Abstract
A method is presented to compute the elastic parameters of a homogeneous medium that is transversely isotropic with a vertical axis of symmetry (VTI). The method requires an initial estimate of the parameters and, using a process similar to common focus point (CFP) analysis, arrives at a set of differential time shifts (DTS). That is, the recorded wavefield, and models of the sources, are propagated to a CFP using extrapolation operators parameterized with vertical slowness q a function of the initial elastic parameters. Cross correlation of the propagated wavefields resolves an angle dependant reflectivity estimate (data along zero lag are used in imaging). When the initial parameters are not correct, the specular reflection corresponding to the CFP will not perfectly align at zero lag, and if the medium is homogeneous VTI, the DTS will appear as a symmetric curve over negative and positive offsets. In the τ p (Radon) domain, the DTS relate error in q to horizontal slowness p—delay-time error as a function of phase angle. Series expansion is used to linearize q with respect to error in the elastic parameters ∆α, ∆e and ∆δ. Least-squares inversion yields ∆α, ∆e and ∆δ for use in updating the initial estimate. Comparison with the exact q for an anisotropic shale shows the linear expression is most sensitive to error in the initial α, followed by δ and is least sensitive to error in e.
Published Version
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