Exercises: Plate tectonics and relief

What is a lithospheric plate and over which layer does it move? State which force is considered today to be the main driving mechanism of its movement.

Name the three types of boundaries between lithospheric plates and give a real example of each (a well-known mountain range, ridge, or fault).

Distinguish between the hypocentre and epicentre of an earthquake, and explain what the moment magnitude scale measures compared to the macroseismic intensity scale.

Name at least six major lithospheric plates and indicate on which one the Iberian Peninsula lies and which plate it contacts to the south.

Explain what the lithosphere is, which layers it is made of and why it behaves rigidly as it moves over the asthenosphere.

Describe the relative movement of the plates at each type of boundary (divergent, convergent and transform) and indicate which process dominates at each (creation, destruction or conservation of lithosphere).

What is a transform fault? Give the best-known example (the San Andreas Fault) and explain which plates it separates and in which direction they move.

Explain why earthquakes and volcanoes are not distributed at random across the planet but instead trace narrow belts, using the Pacific "Ring of Fire" as an example.

Explain what occurs at a mid-ocean ridge and at a subduction trench, stating in which of the two locations new oceanic lithosphere is created and in which it is destroyed.

The Iberian Peninsula experiences earthquakes despite not lying on a simple plate boundary. Explain the role of the contact between the Eurasian and African plates (Azores-Gibraltar) in the seismicity of southern and eastern Iberia.

The diagram shows the three types of boundaries between lithospheric plates. a) State which type of boundary is hidden beneath the "?" symbol and describe the relative motion of its plates. b) Give a real example of each of the three boundaries. c) Indicate in which new oceanic crust is created and in which it is destroyed.

Two earthquakes of the same magnitude occur beneath the same region, one at $30\ \text{km}$ depth and the other at $300\ \text{km}$. Discuss which one will cause more damage at the surface and why, explaining how seismic waves are attenuated with the distance they travel.

When two continents collide, neither of them can subduct easily. Explain what happens to the crust in this collision (shortening, thickening, thrust faults), what relief results, and give the example of the Himalayas.

Define orogen and describe the phases of the orogenic cycle from a marine basin that accumulates sediments to an eroded mountain range, applying it to the case of the Pyrenees.

The Mariana Trench reaches almost $11\ \text{km}$ in depth. Explain which tectonic process forms oceanic trenches, what happens there to the sinking lithosphere, and why volcanic island arcs are usually found next to them.

Outline in words the profile of an ocean-ocean convergent boundary (trench, island volcanic arc, back-arc basin) and explain the origin of each of these three elements and their relationship with subduction.

Consider the following data from two historic earthquakes in the Iberian Peninsula:

• Earthquake A (Lisbon, 1755): Estimated magnitude $M_w \approx 8{,}5$; submarine focus southwest of Cape St. Vincent at a depth of about $40\ \text{km}$; generated a transoceanic tsunami that devastated the coasts of the Gulf of Cádiz and caused building collapses in Madrid and Salamanca.

• Earthquake B (Lorca, 2011): Moderate magnitude $M_w = 5{,}1$; onshore focus at a depth of only $1{,}5\ \text{km}$ on the Alhama de Murcia fault; record ground acceleration of $0{,}37\ g$; caused $9$ fatalities and severe collapses in the town, but at $30\ \text{km}$ away it was barely felt.

1. a) Justify the specific geodynamic context of each seismic event based on the relative motion between the Eurasian and African plates (diffuse transpressive boundary in the southwest versus strike-slip fault system of the Betic Cordillera in the southeast).
2. b) A news reporter states: "The destructive impact of an earthquake depends solely on its magnitude on the Richter scale." Scientifically refute this statement by analyzing how focal depth, wave attenuation with distance, peak ground acceleration, and structural exposure/vulnerability influenced each case.

Currently, the Atlantic oceanic lithosphere is expanding at about $2{,}5\ \text{cm/year}$ from its mid-ocean ridge, while its continental margins are almost entirely passive. In contrast, the Mediterranean represents a relict basin where remnants of the Tethys oceanic crust actively subduct beneath southern Europe at a convergence rate of about $5\ \text{mm/year}$.

