Past exam of the plate tectonics course of the University of Oxford 2023 Question 3 d Solution 2026-10-25
The asthenosphere exists because the mantle's ability to deform is strongly dependent on temperature, pressure, composition, water and deformation mechanism. Cooling from the surface creates a strong lithosphere. Beneath it, hotter mantle deforms by material creep at much lower stress on geological timescales. The asthenosphere is predominantly solid weak rock, not a global ocean of magma. On the much shorter timescale of a seismic wave, it still supports S waves.
The hot shallow mantle can be close to its solidus. Water weakening of rocks and, in some settings, a small connected melt fraction can further lower effective viscosity. At greater depths, changes in pressure, homologous temperature, mineral structure and water storage modify the deformation laws; increasing depth does not imply indefinitely decreasing viscosity. Explaining a weak upper-mantle interval does not require every location to contain the same amount of melt.
There are several physically distinct boundaries to test. The thermal lithosphere-asthenosphere boundary describes a thermal transition, the mechanical boundary a contrast in long-term strength or viscosity, and the seismic lithosphere-asthenosphere boundary a change in seismic velocity or other wave properties. They need not have identical depths. A smooth geothermal gradient can explain broad thermal weakening, but a very sharp decrease of seismic velocity may require changes in melt fraction, hydration, composition or seismic anisotropy. A sharp shallow reflector within a craton might instead be an internal lithospheric boundary.[ref]
A global view of the lithosphere-asthenosphere boundary by Catherine A. Rychert and Peter M. Shearer. Abstract and pp. 495–498: converted-wave sharpness and the possibility that the imaged cratonic discontinuity lies within thicker lithosphere.
Begin with a thermal null model. A half-space cooling model givesIf a thermal boundary corresponds to a fixed temperature , its depth isso it deepens as the square root of plate age. Test that prediction against independently determined seafloor ages, bathymetry and heat flux. An oceanic plate cooling model adds finite thickness and basal heat supply, allowing the old-age depth to approach a finite value. For continents, include radiogenic heating, crustal thickness, the history of continental rifting or tectonic thickening, and advective heating by magma or mantle flow. A cold, dry craton and a recently extended volcanic region should not share the same thermal profile.
Then calculate the observable consequences of competing mechanisms rather than merely assigning a boundary to a map:
- Use receiver functions from both P-to-S conversion and S-to-P conversion to constrain the depth and sharpness of a negative seismic velocity contrast. Check for crustal reverberations and whether the result changes with incident direction or frequency. Combine these with Rayleigh waves, Love waves and seismic tomography to constrain the broader shear-wave velocity profile.
- Measure seismic attenuation and seismic anisotropy. Elevated temperature, small amounts of melt and aligned minerals can all affect apparent seismic velocity, but predict different attenuation, polarization and directional patterns. Convert laboratory elastic and anelastic measurements into synthetic seismic observations at the relevant frequencies.
- Obtain magnetotelluric sounding constraints on electrical conductivity, together with surface heat flux. Connected melt or hydrated material can enhance electrical conductivity, but the interpretation depends on composition and connectivity. Joint thermal, seismic and electrical modelling is more discriminating than any single proxy.
- Use mantle xenoliths and erupted magmas to constrain pressure, temperature, water content, melt depletion and composition, recognizing that transport can alter a sample. Relate these observations to geodynamic modelling of mantle convection, slab flow, mantle plumes and lithospheric rejuvenation.
Compare models against the observed boundary depth and its sharpness, including uncertainty and resolution. An age–depth trend with matching heat flux favours thermal control; a sharp discontinuity that fails the thermal prediction but coincides with an electrical anomaly can support a melt- or hydration-related transition. Neither observation alone proves a unique cause. The spatially varying boundary is best understood as the result of thermal evolution interacting with composition, fluids and deformation history.
Use a high-resolution multichannel seismic reflection survey, with closely spaced crossing lines or a suitable small three-dimensional survey over the turbine locations. It should map the seabed, the sediment–sandstone boundary, local faults, buried channels, and lateral changes relevant to foundations. Seismic reflection responds to acoustic impedance contrasts and can image an irregular boundary without requiring it to be a first-arrival refractor. Here even the seabed has a useful normal-incidence reflection coefficient of despite its zero P-velocity contrast.
