Application of misfit-based model space coordinate system design to seismic AVO inversion
Kristopher A. Innanen
The standard re-expressions used in AVO analysis and inversion (e.g., from velocity-density to modulus-density, or from the Aki-Richards approximation to the Shuey approximation, etc.) are formally coordinate transforms between oblique-rectilinear (i.e., non-Cartesian) coordinate systems. This means alternative re-expressions can be found with favourable updating properties. In a low-dimensional model space like that of AVO (which involves dimensionalities in the low single digits), analytic forms for transformation matrices to systems in which the Hessian operator is an identity matrix can be found. These imply new AVO approximations, within which updates in AVO inversion require no 2nd order objective function information. This may have consequences both for iterative linear AVO inversion algorithms and "weighted stack" algorithms, the latter of which can be based on much simpler weights.