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The dynamic Earth · The dynamics of the geosphere

Structure and Dynamics of the Geosphere

Popocatépetl spews ash from a conduit that begins tens of kilometers beneath our feet, yet no one has ever gone down to see where that material comes from. The deepest hole in the world, the Kola borehole, reached only 12 km, and the center of the Earth is about $6{,}371$ km away. So how do we know what is down there?

Methods for Studying the Earth's Interior

The deepest mines barely reach 4 km, and exploration wells go down about 12 km. Even so, we know that at a depth of 2,900 km a layer of liquid metal begins. How do you explore a planet when we have only scratched its surface?

Cross section of the Earth with crust, mantle, and liquid outer core. Seismic waves leave the hypocenter, travel down through the mantle along curved paths, and return to the surface at stations A and B. hypocenter station A station B crust seismic waves mantle outer core (liquid) not to scale
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The deepest mine in the world reaches a depth of barely $4\ \text{km}$, while the radius of the Earth is about $6\,370\ \text{km}$. Explain why almost everything we know…

The deepest mine in the world reaches a depth of barely $4\ \text{km}$, while the radius of the Earth is about $6\,370\ \text{km}$. Explain why almost everything we know about the Earth's interior comes from indirect methods, and give one example of a direct method and one of an indirect method.

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S-type seismic waves do not pass through the outer core, whereas P-waves do, although their speed is reduced. What does this fact tell us about the physical state of the…

S-type seismic waves do not pass through the outer core, whereas P-waves do, although their speed is reduced. What does this fact tell us about the physical state of the outer core? Reason your answer.

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Measuring the Distance to an Earthquake

Because P waves travel faster than S waves, the farther away the earthquake occurs, the more their arrival times separate. If the delay between them is $\Delta t$, the distance $d$ satisfies:

$$\Delta t = \frac{d}{v_S} - \frac{d}{v_P} \quad\Rightarrow\quad d = \frac{\Delta t}{\dfrac{1}{v_S}-\dfrac{1}{v_P}}$$

The Model Based on Chemical Composition

Diagram of the layers of the geosphere according to the compositional model: crust, mantle, and core crust mantle core

From the outside toward the center, the order is: crust, mantle, outer core, and inner core. The crust is so thin that it is greatly exaggerated in the drawing.

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Order the following layers of the geosphere from the surface to the center of the planet: inner core, mantle, outer core, crust. Then state which of them occupies the…

Order the following layers of the geosphere from the surface to the center of the planet: inner core, mantle, outer core, crust. Then state which of them occupies the largest part of the Earth's volume.

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During an exploration mission on a rocky planet of similar size to Earth, a seismograph records an earthquake generated at a depth of $100\ \text{km}$. It is observed…

During an exploration mission on a rocky planet of similar size to Earth, a seismograph records an earthquake generated at a depth of $100\ \text{km}$. It is observed that, starting at a depth of $2\ 900\ \text{km}$, the velocity of P waves drops abruptly from $13.7\ \text{km/s}$ to $8.1\ \text{km/s}$, and S waves cease to be detected entirely.

  1. a) Interpret what physical changes (density and state of aggregation of matter) occur at that depth and name the analogous terrestrial seismic discontinuity, indicating which layers it separates on our planet.
  2. b) Predict what types of waves a second seismic station located at the planet's antipodes ($180^{\circ}$ relative to the seismic focus) would record and justify why a seismic "shadow zone" exists for S waves.
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The Model Based on Mechanical Behavior

During an earthquake, rocks at the surface break suddenly, yet in the mountain ranges we see layers of rock folded like clay. Why do the same materials behave so differently depending on depth?

Cross section of the Earth's outer layers according to their mechanical behavior: rigid lithosphere broken into plates, which includes the crust and the upper part of the mantle; plastic asthenosphere of the upper mantle that flows slowly; and the mesosphere, the more rigid lower mantle plate boundaries crust upper mantle lithosphere rigid, in plates asthenosphere plastic: flows very slowly (upper mantle) mesosphere more rigid (lower mantle) thicknesses not to scale
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Explain in your own words what the lithosphere is, which layers of the geosphere form it, and how it differs from the crust.

Explain in your own words what the lithosphere is, which layers of the geosphere form it, and how it differs from the crust.

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The Geothermal Gradient and Convection Currents

In deep mines, such as the silver mines of Guanajuato or the gold mines of South Africa, the heat from the walls forces workers to ventilate and cool the air. At what rate does the Earth's interior heat up, and what effect does that heat have on deep rocks?

Animation of mantle convection currents: dots rising along the blue paths (hot material) and sinking along the green ones (cold material), staggered in a slow loop. heat from the core and radioactive decay
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Look at the diagram of the Earth's interior. Name the layers marked with numbers 1 to 4 and state one characteristic of each (physical state or composition).

Look at the diagram of the Earth's interior. Name the layers marked with numbers 1 to 4 and state one characteristic of each (physical state or composition).

1 2 3 4 1 → ? 2 → ? 3 → ? 4 → ?
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Convection currents exist in the mantle: hot material rises and cold material sinks. Explain what causes these currents and how they relate to the movement of the…

Convection currents exist in the mantle: hot material rises and cold material sinks. Explain what causes these currents and how they relate to the movement of the lithosphere.

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At a seismological station, the arrival of P waves is recorded at 10:14:20 and that of S waves at 10:14:49 (a delay of $\Delta t = 29\ \text{s}$). It is known that in…

At a seismological station, the arrival of P waves is recorded at 10:14:20 and that of S waves at 10:14:49 (a delay of $\Delta t = 29\ \text{s}$). It is known that in this region of the crust, P waves travel at an average velocity $v_P = 8.0\ \text{km/s}$ and S waves at $v_S = 4.5\ \text{km/s}$.

  1. a) Deduce the algebraic expression relating the time interval $\Delta t$ to the distance to the epicentre ($d$) and calculate the exact distance from the station to the epicentre (assume the depth of the hypocentre is negligible).
  2. b) A technician states: "Since we know the exact distance, we can now locate the epicentre on the map by drawing a straight line". Refute their statement by explaining what geometric indeterminacy exists, and design the method that seismologists must use (minimum number of stations and graphical procedure) to locate the epicentre accurately.
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In a mine at a depth of $2\ \text{km}$, the temperature of the rocks is $75\ ^{\circ}\text{C}$, while at the surface it is $15\ ^{\circ}\text{C}$. Calculate the…

In a mine at a depth of $2\ \text{km}$, the temperature of the rocks is $75\ ^{\circ}\text{C}$, while at the surface it is $15\ ^{\circ}\text{C}$. Calculate the geothermal gradient (the variation in temperature per kilometer of depth) for that area and explain why the temperature increases with depth.

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Back to the beginning: the material from Popocatépetl comes from deep zones that no one has visited, but we know about them through indirect methods such as seismic waves. In the Kola borehole, at a depth of 12 km, the temperature reached about $180\ ^{\circ}\text{C}$ (the average gradient there was lower than the typical $30\ ^{\circ}\text{C/km}$). The rock, hot and under enormous pressure, behaved plastically and tended to close the hole, which made it impossible to keep drilling.

Summary

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