Approaches to Geometric models

• Fixed depositional geometries are assumed

• Conservation of mass • Simple computations through general

nonlinear dynamic models • Variations in depositional geometries• Variations in surface slope vs discharge • Rigid Model with simplest geometry ,

horizontal plane at sea level.

2D Rigid –Lid Model (Geometrical Model)

Sketch showing the stratigraphic effects of two scenarios for time change on flexural rigidity at basin margin

a) Onlap associated with increasing rigidity due to cooling

b) Off lap associated with decreasing rigidity due to long term viscoelastic relaxation

2D Rigid – Lid Model Strata relation can be investigated by using 2-D subsidence

models particularly when flexural effects are included.The effect of variable rigidity is important to stratigraphic modeling because it could easily be misinterpreted as being caused by sea level change.Oceanic lithosphere tends to stiffens (increase in lithosphere flexural rigidity) as it cools.For passive margins, this increase in rigidity causes the flexture at the margins to widen with time, producing stratigraphic onlap(fig.1a)The opposite effect-stratal offlapping of the basin margin- can be produced by viscoelastic behavior of the lithosphere.

(Geometrical Model)

1-D Geometric modelfor carbonate platform

The depth control of carbonate sedimentation makes it possible to model carbonate sedimentation in 1-Dimension.

The fact that many shallow water platform sequences are laterally continuous but shows rapid vertical variation makes it to do 1-D geometrical modeling.

The models explains the carbonate sequence in terms of superposition of cyclical eustatic force and depth dependent sedimentation.

Carbonate platforms also shows significant lateral variation , particularly near the margin.Two dimensional model have been accounted for such features by including geometrical treatment of sediment redistribution by physical transport.The strong depth dependence of carbonate platforms tends to produce steep edged platforms (fig.2).Strong offshore transport by physical process reduces this sharpening tendency leading to ramp rather than platform geometries.Progradation of carbonate platform by physical transport produces clinoforms whose shape is related to the interplay of eustasy,transport and subsidence.

Figure 2.

Fig2Carbonate stratal geometry produced from various models under various scenarios.In each case variable being changed between the left image and the right image is given on the far right along with (italics)the imposed forcing.The continuous lines are equally spaced time lines. where an additional variable has been mapped onto the time lines it is shown in grey with a relative scale bar below.A. effect of changing subsidence rate b.Effect of changing amplitude of sea level fluctuation(Bice,1991)c.Effect of changing amplitude of sea level fluctuation(Read et al)d.Effect of changing amplitude of sea level fluctuation(Spencer anD Demicco,1989)Sawteeth indicate sub aerial exposures e.Effect of changing carbonate production rate (Bosence et al.)f.Effect of changing water base (Bosence et al.)

2-D geometrical model for clastic and mixed sediments

Comprehensive two-dimensional for clastic sequence stratigraphy has been described by Jervey(1988) and Ross et al.(1995)The Ross et al model for clastic sediments focussed on partioning mud and sand among fluvial, shelf and turbidities systems and stands out as first to separate the shoreline from the shelf break.Both papers shows how a geometrical model based on sea level, sediment supply and subsidence can be used to reproduce pattern in both lithostratigraphy (fig.3) and time- space diagrams(fig.3).The Jevrey”s approach was adopted in the SEDPAK model.SEDPAK is for both clastic and carbonate sedimentation. it is biased toward sediment rather than subsidence. In sediment column it includes the compaction along with deposition in fluvial,clastic shelf, carbonate shelf, continental slope, and deep marine environment.Because of the many geometric parameter ,SEDPAK requires a good deal of input from user and is highly tunable.

Fig3 A catalogue of clastic stratal geometries produced using geometric models under various scenarios.Layout,disclamer and explanation are the same as for fig.2 (e)effect of changing amplitude of sea level cycle (f)effect of changing sediment supply(g)effect of changing relative phase of sediment-supply and sea level cycles.

Advantage of using SEDPACK: In comparison with seismic stratigraphy of the great Bahamas Bank (fig 4) SEDPAK reproduces a major feature of the observed section using the Haq et al .(1987) sea level curve and reasonable parameter values.SEDPAK is a simulation rather than an analytical model. It is a very flexible tools for converting ideas about depositional geometry and external forcing into stratigraphy. In this regards it is useful as a way of systemizing and refining conceptual sequence-stratigraphic model.

Fig 4.

CONCLUSION OF GEOMETRIC MODELLINGGeometric models estimate maximum rates of change in the three controlling variables sediment supply, subsidence, and sea level

Combining these with other limits derived from field observations, we can plot a solution set to define the most likely range of variations in these three primary controls on shoreline migration.

This approach shows the amount each controlling factor must change alone, or in concert, to account for the stratigraphy..

Although a unique solution may not be available, we can calculate the required parameters for the observed shoreline migrations, which provide a basis for informed interpretations.

REFERENCES1. Sedimentology: Millenium Reviews - The Journal of the International ... By Jim Best, C. R. Fielding, Ian Jarvis, Peter Mozley2. Sedimentary basins: evolution, facies, and sediment budget By Gerhard Einsele