Assignment 2 Due March 4, 2019 Show all work and turn in answers on separate pages, not on these pages. Circle your final answers for clarity. Be sure to show/explain all of your reasoning and that your work is neat. If I cannot read or understand what you did, you will lose points. (1) Computational Modeling of Impact Cratering There are a couple of online impact cratering calculators: http://www.lpi.usra.edu/lunar/tools/lunarcratercalc/ (this one is specific to the Moon) http://keith.aa.washington.edu/craterdata/scaling/index.htm (more general) that we can use to do some quantitative exploration of the cratering process. These tools allow you to determine the crater size, shape, and other characteristics of both explosion and impact craters for a very wide range of conditions. The first tool is already set up for impacts. If you use the second tool, be sure to click on the Impacts button at the top. In either tool, you can set the conditions describing the event, with many changeable preset/default values indicated. The results of the simulation are continuously updated in the window as the values of the various input parameters are updated. For cases where a complex impact crater is produced, additional results appear with the complex crater size indicated. Another way of using these tools for impact craters is to choose the crater diameter, and, while keeping all other parameters fixed, have the program solve for the impactor size. The scaling laws underlying the calculations are based on both field and laboratory experimental data for explosions and impacts. The complete database of events and a document describing the equations underlying the calculations ( Theory and Equations for Crater Scaling ) are available through links on both of the tool websites. Note that, because of the extreme complexity of modeling the material behavior of rocks and soils under the extreme conditions of an impact, all the results should be considered approximate. 1
1. Investigate the effects of target geology type on the resulting crater for: (a) a 10-m impactor; and (b) for a 1-km impactor. Do this by changing the target type in the simulation tool. In both cases, assume a rocky body impacting at a 45 angle at 15 km/s. How do your results in each case differ if you are impacting the Earth rather than the Moon (i.e. change the acceleration of gravity in both cases)? Illustrate your answers with plots as you see appropriate. 2. Investigate the effects of impactor size and composition for a 500-m impactor hitting the Earth at a 45 angle. For a rocky (asteroid) impactor use 15 km/s impact velocity and for a comet use both 30 km/s (shortperiod comet) and 50 km/s (long-period comet). Vary the impactor size for the asteroid and cometary cases. Illustrate your answers with plots as you see appropriate. 3. Explore the boundary between the gravity and the strength regimes. Do this by running a series of experiments where you keep the target and impactor compositions and the impactor angle and velocity fixed and only change the size of the impactor. Construct plots of: impactor size vs. crater depth; impactor size vs. crater diameter; crater depth vs. crater diameter; and any others you feel are appropriate. Note on the plots the fields where you have created a crater in one regime or the other. How does this relate to complex vs. simple crater morphologies? How do your results change for Earth vs. the Moon? 2
(2) Crater Counting and Geochronology Impact craters are the dominant landforms on most of the solid surfaces in our solar system. These impact craters have accumulated on the surfaces of planetary bodies over the entire age of our solar system, and the number of craters on a surface increases with the length of time that surface has been exposed to space. These rather simple ideas are the basis for a very powerful tool, called crater counting, that planetary scientists use to unravel the history of a planetary surface. The basic idea is that an old surface will have more impact craters than a younger surface*. For example, on a given planetary surface, by counting the number of craters in some defined area (i.e. determining its crater density ) and comparing that to the crater density for a same-sized area elsewhere, you can determine the relative ages of the two surfaces. A more sophisticated, quantitative chronologic method further examines the density of craters of a range of sizes. The resulting size-density distribution can then be compared to calibrated size-density distributions to determine absolute surface ages. To calibrate these size-density distributions, an independent way of getting absolute ages of rocks that can be related to impacts is needed. Fortunately, the Apollo missions to the Moon brought back impact rocks (melts and breccias) from six sites on the lunar surface. By radiometrically determining the ages of these rocks, and then also measuring the crater size-density distributions for the impact craters the samples came from, we can determine how crater density is related to the absolute age of a surface. We can then measure the crater size-density distribution of any part of the Moon (from images, for example) and compare it to the crater density at the Apollo sites to determine relative ages of surfaces on the Moon. Furthermore, if we make the simple (yet common) assumption that the cratering rate on the Moon is typical of the cratering rate for the entire (inner) solar system, we can extend our measurements of the crater size-density distribution (and relationship to absolute age) for the Moon to estimate surface ages on other planetary surfaces*. 3
