Basin Histories and Properties

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Geohistory, Backstrip Diagram Corrections

To apply eustatic corrections we need a curve that shows the elevations of sea level relative to a fixed reference elevation during the time span of the analysis. We can use the elevation of sea level at present or at a particular time in the past as a reference elevation. Eustatic curves showing absolute sea level through time are not available for much of geologic time, because absolute magnitudes of eustatic variations are poorly known. Instead, we use relative sea-level curves, such as the Haq et al. (1987) curve. Until an absolute eustatic curve becomes available, relative sea-level curves that have been calibrated to a fixed reference elevation provide the most adequate substitute.

To correct a geohistory diagram for eustatic variations, we subtract the magnitude of eustatic rise (or add the magnitude of eustatic fall) to the waterdepth corrected depth of each stratigraphic unit (Figure 1, Correction of units in a geohistory diagram for eustatic variations.

Correction of units in a geohistory diagram for eustatic variations, Basin Histories and Properties, Basin History, Sedimentology, Geohystory — **FIGURE 1** Correction of units in a geohistory diagram for eustatic variations

W_d is water depth at time T₂ during deposition of Unit 2. ΔSL is the magnitude of eustatic rise at time T2 measured form a fixed reference elevation. ΔSL is positve for a eustatic rise and negative for a eustatic fall. On the left column, depth to Unit 1 at time T2 in a relative reference frame, Z_r, is measured from the elevation of eustasy at time T2. In an absolute reference frame, Z_r is equal to the sum of ΔSL and the depth to Unit 1 in an absolute reference frame, Z_a, using Equation 1.

$Z_a = Z_r - \Delta SL$ $\quad$ (1)

where:

Z_a= the depth to a unit in an absolute reference frame

Z_r= the depth to a unit in a relative reference frame, and

ΔSL = the magnitude of eustatic rise

Z_r equals the water depth corrected depths of stratigraphic units. ΔSL is positive for a eustatic rise and negative for a eustatic fall.

To correct a water-filled backstrip diagram for eustatic variations, we must remove the eustatic component of loading, and we must calculate the lithospheric response to the change in load using an appropriate compensation model. In the case of eustatic rise, we subtract the thickness of the water column due to the rise, and then calculate uplift due to removal of this water load Figure 2, Correction of water-filled backstrip diagram for eustatic variations using an Airy compensation model.

Correction of water-filled backstrip diagram for eustatic variations using an Airy compensation model, Basin Histories and Properties, Basin History, Sedimentology, Geohystory — **FIGURE 2** Correction of water-filled backstrip diagram for eustatic variations using an Airy compensation model

Z_r is the depth to basement for a water-filled backstrip diagram with a relative reference frame. Z_a is the eustasy-corrected depth to basement for a water-filled basin with an absolute reference frame.). In the case of an eustatic fall, we add the thickness of the water column lost due to the fall, and then calculate the depression due to addition of this water load. Depth to basement, in an absolute reference frame, Z_a, equals

$Z_a = Z_r - \Delta SL - w$ $\quad$ (2)

where:

Z_r = depth to basement in a relative reference frame, and

w = uplift due to removal of the water load

For calculating a eustasy-corrected subsidence curve, Z_r equals depth to basement corrected for removal of sediment for a water-filled curve. The uplift due to removal of the load of a eustatic rise assuming a water-filled basin is:

$w = \dfrac{\rho_w}{\rho_m - \rho_w}\Delta SL$ $\quad$ (3)

Substituting Equation 3 into Equation 2 gives an expression for depth to basement for a water-filled basin:

$Z_a = Z_r - \dfrac{\rho_w}{\rho_m - \rho_w}\Delta SL$ $\quad$ (4)

Substituting Equation 7 into Equation 4 gives a more complete expression for depth to basement in a water-filled basin:

$Z = W_d + \dfrac{\rho_m - \rho_s}{\rho_m - \rho_w}\cdot t_s - \dfrac{\rho_w}{\rho_m - \rho_w}\Delta SL$ $\quad$ (5)

Geohistory diagrams illustrate the stratigraphic and tectonic history of a section of sedimentary rock, and show process/response histories in a continuous time frame, rather than only in the physical dimension of depth or stratigraphic thickness. In contrast, unconformities and depositional hiatuses are represented by intrastratal surfaces rather than by strata. Therefore, where an unconformity is present within a stratigraphic column, we must model the rise and fall of earlier stratigraphic units and surfaces during the time not represented by rock. To reconstruct the stratigraphic history during the time span represented by an unconformity, we must first infer the processes that formed the unconformity, and second, determine the rates, magnitudes, and timing of the responses to those processes.

Unconformities are formed by three general processes: 1) non-accumulation of sediment by sediment bypass; 2) non-accumulation by sediment starvation; or 3) loss of previously deposited sediment mass by subaerial or subaqueous erosion. The different types of unconformities show different thickness and elevation changes of stratigraphic units and surfaces on geohistory diagrams as seen in (Figure 3).

