---
title: "From Continental Drift to Seafloor Spreading"
book: "High School Earth and Space Sciences"
subject: earth
language: en
chapter: 10
exercises: 15
source: https://one-course.com/books/earth/2/en/chapter/10-from-continental-drift-to-seafloor-spreading
license: CC-BY-NC-SA-4.0
credit: "One Earth and Space Sciences Book, One Course (one-course.com)"
---

# Chapter 10 — From Continental Drift to Seafloor Spreading

In the early 1950s, at the Lamont laboratory of Columbia University, a young geologist named Marie Tharp sat in front of long rows of numbers. Each was a depth of the North Atlantic, measured by a ship’s echo sounder, one after another along the ship’s track. Plotting them one by one, she drew the shape of the ocean floor along the tracks of ships that had crossed the ocean. In the middle of the ocean the floor rose into a mountain range — and on every track, along the crest of the range, the floor dropped again into a deep cleft, as if the mountains had been split down the middle. This chapter follows how such measurements of the ocean floor turned a rejected idea, the drift of the continents, into a theory: the ocean floor is made at the ridges and spreads away from them, and it carries in its rocks a record of its own age.

**You already know.**

Continental drift is the idea that the continents move; Alfred Wegener defended it from 1912 with the fit of the coasts, fossils, rocks and ancient climates, but could not say what moved them. The surface of the Earth is made of rigid plates, which meet at divergent, convergent and transform boundaries; they move a few centimetres a year, and $1\,\mathrm{cm}$ a year is $10\,\mathrm{km}$ per million years (Book 1, grade 7). The ocean floor has its continental shelf, its abyssal plains, its ridges and its trenches (Book 1, grade 8). The Earth has a magnetic field, with a north and a south magnetic pole, that a compass needle follows; a sound pulse sent into the water returns as an echo after a time that gives the distance (the physics books).

## 10.1 Why drift was rejected

Wegener’s evidence showed that the continents had once been joined. What it did not show was how they could have moved. Wegener imagined the continents ploughing through the rock of the ocean floor, and physicists answered that no force known could push a continent through solid rock without crushing it. For half a century most geologists concluded that the continents had not moved at all.

Two things were missing. The first was a mechanism. The second, which led to the first, was knowledge of the floor of the oceans, which covers most of the Earth’s surface and which, in 1912, almost no one had seen: it was assumed to be an almost featureless plain.

## 10.2 Mapping the ocean floor

An echo sounder sends a short pulse of sound from the hull of a ship to the sea floor and times its echo. Sound travels through sea water at about $1500\,\mathrm{m}/\mathrm{s}$; the pulse goes down and comes back, so a delay $t$ means a depth

$$
d = \frac{v\,t}{2}.
$$

A delay of $6.0\,\mathrm{s}$, for example, means $1500 \times 6.0/2 =
4500\,\mathrm{m}$ of water. In the nineteenth century, depths had been measured one at a time, by lowering a weighted line to the bottom. After the First World War, echo sounders took over, and the records of their echoes showed a floor far more rugged than anyone had thought; in the 1950s surveys by ships of many nations showed that a great mountain range on the ocean floor runs almost all the way around the Earth.

**History — Marie Tharp and the rift valley, 1952.**

From 1947, the geophysicist Bruce Heezen had gathered echo-sounding profiles across the North Atlantic. Marie Tharp, who was not allowed on the research ships at the time, turned what she later called “interminable rows of sounding numbers” into drawings of the sea floor. By 1952, with the east–west tracks arranged in order from north to south, she saw that one feature lined up from track to track: a cleft along the crest of the Mid-Atlantic Ridge, a rift valley. Heezen at first thought it was an error. Then the epicentres of the earthquakes of the Atlantic, plotted at the same scale, were found to fall in the rift valley itself. Tharp and Heezen’s map of the world’s ocean floor, painted by the artist Heinrich Berann in 1977, gave people the first realistic picture of the ocean floor; in 1997 the Library of Congress named her one of the four great cartographers of the twentieth century.

The mid-ocean ridges form a single, nearly continuous system about $65\,000\,\mathrm{km}$ long, more than nine tenths of it under water; the crest lies on average $2500\,\mathrm{m}$ below the surface. Along the slow Mid-Atlantic Ridge, the crest is cut by a rift valley; along the faster East Pacific Rise it is a smooth, gentle summit. The earthquakes of the oceans follow the ridges closely. Everything pointed to the ridge as a place where something was happening — but what?

