Estimation of elastic stiffness parameters in weakly anisotropic rotated HTI media

David Cho and Gary F. Margrave

ABSTRACT

The presence of fractures and directional in-situ stress fields in the subsurface has profound implications for numerous geophysical and engineering applications. These phenomenon manifest as azimuthal variations in the seismic response and can be detected in the amplitudes of the scattered wavefield. Therefore, the study of the azimuthal amplitude variation with offset (AVO) can provide information regarding the fracturing or the stress state of the subsurface. In this study, a transversely isotropic medium with a horizontal axis of symmetry (HTI) was used to model the presence of fractures and directional in-situ stress fields. Previous formulations of the reflections from HTI media invoke conditions that are often unrealistic in the natural world. Therefore, a more generic HTI reflection model was presented. This involves a transformation of the elastic stiffness matrix to represent an unknown symmetry axis azimuth where it is allowed to vary as a function of depth. In addition, we investigate the effect of dipping fracture sets and when the vertical stress is not equal to one of the principle stresses. It is shown that the corresponding reflection coefficients for a transformed HTI medium is capable of resolving the symmetry axis azimuth but lacks the complete set of parameters required to characterize the dipping fractures or when the vertical stress is not equal to one of the principle stresses. However, a different parameterization of the model space in the parameter estimation problem can provide an inference as to the presence of dipping fractures or a non-vertical principle stress component. These concepts are illustrated through a numerical example.

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