---
title: "The Continental Crust"
book: "High School Earth and Space Sciences"
subject: earth
language: en
chapter: 19
exercises: 15
source: https://one-course.com/books/earth/2/en/chapter/19-the-continental-crust
license: CC-BY-NC-SA-4.0
credit: "One Earth and Space Sciences Book, One Course (one-course.com)"
---

# Chapter 19 — The Continental Crust

In northwestern Canada, near the Acasta River, crops out a grey rock streaked with pale and dark bands. It has been dated at 4.00 to 4.03 billion years: the Acasta gneiss, the oldest rock known. Older still are grains of the mineral zircon, each a fraction of a millimetre long, found in old sedimentary rocks of the Jack Hills of Western Australia. Worn from older rocks and carried by water before they were buried, they crystallised 4.4 billion years ago, and they show that a crust existed then. No ocean floor is even a twentieth as old. This chapter asks what the continents are made of, and why they last.

![Left: a piece of the Acasta gneiss, 4.03 billion years old, in a museum display. Photograph Pedroalexandrade (CC BY-SA 3.0). Right: two zircon grains from the Jack Hills, Western Australia, seen with an electron microscope; each scale bar is 100\, µ m. The upper grain was rounded as it was carried by water, the lower one kept its crystal faces. Images A. Cavosie and J. Valley (public domain).](https://one-course.com/images/onecourse/chapters/earth-2/g12-continental-crust/img-13336bc1a292.jpg)

![Left: a piece of the Acasta gneiss, 4.03 billion years old, in a museum display. Photograph Pedroalexandrade (CC BY-SA 3.0). Right: two zircon grains from the Jack Hills, Western Australia, seen with an electron microscope; each scale bar is 100\, µ m. The upper grain was rounded as it was carried by water, the lower one kept its crystal faces. Images A. Cavosie and J. Valley (public domain).](https://one-course.com/images/onecourse/chapters/earth-2/g12-continental-crust/img-eadcc869905f.jpg)

*Left: a piece of the Acasta gneiss, 4.03 billion years old, in a museum display. Photograph Pedroalexandrade (CC BY-SA 3.0). Right: two zircon grains from the Jack Hills, Western Australia, seen with an electron microscope; each scale bar is $100\,\text{µ}\mathrm{m}$. The upper grain was rounded as it was carried by water, the lower one kept its crystal faces. Images A. Cavosie and J. Valley (public domain).*

**You already know.**

The crust ends at the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho), below which lies the denser mantle ([Chapter 11](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#ch-g11-seismic-structure)). The [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) is about $7\,\mathrm{km}$ of basalt and [gabbro](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-gabbro) made at the ridges ([Chapter 14](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#ch-g11-ocean-ridges)), and it is never older than about 190 million years ([Chapter 10](https://one-course.com/books/earth/2/en/chapter/10-from-continental-drift-to-seafloor-spreading#ch-g11-drift-to-spreading)). The outer layers float on the [asthenosphere](https://one-course.com/books/earth/2/en/chapter/12-lithosphere-and-asthenosphere#def-g11-lithosphere-asthenosphere-lithosphere): in Airy’s model, a region that stands a height $h$ higher has a crust thicker by $h\,\rho_m/(\rho_m -
\rho_c)$ ([Chapter 12](https://one-course.com/books/earth/2/en/chapter/12-lithosphere-and-asthenosphere#ch-g11-lithosphere-asthenosphere)). Igneous rocks are named by their [texture](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-texture) and their silica content: [mafic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic) from 45 to $55\,\%$ $\ce{SiO2}$, [intermediate](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic) from 55 to 65, [felsic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic) from 65 to 75 ([Chapter 17](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#ch-g11-igneous-rocks)). Radioactive elements decay at a steady rate, which gives rocks their ages (the physics books; [Chapter 25](https://one-course.com/books/earth/2/en/chapter/25-radiometric-dating-and-the-age-of-the-earth#ch-g12-age-of-the-earth)).

## 19.1 What the continents are made of

**Definition 19.1 (Continental crust).**

The *continental crust* is the crust that forms the continents, including the parts of them under shallow seas. It is thick, of granitic composition on average in its upper part, light, and it can be very old.