## 10.3 Seafloor spreading

**History — Hess and the conveyor belt, 1962.**

In 1962 Harry Hess, a geologist at Princeton University and an admiral of the naval reserve, published *History of Ocean Basins*. He proposed that hot rock rises beneath the ridges and becomes new ocean floor, which then moves away on both sides like a conveyor belt, and sinks back into the mantle at the trenches. Robert Dietz, who reached the same idea, gave it its name: [seafloor spreading](#def-g11-drift-to-spreading-spreading). The idea explained why the Earth does not grow although new floor is always being made, why so little sediment lies on the ocean floor, and why the rocks of the ocean floor are much younger than those of the continents.

**Definition 10.1 (Seafloor spreading).**

*Seafloor spreading* is the process by which new ocean floor forms along the crest of a mid-ocean ridge, where molten rock rises from the mantle and solidifies, and then moves away from the ridge on both sides, so that the ocean floor grows older with distance from the ridge.

**Definition 10.2 (Spreading rate).**

The *full spreading rate* of a ridge is the speed at which the two plates on either side of it move apart. The *half spreading rate* is the speed at which the floor on one side moves away from the ridge axis. When spreading is symmetric, the full rate is twice the half rate.

Ridges spread at very different speeds. The Mid-Atlantic Ridge opens at $2\text{ to }5\,\mathrm{cm}$ a year, the East Pacific Rise at $6\text{ to }16\,\mathrm{cm}$ a year. Of the ocean floor that exists today, about a third was made at slow ridges (full rates of $20\text{ to }55\,\mathrm{mm}$ a year) and about two fifths at fast ones ($75\text{ to }180\,\mathrm{mm}$ a year).

Hess’s idea was bold, and at first it had little direct evidence. The evidence came from two unexpected directions: the magnetism of the ocean floor and its sediments.

## 10.4 Magnetic reversals and the striped sea floor

### 10.4.1 A rock remembers the field

The basalt of the ocean floor contains small grains of magnetite, an iron oxide that is strongly magnetic. When basalt lava erupts, it is far too hot to hold any lasting magnetisation; as it cools, the grains become magnetised parallel to the Earth’s field around them, and that direction is then locked into the rock.

**Definition 10.3 (Remanent magnetisation; Curie temperature).**

The *Curie temperature* of a magnetic mineral is the temperature above which it cannot keep a magnetisation of its own: about $580\,{}^{\circ}\mathrm{C}$ for magnetite. A rock whose magnetic grains cool through their Curie temperature in the Earth’s field keeps a magnetisation parallel to the field of that time, the *remanent magnetisation*. It lasts long after the field has changed, unless the rock is heated again above the Curie temperature.

![A lava flow cooling (schematic, Northern Hemisphere, where the field points north and down). The top of the flow has cooled below the Curie temperature of magnetite: its magnetic grains (black arrows) keep the direction of the field. The interior, still hotter, records nothing yet; it will record the field of the moment it cools.](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/fig-a88e80f92352.svg)

*A lava flow cooling (schematic, Northern Hemisphere, where the field points north and down). The top of the flow has cooled below the [Curie temperature](#def-g11-drift-to-spreading-remanence) of magnetite: its magnetic grains (black arrows) keep the direction of the field. The interior, still hotter, records nothing yet; it will record the field of the moment it cools.*

### 10.4.2 The field reverses

Early in the twentieth century, Bernard Brunhes (in 1906) and then Motonori Matuyama (in the 1920s) found that volcanic rocks fall into two groups. In some, the magnetisation points the way the present field does; in the others it points the opposite way, as if the north and south magnetic poles had changed places. The field itself had reversed, again and again.

**Definition 10.4 (Magnetic reversal; normal and reversed polarity).**

A *magnetic reversal* is an exchange of the Earth’s north and south magnetic poles. A time when the field pointed as it does today is a time of *normal polarity*; a time when it pointed the opposite way, a time of *reversed polarity*. A rock magnetised during either time has the same polarity.

Dated lavas give the succession of normal and reversed intervals: the *geomagnetic polarity time scale*. Its long intervals are named after scientists who studied the Earth’s magnetism (Brunhes, Matuyama, Gauss, Gilbert); the short events within them, after the places where they were first found.

![The geomagnetic polarity time scale for the last 5.5 million years: black for normal polarity, white for reversed. The present normal interval began 780\,000 years ago; there were twenty reversals in the last five million years. Data: Cande and Kent (1995).](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/fig-1cc47167826b.svg)

*The geomagnetic polarity time scale for the last 5.5 million years: black for [normal polarity](#def-g11-drift-to-spreading-reversal), white for reversed. The present normal interval began $780\,000$ years ago; there were twenty reversals in the last five million years. Data: Cande and Kent (1995).*

### 10.4.3 Stripes on the ocean floor

From the 1950s, ships towed magnetometers behind them across the oceans, and found that the field at the sea surface was not the smooth field expected from the Earth’s core: it was a little stronger here, a little weaker there.

