Exercises: The structure of the geosphere

The cross-section in the figure shows the concentric layers of the geosphere, but one of them is marked with "?". State the name of that layer and list all the layers in order from the shallowest to the deepest.

Name the three layers of the geosphere and state which is the outermost and which is the deepest. Which layer do we live on?

If the Earth were a peach, explain which part of the fruit would represent the crust, the mantle, and the core, and point out one limitation of this comparison.

Explain what the geosphere is and name which other parts of the Earth it is in contact with at the surface (air, water, and living things), writing the technical name for each one.

Which layer of the geosphere lies just below the crust? And which one occupies the centre of the planet? Order the three layers from the outside inwards.

State the physical state of the materials of the outer core and the inner core, and explain which two metals they are mainly made of.

The iron in the core causes the Earth to behave like a giant magnet.

1. a) Explain which everyday device makes use of this magnetism to navigate.
2. b) Reason out what would happen to that device if the core were not magnetic.

Which is the thinnest layer of the geosphere? Compare its maximum thickness ($70\ \text{km}$) with that of the mantle (about $2\,900\ \text{km}$) and explain what that difference means.

The crust is between $5\ \text{km}$ and $70\ \text{km}$ thick, the mantle extends about $2\,900\ \text{km}$ beneath it, and the core has a radius of about $3\,480\ \text{km}$. Calculate the approximate distance from the surface to the centre of the Earth, estimate how many times a journey from Dublin to Cork (about $620\ \text{km}$) fits into that distance, and explain what a tiny fraction of the total distance is represented by the crust, the layer we live on.

Distinguish between continental crust and oceanic crust: which of the two is thicker, where each one is located, and what types of materials predominate in them.

The core has a liquid outer part and a solid inner part, even though both are made of iron and nickel. Explain how it is possible for the inner core, being the hottest region of the planet, to remain solid.

The deepest borehole ever drilled reached about $12\ \text{km}$, and the distance from the surface to the centre of the Earth is about $6\,370\ \text{km}$. Calculate what percentage of the way to the centre we have managed to drill and explain which two difficulties (temperature and pressure) hold back deep drilling.

Continental crust is thicker and less dense than oceanic crust. Using the analogy of two icebergs of different thickness, explain why continents rise above sea level while oceanic crust remains submerged.

Where does the heat inside the Earth come from? Explain two sources of this heat (the heat left over from the formation of the planet and the heat generated by certain materials inside it) and name two pieces of evidence of this heat that we can observe at the surface, such as volcanoes or hot springs.

Where do you think the crust is thicker: under the Himalaya mountain range or under the Pacific Ocean? Justify your answer and explain the relationship between high mountains and the deep "roots" of the crust.

Compare the Earth with a boiled egg (shell, white, and yolk): explain which layer each part represents and point out two things the egg model does not represent well about the Earth's interior.

The average density of the entire Earth is approximately $5.5\ \text{g/cm}^3$. However, the rocks that make up the continental crust only have an average density of about $2.7\ \text{g/cm}^3$, and the peridotites that some deep volcanoes rip from the mantle reach $3.3\ \text{g/cm}^3$. On the other hand, many metallic meteorites that fall from space are made of iron and nickel with densities exceeding $7.5\ \text{g/cm}^3$.

1. a) Using these density data, demonstrate why it is impossible for the Earth to be homogeneous inside.
2. b) Deduce which layer of the Earth's interior must correspond to the composition of metallic meteorites so that the overall average density of the planet matches $5.5\ \text{g/cm}^3$.
3. c) Justify how the study of asteroid and meteorite debris from space allows us to know the composition of the center of our planet without needing to reach it.

The Mponeng gold mine (South Africa) is the deepest human excavation on Earth: it reaches nearly $4\ \text{km}$ beneath the surface. In that area, the surface temperature is $20\ ^\circ\text{C}$ and the average geothermal gradient is $2.5\ ^\circ\text{C}$ for every $100\ \text{m}$ of depth.

1. a) Calculate what temperature the rock at the bottom of the mine would reach if no artificial air conditioning system were operating.
2. b) A miner can only work safely if the ambient temperature does not exceed $32\ ^\circ\text{C}$. Calculate the maximum depth at which this safety limit would be reached without cooling.
3. c) If we applied that same gradient continuously to the center of the Earth ($6\,371\ \text{km}$), what absurd theoretical temperature would be obtained in the core? Deduce what this calculation teaches us about how the geothermal gradient varies in the deepest layers.

In science class, two observations arise that seem contradictory:

1. S seismic waves generated by earthquakes only travel through solid media, and they cross the entire Earth's mantle without disappearing.

2. Continents move a few centimeters per year because the mantle on which they float flows, forming convection currents over millions of years.

