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Oceanic Lithosphere: Sink or Swim

The fate of oceanic plates depends on their density—how does it change?

Thomas JusterDepartment of Geology, University of South Florida© 2011 University of South Florida Libraries. All rights reserved.

SSAChaz.TCJ.3(trad)

Core Quantitative IssueWeighted average

Supporting Quantitative IssuesProportions, percentage

Core Geoscience IssuesPlate tectonics, lithosphere

The module you are viewing is a Powerpoint slide presentation.

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You can and probably should have a spreadsheet open in a separate window, so you can try out things that are explained in the presentation.

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The paradox of oceanic lithosphere

Oceanic lithosphere plays two very important roles in plate tectonics. First, it is what the oceanic plates are made of, and thus underlies 70% of Earth’s surface. Second, it is thought to provide the most important driving force for the motion of the plates as it sinks into the asthenosphere at subduction zones, dragging the rest of the plate along with it (a process called “slab pull”).

Here the oceanic lithosphere is less dense than the asthenosphere, causing it float. This is a good thing, because foundering of the oceanic plate would destroy the oceans and all life on Earth!

Figure from USGS web site

Here in the subduction zone the oceanic lithosphere is denser than the asthenosphere, causing it to sink. This tugging force drags the entire plate along, causing it to move on the surface.

So how can the density of the lithosphere be both greater and less than the density of the asthenosphere? This is the paradox of the oceanic lithosphere.

(For a review of density, see Endnote 1)

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Objectives of this module

Upon completion of this module you should be able to:•Explain what the weighted average is, and compare it to the simple non-weighted average;•Compute the weighted average;•Compute the density of the oceanic lithosphere given different proportions of mantle and crustal rock;•Explain how oceanic lithosphere thickens as it ages, and how its density changes during this process•Explain how oceanic lithosphere can be both less dense than the underlying asthenosphere (in the ocean basins) and more dense than the underlying asthenosphere (in subduction zones)

First, extract the embedded Excel spreadsheet where you will do your homework. Remember to immediately save it under a new, unique name.

Q1. Quick review: what kinds of geologic hazards are commonly at subduction zone plate boundaries, like the boundary shown in the diagram to the left? Go directly to End-of-Module Questions

Lith_Density

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Math concept: what is a weighted average?

But here’s the key point: the weights don’t have to all be equal. And If they’re not all equal, then some terms will get more weight than others in computing the average.

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Weighted average, con’t.

When would the weights be unequal? When we’re taking the average of numbers that don’t represent individual values, but groups of values. For example, suppose we wanted to calculate the average age of students at a college given these data:

A simple average wouldn’t be appropriate because it would weigh each class equally in the average, but the classes aren’t equal—there are more freshman, for example, than seniors. To calculate an accurate average we need to weigh the averages for each class by the fractions of each class in the whole population, so that classes—like the freshman class—which contain a higher percentage of the college’s students, contribute more to the average.

ClassNumber of students

% of college population

Average age of class (yrs)

Freshman 135 33.75% 18.25

Sophomore 107 26.75% 19.37

Junior 85 21.25% 20.83

Senior 73 18.25% 22.09

Whole college 400

Q2. If we didn’t use a weighted average, what would the weights equal for a simple average? (HINT: we would be simply averaging four numbers)Go directly to End-of-Module Questions

An example: what is the average asking price of a house in Tampa?

Real estate brokers list homes, and you can use these data to compute the average asking price. In many cases the data are broken down by the number of bedrooms (groups of values). For example, here are the data for home listings in Tampa, Florida, in December 2010:

Looking at the data, you can see the obvious—larger houses in general cost more than small ones, and the largest houses—those that have five or more bedrooms—can cost millions.

Data from trulia.comYou could compute an average of these prices, but what does this mean? The average is heavily influenced by the cost of the largest houses, but there were only 500 of them.

Instead you calculate a weighted average, with the weights equal to the proportion of listings.

Total of all listings using the SUM() function

Weight (W) for each size house computed as the number of listings divided by the total of all listings. The weights should sum to one.

Multiply the weight (W) times the average price for each size

The sum of these values is the weighed average asking price.

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An example: what is the average asking price of a house in Tampa?

Here’s what the Excel cell formulas look like. Study them so you can create your own spreadsheet to calculate a weighted average. This table is also found on the embedded spreadsheet file.

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=SUM(E11:E15)

=E11/$E$16

Copy and paste the formula in cell G11 into these cells

=F11*G11

Copy and paste the formula in cell H11 into these cells

=SUM(H11:H15)

Q3. What does the reference $E$16 mean (it’s found in the formula for cell G11)Go directly to End-of-Module Questions

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Another example: what is the average tuition paid by USF students?

Here’s another example: what is the average tuition paid by USF students? If you look it up you will find that the tuition depends on whether a student is in-state or not, and it’s a big difference!

In state tuition: $5,124

Out of state tuition: $15,933

However, there are far more in-state students than out-of-staters, so we need to use the weighted average to compute the average tuition. Here are the complete data:

Q4. Fill in the rest of the this table, which computes the weighted average of tuition for USF students, both in-state and out-of-state. Note that some of the computed values are revealed so you can check your formulas.

Q5. Here is the weighted average. Is it closer to the in-state or out-of-state tuition? Why?

Go directly to End-of-Module Questions

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Review: what is lithosphere?

Core: Iron (Fe) metal

Mantle: Ultramafic rock

Crust: Intermediate or mafic rock covered by sediment, 7-30km thick

Layering based on composition

Liquid Metal

Asthenosphere: Solid rock that can

flow

Plates: Lithosphere: Rigid rock

Layering based on style of deformation

100-250 km, 1,300°C

Recall that the lithosphere is the relatively cool, rigid outer layer of Earth, and is underlain by the asthenosphere, solid rock that is hot enough to flow like a fluid.