**Definition 10.5 (Magnetic anomaly).**

At a point of the sea surface, the *magnetic anomaly* is the measured strength of the magnetic field minus the strength expected there from the Earth’s field alone. It is positive where the rocks below add to the field, negative where they oppose it. It is small compared with the field itself, and measured in nanoteslas ($\mathrm{nT}$).

Mapped over a wide region, the anomalies drew stripes parallel to the ridge crest, alternately positive and negative, like a zebra’s coat — and the pattern on one side of the ridge was the mirror image of the pattern on the other side.

**History — Vine and Matthews, 1963.**

In September 1963, Fred Vine and Drummond Matthews published a short paper in the journal *Nature*, *Magnetic anomalies over oceanic ridges*. They put Hess’s spreading and the reversals of the field together. If new floor forms at the crest and moves away while the field reverses, each strip of floor records the polarity of the time when it cooled. The floor becomes a striped tape, unrolling on both sides of the ridge: positive anomalies above normal strips, negative above reversed ones, the same sequence on both sides.

![The striped ocean floor (schematic, computed for a ridge spreading at 7.5\, cm a year on each side, over the last 4 million years). Each strip of floor kept the polarity of the field at the time it cooled at the axis; the pattern on one side is the mirror image of the other.](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/fig-9ba6f4fcce1d.svg)

*The striped ocean floor (schematic, computed for a ridge spreading at $7.5\,\mathrm{cm}$ a year on each side, over the last 4 million years). Each strip of floor kept the polarity of the field at the time it cooled at the axis; the pattern on one side is the mirror image of the other.*

**Proposition 10.6 (Distance of a stripe from the axis).**

If a ridge spreads symmetrically at a constant half rate $u$, the floor that formed at the axis a time $t$ ago now lies at a distance

$$
x = u\,t
$$

on either side of the axis. In particular, the boundary between two stripes that records a reversal of age $t$ lies at the distance $u\,t$ on both sides.

**Proof.** A piece of floor formed at the axis a time $t$ ago has since moved away from the axis at the speed $u$, for the time $t$: it has covered the distance $u\,t$. A piece formed at the same moment on the other side of the axis moves the other way at the same speed, and lies at the same distance. The floor on each side of a reversal boundary formed just before and just after the reversal, so the boundary lies where floor of age $t$ lies: at $u\,t$. ∎

The anomalies can be computed from the time scale. In the profiles below, the magnetised layer is a sheet of rock $1\,\mathrm{km}$ thick whose top lies $3\,\mathrm{km}$ below the sea surface, divided into blocks of normal and [reversed polarity](#def-g11-drift-to-spreading-reversal) by the proposition; the field of each block at the sea surface is added up. Above a wide strip, the anomaly is strongest near its edges, where the polarity changes, and weaker over its middle; but its sign follows the polarity of the strip below.

![Magnetic anomalies computed across a fast and a slow ridge from the polarity time scale, for floor up to 5 million years old on each side. Under each profile, the strips of floor (black: normal; white: reversed). The anomaly is positive above normal strips and negative above reversed ones; it changes sign at the boundaries. The dashed lines mark the boundary of 3.58 million years. Note the different scales of distance: the slow ridge packs the same history into a sixth of the width, and its shortest events blur together. A model computed with chosen values (a layer magnetised at 5\, A/ m, magnetised vertically, as at high latitudes); time scale from Cande and Kent (1995).](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/fig-f2dd72c5f4af.svg)

*Magnetic anomalies computed across a fast and a slow ridge from the polarity time scale, for floor up to 5 million years old on each side. Under each profile, the strips of floor (black: normal; white: reversed). The anomaly is positive above normal strips and negative above reversed ones; it changes sign at the boundaries. The dashed lines mark the boundary of 3.58 million years. Note the different scales of distance: the slow ridge packs the same history into a sixth of the width, and its shortest events blur together. A model computed with chosen values (a layer magnetised at $5\,\mathrm{A}/\mathrm{m}$, magnetised vertically, as at high latitudes); time scale from Cande and Kent (1995).*

**Method 10.7 (A spreading rate from a magnetic profile).**

1. Find the ridge axis: the centre of symmetry of the profile, in the middle of the central positive anomaly.
2. Recognise a reversal boundary on both sides — a sign change of the anomaly that the time scale dates — and measure its distance from the axis on each side.
3. Divide each distance by the age of the reversal: this gives the half rate on each side, in kilometres per million years ( $10\,\mathrm{km}$ per million years is $1\,\mathrm{cm}$ a year).
4. Add the two half rates to get the full rate.

