[4] The goal of inverse theory is to determine the spatial distribution of some variable (for example, density or seismic wave velocity).
Fractal sets have a number of common features, including structure at many scales, irregularity, and self-similarity (they can be split into parts that look much like the whole).
[6] Data assimilation combines numerical models of geophysical systems with observations that may be irregular in space and time.
For these equations to make good predictions, accurate initial conditions are needed.
Data assimilation methods allow the models to incorporate later observations to improve the initial conditions.
[7] Some statistical problems come under the heading of mathematical geophysics, including model validation and quantifying uncertainty.
Brag's equation is also useful when using an electron microscope to be able to show relationship between light diffraction angles, wavelength, and the d-spacings within a sample.
There are many applications which include gravity, magnetic, seismic, electric, electromagnetic, resistivity, radioactivity, induced polarization, and well logging.
[9] Gravity and magnetic methods share similar characteristics because they're measuring small changes in the gravitational field based on the density of the rocks in that area.
[13] It can be mathematically modeled with Hooke's Law to show the elastic characteristics while using Lamé constants.
[13] Generally the ice has its linear elasticity constants averaged over one dimension of space to simplify the equations while still maintaining accuracy.