Diffraction Traveltime Approximation for an Arbitrary Anisotropic Medium - A Case Study

DEDICATED - Case Studies in Diffraction Imaging and Interpretation. In this case study, we derive an approximation of the diffraction response for an inhomogeneous anisotropic medium. Our traveltime expression is formulated as a double-square-root that allows us to accurately and reliably approximate diffraction response. In the inhomogeneous anisotropic medium, the location of the diffraction apex might be shifted with respect to the diffractor location. The magnitude of the shift depends on the angle of emergence of the fastest ray emitted from the diffractor. In general, our approximation depends on four independent parameters: emergence angle of the fastest ray, ray velocity along this ray, and first and second-order derivatives of the ray velocity with respect to the ray angle. Since we also consider a heterogeneous medium, our anisotropy parameters represent effective parameters. We determine them as stacking parameters by fitting calculated traveltimes to the data using a coherence measure. For this purpose, we perform a simultaneous parameters search. The effective anisotropic parameters can be further used to reconstruct real anisotropic parameters, e.g., by a least-square based inversion. The application of the method to synthetic data with different types of transversely anisotropy shows promising results.