**Example 10.8 (The fast ridge).**

On the fast profile, the boundary between the Gauss and Gilbert intervals, $3.58$ million years old, lies $268.5\,\mathrm{km}$ from the axis on each side. The half rate is $268.5/3.58 = 75\,\mathrm{km}$ per million years, that is $7.5\,\mathrm{cm}$ a year; the full rate is $15\,\mathrm{cm}$ a year, the rate of the fastest parts of the East Pacific Rise.

The magnetic stripes do more than confirm spreading: once a profile has been matched to the time scale, every stripe gives the age of the floor beneath it. In the 1960s, older stripes were dated by assuming a constant rate; a test of the whole theory was to date the floor in a completely different way.

## 10.5 Ages from the sediments

Sediment — the shells of tiny plankton, clay, dust — settles slowly onto the ocean floor and piles up over it. The oldest sediment lying directly on the basalt was deposited soon after the basalt formed; its fossils, which change from one age to the next, date it.

In 1968, the drilling ship *Glomar Challenger*, built to drill into the deep ocean floor and bring back cores, crossed the Mid-Atlantic Ridge between South America and Africa. At seven sites along a line near latitude $30{}^{\circ}$ South it drilled through the sediment into the basalt beneath, at distances of $191\,\mathrm{km}$ to $1270\,\mathrm{km}$ from the ridge axis.

![Age of the oldest sediment on the basalt at the seven drill sites of 1968 (numbered), against their distance from the axis of the Mid-Atlantic Ridge; the squares give the ages of the magnetic stripes at the sites where they were identified. The line is the constant half rate that fits the sediment ages best. Data: Deep Sea Drilling Project, Leg 3 (1970).](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/fig-f96fd745f7d8.svg)

*Age of the oldest sediment on the basalt at the seven drill sites of 1968 (numbered), against their distance from the axis of the Mid-Atlantic Ridge; the squares give the ages of the magnetic stripes at the sites where they were identified. The line is the constant half rate that fits the sediment ages best. Data: Deep Sea Drilling Project, Leg 3 (1970).*

The ages grow steadily with distance from the ridge, on both sides of it: the two sites drilled on the African side fall on the same line as those on the American side. The best constant half rate is $1.9\,\mathrm{cm}$ a year, and the fossil ages agree with the ages predicted from the magnetic stripes. The scientists of the expedition concluded that the floor had spread at a little less than $2\,\mathrm{cm}$ a year on each side for at least the last 66 million years. [Seafloor spreading](#def-g11-drift-to-spreading-spreading) had passed a test it could have failed.

![The drilling ship JOIDES Resolution, which succeeded the Glomar Challenger: the tall tower is its drilling derrick, and the ship carries more than 9000\, m of drill pipe. Photograph: Ocean Drilling Program, Texas A&M University (public domain).](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/img-8e59a3f9235d.jpg)

*The drilling ship *JOIDES Resolution*, which succeeded the *Glomar Challenger*: the tall tower is its drilling derrick, and the ship carries more than $9000\,\mathrm{m}$ of drill pipe. Photograph: Ocean Drilling Program, Texas A&M University (public domain).*

Since then, thousands of magnetic profiles and hundreds of drill holes have been put together into a map of the age of the whole ocean floor.

![The age of the ocean floor. Youngest (red) along the ridges, it grows older away from them on both sides; the oldest floor (blue and purple) lies at the edges of the oceans, against the continents and along the trenches. Data: Seton and others (2020), in 1-degree cells; land outlines: Natural Earth.](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/fig-e81defaa298a.svg)

*The age of the ocean floor. Youngest (red) along the ridges, it grows older away from them on both sides; the oldest floor (blue and purple) lies at the edges of the oceans, against the continents and along the trenches. Data: Seton and others (2020), in 1-degree cells; land outlines: Natural Earth.*

The map confirms everything at once. Along every ridge the floor is young, and its age grows symmetrically away from it. No ocean floor is older than about $190$ million years: the oldest lies in the western Pacific and off the east coast of North America (a few small basins of the eastern Mediterranean are counted apart). The mean age of the ocean floor is about $64$ million years, and about three quarters of it is younger than 100 million years — while the continents keep far older rocks. The ocean floor is young because it is always being made at the ridges and, as Hess saw, destroyed somewhere else: where, is the subject of [Chapter 15](https://one-course.com/books/earth/2/en/chapter/15-subduction-zones#ch-g11-subduction-zones).

