Exercises: The theory of plate tectonics

What is a lithospheric plate and over which more ductile layer does it move? Explain the difference between the lithosphere and the asthenosphere.

Name the three types of lithospheric plate boundaries and describe the relative movement of the plates at each of them.

Why are earthquakes and volcanoes not randomly distributed across Earth's surface, but concentrated in narrow, elongated belts?

What is the Earth's crust and how does it differ from the mantle? Which discontinuity separates them and how was it detected?

Name at least two forces that contribute to the movement of the lithospheric plates, such as ridge push, mantle drag or the slab pull of the subducting plate, and briefly describe each one.

What is an oceanic trench and at what type of plate boundary does it form? Give a present-day example.

Compare oceanic and continental crust in terms of dominant composition, density, thickness, and maximum age of their rocks.

What is a hot spot? Give an example and explain why its volcanism is not associated with any plate boundary.

The diagram shows three plate boundaries (a, b, and c). Identify the type of boundary in each panel, describe the plate movement taking place, and give a real-world example of each.

At a mid-ocean ridge, each flank moves away from the axis at a rate of $2.5\ \text{cm/year}$. Calculate how many kilometers the ocean will have widened after $10\ \text{Ma}$, taking into account that total widening is the sum of both flanks.

At a convergent subduction boundary, earthquakes become progressively deeper away from the trench toward the continent. Explain the cause of this distribution (Benioff zone).

At the East Pacific Rise each flank moves away from the axis at $8\ \text{cm/year}$. Calculate how much that ocean will have widened in $5\ \text{Ma}$ and compare that rate with that of the Atlantic ridge, $2.5\ \text{cm/year}$ per flank.

The magnetic anomalies of the ocean floor form symmetrical bands on both sides of the ridge. Explain what these bands record and how they demonstrate that the ocean floor is spreading.

In volcanic arcs, magma is generated some $100\ \text{km}$ above the subducting plate. Explain the role played by the water released by the plate as it dehydrates in the melting of the overlying mantle.

Transform boundaries have abundant earthquakes but hardly any volcanism. Explain why, relating it to the type of movement and to the fact that lithosphere is neither created nor destroyed there.

Two GPS stations located on either side of a ridge move apart at a total rate of $4\ \text{cm/year}$. Estimate the age of the oceanic crust located $240\ \text{km}$ from the ridge axis and state the assumption you make about the constancy of the spreading rate.

A preliminary technical report for the siting of a strategic nuclear facility compares two candidate locations: the Reykjanes Peninsula (Iceland) and a sector on the granitic basement of the Iberian Central Meseta. An analyst states: "Both areas have abundant igneous rocks and are part of the lithosphere of the Eurasian plate, so their long-term geological hazard ($100,000\ \text{years}$) is equivalent."

1. a) Rebut the analyst's statement in a well-founded manner, contrasting the geodynamic context (lithosphere type, thermal regime, tectonic stresses, and proximity to plate boundaries) of both locations.
2. b) Reasonably predict three geological processes or hazards that would completely rule out the Icelandic site compared to the stability of the Meseta block.
3. c) Does the low seismicity of the Meseta mean that there are no tectonic stresses within it? Justify your answer considering the intraplate transmission of stress.

Along a section of the San Andreas Fault, two GNSS (geodetic GPS) stations located in the crust $15\ \text{km}$ on either side of the main trace have recorded no relative displacement between them over the last $160\ \text{years}$. However, regional stations located more than $100\ \text{km}$ on both sides of the fault record a continuous and steady relative motion of $35\ \text{mm/year}$. Furthermore, paleoseismic studies show that a $40,000\text{-year-old}$ Quaternary alluvial fan is laterally offset by a total of $1.4\ \text{km}$ along the fault.