The continents are larger than the land. The edges of the [continental crust](#def-g12-continental-crust-continental-crust) lie under the sea, on the continental shelves: mapped this way, the [continental crust](#def-g12-continental-crust-continental-crust) covers $210$ million $\mathrm{km}^{2}$, $41\,\%$ of the Earth’s surface, of which almost a third, $30.6\,\%$, is submerged. Counted with its submerged parts, the mean height of the [continental crust](#def-g12-continental-crust-continental-crust) is only about $120\,\mathrm{m}$ above sea level.

At the surface, the continents show every kind of rock — sediments, [volcanic rocks](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-volcanic-plutonic), metamorphic rocks — but beneath the sedimentary cover the [continental crust](#def-g12-continental-crust-continental-crust) is made mostly of granitic rocks and of the metamorphic and [plutonic rocks](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-volcanic-plutonic) of old mountain [roots](#def-g12-continental-crust-root). On average, the whole [continental crust](#def-g12-continental-crust-continental-crust) holds $60.6\,\%$ silica; its upper part is richer, $66.6\,\%$, so its deeper part must be poorer.

![Composition of the continental crust compared with a mafic magma, the kind that makes the oceanic crust: the main oxides, in percent of the mass (FeO counts all the iron). The continental crust is richer in silica, sodium and potassium, poorer in iron, magnesium and calcium. Data: Rudnick and Gao (2014); mafic range from S. Earle, Physical Geology (CC BY 4.0).](https://one-course.com/images/onecourse/chapters/earth-2/g12-continental-crust/fig-ced74f166c3b.svg)

*Composition of the [continental crust](#def-g12-continental-crust-continental-crust) compared with a [mafic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic) magma, the kind that makes the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere): the main oxides, in percent of the mass ($\ce{FeO}$ counts all the iron). The [continental crust](#def-g12-continental-crust-continental-crust) is richer in silica, sodium and potassium, poorer in iron, magnesium and calcium. Data: Rudnick and Gao (2014); [mafic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic) range from S. Earle, *Physical Geology* (CC BY 4.0).*

## 19.2 A thick, light crust

Seismic surveys find the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) beneath the continents at very different depths. Averaged over all continents, weighted by area, the crust is about $41\,\mathrm{km}$ thick; it is thinner, about $30\,\mathrm{km}$, where the crust has been stretched, and thicker, about $46\,\mathrm{km}$ on average, in mountain belts. Away from mountain belts it is commonly 35 to $40\,\mathrm{km}$ thick; under the highest ranges, 50 to $70\,\mathrm{km}$, about $70\,\mathrm{km}$ under parts of Tibet. The [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) is about $7\,\mathrm{km}$ thick: the [continental crust](#def-g12-continental-crust-continental-crust) is five to ten times thicker.

![Thickness of the crust from seismic measurements. Data: White, McKenzie and O’Nions (1992) for the oceanic crust; Christensen and Mooney (1995) for the continental averages; Karplus and others (2019) for Tibet.](https://one-course.com/images/onecourse/chapters/earth-2/g12-continental-crust/fig-53a3aaf57e4f.svg)

*Thickness of the crust from seismic measurements. Data: White, McKenzie and O’Nions (1992) for the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere); Christensen and Mooney (1995) for the continental averages; Karplus and others (2019) for Tibet.*

The [continental crust](#def-g12-continental-crust-continental-crust) is also light. Its mean density is about $2830\,\mathrm{kg}/\mathrm{m}^{3}$. The basalt and [gabbro](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-gabbro) of the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere), rich in pyroxene and olivine, come to about $3000\,\mathrm{kg}/\mathrm{m}^{3}$ ([Chapter 16](https://one-course.com/books/earth/2/en/chapter/16-minerals#ch-g11-minerals)), and the mantle just beneath the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) to about $3380\,\mathrm{kg}/\mathrm{m}^{3}$. A thick and light crust floats high: this is why the continents stand above the ocean floor, and why a continent cannot be dragged down at a [subduction zone](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction). Where a continent arrives at a trench, it is too light to sink; [subduction](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction) stops, and the two continents collide ([Chapter 20](https://one-course.com/books/earth/2/en/chapter/20-building-mountains#ch-g12-mountain-building)). [Continental crust](#def-g12-continental-crust-continental-crust), once made, is hard to destroy.

