GEOL212 Due 10/9/17 Homework VI

Size: px

Start display at page:

Download "GEOL212 Due 10/9/17 Homework VI"

Ethan Carson
6 years ago
Views:

1 GEOL212 Due 10/9/17 Homework VI General instructions: Although you are allowed to discuss homework questions with your classmates, your work must be uniquely your own. Thus, please answer all questions in your own intelligible words. (When in doubt, use complete sentences.) If calculations are involved, show all work (so that I will have some basis for giving partial credit.) Be sure to use appropriate units and significant digits, where appropriate. Chondrite normalization: Because they often lack other sources of data and have very limited access to specimens (!), planetary scientists must rely especially heavily on chemical data. The purpose of this assignment is to make sure you are comfortable with one of the standard methods of the representation of such data. CI carbonaceous chondrite meteorites represent the original condensate of the Solar System. If you omit very light or volatile substances like hydrogen and helium, the relative concentrations of elements in CI carbonaceous chondrite meteorites match those seen in the absorption spectra of the Sun. I.e. in composition, CI carbonaceous chondrites represent little samples of solar composition, minus the hydrogen and helium. Thus, it is common to refer to the concentrations of trace substances in rock samples by comparison to their concentrations in these chondrites, the ultimate standards for the Solar System. An element s chondrite normalized composition is simply the ratio of its concentration in the sample to the average in CI carbonaceous chondrites. In the example below, lines A and B show elemental concentrations for separate samples. Specimen B, for example, is depleted in iron (Fe) compared to specimen A, but is enriched in silicon (Si). Typically, data of this sort is reported for several elements simultaneously in spider diagrams or spidergrams. Note: typically, the y axis would bear a logarithmic scale.

2 Rare Earth Elements (REEs): Although you could present information on any element in this manner, geochemists tend to focus on rare earth elements (REEs). These elements from lanthanum (atomic number 57) to lutetium (71) are, as the name implies, rare enough that they occur as impurities in minerals but don't form minerals in which they predominate. Moreover, they are lithophile, giving them enriched concentrations in most of the samples that a geologist would study. (Recall the lithophile and siderophile elements of the Goldschmidt classification system. See - REEs tend to behave similarly in most chemical systems. Therefore, the processes that cause them to show distinct patterns of concentration tend to be easier to identify. In the above example, lighter REEs are enriched relative to heavier ones.

3 Interpreting spidergrams: 1.) The spidergram above shows chondrite-normalized concentrations for several elements (x-axis) taken from several rock samples. (Each sample has a special symbol and number.) In these samples, are concentrations of the indicated elements enriched or depleted with respect to chondritic concentrations? 2.) The roster of elements shown here seems haphazard at first. Referring to the periodic table in the course notes for our discussion of the Goldschmidt classification system, to what Goldschmidt group do these elements belong? 3.) Generally speaking one sample is more enriched in the various sampled elements than the others. What is its number? All of the specimens are conspicuously less enriched in three elements than in the others. Which elements are these? (Careful! Look at the numbers on the y-axis.)

4.) Identify the line for sample MSS-99-4-17(1a/b).

4 4.) Identify the line for sample MSS (1a/b). Approximately what is the ratio (not the difference) of its chondrite normalized concentration in thorium (Th) to its concentration of lutetium (Lu). (It is understood that answers will not be exact.) 5.) The elements in the spidergram above are also enriched above their chondritic concentrations. Referring to the Goldschmidt system, how do the elements given differ from those in the first spidergram? Based on what you know, would you expect the indicated samples (meteorites in this case) to have originated in a planetary mantle or core?

5 Seismology: The study of seismic waves gives us a means of indirectly sampling places in planetary interiors that we can t get to directly. Let s look at a couple of their applications. Identifying earthquake epicenters: The place beneath a planetary body s surface where rocks actually fracture (i.e. the earthquake, itself) is called the focus. The place directly above it on the surface is the epicenter. Seismic waves can be used to identify the epicenter. As discussed in lecture, P-waves travel faster than S-waves. Thus, as the schematic above suggests, the farther a seismic station is from the epicenter, the greater the time lag is between the arrival of P and S-waves. This lag can be used to calculate the P-waves' actual travel time using this equation: (5 km s -1 ) * t p = (3 km s -1 ) * (t p + t lag s) Where: t p = P-wave travel time t lag = P and S-wave arrival lag time To find P-wave travel time, simply rearrange and solve for t p Rearranging, we get: ((5 km s -1 ) * t p s)/ (3 km s -1 ) = (t p s + t lag s) (5/3) * t p s - t p s = t lag s (2/3) * t p s = t lag s t p s = t lag s/(2/3)

6.) If the lag time between P and S-waves is 10 seconds, what was the travel time of the P-waves? 7.) Assuming the P-waves travel at 5 km s -1, how far away was the epicenter?

6 6.) If the lag time between P and S-waves is 10 seconds, what was the travel time of the P-waves? 7.) Assuming the P-waves travel at 5 km s -1, how far away was the epicenter? The year is 2675 and you are on a survey team exploring an exoplanet orbiting the star Tau Ceti. You have just set up a small network of seismic stations on the landmass pictured above, when a major earthquake occurs. The stations record the following lag times between P and S-wave arrival. Assuming that P-waves travel at 5 km/s and S-waves travel at 3 km/s, calculate the P-wave travel times.

7 8.) Now calculate the distances to the epicenter for each station. Station 1 Time lag 48.5 s P-wave travel time Distance to epicenter Station s Station s

8 9.) Using the scale provided and a compass (or some equivalent) draw circles around each seismic station whose radius is equal to the distance to the epicenter. Then label the epicenter. 10.) Also orbiting Tau Ceti (but at a greater distance) is an icy planet that superficially resembles Europa. You set up a similar seismic network on it but are frustrated to find that you are unable to use the lag-time method to pinpoint epicenters because, for some reason, your stations are not picking up S-waves from earthquakes more than a 30 km away. Why might this be?

Lecture 31. Planetary Accretion the raw materials and the final compositions

Lecture 31. Planetary Accretion the raw materials and the final compositions Lecture 31 Planetary Accretion the raw materials and the final compositions Reading this week: White Ch 11 (sections 11.1-11.4) Today 1. Boundary conditions for Planetary Accretion Growth and Differentiation