# GEOS 1300 – Kent Geophysical Worksheet-University of Maine at Fort.

GEOS 1300: Physical Geology – Lab 2: Numerical Earth Structure Model Overview One of the course objectives is to develop “a detailed understanding of earth’s internal structure.” In today’s lab exercise, we will use a numerical earth model to investigate Earth’s internal structure in more detail. Generally speaking, a numerical model is a simplified representation of some aspect of nature. In this case, the model that we will work with represents the layered structure of earth’s interior. As we’ve discussed in lecture, a model’s scientific value is determined by (i) how accurately it represents existing scientific data, and (ii) how reliably it can be used to make predictions. Just as a scientific hypothesis is considered invalid if it contradicts scientific fact, a model is invalid if it doesn’t accurate reflect empirical observations. Although the numerical model that you will work with in today’s lab is a simplified representation of earth’s structure, it is remarkably consistent with existing geophysical data. Our objectives today are to: ✓ gain practice utilizing MS Excel as a computational and graphing tool ✓ utilize a model to more thoroughly investigate earth’s internal structure Activity You have been given a spreadsheet that has been populated with data on density, bulk modulus and shear modulus vs. depth for a 1-dimensional (1-D) transect (line) starting at the surface and going to the center of the Earth. You will use these data to calculate S-wave and P-wave velocities along a depth transect. You will then plot these data in order to answer questions about earth’s internal structure. Instructions: 1. Open the spreadsheet provided. Save this spreadsheet with you own unique filename that includes GEOS1300, Lab 7, and your last name. 2. Take a minute to examine the data in the columns and how they are organized. Notice that the first cell in each column includes the name of one variable (e.g., Radius, Depth, Rho, etc.) and the second cell notes the unit of measure for that variable (e.g., km, km, kg/m3, etc.). Importantly, you should also note that there are no units reported for the numerical values in the cells below. MS Excel cannot calculate or graph text, so cells with numbers (i.e. quantitative data) should not include text (that’s why they are shown at the top). 3. Now, label columns F & G “S-Wave Velocity” (m/sec) and “P-Wave Velocity” (m/sec), respectively. 4. In Column F, work with your team to enter the equation for S-wave velocity. Please format the cells so the values are represented in scientific notation (select cells, right click, format cell). It is good practice to learn how Excel can be used as a calculator because it can save a significant amount of time. Excel works a bit different than your calculator and needs to be 1 told up front if a cell is going to be used to perform a calculation. This means that in contrast to your calculator, Excel requires the equal sign be entered first followed by the desired computation. The powerful thing about Excel is that the cells can be used to represent the variables in your equation. For example, if you wanted to calculate the sum of 2 + 3 multiplied by 4 in Excel you would put these values into different cells, say B1 = 2, B2 = 3 and B3 = 4. You would then enter the following equation into cell B4 to compute the answer: = (𝐵1 + 𝐵2) ∗ 𝐵3 (Equation 1) Excel doesn’t always honor your preferred order of operations so you must make use of parentheses in your equations. Without the parentheses in equation 1, Excel would follow normal algebraic order of operations and first multiply B2 * B3 and then add that product to B1. MS Excel needs to be told explicitly what operations to do first, second, etc. Note that once an equation has been entered into a column, it can be copied & pasted down the column. This allows you to do hundreds of calculations in seconds, rather than wasting time calculating them one at a time. 5. Now enter an equation to calculate P-wave velocity at each depth. Please format the cells so the values are represented in scientific notation (select cells, right click, format cell). 