![A continent and an ocean side by side (depths to scale, widths not; the ocean drawn 4\, km deep): the continental crust is thicker, lighter and much older than the oceanic crust.](https://one-course.com/images/onecourse/chapters/earth-2/g12-continental-crust/fig-c099ef05212b.svg)

*A continent and an ocean side by side (depths to scale, widths not; the ocean drawn $4\,\mathrm{km}$ deep): the [continental crust](#def-g12-continental-crust-continental-crust) is thicker, lighter and much older than the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere).*

**Method 19.2 (Comparing continental and oceanic crust).**

To tell which kind of crust lies under a place, compare five properties:

1. the thickness: about $7\,\mathrm{km}$ for [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) , 30 to $70\,\mathrm{km}$ for [continental crust](#def-g12-continental-crust-continental-crust) ;
2. the rocks: basalt and [gabbro](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-gabbro) , or granite, gneiss and their relatives, under a cover of sediments;
3. the composition: about $50\,\%$ silica, or about 60 and more;
4. the density: about $3000\,\mathrm{kg}/\mathrm{m}^{3}$ , or about $2830\,\mathrm{kg}/\mathrm{m}^{3}$ ;
5. the age: less than 200 million years, or up to 4 billion years.

The elevation is a clue, not a test: most of the ocean floor lies kilometres deep, but the edges of the continents lie under shallow seas.

**Example 19.3 (A shallow sea floor).**

A survey ship finds a sea floor $150\,\mathrm{m}$ deep. Seismic profiles put the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) $32\,\mathrm{km}$ below the sea floor; a drill core brings up, under the sediments, a coarse-grained rock of quartz, feldspar and mica. Which crust lies there?

*Solution.* Thickness about $32\,\mathrm{km}$: continental, thinner than average, as where it has been stretched. A granite under the sediments: continental. The sea floor is a continental shelf, one of the submerged parts that make up almost a third of the continents.

How heavy is all this crust? A layer that is thin compared with the Earth’s radius has a simple mass.

**Proposition 19.4 (The mass of a thin layer).**

A layer of thickness $H$ and density $\rho$ covering a fraction $f$ of the surface of a planet of radius $R \gg H$ and mean density $\bar\rho$ has a mass $m \approx 4\pi R^2 f H \rho$, and its share of the planet’s mass $M$ is

$$
\frac{m}{M} \approx 3 f\,\frac{H}{R}\,\frac{\rho}{\bar\rho}.
$$

**Proof.** The surface of the planet is $4\pi R^2$; the layer covers $4\pi R^2 f$ and, being thin, has a volume close to that area times $H$, so $m \approx 4\pi R^2
f H \rho$. The planet’s mass is $M = \tfrac{4}{3}\pi R^3 \bar\rho$. Dividing, $m/M \approx 4\pi R^2 f H \rho / (\tfrac{4}{3}\pi R^3 \bar\rho) = 3 f (H/R)
(\rho/\bar\rho)$. ∎

For the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) — the remaining $59\,\%$ of the surface, $7.1\,\mathrm{km}$, about $3000\,\mathrm{kg}/\mathrm{m}^{3}$ — with $R = 6371\,\mathrm{km}$ and $\bar\rho = 5513\,\mathrm{kg}/\mathrm{m}^{3}$, the share is $3 \times 0.59 \times
(7.1/6371) \times (3000/5513) \approx 0.0011$: about a tenth of a percent of the Earth’s mass. The weekend problem does the same for the continents.

## 19.3 An old crust

The ocean floor is young everywhere: three quarters of it is younger than 100 million years, and almost none older than 190 million years. The continents are another matter. Their rocks span almost the whole history of the Earth, from the Acasta gneiss, 4.03 billion years old, to lavas erupted today, and grains of zircon carry the record back to 4.4 billion years.