The different types of unconformities, Basin Histories and Properties, Basin History, Sedimentology, Geohystory — **FIGURE 3** The different types of unconformities

Each diagram has an absolute reference frame, and thickness changes due to compaction are not illustrated. Time increases to the right, equivalent to previous geohistory displays with age before present increasing to the left. The dashed lines delineate the time span of section not represented by rock, Δt. T_b is the time of deposition of the youngest preserved sediment below the unconformity, T_t is the time of deposition of oldest preserved sediment above the unconformity, and T_o is the time that sedimentation was initiated. The lines labeled “Base” and “Top” depict elevation changes of the base and top of the stratigraphic column through time. A dashed line marks the top of the stratigraphic column that has been eroded. Within the preserved and eroded stratigraphic column, several “time lines” show elevation changes of sedimentary units within the column. The area below the base of the column is shaded to depict basement movements of subsidence and uplift caused by tectonic and surface loading. The area above the top of the column is patterned to depict processes controlling changes in the sediment-air or sediment-water interface such as sedimentation, erosion, or sediment bypass. Each diagram has an equivalent preserved sediment record, but accumulation histories differ during the time span of unconformity formation due to different processes of unconformity genesis: [a] unconformity caused by base level fall; [b] unconformity caused by tectonic uplift; [c] hiatus caused by sedmient bypass [non-deposition] We must determine which processes occurred because the elevation changes and thicknesses of eroded sedimentary units can influence the results of thermal maturation, decompaction, and tectonic subsidence calculations.

The processes that form an unconformity may act singularly or in combination. Previously deposited sediment may be eroded either when base level falls (Figure 3 [a] ), or when tectonic uplift occurs (Figure 3 [b] ). If there is neither erosion nor deposition, a hiatus forms due to either sediment bypass or sediment starvation (Figure 3 [c] ). As illustrated in Figure 3 , the base of a stratigraphic column changes elevation due to tectonic or surface-load induced subsidence or uplift; basal movements indicate long-term changes in accommodation space. The top of a stratigraphic column changes elevation due to the addition or removal of sediment in response to changes in base level or accommodation space. During the time span of the unconformity, Δt, elevation changes at the top and base of a stratigraphic column and the thicknesses of eroded sediment are depicted differently for different processes of unconformity formation.

Because there is no preserved section associated with the time of unconformity formation, we have no direct measure of how the unconformity formed. The signature of preserved sediment encasing an unconformity on a geohistory diagram (e.g., T_o < time < T_b and time > T_t) is non-unique with respect to the processes which formed the unconformity. Consequently, we must infer the processes of unconformity formation from other data such as stratigraphic sequences, depositional systems, successions of depositional systems, geothermometers, and tectonic histories.

We then plot the sediment accumulation history on a geohistory diagram using estimates of timing and magnitudes of deposition, non-deposition and erosion of any strata missing at the unconformity surface. Which portions of the time span of the unconformity were depositional, erosional, and non-depositional? Did tectonic uplift occur, and if so, was erosion initiated synchronously with uplift? Was there a time lag between uplift and initiation of erosion? How much sediment was deposited and then eroded? We can best answer these questions by using a sequence-stratigraphic framework to predict which facies and succession of facies may have been deposited and later eroded. The portions of time represented by deposition, non-deposition and erosion depend on geographic position with respect to a base-level transit cycle (Figure 4, Wheeler diagram of a base level transit cycle, or a rise and fall of base level.

Wheeler diagram of a base level transit cycle, Basin Histories and Properties, Basin History, Sedimentology, Geohystory — **FIGURE 4** Wheeler diagram of a base level transit cycle

Position of sediment column of Figure 5 is shown and Figure 5, Geohistory diagram including an unconformity caused by a fall in base level [Figure 4].

Geohistory diagram including an unconformity, Basin Histories and Properties, Basin History, Sedimentology, Geohystory — **FIGURE 5** Geohistory diagram including an unconformity

Key for shading is shown in Figure 3 [c]. t_s is the total thickness of sediment previously deposited, but eroded during base level fall. The bypass line is the line of no net accumulation that is preserved. This line parallels movements of the base of the column, assuming no thickness changes due to compaction.). For example, as the position of the stratigraphic column moves further landward, the duration of time represented by erosion increases.

A sequence-stratigraphic framework constrains estimates of depositional environments and duration of erosion and, therefore, constrains estimates of magnitudes of accumulation and erosion during the time span of the unconformity. The magnitude of accumulation during the unconformity equals the maximum thickness of eroded sediment above the bypass line (t_s, Figure 5). The rate of accumulation during the time span of the unconformity equals the rate of increase of column thickness above the bypass line. Similarly, the magnitude of erosion equals the maximum thickness of eroded sediment above the bypass line, and the rate of erosion equals the rate of decrease of column thickness above the bypass line.