1. a) Reasonably predict the geodynamic evolution of the Atlantic-Iberian and North American margins: explain what critical physical change the oceanic lithosphere will undergo as it moves away from the ridge and cools, and deduce what new plate boundary structure will form spontaneously so that the Atlantic Ocean initiates its closure within the Wilson cycle.
2. b) Design a tectonic model for the Mediterranean Sea $40-50$ million years from now: deduce what resulting landform will replace the current marine basin after the definitive continental collision between Africa and Eurasia, what deformation geological structures will predominate in the suture zone, and how this closure will affect thermohaline exchange between the Atlantic and Indian Oceans.

A seismological observatory records two seismic events in the same province:

• Earthquake 1: Magnitude $M_w = 7{,}0$; hypocentre at a depth of $60\ \text{km}$ in a mountainous rural area. The nearest city is $90\ \text{km}$ away, founded on competent granite massifs and with buildings constructed under earthquake-resistant regulations.

• Earthquake 2: Magnitude $M_w = 5{,}0$; hypocentre at a depth of only $2\ \text{km}$, located beneath a historic city centre built on an unconsolidated alluvial plain.

1. a) The energy released by an earthquake is governed by the relationship $\log E = 4{,}8 + 1{,}5 M_w$. Calculate with justification how many times more mechanical energy Earthquake 1 released than Earthquake 2.
2. b) In the city near Earthquake 1, the recorded intensity was grade IV (widely felt, no damage), whereas in the city centre of Earthquake 2 the intensity reached grade VIII (severe structural damage and partial collapses). Interpret this apparent discrepancy by explaining the role of hypocentral distance (geometric attenuation), the "site effect" due to wave amplification in soft sediments, and building vulnerability.

Analyse the following three geophysical facts:

1. The distance between the crest of the East Pacific Rise and the Japan subduction trench is approximately $10\,000\ \text{km}$, and the Pacific Plate moves westward at a constant average velocity of $8\ \text{cm/year}$.

2. No deep ocean drilling by the IODP project has ever found in situ basaltic oceanic crust older than about $180-200\ \text{Ma}$.

3. In continental cratons (such as the Greenland Shield or the Canadian Shield), rocks older than $3\,800\ \text{Ma}$ crop out.

1. a) Calculate the time (in millions of years) it takes for a portion of basaltic lithosphere to travel from its formation at the Pacific Rise to its subduction at the trench. Assess whether the result obtained is consistent with the maximum age observed on the world's ocean floors.
2. b) Justify, based on the physical and petrological properties of oceanic versus continental lithosphere (average density, crustal thickness, temperature, and isostatic behaviour during thermal cooling), why oceanic lithosphere is ephemeral and continuously recycled into the mantle, whereas continental lithosphere cannot subduct en masse and endures for billions of years.

On 26 December 2004, an earthquake of $M_w = 9{,}1$ off the western coast of Sumatra generated a tsunami of catastrophic proportions. In contrast, large earthquakes of magnitude $M_w > 7{,}5$ associated with transform faults (such as the San Andreas Fault or the Azores-Gibraltar transform fracture) virtually never trigger destructive far-field tsunamis.

1. a) Using elastic rebound theory, explain step by step the mechanical deformation experienced by the accretionary prism and the overriding plate in a subduction zone before and during seismic rupture, and justify why this coseismic displacement generates a catastrophic sea wave whereas a pure strike-slip transform fault does not.
2. b) A tsunami in open water behaves like a shallow-water wave whose speed is approximated by $v = \sqrt{g \cdot h}$ ($g = 9{,}8\ \text{m/s}^2$; $h$ = ocean depth). If the average depth in the Indian Ocean is $4\,000\ \text{m}$, calculate the tsunami's propagation speed in the open sea (in $\text{km/h}$). Then, predict what will happen to the speed, wavelength, and wave amplitude when it reaches a coastal bay only $10\ \text{m}$ deep, justifying the physical principle of conservation of energy flux involved.
3. c) Design and justify the structure of a tsunami early warning system: explain why detecting the seismic wave using terrestrial seismographs is not enough and why it is essential to incorporate ocean-bottom pressure sensors connected to surface buoys (DART-type networks).