![How old the ocean floor is: the share of its area in each band of 10 million years. The young floor dominates; almost nothing is older than 190 million years (a few old basins of the eastern Mediterranean are left out). Data: Seton and others (2020), computed.](https://one-course.com/images/onecourse/chapters/earth-2/g12-continental-crust/fig-a0ba2aba71e3.svg)

*How old the ocean floor is: the share of its area in each band of 10 million years. The young floor dominates; almost nothing is older than 190 million years (a few old basins of the eastern Mediterranean are left out). Data: Seton and others (2020), computed.*

The oldest parts of the continents form their cores.

**Definition 19.5 (Craton).**

A *craton* is an old and stable core of a continent: [continental crust](#def-g12-continental-crust-continental-crust) formed and deformed more than a billion years ago, which has since cooled and no longer deforms. Its rocks are mostly metamorphic and [plutonic rocks](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-volcanic-plutonic), the deep [roots](#def-g12-continental-crust-root) of former mountains.

Around the [cratons](#def-g12-continental-crust-craton) lie belts of younger deformed rocks, the eroded [roots](#def-g12-continental-crust-root) of mountain ranges built later; the belts tend to be younger towards the edges of a continent. A continent has grown by mountain building that welded new crust to its edges, around an ancient core. In Canada, where the [craton](#def-g12-continental-crust-craton)’s rocks lie at the surface, gneisses and granites 1 to 3 billion years old crop out, here on a lakeshore.

![Gneisses and granites 1 to 3 billion years old on a lakeshore in Canada, part of the ancient core of North America. Photograph Chris Light (CC BY-SA 4.0).](https://one-course.com/images/onecourse/chapters/earth-2/g12-continental-crust/img-a6fe04de55fe.jpg)

*Gneisses and granites 1 to 3 billion years old on a lakeshore in Canada, part of the ancient core of North America. Photograph Chris Light (CC BY-SA 4.0).*

Why does the [continental crust](#def-g12-continental-crust-continental-crust) last, while the ocean floor is always young? The [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) is dense: it sinks back into the mantle at [subduction zones](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction), and none of it survives much more than 200 million years. The [continental crust](#def-g12-continental-crust-continental-crust) is too light to sink; it can be worn down by erosion, stretched or crumpled, but it stays at the surface. The rocks of a continent are an archive of four billion years.

## 19.4 Mountain roots

The higher the mountains, the thicker the crust beneath them.

**Definition 19.6 (Mountain root).**

The *root* of a mountain range is the part of its thickened crust that reaches down into the mantle below the level of the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) beneath the surrounding lowlands.

Airy’s model predicts the [root](#def-g12-continental-crust-root): a range standing $h$ above its surroundings has a [root](#def-g12-continental-crust-root) $r = h\,\rho_c/(\rho_m - \rho_c)$, about five times its height with $\rho_c = 2830\,\mathrm{kg}/\mathrm{m}^{3}$ and $\rho_m =
3380\,\mathrm{kg}/\mathrm{m}^{3}$ ([Proposition 12.5](https://one-course.com/books/earth/2/en/chapter/12-lithosphere-and-asthenosphere#prop-g11-lithosphere-asthenosphere-airy)). Two kinds of measurements see the [roots](#def-g12-continental-crust-root). Seismic surveys find the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) deeper under ranges: 50 to $70\,\mathrm{km}$ under many mountain belts, about $70\,\mathrm{km}$ under parts of Tibet. Gravity is weaker over mountain ranges than their visible mass would suggest: the light [root](#def-g12-continental-crust-root), standing in place of denser mantle, makes up a deficit of mass at depth, and the measured gravity anomalies follow the topography and the thickness of the crust found by seismology. The continents float, and their mountains float highest.

## 19.5 Exercises

**Exercise 19.1 ★.**

Copy and complete for the continental and the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere): thickness; main rocks; silica content; density; greatest age.

