Correlation of Middle and Upper Ordovician Rocks Of Estonia Using Constrained Optimization Introduction 1. 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. Objective This 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 Questions 1. 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 Optimization Traditional 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 optimization Finding 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 Conclusions 1. 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 Fig. From Kemple Upper Ordovician stage boundaries are nearly synchronous wheras middle Ordovician stage boundaries tend to vary significantly. 1.Ruhnu 2.Valga 3.Taga-Roostoja 4.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 synchronous 2. Locate rocks of identical age in multiple sections 3. Identify gaps in local sections 4. Draw conclusions about regional environmental and sea level changes Results 3 2 References 3 2