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# Mathematical geophysics

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 Title: Mathematical geophysics Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Mathematical geophysics

Mathematical geophysics is concerned with developing mathematical methods for use in geophysics. As such, it has application in many fields in geophysics, particularly geodynamics and seismology.

## Areas of mathematical geophysics

### Geophysical fluid dynamics

Geophysical fluid dynamics develops the theory of fluid dynamics for the atmosphere, ocean and Earth's interior. Applications include geodynamics and the theory of the geodynamo.

### Geophysical inverse theory

Geophysical inverse theory is concerned with analyzing geophysical data to get model parameters. It is concerned with the question: What can be known about the Earth's interior from measurements on the surface? Generally there are limits on what can be known even in the ideal limit of exact data.

The goal of inverse theory is to determine the spatial distribution of some variable (for example, density or seismic wave velocity). The distribution determines the values of an observable at the surface (for example, gravitational acceleration for density). There must be a forward model predicting the surface observations given the distribution of this variable.

Applications include geomagnetism, magnetotellurics and seismology.

### Fractals and complexity

Many geophysical data sets have spectra that follow a turbulence.

### Data assimilation

Data assimilation combines numerical models of geophysical systems with observations that may be irregular in space and time. Many of the applications involve geophysical fluid dynamics. Fluid dynamic models are governed by a set of partial differential equations. For these equations to make good predictions, accurate initial conditions are needed. However, often the initial conditions are not very well known. Data assimilation methods allow the models to incorporate later observations to improve the initial conditions. Data assimilation plays an increasingly important role in weather forecasting.

### Geophysical statistics

Some statistical problems come under the heading of mathematical geophysics, including model validation and quantifying uncertainty.