**Solution of Exercise 19.1.**

[Continental crust](#def-g12-continental-crust-continental-crust): 30 to $70\,\mathrm{km}$, about $41\,\mathrm{km}$ on average; granitic rocks, gneisses and other metamorphic and [plutonic rocks](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-volcanic-plutonic) under a sedimentary cover; about $61\,\%$ silica on average; about $2830\,\mathrm{kg}/\mathrm{m}^{3}$; up to 4.03 billion years (grains 4.4). [Oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere): about $7\,\mathrm{km}$; basalt and [gabbro](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-gabbro); about $50\,\%$ silica; about $3000\,\mathrm{kg}/\mathrm{m}^{3}$; less than 200 million years.

**Exercise 19.2 ★.**

The whole [continental crust](#def-g12-continental-crust-continental-crust) holds $60.6\,\%$ silica, its upper part $66.6\,\%$. Using the silica classes of igneous rocks, is each [mafic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic), [intermediate](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic) or [felsic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic)? Name a [plutonic rock](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-volcanic-plutonic) of the same composition.

**Solution of Exercise 19.2.**

$60.6\,\%$: [intermediate](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic), like a [diorite](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-rock-names). $66.6\,\%$: [felsic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic), like a granite.

**Exercise 19.3 ★.**

Why can the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) sink into the mantle at a [subduction zone](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction), and not the [continental crust](#def-g12-continental-crust-continental-crust)? Answer with densities.

**Solution of Exercise 19.3.**

The [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere), about $3000\,\mathrm{kg}/\mathrm{m}^{3}$, sits on lithospheric mantle, and the old, cold [oceanic lithosphere](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) as a whole is dense enough to sink. The [continental crust](#def-g12-continental-crust-continental-crust), about $2830\,\mathrm{kg}/\mathrm{m}^{3}$, far lighter than the mantle (about $3380\,\mathrm{kg}/\mathrm{m}^{3}$), is too buoyant: a continent arriving at a trench stops [subduction](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction).

**Exercise 19.4 ★.**

(1) What is a [craton](#def-g12-continental-crust-craton)? (2) How old are the rocks of a [craton](#def-g12-continental-crust-craton) at least? (3) Which kinds of rocks make it up?

**Solution of Exercise 19.4.**

(1) An old, stable core of a continent, which no longer deforms. (2) More than a billion years. (3) Metamorphic and [plutonic rocks](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-volcanic-plutonic), the deep [roots](#def-g12-continental-crust-root) of former mountains.

**Exercise 19.5 ★.**

The oldest ocean floor is about 190 million years old, the Acasta gneiss 4.03 billion years. How many times older is the gneiss? Why is there no ocean floor as old?

**Solution of Exercise 19.5.**

$4030/190 \approx 21$ times. The ocean floor is made at the ridges and destroyed at [subduction zones](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction): none survives much more than 200 million years.

**Exercise 19.6 ★★.**

The [continental crust](#def-g12-continental-crust-continental-crust) covers $210.4$ million $\mathrm{km}^{2}$, of which $30.6\,\%$ is under the sea. (1) What area of [continental crust](#def-g12-continental-crust-continental-crust) lies under the sea? (2) What area stands above it? (3) The Earth’s surface is $4\pi R^2$ with $R = 6371\,\mathrm{km}$. What share of the surface does the [continental crust](#def-g12-continental-crust-continental-crust) cover?

**Solution of Exercise 19.6.**

(1) $0.306 \times 210.4 \approx 64.4\text{ million }\mathrm{km}^{2}$. (2) $210.4 - 64.4 = 146.0\text{ million }\mathrm{km}^{2}$. (3) $4\pi \times 6371^2 \approx 5.10 \times 10^{8}\,\mathrm{km}^{2}$; $210.4/510.1 \approx
0.41$: $41\,\%$.

**Exercise 19.7 ★★.**

Compute the mass of a column of crust $1\,\mathrm{m}^{2}$ in cross-section, from the surface to the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho): (1) through $41.1\,\mathrm{km}$ of [continental crust](#def-g12-continental-crust-continental-crust) at $2830\,\mathrm{kg}/\mathrm{m}^{3}$; (2) through $7.1\,\mathrm{km}$ of [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) at $3000\,\mathrm{kg}/\mathrm{m}^{3}$. (3) How many times heavier is the first?

