How do you calculate absolute dating
Geologists often need to know the age of material that they find. They use absolute dating methods, sometimes called numerical dating, to give rocks an actual date, or date range, in number of years. This is different to relative dating, which only puts geological events in time order. Most absolute dates for rocks are obtained with radiometric methods. These use radioactive minerals in rocks as geological clocks. The atoms of some chemical elements have different forms, called isotopes.
We have already discussed determining the relative ages of events. We will now discuss absolute age determination, which assigns a quantitative estimate of the number of years ago an event occurred. For a series of horizontal, depositional layers that are not overturned, the relative age of each layer with respect to the other layers may be known by invoking the Law of Superposition: Thus, in a series, the layers are successively younger, going from bottom to top.
What may not be known is how long ago in years or some other unit or units of time any of the layers formed their absolute ages. In some circumstances, the absolute age may be readily determined. Consider a flat-floored valley in which a river flows. On April 1, the river flooded diagram A. When the flood waters receded on May 1, , it was seen that a layer of sediment layer 'f' had been deposited on the valley floor diagram B.
Next year, on April 1, , the river flooded again, covering the valley floor. And once again, when the flood waters receded on May 1, , it was seen that another layer of sediment layer 'g' had been deposited on the valley flood diagram D. The flooding and deposition have occurred through the years on an annual basis, gradually filling the valley with a stack of layers a through g.
A pottery bowl was incorporated into the sediment at location X when layer 'c' was being deposited. On May 1, a farmer drilling a well discovers the pottery bowl. To calculate how many years ago the bowl was buried, the farmer counted the number of layers from the surface down to the layer in which the bowl was incorporated. The bowl is in the 5th layer beneath the surface.
Knowing that the depositional cycle is one layer per year, the farmer calculates that the bowl was buried four cycles before the most recent layer was formed. If the farmer had waited until October 1, to do the calculation, the time of the burial would have been 0. The formula for calculating absolute age of a layer by this method of counting is: If the duration of the cycle is not a constant, but durations of individual cycles do not vary very much, the average duration of the cycle may be used without losing much accuracy.
This simple counting method has been famously used for dating artifacts buried in the floodplain deposits of the Nile River. Before the completion of the Aswan High Dam in , a new layer of soil was deposited every year during annual flooding. To determine the age within one year of any layer, all that needed to be done was to count the number of layers down to the artifact and that was equal to the absolute age of the artifact's burial.
To get the age of the burial of an artifact, therefore, the time elapsed since has to be added to the number of layers. In , 36 years would have to be added. In actuality, the Aswan Dam was built in several stages, starting in , so the interval between deposition of the uppermost layers is actually irregular, voiding simple application of the formula. Photo by NASA.
In areas with glaciers, the ice undergoes melting every spring and summer. The meltwaters carry away sediment that was trapped in the ice. Where the sediment-laden meltwaters flow into a lake, a layer of sediment is deposited on the lake floor every year. Coarse sediment is deposited quickly; fine sediment remains suspended in the water until it has a chance to gradually settle out during the cold months when the surface of the lake is frozen over and the water is quiet. Each annual layer, therefore, has two parts: The coarse-fine couplet is known as a varve 'varv' is Swedish for 'layer'.
If the process of annual varve deposition continues today or only ceased in historic time, and the date of cessation was recorded, then simple counting can reveal the absolute age of any layer within the lake basin, using the formula developed above: However, deposition of varves may cease because the glaciers have melted away completely or because the lake basin has been completely filled by sediment. If annual deposits ceased before human records dating the event were kept, then the length of time that has elapsed since the top layer was deposited must be determined in some other fashion.
Correlation of time-equivalent layers may be accomplished by 'pattern matching'. It has been observed that in any given year , varve thicknesses vary from places to place. This is not surprising, since different meltwater streams carry different sediment loads. Also, in any given place varve thicknesses vary from year to year, being thicker when temperatures are higher and meltwaters are more voluminous and flow faster, and thinner when temperatures are lower and stream volume and velocity are diminished.
Such yearly changes in stream volume and velocity and thickness of depositional layers tend to be regional: Throughout the region, all layer thicknesses may be double what they were the year before. Through time, therefore, although layer thicknesses vary from place to place, the ratio of layer thicknesses to each other at one site are the same as the ratio of layer thicknesses to each other at a different site.
The diagram on the right shows varves that accumulated simultaneously during the same 8-year time interval at locations A, B, and C. Note that although the thicknesses vary from location to location, the ratios of thicknesses remain constant. At location A, from oldest to youngest, the thicknesses for the layers are 0. The ratio of the thicknesses is 5: That is, the pattern is the same at at the three locations. It is important to note that the pattern is random.
The position within the series of any layer, therefore, is unique. Layers formed at the same time, such as layer 'X', may be recognized. That is, equivalent layers may be correlated. Correlation using pattern matching makes it possible to determine, in a location where deposition has ceased, the absolute ages of the layers. This is accomplished by comparison with a location where annual deposition continues. Consider the varve sequences at locations A, B and C. At A, yearly deposition continues, so the absolute ages of layers can be determined by counting down from the top.
