A novel modeling approach for diffusion-dominated systems

Lipovsky, Brad; Funning, Gareth
UC Riverside, Riverside, CA, USA, lipovsky@ucr.edu

We present a novel and succinct method for analyzing diffusion-dominated systems using an eigen-decomposition method. It is well known that eigen-decomposition methods such as Principal Component Analysis (PCA) can be used to decompose large data sets into statistically representative patterns, however, a major limitation of this method is often that these patterns need correspond to any physical event or process. We present a geodetic data set that does not have this encumbrance. We use an eigen-decomposition on a data matrix, D, to achieve a separation of variables, D(x,t) = X(x) * T(t). We show that the separated functions satisfy a simple diffusion equation. We demonstrate this new technique in the Evergreen Basin, CA, and show that a persistent scatterer InSAR data set with O(10^5) data points may be elegantly represented with only several physical parameters.