Physical processes of the Earth: seismology (elastic wave propagation), geomagnetism (geodynamo), gravity anomalies, heat flow, plate tectonics, fluid geophysics (ocean/atmosphere).
Geophysics
Seismic P wave
Compressional elastic wave in rock; fastest body wave (v_p = √((K + 4μ/3)/ρ)); propagates through solids and fluids.
Seismic S wave
Transverse elastic shear wave; slower than P (v_s = √(μ/ρ)); cannot propagate through fluids — basis for inferring the Earth's liquid outer…
Surface waves (Rayleigh/Love)
Elastic waves confined to a free surface; Rayleigh (retrograde elliptical in the sagittal plane), Love (horizontal, requires a layered…
Seismic tomography
Inverse method reconstructing 3D seismic-velocity structure from travel-time/amplitude data of many ray paths; analogous to medical CT.
Plate tectonics
Earth's lithosphere divided into rigid plates moving ~cm/yr; boundaries accommodate subduction, spreading, or transform faulting. Driving…
Geodynamo
Self-sustaining magnetic-field generation by MHD convection in Earth's liquid iron outer core; responsible for the geomagnetic field and…
Gravity anomaly
Spatial variation of the Earth's gravity field (Bouguer, free-air, isostatic) revealing subsurface density contrasts (ore bodies, magma…
Earth's free oscillations (normal modes)
Discrete spheroidal (₀S_n) and toroidal (₀T_n) eigenmodes of the whole Earth excited by great earthquakes; mode frequencies constrain…
Mantle convection
Rayleigh-Bénard-style thermal convection driving plate tectonics. Whole-mantle vs layered debate; plumes (Iceland, Hawaii), LLSVPs,…
Paleomagnetism & geomagnetic reversals
Magnetisation of igneous rocks records past field. Matuyama-Brunhes boundary 781 ka. Cornerstone evidence for seafloor spreading;…
Moho & internal structure
Crust-mantle boundary (Mohorovičić 1909) from P-wave velocity jump 6.8→8.1 km/s. PREM reference model; core-mantle boundary, inner-core…
Climate feedbacks (Earth system)
Planck (negative), water vapor (strong positive), lapse rate, surface albedo (ice-albedo), clouds (uncertain). Climate sensitivity 2.5-4 K…
Seismic wave propagation
P, S, Rayleigh, Love waves through layered Earth; wave equation with variable (λ, μ, ρ); 3D full-waveform inversion images interior.
Plate tectonics
Lithospheric plates move ~cm/yr driven by mantle convection + slab pull; mid-ocean ridges spread, trenches subduct; ~50 yr old theory…
Gutenberg–Richter law
log N(M) = a - bM with b ≈ 1; power-law earthquake magnitude frequency; self-organized criticality interpretation.
PREM: preliminary reference Earth model
1D seismic velocity, density vs depth; inner solid core, outer liquid core, mantle, crust; Bullen regions.
Geodynamo & dipole reversals
Convection + rotation in liquid outer core generates self-sustaining B-field via α-Ω dynamo; random reversals ~Myr timescale recorded in…
Paleomagnetism & magnetic reversals
Ferromagnetic minerals record ancient B-field orientation; seafloor magnetic stripes confirmed seafloor spreading.
Gravity anomalies & isostasy
Free-air, Bouguer, isostatic corrections; Airy/Pratt compensation of mountain roots; GRACE satellites measure mass changes.
Core–mantle boundary (CMB) dynamics
Chemical, thermal, magnetic interactions at 2891 km depth; ultra-low-velocity zones; D'' layer, post-perovskite phase.
Milankovitch cycles
Eccentricity (100 kyr), obliquity (41 kyr), precession (23 kyr) modulate insolation → glacial cycles; Pleistocene ice ages.
Atmospheric thermodynamics
Dry/moist adiabatic lapse rate, potential temperature θ; CAPE, LFC/LCL; controls convection and storm formation.
Geostrophic balance & Coriolis
2Ω×v = -(1/ρ)∇P for large-scale atmospheric/oceanic flow; Rossby number Ro = U/(fL) ≪ 1; cyclones, Gulf Stream.
Rossby waves
Planetary-scale waves in rotating stratified fluids from β = df/dy; westward propagation; drive mid-latitude weather patterns.
ENSO / El Niño Southern Oscillation
Coupled ocean-atmosphere mode in tropical Pacific; warm (El Niño) / cold (La Niña) phases every 2-7 yr; delayed-oscillator mechanism.
Thermohaline circulation (AMOC)
Global overturning driven by T, S differences; Atlantic Meridional OC slowing with climate change; abrupt-change risk.
Earth's magnetosphere
Bow shock, magnetopause at 10 R_E, magnetotail; Van Allen radiation belts; auroral oval from magnetotail reconnection.
Geomagnetic storms (Dst index)
Solar CMEs inject plasma; ring current intensifies; Dst < -300 nT in super-storms; Carrington event 1859; impacts power/satellites.
Volcanic eruption dynamics
Magma chamber overpressure, conduit flow, fragmentation at critical vesicularity; VEI scale; plume dynamics inject SO₂ to stratosphere.
Elastic seismic wave equation and P/S wave speed ratio (geophysics)
Geophysics application of L0 wave-equation-PDE and Sturm–Liouville theory. Infinitesimal elastic displacements u(x, t) in an isotropic…
Rossby wave dispersion from β-plane geostrophy (geophysics)
Geophysics application of L0 linear-ODE and Fourier-series theory. On a rotating planet the Coriolis parameter f = 2Ω sin φ varies with…