At locations B and C, deposition stopped at some time in the past. Indeed, some of the top layers may have been removed by erosion. However, by pattern matching, five layers within the series at A can be correlated with five layers at the top of B. Similarly, by pattern matching, five layers in the series at B can be correlated with five layers at the top of C. Since the ages of the layers at A are known by counting down from the top, layers at B that correlate with them can also be assigned ages.
Then, the ages of the rest of the layers at B may be determined by counting down. In similar fashion, layers at C that correlate with layers at B may be assigned ages, and the rest of the layers at C may be assigned by counting down. Using this method, ages of varves that formed tens of thousands of years ago may be determined. For example, varves close to forty thousand years old have been dated in Japan.
Pattern matching is also used to date trees by examining growth rings dendrochronology. Ages up to 14, years have been determined in this fashion. An archeologist finds a dried out, abandoned flood plain at location 'A'. He drills a hole and extracts a drill core that shows a series of layers of sediment one of which contains pottery fragment 'X'. The archeologist then contacts his colleague who is working in a nearby area location 'B' where there is a modern floodplain to which a layer of sediment is added every year.
He asks his colleague to extract and send him a drill core from location 'B', making sure to include and label the most recent layer, deposited in She does so, and also includes another drill core from a third location 'C', where she has recently worked. She tells him that location 'C', like location 'A', is also a dried out, abandoned floodplain.
The first archeologist wants to know in what year the layer containing pottery fragment 'X' was deposited. Question 1: In what year was the layer formed that contains pottery fragment 'X'? My answer to Question 1: The layer containing 'X' was deposited in: Indeed, dating of lake sediments using varves was undertaken as early as Their disadvantage is that they are restricted to sites where annual deposition has occurred and the absolute age of at least one layer can be determined with confidence by some other means for example, by counting or by pattern matching with places where annual deposition continues through to today.
Places satisfying these requirements are relatively few. Another disadvantage is that over geologic time, preservation of such layers is limited. Absolute age determination by varve counting is only suitable for materials less than several tens of thousands of years old. These limitations are overcome in radiometric dating. Radioactive elements, such as certain isotopes of uranium, thorium, rubidium, potassium, carbon and others, have the property that over set periods of time, known as their 'half lives' which are different for each radioactive element , half of their atoms decay to form atoms of different elements.
For example, over the course of million years, half the atoms of the 'parent' element uranium U decay to form atoms of the 'daughter' element lead Pb Over the next million years, half of the remaining U atoms change to Pb, and so on. By comparing the ratios of U to Pb that are found in the material today, the time when the process started may be ascertained see table below. Examples of radioactive parent-daughter pairs and their half lives include: U - Pb 4. An error of that magnitude may be quite acceptable for such old rocks.
After careful analysis, a geochronologist determines that an unweathered, unmetamorphosed mineral sample contains 7 trillion atoms of the radioactive element K and trillion atoms of its decay product A How many years ago was the sample formed? The number of years ago that the sample formed is: It is important to choose a radioactive parent-daughter pair whose half life is appropriate for the age of the material being dated. On the one hand, the half life should be short enough so that a measurable amount of the daughter element has formed.
On the other hand, if the half life is too short, the amount of parent element left may not be measurable. Thus, K-Ar dating would not be appropriate for a material that is 50, years old, as hardly any daughter element would have formed. Similarly, C dating is not be appropriate for materials older than about 70, years as the amount of the parent element left becomes too small to be measured accurately.
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During natural radioactive decay, not all atoms of an element are instantaneously changed to atoms of another element. The decay process takes time and there is value in being able to express the rate at which a process occurs. Half-lives can be calculated from measurements on the change in mass of a nuclide and the time it takes to occur. The only thing we know is that in the time of that substance's half-life, half of the original nuclei will disintegrate.
Radiometric dating , radioactive dating or radioisotope dating is a technique used to date materials such as rocks or carbon , in which trace radioactive impurities were selectively incorporated when they were formed. The method compares the abundance of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay.
We have already discussed determining the relative ages of events. We will now discuss absolute age determination, which assigns a quantitative estimate of the number of years ago an event occurred.
Despite seeming like a relatively stable place, the Earth's surface has changed dramatically over the past 4. Mountains have been built and eroded, continents and oceans have moved great distances, and the Earth has fluctuated from being extremely cold and almost completely covered with ice to being very warm and ice-free. These changes typically occur so slowly that they are barely detectable over the span of a human life, yet even at this instant, the Earth's surface is moving and changing. As these changes have occurred, organisms have evolved, and remnants of some have been preserved as fossils. A fossil can be studied to determine what kind of organism it represents, how the organism lived, and how it was preserved. However, by itself a fossil has little meaning unless it is placed within some context.
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Absolute dating is the process of determining an age on a specified chronology in archaeology and geology.
5.7: Calculating Half-Life
.Radiometric or Absolute Rock Dating