Earth sciences 10 topics
Earth sciences
Geophysics
10 topics 13 math concepts connects to 3 fields
Geophysics applies physics to study the Earth's interior and surface. Seismic wave equations, potential field theory, and inverse problems are central mathematical tools.
Topics in this field
Earthquake Seismology
Moment tensors, seismic moment, and the Gutenberg-Richter law characterise earthquake sources and their statistical recurrence.
probability theory linear algebra spectral analysis
Electrical Methods
Resistivity surveys and IP measurements map subsurface conductivity by injecting current and measuring potential differences.
partial differential equations linear algebra numerical methods
Geodesy
Reference ellipsoids, geoid undulations, GPS trilateration, and InSAR measure Earth's shape, gravity field, and crustal deformation.
differential geometry linear algebra optimization
Geostatistics
Variograms, kriging, and sequential simulation quantify spatial uncertainty in subsurface property estimation.
gaussian distribution linear algebra probability theory
Gravity Methods
Bouguer anomalies and gravitational potential inversion reveal subsurface density contrasts.
partial differential equations linear algebra optimization
Ground-Penetrating Radar
Electromagnetic wave propagation and reflection imaging reveal shallow subsurface structure with centimetre-scale resolution.
partial differential equations fourier transform wavelet transform
Magnetic Methods
Total-field anomaly maps, Euler deconvolution, and susceptibility inversion image subsurface magnetic sources.
partial differential equations linear algebra optimization
Potential Field Theory
Laplace's equation, harmonic functions, and spherical harmonics underpin gravity and magnetic field modelling.
partial differential equations fourier transform hilbert spaces
Seismic Tomography
Ray-path integrals and least-squares inversion map 3D velocity structure inside the Earth.
linear algebra optimization numerical methods
Seismic Waves
P and S waves, the elastic wave equation, and Snell's law govern how seismic energy travels through the Earth.
partial differential equations fourier transform spectral analysis