6. Construct the following graphs by making cross plots using the “Scatter with Straight Lines” option. Be sure to show depth increasing to the right. Label all axes (with titles and units). a. Figure 1. Plot Density, P-Wave velocity and S-Wave Velocity as a function of Depth (from 0-6371 km). i. Label plot with the inner core, outer core, mantle, crust, Oldham-Guttenberg Discontinuity, Bullen Discontinuity, and the Moho Discontinuity b. Figure 2. Plot Shear Modulus and Bulk Modulus vs. Depth (from 0-6371 km). i. Label plot with Lehm Bullen ann and Moho Discontinuities c. Figure 3. Plot Density, P-Wave velocity and S-Wave Velocity as a function of Depth (from 0-1000 km). i. Label this plot with the upper mantle, lower mantle, mantle transition zone and crust. d. Figure 4. Plot P-Wave velocity and S-Wave Velocity as a function of Depth (from 0450 km). i. On this plot label the upper mantle, crust, and the Moho Discontinuity. Also label the low velocity zone, asthenosphere, and lithosphere. e. Notes: i. You need to label the plots so that it is very clear where the layers and discontinuities are. If it is not clear it’s wrong. ii. You will need to do some research to correctly label the plots with the various layers and discontinuities. You are going to find different answers from different sources. This is because there are slight variations in earth 2 structure along different depth profiles. The important point here is to make sure that your labels are consistent with the 1-D model you made. For instance, don’t label seismic discontinuities in places where your model doesn’t show a seismic discontinuity just because Wikipedia said so… Discussion questions (One well-written paragraph with citations for each question): 1. What is the Oldham-Gutenberg Discontinuity, the Moho Discontinuity, and the Bullen Discontinuity? Where do they occur, and what do they tell us? 2. Why do geologists distinguish between the asthenosphere & the lithosphere AND between the crust & the mantle? You’ll need to do some research to understand why geologists use multiple ways to talk about the uppermost layers of the Earth. 3. What is the low velocity zone and what does it tell you about the mechanical properties of the mantle? Be sure to write your responses in your own words and properly cite all sources. Refer to the academic dishonesty definitions in the course syllabus for clarification. What to Turn In Complete lab report including an introduction stating the goal of the lab, how the data was handled (methods), a description of the results, including figures 1, 2, 3, 4 (properly ordered, numbered, captioned and labeled), a short discussion that includes answers to the questions posed above, and a conclusion. Cite all references and include a bibliography at the end of your lab report. 3 Radius (km) 0 200 400 600 800 1000 1200 1222 1222 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3480 3480 3600 3630 3630 3800 4000 4200 4400 4600 4800 5000 5200 5400 5600 5600 5701 5701 5771 5771 Depth (km) 6371 6171 5971 5771 5571 5371 5171 5150 5150 4971 4771 4571 4371 4171 3971 3771 3571 3371 3171 2971 2891 2891 2771 2741 2741 2571 2371 2171 1971 1771 1571 1371 1171 971 771 771 670 670 600 600 ρ (kg/m3) 13088,5 13079,8 13053,6 13010,1 12949,1 12870,7 12774,9 12763,6 12166,3 12069,2 11946,8 11809 11654,8 11483,1 11293 11083,4 10853,2 10601,5 10327,3 10029,4 9903,49 5566,45 5506,42 5491,45 5491,45 5406,81 5307,24 5207,13 5105,9 5002,99 4897,83 4789,83 4678,44 4563,07 4443,17 4443,17 4380,71 3992,14 3975,84 3975,84 µ (Pa) 1,761E+11 1,755E+11 1,739E+11 1,713E+11 1,676E+11 1,630E+11 1,574E+11 1,567E+11 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 0,000E+00 2,938E+11 2,907E+11 2,899E+11 2,899E+11 2,794E+11 2,675E+11 2,559E+11 2,445E+11 2,331E+11 2,215E+11 2,098E+11 1,979E+11 1,856E+11 1,730E+11 1,730E+11 1,548E+11 1,239E+11

1,210E+11 1,210E+11 K (Pa) 1,425E+12 1,423E+12 1,416E+12 1,405E+12 1,390E+12 1,370E+12 1,346E+12 1,343E+12 1,305E+12 1,268E+12 1,224E+12 1,178E+12 1,127E+12 1,074E+12 1,016E+12 9,542E+11 8,889E+11 8,202E+11 7,484E+11 6,743E+11 6,441E+11 6,556E+11 6,440E+11 6,412E+11 6,412E+11 6,095E+11 5,744E+11 5,409E+11 5,085E+11 4,766E+11 4,448E+11 4,128E+11 3,803E+11 3,471E+11 3,133E+11 3,133E+11 2,999E+11 2,556E+11 2,489E+11 2,489E+11 5871 5971 5971 6061 6151 6151 6221 6291 6291 6347 6347 6356 6356 6368 500 400 400 310 220 220 150 80 80 24 24 15 15 3 3849,8 3723,78 3543,25 3489,51 3435,78 3359,5 3367,1 3374,71 3380,76 3380,76 2900 2900 2600 2600 1,051E+11 9,060E+10 8,060E+10 7,730E+10 7,410E+10 6,560E+10 6,650E+10 6,740E+10 6,820E+10 6,820E+10 4,410E+10 4,410E+10 2,660E+10 2,660E+10 2,181E+11 1,899E+11 1,735E+11 1,630E+11 1,529E+11 1,270E+11 1,287E+11 1,303E+11 1,315E+11 1,315E+11 7,530E+10 7,530E+10 5,200E+10 5,200E+10 Radius Region Inner Core Outer Core D” Transitio n Zone LVZ LID Crust (km) 0 400 800 1200 1221,5 1221,5 1600 2000 2400 2800 3200 3480 3480 3630 3800 4200 4600 5000 5400 5701 5701 6016 6221 6331 6356 6371 Depth (km) 6371 5971 5571 5171 5149,5 5149,5 4771 4371 3971 3571 3171 2891 2891 2741 2571 2171 1771 1371 971 670 670 355 150 40 15 0 T (K) 5101 5087 5041 4965 4961 4961 4846 4693 4501 4265 3981 3750 3750 3564 3018 2712 2509 2313 2109 1950 1950 1750 1550 930 630 300 Tm (K) 5162 5140 5075 4966 4961 4961 4812 4618 4377 4081 3723 3429 3840 3850 3790 3640 3500 3240 3130 2750 2750 2070 1880 1590 1530 1500