Correlation of Middle and Upper Ordovician Rocks Of Estonia Using Constrained Optimization

Introduction1. Fundamental to the understanding and inquiry of geologic history, the geologic time scale provides a framework for putting geologic evidence into a precise temporal context. The modern time scale is built of successions of fossil organisms through time. This succession puts corresponding rock units into a temporal context. 2. Fossils that are especially conducive to time scale applications are called index fossils. Good index fossils possess a number of characteristics including short stratigraphic ranges, rapid morphological change over time, widespread distribution and good preservation potential. (pic of index fossils)

3. Index fossils allow the time scale to be applied to local section with high precision. The interpretation of age relationships between sections or to the time scale is called correlation.4. Index fossil data from 4 Estonian drill cores was used to generate a solution.

ObjectiveThis project conducted a computer based analysis

called constrained optimization to generate a high resolution interpretation of correlation between northern and southern Estonian sections. The resulting solution is used to better understand the geologic and stratigraphic relationships

Research Questions1. Do the Estonian stage boundaries represent real cronostratigraphic horizons? 2. What fossil groups appear to provide the best biostratigraphical information?3. Based on microfossil correlations, what can we say about gaps in Estonian sections?

Methods: Constrained OptimizationTraditional correlation methods: integrate data one section at a time to develop an increasingly complete composite section. (subjective and difficult to repeat)

Constrained optimization approaches the problem from the opposite direction 1. Constraint: define the parameters of solutions that are possible. 2. Optimization: find a solution that best fits the data using a probabilistic search algorithm.

Simplified analogy for constrained optimizationFinding the solution that best fits the data is like fitting a line to a scatter of points. (Kemple 1995) If we consider a graph of all possible lines where x is slope, y is intercept and z is a quantity representing the level of fit then the goal of the search is to move to the lowest point on the graph

Greg Miller and Dan Goldman PhD. Department of Geology, University of Dayton

Conclusions1. Gaps: compared to the synthesized

composite section the Tartu and Taga-Roostoja cores have significantly more gaps than their southern counterparts and gappiness increases up section.

Kemple, William; Sadler, Peter; Strauss, David. Extending Graphic Correlation to Many Dimensions: Stratigraphic Correlation As Constrained Optomization. SEPM Special Publication No. 53 1995

Fig. From Kemple 1995

2. Upper Ordovician stage boundaries are nearly synchronous wheras middle Ordovician stage boundaries tend to vary significantly.

1.Ruhnu2.Valga3.Taga-Roostoja4.Tartu

Locations of Estonian Drill cores

Are the stage boundaries synchronous?Relaxed fit curves map out the interval through which the events fit the solution equally well. U shaped curves show how well each event is constrained by the data

Left: A well constrained event, Above: A poorly constrained event

By plotting each local stage boundary separately we can compare their positions in the composite

By comparing local sections to the best fit composite section, we can interpret precise age relationships between local sections. This information allows one to:1. Assess to what extent the Estonian stage boundaries are actually synchronous2. Locate rocks of identical age in multiple sections3. Identify gaps in local sections4. Draw conclusions about regional environmental and sea level changes

Results

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References32