Stochastic geodynamic modelling of volcanic sedimentary basins
More than a hundred power-law distributions have been identified in physics (e.g. sandpile avalanches), biology (e.g. species extinction and body mass), and the social sciences (e.g. city sizes and income). Examples in geophysics are the frequency-dependency of acoustic attenuation in complex media; the Burridge-Knopoff model that reproduces the Gutenberg–Richter and Omori's empirical laws. The dimensions of dike and sill intrusions obey a power law analogous to the Gutenberg-Richter relation, and the long-term release of geodetic moment is governed by a relationship consistent with the Omori law.
Magmatism and volcanism exhibit spatial and temporal clustering on a wide range of scales. We will address this by quantifying the spatial clustering of magmatism and volcanism in several data sets in the east Barents Sea and North Atlantic.
The spatial correlation function will be estimated based on a two-point statistics. The temporal pair-correlation function will be used to identify temporal clustering of magmatism and volcanism in the radiometric age data in the east Barents Sea and North Atlantic. At the global scale, isotropic Gaussian random fields on the sphere can be characterized by Karhunen–Loeve expansions with respect to the spherical harmonic functions and the angular power spectrum.
The stochastic heat equation on the sphere driven by an isotropic Gaussian random field of temperature anomalies in the upper mantle can be considered and its gravity spectrum will be compared with the observations.
We will also address the methods to validate the statistical relations retrieved from the data, since a simple fitting of the observation may give some biased results.