This course comprises the mathematical basis, procedures, field application, and instruments used by non-invasive geophysical methods. In particular, we will draw from the experience gained over decades of development of such methods for the exploration of our own planet to lay a path in which we will learn how such methods have been adapted (or could potentially be adapted) to gain insight on the hidden physical properties of other extraterrestrial bodies.
Topics:
Structure, Terminology, and workflow of geophysical methods.

Gravity: Laws of gravitation; Earth gravity models; Spheroid and Geoid; Gravity measurements and Instrumentation; Correction to gravity measurements and gravity anomaly; The meaning of gravity anomaly; Isostasy; Interpretation of Gravimetric Maps; Gravity anomaly from bodies of irregular shape; Deploy of a gravimetric survey; Gravity surveys beyond our planet.

Magnetism: Basic physical laws. Magnetic properties and behavior of solids. Magnetic Hysteresis; Residual Magnetization; Magnetic field from a dipole; The Earth magnetic field. Variations of the Earth's magnetic field; Paleomagnetism; Magnetic measurement methods and Instrumentation; Sources of noise; Examples of magnetic surveys; Origins of the Earth's magnetic field; Magnetic surveys beyond our planet.

Electro-Magnetic Methods: Maxwell Equations; Low-Frequency E. M. methods; Time Domain Electromagnetics; Inversion Methods; High-Frequency E. M. Methods (Ground Penetrating Radar);

Electric Resistivity Methods: Basic principles; Vertical Electrical Soundings; Electrical Resistivity Tomography; Induced Polarization and Spectral Induced Polarization; Self-Potential;

Seismic Methods: Theory of Elasticity in a Continuum. Stress-Strain relation; Classification of seismic waves; Energy loss and Spherical divergence; Seismic waves reflection and refraction laws; Head Waves; “Dromocrone” of reflected and refracted waves. Surface waves; Seismic Reflection Method; Seismic refraction Method; Surface waves methods: SPAC, SASW; MASW; SPAC; ESAC; Re.Mi; HVSR;

Fourier Series and Fourier Transform Theory: Theory; Multy-dimensional Fourier Transforms; Convolution and Correlation; Signal sampling and aliasing. Examples;

Data Inversion Theory: Introduction; Linear inversion; Multi-Parametric Regression; Stochastic global Inversion methods; Local Inversion Methods; Ill-posed problems and Tickhonov regularization; Gauss-Newtom method; Non-linear inversion; Occam’s Method.