3.05 Sea Level

This section describes how SEDPAK represents and manipulates sea level fluctuations. The simulation characterizes sea level variation as a single composite curve. This curve may be generated from: 1) digitized data sets; 2) sinusoidal and/or sawtooth data sets; or 3) a combination of 1 and 2. The resulting composite sea level curve is generated from the sum of several sets of linear time-depth pairs, allowing some flexibility in the manner that the program handles eustasy. For example, Milankovitch cyclicity can be superimposed upon the Haq et al. (1987) curve.

Inputs: Sea Level

Input for each of the digital values is a time-depth pair. Figure 3.5.1 depicts the inputs required to set up the digitized linear components.

SEDPAK fits each set of pairs with a piecewise linear curve z(t) as depicted in Figure 3.5.1. Sinusoidal and/or sawtooth curves may also be entered using the calculator (see Section 2.12).

Discussion: Sea Level

Construction of curves is accomplished by selecting Digitized Curves from the Sea Level menu on the SEDPAK EDIT panel. The plotter for Sea Level (Figure 3.5.2) is used in the standard manner described in Section 2.10. The vertical axis of the graph on the sea level plotter is depth in meters or feet, and the horizontal scale is time in millions of years. The sea level position is delimited as a series of piecewise straight lines connecting time-depth pairs. The data points can be selected and dragged to new locations on the graph, thereby changing the sea level position, and their entry on the data sheet, or the locations can be entered by typing the values on the data sheet. Figure 3.5.3 shows a data sheet for a digitized sea level curve similar to those shown in Figure 3.5.2.

More than one digitized sea level curve may be defined using the New Curve or Copy Current Curve pull-down menu under Curve. An identifier (Curve ID which is a unique real number) must be assigned to each sea level curve.

Cyclic curves are constructed using the Cycle Description on the calculator (see Section 2.12) and the data sheet. The data sheet is invoked by selecting Cyclic Data from the Sea Level pull down menu on the sea level plotter. The Create Range button is depressed and a range of data values is entered on the data sheet using the Create Range dialog (Figure 2.11.2, and see Section 2.11). The columns of data on the data sheet are selected and the calculator is used to produce sine or sawtooth curves (see Section 2.12) with the Cycle Description dialog (Figure 2.12.2). Cycle Period, Amplitude, Phase and Damping values are entered on this dialog and then Applied. The purpose of this type of entry is to reproduce the sea level responses that Milankovitch and others have ascribed to planetary orbital behavior. There is no limit to the number of curves that may be entered to the sea level plotter. It is important to ensure that the period of the sea level curve does not exceed the time resolution defined by the number of time steps and the start and end times of the simulation (see Section 1.11 on aliasing). NB: It is necessary to give all digitized curves an ID number greater than that of the last cyclic curve.

The cyclic curves created on the sea level plotter may be viewed and edited. Figure 3.5.2 displays both an example of a cyclic curve which was specified on the cycle description portion of the calculator and a digital curve.

The resulting composite sea level curve produced by the summation of these two curves may be viewed by selecting Composite Curve from the Sea Level pull down menu (Figure 3.5.4). There is no capability for interactive modification of the composite curve, as the plotter for the Composite Curve is for viewing purposes only. The generation of a composite curve requires the definition of at least two curves. A composite curve from one sea level curve alone can be displayed but has little meaning.

A final note of caution: when running the program with clastic sediment deposition, sea level for each time step must intersect the evolving initial basin surface somewhere within the cross section. If a shoreline is not present, a Shore Error will occur. This problem can be avoided by setting clastic deposition to zero for the side of the basin which lies above sea level, and for the time interval during which the Shore Error is produced. Similarly, remember that aliasing may occur if the frequency of the sea level time-depth pairs exceeds the number of time steps specified in the Setup dialog (see Section 3.3).

The actual values used to specify sea level behavior are a matter of choice. An extensive discussion on the geological evidence for eustasy can be found in Burton et al. 1987. Values provided by the Haq et al. (1987) Tertiary and Mesozoic sea level curves can be entered directly into SEDPAK. For several stratigraphic sections from the Paleozoic, we have in the past used a combination of our own intuition and curves by Vail et al. (1977), and Ross and Ross (1987) and (1988). We have included these curves in some of the Benchmark files.

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3.06 Subsidence

This section deals with tectonic movement in the vertical plane, representing either subsidence or uplift.

Inputs: Regional Subsidence/Uplift

Subsidence behavior can be determined from burial and crustal subsidence curves or from seismic data and can be input directly into the simulation. Subsidence points are entered in the same manner as the initial basin surface and sea level points. The editor is set up to enter a subsidence curve at a particular location. Locations where the rate of subsidence changes can be defined to create a series of subsidence curves across the basin.

To enter subsidence data, select Subsidence from the SEDPAK EDIT menu. The resulting pull-down menu has two options: View curves and View table. Select View curves to access the plotter (Figure 3.6.2) for editing particular curves. The curve, listed by location, is selected from a list at the bottom of the Subsidence plotter. Select View table from the pull down menu to display a summary table (Figure 3.6.4) which lists subsidence rates as a function of time for all locations across the basin. This table cannot be edited.