The Mid-Atlantic Ridge is typically submerged at a depth of about $2\,500\ \text{m}$, but in Iceland it rises to form an extensive emergent island whose crust reaches between $30$ and $40\ \text{km}$ in thickness (about four times the thickness of normal oceanic crust).

1. a) Justify this orographic and crustal anomaly geodynamically by explaining the interaction between two independent endogenous mechanisms: a divergent plate boundary and a deep mantle plume (hotspot). What physical-chemical process in the upper mantle generates such an extraordinary volume of basaltic magma beneath Iceland?
2. b) In the Thingvellir valley, a rift valley or graben crossed by large open fissures (such as Almannagjá) is visible. Deduce the stress regime acting in the area, the kinematic type of the faults that bound the valley, and predict what will happen to the width of Iceland if the spreading rate of $2\ \text{cm/year}$ continues for the next $5$ million years.
3. c) Iceland exhibits local geothermal gradients of up to $150-200\ ^\circ\text{C/km}$ (compared to $30\ ^\circ\text{C/km}$ for average continental crust). Evaluate the geological hazards (induced seismicity, magmatic gas emissions, volcanic deformation) that must be considered when drilling high-enthalpy geothermal wells in the vicinity of active magma chambers.

The Red Sea and the Gulf of California are two classic examples of ocean basins in a juvenile stage. In the central axis of the Red Sea, symmetrical magnetic anomalies from the basaltic floor, metalliferous hydrothermal brines at over $60\ ^\circ\text{C}$, and a divergence rate of $1{,}5\ \text{cm/year}$ are already detected. At the same time, the Baja California peninsula is separating from the American continent at a rate of $4{,}5\ \text{cm/year}$, combining extension and strike-slip faulting.

1. a) Analyse the rheological, isostatic, and structural evolution of the lithosphere during the transition from an intracontinental rift (East African Rift Valley stage) to a juvenile ocean (Red Sea stage). Explain the exact moment at which complete lithospheric rupture ("continental breakup") occurs and how the associated type of volcanism and sedimentation changes.
2. b) A geologist claims that the warm brines and linear, symmetrical magnetic anomalies of the Red Sea prove that a miniature ocean ridge is already operating there. Justify the scientific validity of both pieces of evidence.
3. c) Reasonably predict the paleogeographic configuration of the Baja California region in $30$ million years if the current displacement continues: deduce the relative position of the peninsula, the nature of the marine crust that will separate it from North America, and the structural fate of the San Andreas Fault.

Although the main orogenic collision between Iberia and Eurasia ended more than $20\ \text{Ma}$ ago and current GNSS/GPS measurements record an almost negligible horizontal tectonic shortening rate ($< 0{,}3\ \text{mm/year}$), geodetic levelling profiles reveal that the axial zone of the Pyrenees continues to rise vertically at a net rate of $0{,}5$ to $1{,}2\ \text{mm/year}$.

1. a) Resolve this apparent paradox: if active tectonic convergence is not the primary driving cause of the current uplift, justify what endogenous physical mechanism—based on Airy's isostasy model and the presence of a deep crustal root—drives the mountain range's uplift as external agents erode it.
2. b) In a Pyrenean valley, a stepped sequence of four river terraces incised into bedrock is identified. The upper terrace (T1) is located at $+120\ \text{m}$ above the current riverbed, and its alluvial sediment has been dated to $150\,000$ years ago. Calculate the average rate of river incision (in $\text{mm/year}$) and interpret what this data reveals about the equilibrium between river incision and the uplift of the mountain range during the Quaternary.
3. c) Refute the following statement: "Since erosion removes thousands of tonnes of rock per year, the Pyrenees will be reduced to a peneplain at sea level in a few million years." Explain the role of delayed isostatic compensation in the longevity of mountainous relief.