## 10.6 Exercises

**Exercise 10.1 ★.**

Define [seafloor spreading](#def-g11-drift-to-spreading-spreading). What is the difference between the full and the half [spreading rate](#def-g11-drift-to-spreading-spreading-rate) of a ridge?

**Solution of Exercise 10.1.**

[Seafloor spreading](#def-g11-drift-to-spreading-spreading) is the making of new ocean floor at the crest of a mid-ocean ridge, where molten rock rises and solidifies, followed by its motion away from the ridge on both sides. The full rate is the speed at which the two plates move apart; the half rate is the speed at which the floor on one side moves away from the axis. For symmetric spreading, full rate $= 2
\times$ half rate.

**Exercise 10.2 ★.**

Why does a lava record the direction of the Earth’s field only once it has cooled below about $580\,{}^{\circ}\mathrm{C}$? What happens to that record if the rock is later heated to $700\,{}^{\circ}\mathrm{C}$?

**Solution of Exercise 10.2.**

Above its [Curie temperature](#def-g11-drift-to-spreading-remanence), about $580\,{}^{\circ}\mathrm{C}$, magnetite cannot keep a magnetisation of its own; only when it cools below it do its grains become magnetised along the field and keep that direction. Heated again to $700\,{}^{\circ}\mathrm{C}$, above the [Curie temperature](#def-g11-drift-to-spreading-remanence), the rock loses its old record; as it cools again it records the field of that new time.

**Exercise 10.3 ★.**

An echo sounder hears the echo of its pulse $5.2\,\mathrm{s}$ after sending it. Taking the speed of sound in sea water as $1500\,\mathrm{m}/\mathrm{s}$, how deep is the sea floor?

**Solution of Exercise 10.3.**

The sound goes down and back: $d = 1500 \times 5.2/2 = 3900\,\mathrm{m}$.

**Exercise 10.4 ★.**

On the polarity time scale of this chapter: how long has the present normal interval lasted? How long did the Jaramillo event last? How many reversals happened in the last five million years?

**Solution of Exercise 10.4.**

The present normal interval began $0.78$ million years ago: it has lasted $780\,000$ years. The Jaramillo event lasted $1.07 - 0.99 = 0.08$ million years, $80\,000$ years. Counting the boundaries younger than five million years (0.78, 0.99, 1.07, 1.77, 1.95, 2.14, 2.15, 2.581, 3.04, 3.11, 3.22, 3.33, 3.58, 4.18, 4.29, 4.48, 4.62, 4.80, 4.89, 4.98): twenty reversals.

**Exercise 10.5 ★.**

The mid-ocean ridges are about $65\,000\,\mathrm{km}$ long. The circumference of the Earth is about $40\,000\,\mathrm{km}$. How many times around the Earth would the ridges go?

**Solution of Exercise 10.5.**

$65\,000/40\,000 \approx 1.6$: the ridges would go about one and a half times around the Earth.

**Exercise 10.6 ★★.**

On a magnetic profile, the boundary between the Brunhes and Matuyama intervals ($0.78$ million years) lies $20\,\mathrm{km}$ from the ridge axis. Compute the half rate and the full rate in centimetres a year.

**Solution of Exercise 10.6.**

$20/0.78 \approx 25.6\,\mathrm{km}$ per million years, that is a half rate of about $2.6\,\mathrm{cm}$ a year; the full rate is about $5.1\,\mathrm{cm}$ a year.

**Exercise 10.7 ★★.**

On another profile, the Gauss–Gilbert boundary ($3.58$ million years) lies $45\,\mathrm{km}$ west and $44\,\mathrm{km}$ east of the axis. Compute the half rate on each side and the full rate. Is the spreading symmetric?

**Solution of Exercise 10.7.**

West: $45/3.58 \approx 12.6$ km per million years, $1.26\,\mathrm{cm}$ a year; east: $44/3.58 \approx 12.3$ km per million years, $1.23\,\mathrm{cm}$ a year. Full rate: $1.26 + 1.23 \approx 2.5\,\mathrm{cm}$ a year. The two half rates differ by about $2\,\%$: the spreading is very nearly symmetric.

**Exercise 10.8 ★★.**

Site 19 of the 1968 drilling lies $990\,\mathrm{km}$ from the axis of the Mid-Atlantic Ridge. Using a half rate of $1.9\,\mathrm{cm}$ a year, predict the age of the floor there, and compare with the $49$ million years of its oldest sediment.