**Solution of Exercise 19.7.**

(1) $41100 \times 2830 \approx 1.16 \times 10^{8}\,\mathrm{kg}$. (2) $7100 \times 3000 =
2.13 \times 10^{7}\,\mathrm{kg}$. (3) About 5.5 times.

**Exercise 19.8 ★★.**

A range stands $2.5\,\mathrm{km}$ above lowlands whose crust is $35\,\mathrm{km}$ thick. With $\rho_c = 2830\,\mathrm{kg}/\mathrm{m}^{3}$ and $\rho_m =
3380\,\mathrm{kg}/\mathrm{m}^{3}$, compute its [root](#def-g12-continental-crust-root) and the thickness of its crust. Is the result in the range measured under mountain belts?

**Solution of Exercise 19.8.**

[Root](#def-g12-continental-crust-root): $2.5 \times 2830/550 \approx 12.9\,\mathrm{km}$. The crust is thicker by $2.5 \times 3380/550 \approx 15.4\,\mathrm{km}$: about $50\,\mathrm{km}$ in all, within the 50 to $70\,\mathrm{km}$ found under mountain belts.

**Exercise 19.9 ★★.**

From the histogram of ocean-floor ages: (1) what share of the ocean floor is younger than 30 million years? (2) Which band of 10 million years holds the most floor? (3) Why does the share fall towards old ages?

**Solution of Exercise 19.9.**

(1) About $0.103 + 0.100 + 0.102 \approx 0.30$: $30\,\%$. (2) The youngest band, 0 to 10 million years (about $10\,\%$), almost tied with 20 to 30. (3) Old floor has been destroyed at [subduction zones](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction); the older the floor, the more of it has gone.

**Exercise 19.10 ★★.**

Mapped with its submerged parts, the [continental crust](#def-g12-continental-crust-continental-crust) has a mean height of about $120\,\mathrm{m}$. Suppose its submerged parts, $30.6\,\%$ of its area, lie on average $100\,\mathrm{m}$ below sea level. What is the mean height of its emerged part? Why do older estimates that counted only the land give a much higher mean height?

**Solution of Exercise 19.10.**

$120 = 0.694\,h - 0.306 \times 100$, so $h = 150.6/0.694 \approx
217\,\mathrm{m}$. Counting only the land leaves out the low, submerged edges of the continents, and the mean comes out far higher.

**Exercise 19.11 ★★.**

A drill hole on an island far out in an ocean reaches, below a few hundred metres of lavas, a [gabbro](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-gabbro); seismic profiles put the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) $8\,\mathrm{km}$ down. Another drill hole, under a broad, flat plain, reaches gneiss at $2\,\mathrm{km}$, and the [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) lies $38\,\mathrm{km}$ down. Use the method to decide which crust lies under each.

**Solution of Exercise 19.11.**

The island: a [gabbro](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-gabbro) under lavas and a [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) at $8\,\mathrm{km}$, [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) (the elevation of the island does not change that). The plain: gneiss and a [Moho](https://one-course.com/books/earth/2/en/chapter/11-seismic-waves-reveal-the-interior#def-g11-seismic-structure-moho) at $38\,\mathrm{km}$, [continental crust](#def-g12-continental-crust-continental-crust).

**Exercise 19.12 ★★★.**

How good is the approximation of the proposition? (1) Compute the exact volume of a shell of thickness $41.1\,\mathrm{km}$ at the surface of a sphere of radius $6371\,\mathrm{km}$, $\tfrac{4}{3}\pi\bigl(R^3 - (R - H)^3\bigr)$, and the approximate one, $4\pi R^2 H$. (2) What is the relative difference? Compare it with $H/R$.

**Solution of Exercise 19.12.**

(1) Exact: $\tfrac{4}{3}\pi(6371^3 - 6329.9^3) \approx
2.0829 \times 10^{10}\,\mathrm{km}^{3}$; approximate: $4\pi \times 6371^2 \times 41.1
\approx 2.0964 \times 10^{10}\,\mathrm{km}^{3}$. (2) The approximation is too large by about $0.65\,\%$, close to $H/R \approx 0.0065$: for a thin layer the error is negligible.