1. a) Interpret the apparent discrepancy between the lack of local movement over the last $160\ \text{years}$ and the regional velocity measured by GNSS by applying the elastic rebound theory.
2. b) Verify with calculations whether the long-term geological displacement rate (deduced from the alluvial fan) is consistent with the current instantaneous velocity obtained by GNSS.
3. c) Calculate the slip deficit accumulated on the locked fault plane during those $160\ \text{years}$ and predict the expected coseismic displacement if all that elastic strain were released at once in a single earthquake.

At the upper elevations of Mount Everest, at over $8,000\ \text{m}$ altitude, Ordovician and Mesozoic fossiliferous marine limestones outcrop (Qomolangma Formation). Below, the massif consists of gneisses, high-grade schists, and Cenozoic leucogranites. Gravimetric and deep seismic data reveal that the continental crust beneath Tibet and the Himalayas reaches a thickness of up to $75\ \text{km}$, nearly double the global continental average, without an associated active volcanic arc.

1. a) Reconstruct the geodynamic evolution that explains how rocks formed on a shallow sea floor have ended up on the highest peak on the planet, indicating the different types of plate boundaries that operated successively in the region.
2. b) Justify, using the principle of isostasy, the relationship between the $75\ \text{km}$ crustal root and the extraordinary topographic elevation of the orogen.
3. c) Unlike the Andes, active volcanic magmatism is not observed in the Himalayas despite being a zone of intense convergence and seismicity. Mechanically and thermally justify this absence of volcanism.

A geophysical cross-section of the South American Pacific margin at $22^\circ\text{S}$ is analyzed. The following empirical data are observed:

1. A deep oceanic trench with scarce sedimentary infill and oceanic lithosphere of about $45\ \text{Ma}$ subducting with an eastward dip of $30^\circ$.

2. Aligned seismic hypocenters reaching depths of up to $600\ \text{km}$.

3. An active volcanic arc $280\ \text{km}$ east of the trench, erupting predominantly andesitic and dacitic lavas rich in volatiles.

4. A fold-and-thrust belt in the eastern foreland (Subandean zone) with thrust faults that shorten and thicken the continental crust.

1. a) Interpret the thermal and chemical origin of the arc magma: refute the intuitive idea that magma comes from simple frictional melting of the subducting oceanic crust, and explain the fundamental role of the dehydration of hydrous minerals.
2. b) Justify why Andean volcanism is predominantly andesitic-dacitic and highly explosive, in contrast to the effusive basaltic volcanism of mid-ocean ridges.
3. c) Reasonably predict how the tectonic and magmatic dynamics of the margin would evolve if the ocean basin were to close completely and a microcontinent located on the subducting plate were to collide.

The Hawaiian-Emperor seamount chain displays a systematic morphology: the southeastern islands (such as Hawaii) are huge, subaerial shield volcanoes with elevations up to $4,200\ \text{m}$ and ages younger than $1\ \text{Ma}$. Toward the northwest, the islands gradually transition into coral atolls and, further north, into guyots (flat-topped seamounts submerged at depths greater than $1,000\ \text{m}$ with ages up to $80\ \text{Ma}$). Located $3,500\ \text{km}$ northwest of Hawaii is Daikakuji guyot, dated at $47\ \text{Ma}$, at the exact point where the alignment abruptly changes orientation (from NW-SE to N-S).

1. a) Explain the sequence of geological processes (thermal, isostatic, and morphosedimentary) that transform an active volcanic island into a submerged guyot as the lithosphere moves away from the hotspot.
2. b) Calculate the average rate of motion of the Pacific plate between the present day and the formation of the bend $47\ \text{Ma}$ ago, expressing the result in $\text{cm/year}$.
3. c) It is debated whether the Emperor "bend" reflects an abrupt change in the kinematic trajectory of the Pacific plate or the motion of the mantle plume itself. What testable geological evidence (by analyzing other contemporaneous intraplate chains in the Pacific or through paleomagnetism) would allow confirming whether the direction of the plate changed?