**Solution of Exercise 10.8.**

$1.9\,\mathrm{cm}$ a year is $19\,\mathrm{km}$ per million years: $990/19 \approx 52$ million years, a little older than the 49 million years of the oldest sediment (about $6\,\%$).

**Exercise 10.9 ★★.**

A ridge spreads at a half rate of $2\,\mathrm{cm}$ a year. Using the time scale of this chapter, give the distances from the axis of the boundaries at 0.78, 0.99, 1.07, 1.77 and 1.95 million years, and draw the stripes on one side, normal in black.

**Solution of Exercise 10.9.**

At $20\,\mathrm{km}$ per million years: $15.6\,\mathrm{km}$, $19.8\,\mathrm{km}$, $21.4\,\mathrm{km}$, $35.4\,\mathrm{km}$ and $39.0\,\mathrm{km}$. From the axis: normal from 0 to $15.6\,\mathrm{km}$, reversed to $19.8\,\mathrm{km}$, normal to $21.4\,\mathrm{km}$ (Jaramillo), reversed to $35.4\,\mathrm{km}$, normal to $39.0\,\mathrm{km}$ (Olduvai), then reversed.

**Exercise 10.10 ★★.**

The mean age of the ocean floor is about $64$ million years; the Earth is about $4.6$ billion years old. What fraction of the Earth’s age is that? Which of Hess’s arguments does it support?

**Solution of Exercise 10.10.**

$64 \times 10^6/4.6 \times 10^9 \approx 0.014$, about $1.4\,\%$ of the Earth’s age. It supports Hess’s argument that the ocean floor is young because it is always being made and destroyed: no ocean floor has survived from most of the Earth’s history.

**Exercise 10.11 ★★.**

Explain, with a drawing, why the pattern of magnetic stripes on one side of a ridge is the mirror image of the pattern on the other side. What would break this symmetry?

**Solution of Exercise 10.11.**

At any moment the floor forms at the axis with the polarity of that moment, and splits: half moves away on each side at the same speed. Two strips formed at the same time therefore lie at the same distance from the axis, one on each side, with the same polarity: each side is a copy of the other, reflected in the axis. The symmetry is broken if the floor moves away faster on one side than on the other (asymmetric spreading), or if the axis jumps to a new position.

**Exercise 10.12 ★★★.**

Suppose the ridges, $65\,000\,\mathrm{km}$ long in all, spread at an average full rate of $5\,\mathrm{cm}$ a year.

1. What area of new ocean floor do they make each year, in $\mathrm{km}^{2}$ ?
2. The ocean floor covers about $2.9 \times 10^{8}\,\mathrm{km}^{2}$ . How long would the ridges take to make that much?
3. Compare with the oldest ocean floor, about $190$ million years. What must happen to the ocean floor as fast as it is made?

**Solution of Exercise 10.12.**

(1) $5\,\mathrm{cm}$ is $5 \times 10^{-5}$ $\mathrm{km}$: each year a strip $65\,000 \times 5 \times 10^{-5} = 3.25\,\mathrm{km}^{2}$ is added. (2) $2.9 \times 10^8/3.25 \approx 9 \times 10^7$ years, about 90 million years. (3) This is of the same order as the age of the oldest floor (190 million years) and shorter than it: for the ocean floor to stay so young, as much floor must be destroyed, somewhere, as is made at the ridges.

**Exercise 10.13 ★★★.**

The Jaramillo event lasted from $0.99$ to $1.07$ million years ago. How wide is its stripe on each side of a ridge with a half rate of $1.25\,\mathrm{cm}$ a year, and of one with $7.5\,\mathrm{cm}$ a year? The magnetised rock lies about $3\,\mathrm{km}$ below the sea surface. Explain why the event shows clearly on the fast profile of this chapter but hardly at all on the slow one.

**Solution of Exercise 10.13.**

The event lasted $0.08$ million years. At $12.5\,\mathrm{km}$ per million years its stripe is $0.08 \times 12.5 = 1\,\mathrm{km}$ wide; at $75\,\mathrm{km}$ per million years, $0.08 \times 75 = 6\,\mathrm{km}$. Seen from the sea surface, $3\,\mathrm{km}$ above, a stripe much narrower than its depth produces only a weak field, blurred together with the fields of its wide neighbours of the opposite polarity; a stripe twice as wide as its depth stands out.