**Exercise 19.13 ★★★.**

Suppose the upper third of the [continental crust](#def-g12-continental-crust-continental-crust), by mass, holds $66.6\,\%$ silica, and the whole crust $60.6\,\%$. (1) What is the silica content of the lower two thirds? (2) Which class of igneous rock does it match? (3) What does that say about the deep [continental crust](#def-g12-continental-crust-continental-crust)?

**Solution of Exercise 19.13.**

(1) $60.6 = (66.6 + 2x)/3$, so $x = (181.8 - 66.6)/2 = 57.6\,\%$. (2) [Intermediate](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic). (3) The deep [continental crust](#def-g12-continental-crust-continental-crust) is less rich in silica than the upper crust: more [mafic](https://one-course.com/books/earth/2/en/chapter/17-igneous-rocks#def-g11-igneous-rocks-felsic-mafic) minerals, richer in iron, magnesium and calcium.

**Exercise 19.14 ★★★.**

Suppose that new [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) forms at the ridges at about $3\,\mathrm{km}^{2}$ a year, and that the ocean floor covers about $300$ million $\mathrm{km}^{2}$. (1) How long would the ridges take to make an area equal to the whole ocean floor? (2) Compare with the ages of the ocean floor. (3) What must happen to the old floor?

**Solution of Exercise 19.14.**

(1) $3 \times 10^8/3 = 10^8$ years, 100 million years. (2) The same order as the ages of the ocean floor: three quarters younger than 100 million years, none older than about 190. (3) It must be destroyed as fast as it is made: it sinks back into the mantle at [subduction zones](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#def-g11-subduction-zones-subduction).

**Exercise 19.15 ★★★.**

Suppose all the [continental crust](#def-g12-continental-crust-continental-crust), $8.6 \times 10^{9}\,\mathrm{km}^{3}$, had formed at a steady rate since 4.0 billion years ago. (1) Compute the rate in cubic kilometres a year. (2) The zircons of the Jack Hills show that some crust already existed 4.4 billion years ago. Does a steady rate fit a world in which most of the crust might have formed early, or late? What could the oldest rocks tell, and what can they not, given that old crust can be eroded or recycled?

**Solution of Exercise 19.15.**

(1) $8.6 \times 10^9 / 4.0 \times 10^9 \approx 2.2\,\mathrm{km}^{3}$ a year. (2) A steady rate is only one possibility: the crust may have grown fast early and been recycled since, or grown late. The oldest rocks and grains prove that some crust existed early; they cannot tell how much, because old crust can be eroded or carried back into the mantle and leave few traces.

## 19.6 Problem: How Heavy Is the Continental Crust?

**Problem 19.1.**

Weekend problem — the mass of the continents

The [continental crust](#def-g12-continental-crust-continental-crust) covers $210.4$ million $\mathrm{km}^{2}$ (submerged parts included). Seismic surveys give it an average thickness of $41.1\,\mathrm{km}$ and a mean density of $2830\,\mathrm{kg}/\mathrm{m}^{3}$. The Earth has a mean radius of $6371\,\mathrm{km}$, a mass of $5.9722 \times 10^{24}\,\mathrm{kg}$ and a mean density of $5513\,\mathrm{kg}/\mathrm{m}^{3}$.

**Part I — The area.**

1. Compute the area of the Earth’s surface, $4\pi R^2$ , in $\mathrm{km}^{2}$ .
2. What share of it does the [continental crust](#def-g12-continental-crust-continental-crust) cover?
3. $30.6\,\%$ of the [continental crust](#def-g12-continental-crust-continental-crust) lies under the sea. What area is that?
4. What area of the Earth’s surface is left for the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) , assuming the rest is all oceanic?
5. Why is the [continental crust](#def-g12-continental-crust-continental-crust) larger than the land?

**Part II — Thickness and volume.**

6. Why can the volume be computed as area times thickness, though the crust lies on a sphere?
7. Compute the volume of the [continental crust](#def-g12-continental-crust-continental-crust) in $\mathrm{km}^{3}$ .
8. Convert it to $\mathrm{m}^{3}$ .
9. Another estimate of the average thickness is $36\,\mathrm{km}$ . What volume does it give?
10. By how much, in percent, do the two volumes differ?

