Geophysics of Stratigraphic Facies Identification: Emergent Phases of Self Organization and the Mallat Scattering Transformation

A framework for the analysis of stratigraphic facies as emergent phases of self organization will be presented. An example will be given of turbidite deposition that is governed by a system of partial differential equations. It will be shown how the boundary conditions and coefficients of the PDEs parameterize a phase space that is divided into distinct phases, or what is more commonly called facies. A method of renormalization of the texture of geologic outcrops, seismic data, and well logs will be presented that gives the scale dependance of the PDE coefficients and boundary conditions. This specification of the running coupling coefficients or S-matrix of the physics gives the form of the PDE as well as the coefficients and boundary conditions. Practically this gives a unique fingerprint, or "attribute" (technically a metric) of the geologic facies. The mathematical framework is based on the Mallat Scattering Transformation - an iterative wavelet transformation.