**Exercise 10.14 ★★★.**

At the 1968 sites, the sediment is $176\,\mathrm{m}$ thick at site 16, whose floor is about $11$ million years old, and only $72\,\mathrm{m}$ thick at site 20, about $67$ million years old. Compute the average rate at which sediment piled up at each site, in metres per million years. Can the thickness of the sediment be used to date the floor? What is used instead?

**Solution of Exercise 10.14.**

Site 16: $176/11 \approx 16\,\mathrm{m}$ per million years; site 20: $72/67
\approx 1.1\,\mathrm{m}$ per million years. The sediment piles up at very different rates from place to place and from time to time, so its thickness does not give the age of the floor. The age is given by the fossils of the oldest sediment, lying directly on the basalt.

**Exercise 10.15 ★★★.**

On a profile across a ridge, the boundary of $2.581$ million years lies $58\,\mathrm{km}$ west and $70\,\mathrm{km}$ east of the axis.

1. Compute the half rate on each side and the full rate.
2. The floor east of the axis was made faster than the floor west of it. After 10 million years at these rates, how far from the axis would floor of that age lie on each side?
3. Explain why the distance between the two boundaries gives the full rate even if the spreading is not symmetric.

**Solution of Exercise 10.15.**

(1) West: $58/2.581 \approx 22.5\,\mathrm{km}$ per million years, $2.25\,\mathrm{cm}$ a year; east: $70/2.581 \approx 27.1\,\mathrm{km}$ per million years, $2.71\,\mathrm{cm}$ a year; full rate $128/2.581 \approx 49.6\,\mathrm{km}$ per million years, about $5.0\,\mathrm{cm}$ a year. (2) About $225\,\mathrm{km}$ west and $271\,\mathrm{km}$ east. (3) The two boundaries were together at the axis when the reversal happened; since then they have moved apart at the full rate, however the motion is shared between the two sides. Their separation divided by their age is the full rate.

## 10.7 Problem: The Age of the South Atlantic

**Problem 10.1.**

Weekend problem — dating an ocean in three ways

In 1968 the *Glomar Challenger* drilled seven holes across the Mid-Atlantic Ridge near latitude $30{}^{\circ}$ South. The table gives, for each site, its distance from the ridge axis, the age of the oldest sediment on the basalt (from its fossils) and, where the stripe beneath it was identified, the age of that magnetic stripe, in millions of years.

| site | distance from the axis ($\mathrm{km}$) | age of the oldest sediment | age of the magnetic stripe |
| --- | --- | --- | --- |
| 16 | 191 | 11 | 9 |
| 15 | 380 | 24 | 21 |
| 18 | 506 | 26 | — |
| 17 | 643 | 33 | — |
| 14 | 727 | 40 | 38.5 |
| 19 | 990 | 49 | 53 |
| 20 | 1270 | 67 | 71 |

*Data: Deep Sea Drilling Project, Leg 3 (1970); magnetic ages are the middle of the ranges given there.*

![](https://one-course.com/images/onecourse/chapters/earth-2/g11-drift-to-spreading/fig-285e6fc3039b.svg)

**Part I — The drill sites.**

1. Which site lies closest to the ridge, and which farthest? How do their ages compare?
2. Why is the age of the oldest sediment lying on the basalt close to the age of the basalt itself? Is it a little older or a little younger?
3. For each site, compute the ratio of its distance to the age of its oldest sediment, in kilometres per million years.
4. What is the mean of these seven ratios? Convert it to centimetres a year.
5. Sites 17 and 18 lie east of the ridge, the others west of it. Do the eastern sites follow the same trend as the western ones? What does that say about the spreading?

**Part II — The rate from the sediments.**

6. If the floor spread at a constant half rate $u$ , how would the age $t$ of the floor depend on its distance $d$ from the axis?
7. The line through the origin that fits the points best has the slope $u = \sum d\,t / \sum t^2$ . For the seven sites, $\sum d\,t = 208\,276$ and $\sum t^2 = 10\,952$ (in kilometres and millions of years). Compute $u$ in kilometres per million years and in centimetres a year.
8. What is the [full spreading rate](#def-g11-drift-to-spreading-spreading-rate) of the South Atlantic at this latitude?
9. The expedition’s scientists wrote that the rate was “slightly less than $2\,\mathrm{cm}$ a year”. Do you agree?
10. With this rate, predict the age of the floor at site 20, and compare with its oldest sediment.

