Exercises: Structure and composition of the geosphere

Name the layers of the geosphere ordered from the outside to the center of the planet, and state the physical state (solid, fluid) of each one.

Cite two direct methods of studying the geosphere and explain why, even with the deepest boreholes, we directly know only a tiny fraction of the Earth's radius.

Compare continental crust and oceanic crust in terms of their thickness, composition, and density, and relate these differences to their behavior when two plates collide.

Explain how P and S seismic waves differ (type of movement and media they pass through) and how their shadow zones allowed the existence and state of Earth's core to be deduced.

What is a seismic discontinuity? State which layers are separated by the Mohorovičić and Gutenberg discontinuities and at roughly what depths they are located.

The diagram represents a cross-section of the concentric layers of the geosphere. a) Name the layers marked with numbers 1 to 4. b) State the missing approximate depth ("?") and which discontinuity is found at that depth. c) Indicate the physical state of layers 3 and 4 and the evidence that proves it.

A geophysical exploration probe deploys a network of seismometers on a newly discovered rocky planet. Following a major meteorite impact at its north pole ($0^\circ$), the seismographs record:

• Direct P-waves between $0^\circ$ and $105^\circ$ of angular distance.

• A total shadow zone (without direct P- or S-waves) between $105^\circ$ and $142^\circ$.

• Between $142^\circ$ and the antipodes ($180^\circ$), P-waves are recorded again, but they arrive with a noticeable delay, and no direct S-waves are recorded.

1. a) Interpret these records by applying the laws of seismic wave propagation and refraction to deduce the existence of the core, its physical state, and its relative propagation velocity compared to the mantle.
2. b) Predict which new direct seismic phases you would expect to record in the antipodal zone ($142^\circ$-$180^\circ$) if, with the progressive cooling of the planet, a solid inner core were to begin nucleating and growing.

A student proposes the following hypothesis to simplify calculating the travel time of seismic waves: «Given that Earth's mantle is a continuous solid medium down to a depth of $2\,900\ \text{km}$, seismic rays traveling from the focus to a distant seismological station propagate in a straight line at a constant average velocity; therefore, the arrival time is simply calculated by dividing the straight-line geometric distance by said velocity».

1. a) Reasonably refute their hypothesis by explaining why the actual path of seismic rays through the mantle is curved and concave toward Earth's surface (support your reasoning with the variation of elastic properties with depth and Snell's law of refraction).
2. b) Based on the principle of least time (Fermat's principle), justify why, at epicentral distances greater than a few hundred kilometers, a wave following this curved and deep path arrives at the receiving station sooner than a hypothetical wave traveling in a straight line through shallower levels.

Earth's overall average density is $5.5\ \text{g/cm}^3$, whereas that of crustal rocks ranges between $2.7$ and $3.0\ \text{g/cm}^3$ (granite, basalt) and upper mantle peridotites barely reach $3.3\ \text{g/cm}^3$.

1. a) Justify why this contrast conclusively rules out Earth being homogeneous and demonstrates that most of its interior must contain materials with densities far higher than those observed at the surface.
2. b) Two types of meteorites are analyzed: a chondrite (silicate, density $\approx 3.5\ \text{g/cm}^3$) and an iron meteorite (Fe-Ni alloy, density $\approx 7.8\ \text{g/cm}^3$). Interpret the cosmochemical origin of both based on the process of accretion and differentiation of parent asteroids, and reason why iron meteorites constitute the classic indirect evidence supporting the chemical nature proposed for Earth's core.