Consider the following average geophysical data for the lithosphere and asthenosphere:

• Oceanic lithosphere freshly created at the ridge: thickness $\approx 12\ \text{km}$; mean density $\approx 3.05\ \text{g/cm}^3$.

• Mature oceanic lithosphere ($>60\ \text{Ma}$): thickness $\approx 100\ \text{km}$; mean density $\approx 3.35\ \text{g/cm}^3$.

• Typical continental lithosphere: thickness $\approx 150\ \text{km}$; $35\ \text{km}$ crust (density $\approx 2.75\ \text{g/cm}^3$) and $115\ \text{km}$ lithospheric mantle (density $\approx 3.30\ \text{g/cm}^3$); overall mean density $\approx 3.17\ \text{g/cm}^3$.

• Underlying upper asthenospheric mantle: density $\approx 3.25\ \text{g/cm}^3$.

1. a) Based on the principle of buoyancy and the data above, justify why an oceanic ridge can never subduct spontaneously, whereas old oceanic lithosphere can collapse and initiate subduction.
2. b) Explain why continental lithosphere cannot undergo deep and continuous subduction into the asthenospheric mantle, and predict what mechanical response it experiences when a passive continental margin is dragged into a subduction trench.
3. c) During subduction, the basalts and gabbros of the oceanic crust undergo high-pressure, low-temperature metamorphism, transforming into eclogite (density $\approx 3.50\ \text{g/cm}^3$). Justify how this phase transformation affects the slab pull force.

When analyzing the seismicity recorded at two different convergent boundaries (Margin A: Tonga-Kermadec trench; Margin B: Peru-Chile trench at $32^\circ\text{S}$), the following differences are observed:

• At Margin A, hypocenters are distributed along an inclined plane with a dip of $60^\circ$ that penetrates continuously down to a depth of $680\ \text{km}$.

• At Margin B, the seismic plane initially descends at an angle of $30^\circ$ down to $100\ \text{km}$, then becomes subhorizontal ($<10^\circ$) for hundreds of kilometers inland and ceases completely at depths greater than $150\ \text{km}$.

Furthermore, globally no earthquakes are recorded at depths greater than $700\ \text{km}$, even though seismic tomography shows that the cold lithosphere continues sinking into the deep mantle.

1. a) Justify which physical factors (age of the oceanic plate, temperature, convergence rate, or buoyancy) account for the observed differences in the dip and depth of earthquakes between both margins.
2. b) Explain the change in the rheological behavior of the materials and the mineralogical phase transformations that justify the total disappearance of earthquakes below $700\ \text{km}$.
3. c) If a seismological station is located on Margin A at a distance of $180\ \text{km}$ from the trench toward the arc, predict with reasoning the depth range (shallow, intermediate, or deep) in which it will detect earthquakes directly caused by the subducting plate beneath it.

The seismotectonic map of the Iberian Peninsula shows marked heterogeneity: continuous seismicity with periodic destructive earthquakes (such as those in Arenas del Rey in 1884 or Lorca in 2011) is concentrated in the Betic-Rif sector and the Gibraltar Arc, whereas the interior of the Meseta Central is considered virtually aseismic. Nevertheless, GNSS measurements show that the African plate is moving NW relative to Eurasia at a constant rate of $4\text{ to }5\ \text{mm/year}$.

1. a) Justify why the geodynamic contact between Eurasia and Africa in southern Iberia is not manifested as a single discrete fault or a classic trench, but rather as a "diffuse boundary" of crustal deformation hundreds of kilometers wide.
2. b) In the Betic Cordillera, active strike-slip faults and reverse faults coexist. Explain mechanically the coexistence of both types of faults based on the oblique compressive regime induced by plate kinematics.
3. c) Can the probability of an earthquake occurring in the interior of the Meseta Central be considered absolutely zero? Justify your answer taking into account the intraplate transmission of tectonic stresses and the reactivation of Late Variscan faults.