Role of Wavelets in the Physical and Statistical Modelling of Complex Geological Processes

Today, wavelets are recognized to have a wide range of useful properties that allow them to treat effectively multifacet problems, such as data compression, scale-localization analysis, feature extraction, statistics, numerical simulation, visualization, and communication. Second-generation wavelets represent a recent improvement of the wavelet algorithm, allowing for greater flexibility in the spatial domain and other computational advantages. We will show how these wavelets can be employed to extract large-scale coherent structures from (1) three-dimensional turbulent flows and (2) high Rayleigh number thermal convection. We will discuss the concept of modelling via decomposition into coherent and incoherent fields, taking into account the effect of the incoherent field via statistical modelling. We will discuss wavelet properties and how they can be utilized and integrated in handling large-scale problems in earthquake physics and other nonlinear phenomena in the geosciences.