3D edge-diffraction coefficients in the azimuth and emergence domain

The conventional equation for 3D edge diffractions in the Cartesian coordinate system lacks angle information for studying the energy patterns in 3D seismic prestack data. Here, a new calculation method is presented for determining 3D edge-diffraction coefficients in a spherical coordinate system that can formulate the coefficients according to the azimuth and emergence angles. To avoid the singularity phenomenon, a Haar wavelet operator matrix is used for this new method. Analysis of the edge-diffraction coefficients variations with azimuth in the common-shot domain, common-receiver domain, and common-midpoint domain reveals that the variation curves of the coefficients can be used to identify the trend of a fault. The phenomenon of polarity reversal of the edge-diffraction coefficients is observed in the different domains, and the coefficients in the common-shot domain are more sensitive than in other domains.

Spatiotemporal Compound Wavelet Matrix Framework for Multiscale/Multiphysics Reactor Simulation: Case Study of a Heterogeneous Reaction/Diffusion System

We present a mathematical method for efficiently compounding information from different models of species diffusion from a chemically reactive boundary. The proposed method is intended to serve as a key component of a multiscale/multiphysics framework for heterogeneous chemically reacting processes. An essential feature of the method is the merging of wavelet representations of the different models and their corresponding time and length scales. Up-and-down-scaling of the information between the scales is accomplished by application of a compounding wavelet operator, which is assembled by establishing limited overlap in scales between the models. We show that the computational efficiency gain and potential error associated with the method depend on the extent of scale overlap and wavelet filtering used. We demonstrate the method for an example problem involving a two-dimensional chemically reactive boundary and first order reactions involving two species.