*It is important to note, however, that crater count-derived surface ages are estimates for the age of the surface, or, more precisely, the time since that surface was last devoid of craters. Such an event that erases impact craters can be called a resurfacing event, and examples include volcanic eruptions, episodes of weathering and erosion, or tectonic processes. Earth s surface has been largely resurfaced and continues to be, hence the dearth of impact craters and the very young crater counting age one would deduce for the Earth. The same is true for Venus! You will now estimate model ages for resurfacing on two specific regions on Mars using images taken by the Viking 1 and 2 orbiters (see attached). 1. On each of the Mars images you have are 5 white scale bars that represent 128, 64, 32, 16, and 8 km in size. Use these scale bars to create a measuring tool (a ruler) that is divided into several different size ranges (0-8 km, 8-16 km, 16-32 km, etc.). Your measuring tool should look something like this: Use your measuring tool (NOT the example one above it is not drawn at the right scale!) to determine how many craters are in each size range in the Mars images. You may not be able to effectively use all the different size ranges because there may be no craters in some of the larger ranges or too many craters in the smallest ranges. Try to fill in as many of the size ranges as you can. Record the numbers in the Crater Density Table (see attached page). 2. The data for the crater density at the Apollo sites was determined from images covering areas of about 1,000,000 km 2. The total area of the Mars images you 4
have is shown at the bottom of the images. Using the numbers you record in the Crater Density Table and the formula below: determine how many craters of each size range are found in 1,000,000 km 2. Record this number in the Crater Density Table (see attached; alternatively, you can make your own table in Microsoft Excel**). 3. Plot your data points from the Crater Density Table on the Crater Density Graph (see attached; alternatively, you can make your own table and plot in Microsoft Excel**). When plotting, put your points on the graph in the middle of your size range. For example, if you had 200 craters in the 0-8 km size range, you should put your point at the intersection of 200 on the y-axis, and 4 km (half way between 0 and 8 km) on the x-axis. Note that the y-axis of this graph has a logarithmic scale and the x-axis is linear. 4. Determine the age of your surface with the following procedure. Once you have your points plotted, draw a best-fit straight line through the points. You can eyeball this if you are using the attached Crater Density Graph, or you can use the linear regression tools in Microsoft Excel**. Your line should be nearly parallel to the labeled, calibrated age lines on the graph. The best-fit line through your data will be representative of the average age of the cratered surface you have been examining. Estimate the age by interpolating the location of the line you have drawn with respect to the labeled age lines already on the graph. Martian Northern Hemisphere Surface: billion years old 5
Martian Southern Hemisphere Surface: billion years old 5. How accurate are your age estimates (i.e. ±? billion years)? You can quantitatively assess this for each surface by determining the oldest and youngest ages that fit your data. 6. What is (are) the greatest source(s) of uncertainty in the surface ages you get from crater counting? Be as specific and as quantitative as possible. Note that the following are not adequate explanations (although they can contribute): human error, bad eyesight, classmates talking, etc. Instead, think geologically and think about remote sensing. 7. Consider these two facts: (i) the Earth has been hit by as many impactors as the Moon and Mars; (ii) the state of Texas has a total land area of about 696,241 km 2. Using the size-density relationships, calculate how many 5-km-sized craters should have been formed in Texas over the last 4 billion years. Show all of your work. 8. An online database of known terrestrial impact craters is hosted at the Earth Impact Database: http://www.passc.net/earthimpactdatabase/new%20website_05-2018/index.html Use this database to find the known impact craters in Texas. How does this number of craters compare with your calculated predictions? Come up with a hypothesis to explain the results. 6
**If you choose to use Excel, be sure to also turn in an electronic version to me along with the rest of your hardcopy work. 7
Crater size range (km) < 8 Martian Crater Density Data Table Northern Hemisphere Number of Craters in 1,000,000 km 2 Number of Craters in Image Number of Craters in Image Southern Hemisphere Number of Craters in 1,000,000 km 2 8-16 16-32 32-64 64-128 55
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