There are lots of different possibilities. The most used one, I think, are isotopical studies.
This is a good start to begin with that topic:
https://en.wikipedia.org/wiki/Radiometric_dating#Modern_dating_methods
You can also use different stratigraphic principles like event chronology, warve chronology or tephrochronology.
Another possibility is fission track analysis.
Another way may be the biostratigraphy. If you can collect fossils from rocks, you can give a relative age of rock.
Surely not a clear age but if you can use macrofossil you may give the age directly on the field.
In many cases a sure correlation between bioevent and chronological age is possible to do.
A rock can be dated either by relative method or absolute method.
A relative age is the age of a fossil organism, rock, or geologic feature or event defined relative to other organisms, rocks, or features or events.
Paleontological and biostratigraphic correlation methods are common relative dating methods.
Moodern correlation technologies include use of marine stable isotope records, paleomagnetic dating, tephrachronology, geomorphological methods, sedimentation characteristics, and other geochemical and radiometric methods.
Young deposits can be sometimes dated using tree rings, varved-lake sediments, coral growth patterns, and other methods.
Absolute ages can be obtained by 40-K/39-Ar, 40-Ar/39-Ar Geochronology, Uranium Series Methods, Lead-210 Geochronology, Rb-Sr SYSTEM, Sm-Nd SYSTEM, Radiocarbon Geochronology, Fission-Track Geochronology and Luminescence Geochronology
But before dating by these methods we have to see the system is a closed system.
The presence of particular mineral bearing these elements should be present in the rock without any alteration in sufficient quantities to separate it for dating.
Dear Ebrahim: your questions has been already answered by several colleagues, however I must point out two things. First, fossils can only give relative ages, I usually tell my students this funny analogy: Dinosaur bones don't have a tag attached saying "I was born 75 Ma ago!"... So to calibrate relative paleonthologigal ages, and also paleomagnetic time scales, one should have in the first case, a basin which, at the same time, is fossil-rich and has interestratified volcanic tuffs, lava flows or sills, and in the second case, a complete sequence of lavas showing several paleomagnetic inversions, such as MORB lavas or plateau basalts. These fossil+igneous basins could be rift basins, fore-arc or back-arc basins. The igneous tabular bodies present in them can be dated (usually in bentonites from weathered rhyolite tuffs, basalt flows, or diabase sills), and help to give upper and lower age limits to the fossil bearing strata linked to them. And second, that the so called absolute age of a rock has been substituted by a quite more realistic term as apparent age. This is because of what Asoori stated: rocks can be affected by many alteration processes, from metamorphism to hydrothermal alteration to weathering, that isotopic systems can be severely altered and give apparent ages which are not the real crystallisation or metamorphism ages. Systems with soluble cations, such Rb-Sr, and K, or with radiogenic gases, such as Ar, are easily modified by these secondary processes. Therefore the best methods used nowadays for primary crystallisation ages of igneous and metaigneous rocks are those effected in zircon crystals. Zircon, being a mineral resistant to secondary alterations, usually holds the true isotopic content reflecting the radioactive decay of U isotopes to Pb isotopes. It is a sort of miniature "time capsule", whose zoning can even record several successive orogenic or thermal events. Other methods of dating involving inmobile trace elements are: Sm-Nd, Lu-Hf, and Re-Os, applicable to specific rock types, and even to some Cu or Pt ores.
In Paleozoic granites of the Coastal Cordillera of Venezuela K-Ar method in biotite calculated 30 years ago gave quite "young" ages of 33 Ma; 20 years ago Rb-Sr isochrones gave quite "old" ages of about 404 Ma; but more recent U-Pb ages in zircon (LA-ICP-MS) gave even older ages, reaching to almost 500 Ma. It's a difference of almost 100 Ma, quite significant, indeed. The young Tertiary age has been interpreted as the orogenic uplift age, the oldest age, 495 Ma as the crystallisatin age of the plutons, so the 404 Ma Rb-Sr age was an apparent age, which really doesn't relate to either event! Therefore, hydrothermal and/or low metamorphic grade alterations have happened in these rocks disrupting somehow the Rb-Sr isotopic system. That's why absolute ages are no longer called such, they are apparent ages. With regards. Sebastian.
Hii dear,, Simply age of the Rock can be dated by Radio-active isotope method, in which parent element decays to stable daughter elements.There are different radio-active method, to know the age of different rocks, such as U-Pb, Sm-Nd, Rb-Sr and etc.
Dear Ebrahim,
Your question covers each rock type. Igneous and metamorphic rocks, will likely not contain fossils. You must use the radiometric methods while being cautious of remobilizations/ recrystallizations and relics in metamorphic rocks thereby confusing the inexperienced.
