Exercises: Structure and dynamics of the geosphere

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.

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.

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

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.

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).

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.

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.

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.

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.