The lithosphere is not the same thing as the crust, which is the outermost layer of rock on Earth defined on the basis of its chemical composition.

The lithosphere consists of two compositional layers: the crust and the uppermost part of the mantle. The transition from lithosphere to asthenosphere occurs at ≈ 1,300°C, the temperature at which mantle rock begins to flow.

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Review: what is oceanic lithosphere?

Mid-Ocean Ridge

Asthenosphere

1,300°C

Crust

Mantle

8 m.y.20 m.y.70 m.y.140 m.y.

Click here to see how the oceanic lithosphere thickens as

it moves away from the ridge and ages

The oceanic crust is formed at mid-ocean ridges, and consists primarily of mafic volcanic rocks (basalt). Underlying the crust is a small piece of mantle rock cool enough to be rigid, and these two components form the oceanic lithosphere.

Typically, about 7 km of volcanic rocks can accumulate at the mid-ocean ridge to form the oceanic crust before the plate moves away from the source of heat and magma.

As the lithosphere moves away from the mid-ocean ridge and its source of heat, it cools. As it cools more and more of the mantle rock becomes rigid, and the mantle component of the oceanic lithosphere thickens. Notice that as it thickens, the crust becomes a smaller and smaller proportion of the lithosphere.

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Average density of oceanic lithosphere

The average density of the mafic crustal rocks in the oceanic lithosphere is 2,800 kg/m3. The average density of the ultramafic mantle rock in the oceanic lithosphere is 3,400 kg/m3. Because it consists of both crust and mantle, the average density of the lithosphere will therefore be a weighted average of the densities of the crustal and mantle components.

When the oceanic lithosphere is approximately 8 million years old it consists of about 13 km of mantle overlain by 7 km of crust.

Q6a. Fill in the orange cells in this table in Excel that will calculate the average density of the oceanic lithosphere when it is about 8 million years old, and consists of 7 km of crust overlying 13 km of rigid mantle.

Q6b. The density of the asthenosphere below the lithosphere is about 3,350 kg/m3. Based on the density of the lithosphere you just calculated, will the lithosphere float in this asthenosphere or sink through it? Enter “float” or “sink” in this cell.

Go directly to End-of-Module Questions

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Average density of oceanic lithosphere as a function of age

As shown on Slide 10, the oceanic lithosphere gets thicker with age, as the mantle component grows. Now that you know how to compute the average density of the lithosphere using the weighted mean, you can investigate how the density changes with time.

Q7a. Fill in the orange cells in this Excel table that will calculate the average density of the oceanic lithosphere at 9 different ages, from 8 to 140 million years old. Note that the arrangement of the table is a little different from the ones you’ve done before, but the equations are all the same—just make sure you enter the cell references properly. I’ve revealed the density for 25 m.y. old lithosphere so you can check you’re doing it right.

Q7b. In column N calculate the density difference between the lithosphere and the asthenosphere [ρ(asth), shown in column M].

Q7c. Once again, decide whether the lithosphere will float or sink in the asthenosphere, and enter “float” or “sink” in column O.

Go directly to End-of-Module Questions

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Density of oceanic lithosphere under subduction zones

Most geologists think that the motion of the plates is driven by the sinking of oceanic lithosphere at subduction zones (the force is indicated with the arrow).

What is different about the oceanic lithosphere here as opposed to on the surface?

Notice that all the densities are larger because of the greater pressure at 150 km. The greater pressure compresses the minerals so they occupy less volume.

Here’s the big difference: basalt, which forms near the surface and is stable there, transforms at depth into a new rock called eclogite. Eclogite is much denser than basalt. Endnote 2

Q8. Calculate the density of the subducting oceanic lithosphere, and decide whether it floats or sinks.

Go directly to End-of-Module Questions

Basalt Eclogite

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End-of-Module Assignment

Answer all questions in the spaces provided in the embedded spreadsheet (Slide 3), which you should have saved with a different name (e.g., “YourName-density.xls”).

1.Answer questions 1-8 on Slides 3, 5, 7, 8, 11, 12, and 13.

9.How does the density of the subducted oceanic lithosphere change as it warms up? How would this change the “slab pull” driving force for plate tectonics?

10.Continental crust and lithosphere is much thicker than oceanic lithosphere. The average thickness of the continental crust is 30km, and the average thickness of the continental lithosphere is 200km. Calculate the average density of the continental crust assuming that the crustal rocks have a density of 2,700 kg/m3. Show all your work in the spreadsheet.

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Endnotes

1. Density is a measure of the amount of mass per volume. The modern metric unit of density is kilograms-per-square-meter, kg/m3, though many people are more familiar with the older grams-per-cubic-centimeter (g/cm3). Water at normal surface conditions has a density of 1,000 kg/m3 or 1.00 g/cm3. Return to Slide 2.

2. The difference between basalt and eclogite is the mineral composition. Basalt consists primarily of three minerals: olivine, plagioclase, and pyroxene. When exposed to high pressures, the olivine and plagioclase transform into garnet in the rock eclogite. Here are the densities of the pertinent minerals:

You can see that a rock made of pyroxene + garnet (eclogite) will be denser than a rock made of olivine, plagioclase, and pyroxene (basalt). Return to Slide 13.

Mineral Density (kg/m3)

Olivine 3,300

Plagioclase 2,700

Pyroxene 3,400

Garnet 3,500