The Solid Earth

Potential Fields, Seismic Waves and a Deforming Planet in 9 chapters — from “The shape and gravity of the Earth: potential, geoid, isostasy and flexure” to “Faults, the earthquake cycle and seismic hazard”.

Chapters

  1. The shape and gravity of the Earth: potential, geoid, isostasy and flexure
    • The spherical harmonic expansion of the gravity potential
    • MacCullagh's formula and the dynamical form factor
    • Clairaut's theorem and hydrostatic flattening
    • Buried bodies and upward continuation
    • The geoid anomaly of a compensated column
    • Plate bending and the thin-plate flexure equation
    • The degree of compensation
    • Space geodetic positioning and a moving surface
    • Problems
  2. The geomagnetic field: potential, spectrum, induction and the palaeomagnetic record
    • Gauss coefficients of the geomagnetic field
    • The geomagnetic power spectrum and the core surface
    • The magnetic induction equation
    • Magnetic diffusion time and the frozen-flux limit
    • What a self-sustaining dynamo needs
    • Polarity reversal statistics
    • Fisher statistics and the virtual geomagnetic pole
    • Problems
  3. Dating, heat flow and the thermal history of the Earth
    • Two uranium clocks and U-Pb concordia
    • Closure temperature and thermochronology
    • The heat equation with internal heating
    • The continental geotherm and heat production
    • Periodic surface temperature and the skin depth
    • The half-space cooling solution
    • Parameterised thermal history of the Earth
    • Core heat flow and inner-core growth
    • Problems
  4. Stress, strain and elastic waves in the Earth
    • Index notation and principal stresses
    • The Mohr circle and the Coulomb failure criterion
    • Anderson's theory of faulting
    • The infinitesimal strain tensor and isotropic Hooke's law
    • Navier's equation of elastodynamics
    • P and S wave potentials
    • Plane wave polarisation and impedance
    • SH reflection and transmission at an interface
    • Problems
  5. Rays and travel times: from arrivals to a layered planet
    • The ray parameter in a layered medium
    • Head waves and the refraction survey
    • Reflections and normal moveout
    • The spherical ray parameter and the intercept-time function
    • Abel's integral equation and Herglotz-Wiechert inversion
    • Triplications, low-velocity zones and core phases
    • The Adams-Williamson equation for density
    • Problems
  6. Surface waves, free oscillations and seismic tomography
    • The Rayleigh wave on a half-space
    • The Love wave in a surface layer
    • Surface-wave group velocity and dispersion
    • Free oscillations and the Jeans relation
    • Least squares for many unknowns
    • Travel-time tomography
    • Damped least squares and resolution
    • Tomographic images of the mantle
    • Problems
  7. Plates, creep and convection: the mantle in motion
    • Euler poles and relative plate motion
    • Power-law creep and effective viscosity
    • The lithospheric strength envelope
    • Slow viscous flow of the mantle
    • Rayleigh-Benard stability of the mantle
    • Thermal boundary layers and mantle plumes
    • Plate forces and the dynamic geoid
    • Problems
  8. The earthquake source: moment tensor, radiation and spectra
    • Fault orientation and slip
    • The double couple and equivalent forces
    • The seismic moment tensor
    • The radiation pattern of a double couple
    • Focal mechanisms from first motions
    • Source spectra, corner frequency and stress drop
    • Magnitude scales and magnitude saturation
    • Finite rupture and rupture directivity
    • Problems
  9. Faults, the earthquake cycle and seismic hazard
    • Rate-and-state friction
    • The spring-slider instability
    • Interseismic strain accumulation
    • The elastic rebound cycle and recurrence
    • Coulomb stress transfer and Omori's law
    • The Gutenberg-Richter law
    • Poisson exceedance probability and seismic hazard
    • Induced seismicity and early warning
    • Problems