**Part III — Density and mass.**

11. Compute the mass of the [continental crust](#def-g12-continental-crust-continental-crust) with $41.1\,\mathrm{km}$ .
12. Compute the mass of a $1\,\mathrm{m}^{2}$ column through the [continental crust](#def-g12-continental-crust-continental-crust) .
13. Compute the mass of the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) : area from question 4, thickness $7.1\,\mathrm{km}$ , density $3000\,\mathrm{kg}/\mathrm{m}^{3}$ .
14. Which is heavier, and by how many times? Why, though it covers less area?
15. Why is the [continental crust](#def-g12-continental-crust-continental-crust) less dense than the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) ?

**Part IV — Compared with the Earth.**

16. Divide the mass of question 11 by the Earth’s mass.
17. Check the result with the proposition on thin layers.
18. What share of the Earth’s mass is the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) ?
19. The [continental crust](#def-g12-continental-crust-continental-crust) holds the only rocks older than about 200 million years. What share of the Earth’s mass carries the record of almost all of its history?
20. Conclude: what share of the Earth’s mass is the [continental crust](#def-g12-continental-crust-continental-crust) ?

**Solution of Problem 19.1.**

**1.** $4\pi \times 6371^2 \approx 5.10 \times 10^{8}\,\mathrm{km}^{2}$.

**2.** $210.4/510.1 \approx 0.41$: $41\,\%$.

**3.** $0.306 \times 210.4 \approx 64.4\text{ million }\mathrm{km}^{2}$.

**4.** $510.1 - 210.4 \approx 299.7\text{ million }\mathrm{km}^{2}$, $59\,\%$.

**5.** The edges of the continents lie under shallow seas, on the continental shelves.

**6.** The thickness, $41\,\mathrm{km}$, is very small compared with the radius, $6371\,\mathrm{km}$: the curvature changes the volume by less than one percent.

**7.** $210.4 \times 10^6 \times 41.1 \approx 8.65 \times 10^{9}\,\mathrm{km}^{3}$.

**8.** $8.65 \times 10^{18}\,\mathrm{m}^{3}$.

**9.** $210.4 \times 10^6 \times 36 \approx 7.57 \times 10^{9}\,\mathrm{km}^{3}$.

**10.** $(8.65 - 7.57)/7.57 \approx 0.14$: $14\,\%$.

**11.** $8.65 \times 10^{18} \times 2830 \approx 2.45 \times 10^{22}\,\mathrm{kg}$.

**12.** $41100 \times 2830 \approx 1.16 \times 10^{8}\,\mathrm{kg}$.

**13.** $299.7 \times 10^6 \times 7.1 \approx 2.13 \times 10^{9}\,\mathrm{km}^{3}$, that is $2.13 \times 10^{18}\,\mathrm{m}^{3}$; times 3000: about $6.4 \times 10^{21}\,\mathrm{kg}$.

**14.** The [continental crust](#def-g12-continental-crust-continental-crust), about 3.8 times heavier: it is almost six times thicker, which outweighs its smaller area and density.

**15.** It is made of granitic rocks, rich in quartz and feldspars, the lightest rock-forming minerals; the [oceanic crust](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-oceanic-lithosphere) is made of basalt and [gabbro](https://one-course.com/books/earth/2/en/chapter/14-ocean-ridges-and-the-oceanic-lithosphere#def-g11-ocean-ridges-gabbro), rich in pyroxene and olivine.

**16.** $2.45 \times 10^{22}/5.97 \times 10^{24} \approx 0.0041$.

**17.** $3 \times 0.41 \times (41.1/6371) \times (2830/5513) \approx
0.0041$: the same.

**18.** $6.4 \times 10^{21}/5.97 \times 10^{24} \approx 0.0011$: about a tenth of a percent.

**19.** About $0.4\,\%$.

**20.** The [continental crust](#def-g12-continental-crust-continental-crust) is about **$0.4\,\%$ of the Earth’s mass**.