1. a) Resolve this apparent contradiction using the analogy of plasticine or bitumen: explain how a material can behave as a rigid solid under sudden, brief forces (an earthquake) and at the same time deform plastically and flow under continuous forces applied over millions of years.
2. b) Predict what would happen to the Earth's surface (relief, volcanoes, and earthquakes) if the mantle were completely liquid like water or volcanic lava instead of a plastic solid.

Imagine that a space mission installs seismographs all over a newly discovered rocky planet. After an earthquake is recorded at the north pole of that planet, the following data are obtained:

• P seismic waves (which travel through both solids and liquids) are recorded across almost the entire planet, although they undergo a sudden change in direction and speed at a depth of $2\,500\ \text{km}$.

• S seismic waves (which propagate exclusively through solid materials) are detected normally down to $2\,500\ \text{km}$, but they disappear completely below that and do not reach any seismograph in the southern hemisphere.

1. a) Interpret these recordings and deduce the physical state (solid or liquid) of the layer located between $0$ and $2\,500\ \text{km}$, and of the layer located deeper down. Justify your deduction.
2. b) Suppose that at the center of this planet there is also a completely solid inner core. Predict whether S waves originating from the earthquake at the north pole will be able to reach that solid inner core. Reason your answer based on the path they must travel.

It is often said that the Earth's crust is proportionally as thin as the skin of an apple. Let's check with data whether this statement is scientifically accurate:

• Radius of the Earth: $6\,370\ \text{km}$.

• Average thickness of the continental crust: $35\ \text{km}$; of the oceanic crust: $7\ \text{km}$.

• A typical apple has a radius of about $40\ \text{mm}$ and its skin thickness is approximately $0.3\ \text{mm}$.

1. a) Calculate the percentage of the radius represented by the apple's skin and compare it with the percentage represented by the continental crust and the oceanic crust relative to the Earth's radius.
2. b) In light of your calculations, is the popular analogy correct, or is the apple's skin proportionally thicker or thinner than the Earth's crust? Justify it with your results.
3. c) If you made a spherical model of the Earth with a radius of $20\ \text{cm}$ ($200\ \text{mm}$), calculate how many millimeters thick the oceanic crust and the continental crust would be. Could you draw the oceanic crust to scale with the tip of a standard $1\ \text{mm}$ school pencil without exaggerating it?

We have maps of the surface of Mars with a resolution of a few metres thanks to orbiting satellites, but we know the ocean floor of the Earth, located just a few kilometres underwater, in much less detail.

1. a) Explain why high-resolution cameras and radar on orbiting satellites cannot be used to map the deep ocean floor, indicating which physical property of seawater prevents this.
2. b) In the Mariana Trench ($11\ \text{km}$ deep), the pressure is over $1\,100$ atmospheres. If you had to design an underwater robot to descend into that area, what two critical technical difficulties would you need to solve to prevent its destruction and successfully collect data from the seabed?
3. c) Given that light and radar do not penetrate the deep ocean, deduce what type of waves oceanographic vessels use to "see" and map the underwater relief (sonar), and briefly explain how they calculate the depth of the ocean floor.

Two European cities want to build a plant to heat homes using deep geothermal energy, taking advantage of groundwater at $90\ ^\circ\text{C}$. In winter, the surface temperature in both cities is $0\ ^\circ\text{C}$:

• Reykjavik (Iceland): located on an active volcanic ridge, its average geothermal gradient is $15\ ^\circ\text{C}$ per $100\ \text{m}$ of depth.

• Helsinki (Finland): located on an old, cold continental shield, its geothermal gradient is $2\ ^\circ\text{C}$ per $100\ \text{m}$ of depth.

1. a) Calculate the minimum depth each city must drill to reach rock at the required $90\ ^\circ\text{C}$.
2. b) Taking into account the cost and technical difficulty of drilling deep wells, justify why direct geothermal heating is highly profitable in Iceland, but virtually economically unfeasible in most of the European continent.
3. c) Explain the origin of the internal heat utilized by Iceland and reason why it is found at such shallow depths compared to Finland.

In Jules Verne's famous novel Journey to the Centre of the Earth, the protagonists walk down the vent of an extinct volcano and find enormous hollow, passable caverns, an underground ocean, and pleasant temperatures hundreds of kilometres deep.

1. a) Considering lithostatic pressure (the colossal weight of the overlying rocks), predict what would happen to any hollow cave or gallery deeper than $15\ \text{km}$. Why is it physically impossible for open caverns to exist in the Earth's mantle?
2. b) Common steel melts at around $1\,400\ ^\circ\text{C}$ and titanium at $1\,668\ ^\circ\text{C}$. Knowing that the temperature at the boundary between the mantle and the core is around $4\,000\ ^\circ\text{C}$, justify why it is unfeasible to build a vehicle or drill that physically descends to the centre of the planet.
3. c) If the temperature at the centre of the Earth is even higher (reaching almost $6\,000\ ^\circ\text{C}$), how is it possible that the inner core is solid while the outer core, which is at a lower temperature, is liquid? Resolve this apparent contradiction by explaining the role of pressure.