Team 3: Azimuthal elastic inversion for fracture characterization

An increasing amount of the oil and gas produced in North America and the world is from unconventional reservoirs. Understanding the fractures within the reservoir plays an important role in developing this resource. The objective of this project is to infer from P-wave seismic amplitude variations with offset and azimuth (AVAz) the elastic parameters of the earth and then from these elastic parameters characterize the fractures (Figure 1). The forward model is primarily described by two key models, the first describes the functional relationship between the anisotropic elastic parameters and the fractures, and the second describes the AVAz. One possible way of modeling this is to use linear slip theory [7,8] to characterize the fractures and then use a linearized approximation of the Zoeppritz equations [5] to describe the AVAz. It is then possible to estimate the fractures by inverting the nonlinear forward problem using simulated annealing [2].

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:

1. 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


2. J. Downton, and B. Roure, “Azimuthal simultaneous elastic inversion for fracture detection,” SEG, Expanded Abstracts 30 (2010), 269-273


3. J. Downton, B. Roure, and L. Hunt, “Azimuthal Fourier Coefficients,” CSEG Recorder 36, no. 10, (2011): 22-36.


4. M. Eftekharifar and C. M. Sayers, “Seismic characterization of fractured reservoirs: A resolution matrix approach,” SEG, Expanded Abstracts 30, (2011):1953


5. 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.


6. C.M. Sayers, and S. Dean, “Azimuth-dependent AVO in reservoirs containing non-orthogonal fracture sets,” Geophysical Prospecting 49 (2001): 100-106.


7. M. Schoenberg, “Elastic behaviour across linear slip interfaces,” Journal of the Acoustical Society of America 68, no. 5, (1980):1516–1521.


8. M. Schoenberg and C. M. Sayers “Seismic anisotropy of fractured rock,” Geophysics 60 (1995): 204–211
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