For sedimentary rocks there are fossils, macro and micro. Fossil evolutions and extinctions were tied to numerical ages because fortunately, sediments do occur interlayered with extrusive igneous rocks that were dated using radiometric methods. They are the invaluable index fossils.
One cannot use the physico-chemical method on clastic rocks either, because they come from various sources that may not be of the same age; while the clasts carry the age of their parent source, the cement are diagenetic i.e. post depositional. Thus the methods tend to be mutually exclusive between igneous/metamorphic and sedimentary.
Fossil dating or biostratigraphy is not inferior to the physical/chemical daring results when one considers the years of uncertainty involved in the standard deviation of statistics.
Fossil dating is simply so very cheap and fast that it cannot be ignored and some fossils have quite high-resolution which one cannot obtain in the physico-chemical methods. Some rocks can be dated even out in the field based on fossils.
Finally, you can see that how to obtain the age of a rock depends on the type of rock, and the cost implications.
All the best.
Obianuju P. Umeji
I feel there is one big misconception here, which is that fossils would yield only relative ages. This is not true. If you have an age for fossils, you can quite accurately determine the age of units or formations that have formed within the occurrence of two index fossils, or if they contain an index fossil.
Relative dating only means that you can establish (in the field) that one lithologic unit has formed earlier or later relative to the adjacent lithologies. If you have a predetermined absolute age for those adjacent lithologies, you can also give an age for the lithologic unit in question, although the deviation is linked to the determined age of the fossils.
Dear Tilman: Suppose you have a fossil-rich bed, containing index fossils, and below and of top of it you have rhyolitic tuff beds. How can you assure that the fossil has the same age of the tuffs? There's always going to be a lag between the ages, unless the fossil is in one of the tuff beds! So, even the best "dated" index fossil always gives you a quite large age "range", a lot larger than the error inherent in the U-Pb method in zircon, which with the recent techniques is becoming everyday less.
Also, let me point out to Obianuju statement: some low or very low grade metamorphic rocks (metapelites, metacarbonates and metacherts) can contain identifiable fossils, usually somewhat deformed, which could give good approximations to their ages.
Regards ro both, Sebastian.
Dear Sebastian: The point I'm arguing is not whether one method is suited better for dating than the other. My argument is that the definition of absolute and relative dating is stated wrongly. Dating with index fossils will always yield absolute (or apparent) ages, even if it results in a 100 Ma uncertainty. But let's take at look at your proposed example with the index-fossil-bearing layer within tuff beds: of course you can only say that the tuff beds are either older or younger relative to the index-fossil-rich layer. Now, let's say we have sedimentary layers, and in between a tuff bed, on which we have done U-Pb dating in zircons. So also in this case we will only get relative ages for the sedimentary layers, even though we used an isotope-based method!
Dear Ashkan: Yes, I understand it the same way. But I really believe it is wrong as to what the term relative age conveys.
Dear Tilman: let's go back to the example of a fossil rich bed between a lower and an upper tuff bed, of Jurassic age. Both tuff beds will give apparent ages with a degree of error, always. Let's suppose the lower bed gives a U-Pb in zircon age of 156 +-5 Ma, and the upper tuff gives an age of 145 +-6 Ma, very precise results obtainable nowadays with TIMS or LA-ICP-MS methods in zircon crystals. Which is then the "age" of the fossil bed, and that of its possible index fossils? The only thing that all these dating will provide us is a reasonable RANGE in the age of the fossil bed, it is not a relative age, since it is given in Ma, not in stages, or other biostratigraphical units. But it is not an "absolute" age either, since it has a noticeable range of uncertainty! We geologist can only deal with apparent ages, this is always going to be our limitation, and we must learn to cope with it! Regards. Sebastian.
Dear Sebastian: I agree with that. But remember that also U-Pb in zircon only yield a RANGE within the uncertainty (let's forget about standard deviation and confidence interval for now). Now, let's turn your example around: assume we have a lower and upper bed with index fossils (150 +-20 Ma and 120 +-10 Ma, respectively). Yes, the accuracy is much worse than with U-Pb dating, yet we have an apparent range. So, we do have used fossil records for dating here, yet it is not relative age!
Dear Tilman: Surely is it not a relative age, even with an uncertainty from 170 to 110 Ma (60 Ma, almost the whole Tertiary Period!), due to error ranges and the like, it is a NUMERICAL age range that the fossils give us! So it really is an apparent age, callibrated in other world localities through radiometric dating of igneous extrusions! Relative ages are named by WORDS, stages, epochs, periods, not by numbers in Ma. Right? So the controversy is settled. With regards, Sebastian.
It's not nice to answer a question with another question, but what rock?