**Part III — The rate from the magnetic stripes.**

11. From site 16 alone ( $191\,\mathrm{km}$ , stripe of 9 million years), compute a half rate.
12. From site 20 alone ( $1270\,\mathrm{km}$ , stripe of 71 million years), compute a half rate.
13. For the five sites with a magnetic age, $\sum d\,t = 180\,329$ and $\sum t^2 = 9854$ . Compute the best half rate.
14. By how many per cent do the rates from the fossils and from the stripes differ? Do the two methods agree?
15. Why is it important that the two ages were found by completely different methods?

**Part IV — To the edge of the ocean.**

16. Along $30{}^{\circ}$ South, the ridge axis lies at longitude $13.8{}^{\circ}$ West and the ocean floor ends against Africa at $13.8{}^{\circ}$ East. How many degrees of longitude separate them?
17. On a sphere of radius $6371\,\mathrm{km}$ , one degree of longitude measures $111.2\,\mathrm{km} \times \cos(\text{latitude})$ . Compute the length of one degree at $30{}^{\circ}$ South, and the distance from the axis to the edge of the ocean floor beside Africa.
18. If the floor had always spread at the rate of Part II, how long ago would the floor at the edge have formed?
19. The age map, which dates the old floor by its magnetic stripes, gives $130$ million years at the edge. What average half rate does that imply? Was the early opening of the ocean a little faster or a little slower than the opening of the last 66 million years?
20. Conclude: how old is the oldest ocean floor beside Africa at $30{}^{\circ}$ South? The Cretaceous period began about $143$ million years ago: in which period did the South Atlantic begin to open there?

**Solution of Problem 10.1.**

**1.** Site 16 is the closest ($191\,\mathrm{km}$, 11 million years), site 20 the farthest ($1270\,\mathrm{km}$, 67 million years): the farther from the ridge, the older the floor.

**2.** The sediment starts to settle on the basalt as soon as the basalt has formed, so the oldest layer is about as old as the basalt. It can only be a little younger, never older.

**3.** In kilometres per million years: site 16: $191/11 \approx 17.4$; site 15: $380/24 \approx 15.8$; site 18: $506/26 \approx 19.5$; site 17: $643/33 \approx 19.5$; site 14: $727/40 \approx 18.2$; site 19: $990/49
\approx 20.2$; site 20: $1270/67 \approx 19.0$.

**4.** $129.5/7 \approx 18.5$ km per million years, about $1.85\,\mathrm{cm}$ a year.

**5.** Yes: their ratios (19.5) lie among those of the western sites. The floor has spread at about the same rate on both sides: the spreading is symmetric.

**6.** $t = d/u$: the age is proportional to the distance.

**7.** $u = 208\,276/10\,952 \approx 19.0$ km per million years, that is $1.90\,\mathrm{cm}$ a year.

**8.** About $2 \times 1.9 = 3.8\,\mathrm{cm}$ a year.

**9.** Yes: $1.9\,\mathrm{cm}$ a year is slightly less than $2\,\mathrm{cm}$ a year.

**10.** $1270/19.0 \approx 67$ million years, the same as its oldest sediment.

**11.** $191/9 \approx 21.2$ km per million years, $2.1\,\mathrm{cm}$ a year.

**12.** $1270/71 \approx 17.9$ km per million years, $1.8\,\mathrm{cm}$ a year.

**13.** $180\,329/9854 \approx 18.3$ km per million years, $1.83\,\mathrm{cm}$ a year.

**14.** $(1.90 - 1.83)/1.83 \approx 4\,\%$: the two rates agree within the uncertainties of the ages and distances.

**15.** One age comes from fossils in the sediment, the other from the magnetism of the basalt and the time scale of reversals. An error in one method would not appear in the other: their agreement is a strong test of [seafloor spreading](#def-g11-drift-to-spreading-spreading).

**16.** $13.8 + 13.8 = 27.6{}^{\circ}$.

**17.** $111.2 \times \cos 30^\circ \approx 96.3\,\mathrm{km}$ per degree; $27.6 \times 96.3 \approx 2660\,\mathrm{km}$.

**18.** $2660/19.0 \approx 140$ million years.

**19.** $2660/130 \approx 20.5$ km per million years, about $2.0\,\mathrm{cm}$ a year, a little more than $1.9\,\mathrm{cm}$ a year. Since the last 67 million years ran at about $1.9\,\mathrm{cm}$ a year, the earlier opening was a little faster: the floor between site 20 and the edge, $2660 - 1270 =
1390\,\mathrm{km}$, formed in $130 - 67 = 63$ million years, about $2.2\,\mathrm{cm}$ a year.

**20.** **The oldest ocean floor beside Africa at $30{}^{\circ}$ South is about 130 million years old** (140 million years by extrapolating today’s rate): the South Atlantic began to open there in the Cretaceous period.