A seismic refraction survey can provide complementary seismic velocities and geotechnical information, particularly using seabed multicomponent receivers for S waves. Its limitations as the principal imaging method here include the missing water–sediment P refractor, required offsets of hundreds of metres to obtain useful basement first arrivals, and weaker constraints on thin layers or velocity inversions. Variable bathymetry and sediment thickness further complicate simple refraction interpretations.
A shallow-towed boomer seismic source or small sparker seismic source is a sensible initial seismic source for penetrating about 20 m of sediment beneath a 50 m water column. A chirp sub-bottom profiler can add finer imaging of the upper cover where penetration permits; penetration depends on grain size, consolidation, gas, and seismic attenuation. A pilot line should establish the minimum useful source energy and bandwidth. Large low-frequency air-gun arrays are unnecessary for this shallow target. Small coastal vessels, sea state, tow stability and acoustic background constrain usable frequencies and operations. Marine mammals and other local receptors motivate a low-energy effective source, monitoring and appropriate operational mitigation.[ref]
High-resolution multichannel seismic system by United States Geological Survey. The institutional instrument description lists configurable boomer, sparker, hydrophone-streamer and complementary chirp equipment for shallow subsurface mapping.
The expected normal-incidence two-way travel times are for the seabed and for basement, separated by . Source duration, recording sample interval and bandwidth must distinguish them. As an initial vertical seismic resolution estimate, : gives about in the sediment, although usable resolution depends on the whole seismic wavelet and signal-to-noise ratio.
Choose shot and receiver spacing from the shortest useful wavelength, target size, maximum reflector dip, seismic migration needs and achievable navigation accuracy. For a plane event of horizontal seismic ray parameter , avoiding spatial aliasing requires approximately . Source spacing and receiver spacing also set midpoint coverage and seismic acquisition fold; adequate offsets enable moveout correction and velocity estimation. For nearly horizontal shallow reflectors a few-metre shot interval can be practical, whereas steep events at high frequency require denser spatial sampling. These values must be designed together rather than imposing one spacing for every target. Cross-line spacing must resolve lateral features between turbine sites, not merely along each track.
At a vessel speed of , one shot per second gives 2 m shot spacing and ample separation relative to a roughly target return, subject to the longer record needed for seismic multiples and source recovery. Shallow towing limits seismic source ghosts and receiver ghosts, but requires stable tow depth. Accurate positioning, tides, measured water sound speed, bathymetry and checks for seabed seismic multiples are essential for correct target depths.
A gravity anomaly is the difference between observed gravitational acceleration and a specified reference prediction after defined reductions. A free-air gravity anomaly, a Bouguer gravity anomaly, and a residual local gravity anomaly differ because they remove different reference contributions. State the reference ellipsoid, datum, reference density, and regional trend before interpreting an anomaly as a subsurface geophysical density contrast.
On land, tie gravimeter observations to a gravity base, calibrate them, correct instrumental drift and Earth tides, and determine station latitude and elevation accurately. Subtract latitude-dependent normal gravity . Reduce to the reference elevation using a positive free-air correction for a station above that datum: about for in metres. A simple Bouguer gravity anomaly then subtracts attraction of the intervening rock slab and adds the conventional terrain correction:with all acceleration terms expressed consistently. In SI units .
At sea, also correct vessel-motion effects, especially the Eötvös correction from east–west vessel motion and Earth rotation, and vertical ship acceleration; average or filter the moving-platform data appropriately. GPS navigation and tide information specify position and measurement height. Sea-surface measurements give a marine free-air gravity anomaly after motion, latitude, tide and height reductions. A marine Bouguer gravity anomaly additionally allows for measured bathymetry and the replacement of low-density water by reference rock; the simple water-column replacement correction is positive, , relative to the sea-surface free-air value. A consistent three-dimensional bathymetric correction is preferable near irregular coasts. Remove a justified broad regional field if the intended quantity is a residual anomaly of the local body.