# Team 3: Azimuthal elastic inversion for fracture characterization

Figure 1: Fracture direction and magnitude displayed for a carbonate reservoir

The inversion problem is nonlinear, under-resolved and ill-conditioned. In order to make the problem better posed and resolved, assumptions are typically made about the type and complexity of the fractures [4,6]. One of the goals of this project is to understand the resolvability of these models and their parameterizations under different noise conditions. Another goal is to explore different methods to solve this nonlinear problem. Under certain data and parameter transformations [3] it is possible to linearize certain aspects of this problem. For this portion of the problem it is possible to perform a traditional parameter and data resolution analysis [1,4]. In this workshop we would like to explore techniques to understand the resolvability of the parameters for the full nonlinear problem.

**Prerequisites:**

We expect students with a strong background in optimization, numerical analysis, and good computing skills (MatLab or C/C++). Knowledge of statistical methods and stochastic analysis would be an asset.

**References:**

- G. Backus, and F. Gilbert, “Numerical applications of a formalism for geophysical inverse problems,” Geophysical Journal of the Royal Astronomical Society 13 (1967): 247-276
- J. Downton, and B. Roure, “Azimuthal simultaneous elastic inversion for fracture detection,” SEG, Expanded Abstracts 30 (2010), 269-273
- J. Downton, B. Roure, and L. Hunt, “Azimuthal Fourier Coefficients,” CSEG Recorder 36, no. 10, (2011): 22-36.
- M. Eftekharifar and C. M. Sayers, “Seismic characterization of fractured reservoirs: A resolution matrix approach,” SEG, Expanded Abstracts 30, (2011):1953
- I. Pšenčík, and J. L. Martins, “Properties of weak contrast PP reflection/transmission coefficients for weakly anisotropic elastic media,” Studia Geophysica et Geodaetica 45 (2001): 176-197.
- C.M. Sayers, and S. Dean, “Azimuth-dependent AVO in reservoirs containing non-orthogonal fracture sets,” Geophysical Prospecting 49 (2001): 100-106.
- M. Schoenberg, “Elastic behaviour across linear slip interfaces,” Journal of the Acoustical Society of America 68, no. 5, (1980):1516–1521.
- M. Schoenberg and C. M. Sayers “Seismic anisotropy of fractured rock,” Geophysics 60 (1995): 204–211 .