As an example of data entry under Subsidence, consider a 250 km shelf-to-basin section with clastics entering the basin from the right. First, the anchor points (points which are to be held stable throughout the simulation) created for the initial basin surface must also be represented as points on the subsidence curve. Each anchor point must be given a subsidence rate of 0.0 m/ka throughout the run. Because clastics are entering the basin from the right in this example, a subsidence location must be set at 250 km, i.e., the right-hand side of the basin. This is done by selecting New Curve on the Curves pulldown menu on the plotter. A data sheet (similar to Figure 3.6.3) is displayed when New Curve is selected. The location (in km across the basin) must be entered in the text area labeled Curve location at the top of the data sheet. In this example, 250 is entered instead of 147.4. Then the time-rate pairs are entered into the corresponding cells of the data sheet as (-215.0, 0.0) and (-113.0, 0.0) to anchor this point throughout the simulation. This keeps the basin surface from sinking below sea level and causing a Shore Error. Note that only two time-rate pairs are needed to anchor this location though several may be provided.

As with other parameters, the program linearly interpolates between the prescribed rates for particular times. Remember to consider time and space-aliasing problems. If time values or location values are too close together, then the program will read only one value and skip over the other(s). While the program does not handle flexure in response to sediment loading directly, the effects of flexure, if they are already known (as expressed by the subsidence behavior seen on a seismic line) can be matched by the subsidence history input to the program.

Discussion: Hinged Subsidence

If the basin is to subside about a point, this can be achieved by keeping one edge at a fixed subsidence rate while the other edge subsides at a different rate. The program interpolates linearly between these two rates. If it is necessary to add other subsidence locations, the hinged effect will be removed. This capability is perhaps of more interest to those wishing to experiment with hypothetical sedimentary models, but with "real-world" data, it is unlikely that the model will be successfully created.

Discussion: Faulting

Faults are modeled by assuming different rates of subsidence between two adjacent columns. The x-locations which have different rates of movement must be at least within a column width, as the program rounds off to the next adjacent column.

In order to simplify the computations involved with faulting, it is assumed that all faults extend to the bottom of the basin and only the vertical effects of faulting are modeled by the simulation (Figure 3.6.5). In general, the latter is a reasonable approximation within the simulation because vertical sediment geometries in the simulated section are measured in fractions of feet or meters, whereas horizontal distances are of the order of hundreds of feet or meters. For example, if the basin modeled is in reality 150 km wide, subdividing it into 300 equally spaced columns results in a column width of 500 meters. Therefore, for a horizontal dislocation to be large enough to cause significant changes, it would have to exceed 250 meters, or one half the column width. This simplification, while well justified for high angle faults, becomes less accurate for low angle or listric faults.

The data sources for the location and timing of faulting may be seismic cross sections, well data, outcrops, or a combination of these sources. As with the topography of the initial depositional surface, the problem is to extract this information from strata that may have been deformed by tectonic movement and compaction. The best approach is to use seismic lines tied to a well and determine the location and timing of faulting.

Subsidence is used to handle faulting in SEDPAK by simulating tectonic movement along the vertical plane. In order to cause faulting using Subsidence, first identify the location to be faulted. Subsidence points must be created at the columns on either side of each fault. The two points which identify either side of a fault should be set as close together as possible without causing a space-aliasing error, as described earlier. Subsidence points must be defined on either side of a fault because, without them, SEDPAK would interpolate linearly between the differing subsidence rates at the fault and the result would be more of a ramp.

Discussion: Backstripping Calculator

Subsidence curves may also be calculated from interpreted seismic and well data using the Backstripping Calculator. To use the calculator, select Subsidence from the SEDPAK EDIT menu, and then select View curves from the resulting pulldown menu. At the bottom of the plotter window is a button which activates the Backstripping Calculator. This is a data sheet entitled Backstripping Calculator (Figure 3.6.6). Each row on the data sheet represents a sediment layer, ordered from the top down as oldest to most recent.

When all the data are input, activation of the Apply bottom normalizes the data sheet (blank lines are eliminated, and various defaults are filled in), a new subsidence curve is created, and a dialog box which is used to locate the subsidence curve on the simulation cross-section is activated. The new subsidence curve may be edited on the Subsidence plotter and data sheets.

The Backstripping Calculator data sheet is subdivided into columns. The columns Bot (-Ma) and Top (-Ma) should match the ages in millions of years of the bottom and top of each layer, respectively. Thick (m) refers to the thickness of the layer in meters. Porosity refers to the present-day overall porosity of the layer. The Shale (%), Sand (%) and Carb (%) columns refer to lithology data for the layer. The PBath bottom (-m) and PBath top (-m) columns contain the paleobathymetry data expressed as meters below sea level. The left column is for paleobathymetry data from the time the layer is first deposited. The second column is for paleobathymetry of the depositional surface after the layer is deposited.

In certain cases, the program will fill in columns that are left blank. If the lithology data are left blank, 100% shales will be used as a default. Also, porosity can be calculated as a default, provided that lithology consists of 100% shale, 100% sandstone, or 100 % carbonates. (Porosity for non-monotonic lithologies cannot be calculated.) The age, thickness, and paleobathymetry information must be provided for the calculation to work properly.

Should it be necessary to save the Backstripping Calculator data sheet, press the Save button, and a dialog box in which the data sheet to be saved can be given a name and saved to an appropriate directory will appear. Should it be necessary to retrieve this file again for editing, this can be done by pressing the Load button at the base of the Backstripping Calculator data sheet. This activates a dialog from which the required Backstripping Calculator file can be retrieved and edited.

Chapter 3, Section 7

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