The Accommodation Space Equation

Over long time scales (105 - 108 years), sediment accumulation is strongly controlled by changes in eustatic sea level, tectonic subsidence rates, and climatic effects on the production of sedimentary grains. Several of these factors are linked to one another through the accommodation space equation. This balance of terms is most easily explained for marine sediments, but can be easily modified to include terrestrial sedimentation. A number of processes can cause the surface of the oceans to move up and down relative to the center of the earth. The distance from the sea surface to the center of the earth is eustatic sea level. In addition, the lithosphere can also move up and down relative to the center of the earth, and changes in the distance from some arbitrarily chosen reference horizon and the center of the earth are called uplift or subsidence. The distance between this reference horizon and the sea surface is called relative sea level or accommodation space.

Relative Sea Level

Acommmodation space can be filled with sediments or water. The distance between the sediment/water interface and the sea surface is known as water depth. The accommodation space not filled with water is filled with sediment. The rates of change of tectonic subsidence, eustatic sea level, sediment thickness and water depth are linked to one another through the accommodation space equation:

T + E = S + W

where T is the rate of tectonic subsidence, E is the rate of eustatic sea-level rise, S is the rate of sedimentation, and W is the rate of water depth increase (or deepening). These four variables are defined such that positive values correspond to tectonic subsidence and eustatic sea-level rise (factors that increase accommodation space) and sediment accumulation and water depth increase (factors that reflect filling of accommodation space). Reversing the signs of these variables accommodates tectonic uplift, eustatic sea-level fall, erosion, and shallowing of water depth, respectively.

The accommodation space equation represents a simple volume balance, with the terms on the left controlling the amount of space that can be occupied by sediments and water and the terms on the right describing how much water or sediment fills the accommodation space. As written, the equation is an approximation. In reality, sediment thickness and water depth must be corrected for compaction of sediments and for the isostatic effects of newly deposited sediment.

Through section measurement, changes in sediment thickness can be known, and through facies analysis, changes in water depth can be known or approximated. However, without outside information, the rates of eustatic sea-level change and tectonic subsidence cannot be isolated, nor can their effects be distinguished from one another for a single outcrop. In other words, there is no unique solution to this equation as it has two unknowns. Thus, it is impossible in most cases to ascribe water depth or sedimentation changes to eustasy or tectonics without having regional control or outside information. Backstripping is a method of analysis that iteratively solves the accommodation space to measure changes in relative sealevel through time. Although as pointed out earlier that no unique solution exists for this equation, solving it for relative sea level can provide useful insights into eustasy and tectonics. These data may then be used to date the timing of rifting and orogeny, to constrain estimates of lithospheric thickness, and to understand global CO2 cycles and global patterns of sedimentation.

Causes of Eustatic Sea-Level Change

Changes in eustatic sea level arise from either changes in the volume of ocean basins or changes in the volume of water within those basins. The volume of ocean basins is controlled primarily by the rate of seafloor spreading and secondarily by sedimentation in ocean basins. Because hot and young oceanic lithosphere is relatively buoyant, it floats higher on the asthenosphere and displaces oceanic waters upwards and onto continents. Older and colder oceanic lithosphere is denser, floats lower on the asthenosphere, and allows oceanic waters to stay within ocean basins. Long-term (102 k.y. - 105 k.y.) changes in the global rate of seafloor spreading can change the global average age and density of oceanic lithosphere, resulting in tens to a couple hundred meters of eustatic change. Filling of ocean basins with sediments derived from continental weathering is a relatively slow and minor way of changing ocean basin volumes and is capable of meters to tens of meters of eustatic change over tens to hundreds of millions of years.

The three most important controls on the volume of seawater are glaciation, ocean temperature, and the volume of groundwater. Continental and mountain glaciation is perhaps the most efficient and rapid means of storing and releasing ocean water. Due to Archimede's principle, ice caps over polar oceans do not affect eustatic sea level, so frozen seawater must be placed on a landmass to lower eustatic sea-level. Continental glaciation is capable of driving high amplitude (10 - 100 m) and high frequency (1 - 100 k.y.) eustatic changes. Because water expands at temperatures higher and lower than 4 degrees C, and because the depths of the oceans average around 5 km, small changes in the temperature of seawater can lead to significant changes in ocean water volume. Changes in water temperature can drive a few meters of eustatic change over short time scales (0.1 - 10 k.y.). Ocean water is continuously being recycled through continents as groundwater and surface water, such as rivers and lakes. Over relatively short time scales (0.1 - 100 k.y.), changes in the amount of water sequestered on the continents can cause up to a few meters of eustatic change.

Causes of Tectonic Subsidence

Tectonic subsidence is also called driving subsidence and is distinguished from the isostatic effects of sediment and water loads. Tectonic subsidence, as its name implies, is driven by tectonic forces that affect how continental lithosphere floats on the asthenosphere. Three main mechanisms that affect this isostatic balance and therefore drive tectonic subsidence include stretching, cooling, and loading.

Stretching of continental lithosphere in most situations results in the replacement of relatively light continental lithosphere with denser asthenosphere. The resulting stretched and thinned lithosphere sinks, causing tectonic subsidence. Stretching occurs in several types of sedimentary basins including rifts, aulacogens, backarc basins, and cratonic basins.

Cooling commonly goes hand-in-hand with stretching. During stretching, continental lithosphere is heated, becomes less dense, and tends to uplift from its decreased density (the net effect in a stretched and heated basin may result either in uplift or in subsidence). As continental lithosphere cools, it becomes denser and subsides. Cooling subsidence decreases exponentially with time yet can cause a significant amount of subsidence hundreds of millions of years following initial cooling. Cooling subsidence is especially important on passive margins and in cratonic basins.

Tectonic loading can also produce subsidence. The additional weight of tectonic loads such as accretionary wedges or fold and thrust belts causes continental lithosphere to sink, leading to tectonic subsidence. Because the lithosphere responds flexurally, the subsidence occurs not only immediately underneath the load, but in broad region surrounding the load. Tectonic loading is particularly important in orogenic regions such as foreland basins.

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