴露于通过风化消耗 O2 的增加。在 O2 控制中重要的是沉积物在三种不同岩石类型之间的重新分布，而不是总沉积速率。为了增加系统的稳定性，通过在地质上合理地将较高的风化率分配给较年轻的岩石，在建模中提供了对 O2 过度波动的负反馈，从而导致 C 和 S 的快速循环。我们没有使用直接的 O2 负反馈。 C 和 S 的风化或 C 的掩埋，因为风化速率被假定受隆起和侵蚀的限制，而 C 的掩埋速率受沉积物沉积速率的限制。后一种假设是现代沉积物研究的结果，表明海洋有机物埋藏主要发生在含氧浅水中，并且受到河流向海洋供应营养物的速度的限制。模拟结果表明，大气中的 O2 可能在显生宙时期发生了明显的变化。在石炭纪晚期和二叠纪晚期，由于维管植物的兴起和广阔的煤沼泽中有机物质的广泛掩埋，O2 比以前高。晚二叠世 O2 的大量减少可能是由于煤沼泽的干涸和大部分总沉积物沉积在无 C 和 S 的大陆红层中。敏感性研究表明，影响结果的主要参数是煤盆地中的平均 C 浓度以及年轻（快速回收）与老岩储层的相对大小。发现对经历风化的陆地总面积随时间的变化以及使用直接 O2 负反馈对海洋碳埋藏的敏感性较低。通过我们的模型和基于使用稳定碳同位素的独立模型计算出的 C 埋藏率具有良好的一致性，这表明导致大气 O2 水平（以及溶解无机碳的同位素组成）变化的主要因素在海水中）在显生宙时期是沉积而不是风化或高温现象，如玄武岩-海水反应。发现经历风化的陆地总面积随时间的变化以及使用直接 O2 负反馈对海洋碳埋藏的敏感性较低。通过我们的模型和基于使用稳定碳同位素的独立模型计算出的 C 埋藏率具有良好的一致性，这表明导致大气 O2 水平（以及溶解无机碳的同位素组成）变化的主要因素在海水中）在显生宙时期是沉积而不是风化或高温现象，如玄武岩-海水反应。发现经历风化的陆地总面积随时间的变化以及使用直接 O2 负反馈对海洋碳埋藏的敏感性较低。通过我们的模型和基于使用稳定碳同位素的独立模型计算出的 C 埋藏率具有良好的一致性，这表明导致大气 O2 水平（以及溶解无机碳的同位素组成）变化的主要因素在海水中）在显生宙时期是沉积而不是风化或高温现象，如玄武岩-海水反应。