Statistical Characteristics of a Fractured Model from Seismic Data via Topological Analysis of Diffraction Images

A workflow for recovering fracture network characteristics from seismic data is considered. First, the presented discrete fracture modeling technique properly describes fracture models on the seismic scale. The key procedure of the workflow is 3D diffraction imaging based on the spectral decomposition of different combination s of selective images. Selective images are obtained by the prestack asymmetric migration procedure, while spectral decomposition occurs in the Fourier domain with respect to the spatial dip and the azimuth angles. At the final stage, we propose a topological analysis based on the construction of a merge tree from the obtained diffraction images. The results of the topological algorithm are modeling parameters for the discrete fractures. To analyze the effectiveness of the proposed workflow, a statistical comparison of the recovered parameters and true model parameters are provided. We use the Kolmogorov -Smirnov test for a statistical analysis of the fracture lengths, while the behavior of the Morisita index shows the statistical distribution of the modeled fracture corridors. Numerical examples with synthetic realistic models demonstrate a detailed, reliable reconstruction of the statistical characteristics of the fracture corridors.