Geophysics

Physics of the solid Earth: gravity, seismology, geomagnetism, Earth's interior, and exploration methods.

General idea of the topic

Geophysics investigates the solid Earth through continuum elasticity, potential field theory, thermodynamics, and electrodynamics applied to the crust, mantle, and core. It maps the inaccessible deep interior of the planet by analyzing seismic wave speeds, gravimetric field anomalies, and the self-sustaining magnetohydrodynamic geodynamo operating in the liquid outer core.

This node covers continuum elastodynamics (P, S, Rayleigh, and Love waves), seismic tomography, gravimetry and Bouguer density anomalies, geomagnetism, and mantle thermal convection.

What you will truly understand

You will understand how the physical inability of transverse shear waves (S-waves) to propagate across liquids ($G=0$) definitively proved that Earth's outer core is liquid at $2890\text{ km}$ depth (Gutenberg discontinuity).

You will invert radial density profiles using the Adams-Williamson equation and compute gravimetric anomalies by applying free-air and Bouguer slab corrections.

Recommended learning route

1. Elasticity theory and seismic body waves: stress/strain tensors, bulk and shear moduli ($K, G$), longitudinal P-waves ($v_p = \sqrt{(K + 4/3 G)/\rho}$), and transverse S-waves ($v_s = \sqrt{G/\rho}$).
2. Ray theory and planetary discontinuities: seismic ray tracing, Snell's law at boundaries, Mohorovičić discontinuity, and core shadow zones.
3. Gravimetry and isostasy: geoid vs reference ellipsoid, Bouguer gravity anomalies, and Airy/Pratt isostatic compensation.
4. Geomagnetism and planetary heat flow: MHD dynamo action in the molten iron outer core, geomagnetic field reversals, and mantle convective plumes.

Physical criterion you must acquire

Recognizing that dispersive surface waves (Rayleigh and Love) constrain shallow crustal shear velocity profiles, whereas deep body waves (P and S) probe the deep mantle and inner/outer core boundary.

Connection with real problems

• Earthquake early warning systems and structural seismic hazard mitigation in civil engineering.
• Non-invasive geophysical exploration for groundwater reservoirs and mineral deposits.
• Volcanic unrest monitoring and deep geothermal energy reservoir modeling.

Final goal of the topic

Master elastic wave mechanics, potential fields, and planetary thermodynamics to model Earth's internal structure and geophysical dynamics.