Parameter inversion and angle migration in anisotropic elastic media

Seismic parameter inversion using the inverse generalized Radon transform (GRT) was originally formulated as an integral over source and receiver surface coordinates, involving a Jacobian from angle to surface coordinates. By formulating the inversion directly in terms of angle coordinates at the subsurface image point, I obtain simplified inversion formulas for point scatterers and subsurface reflectors. Amplitudepreserving angle migration based on the inverse GRT gives an estimate of the scattering coefficient in the Born integral as a function of scattering angle and azimuth. The scattering coefficient is directly related to the linearized plane-wave reflection coefficient between two anisotropic media, which limits the result to small angles and small contrasts in the elastic parameters. I use the Kirchhoff modeling integral for anisotropic media to formulate a Kirchhoff angle-migration integral that is valid for large angles and large parameter contrasts. It gives an estimate of the plane-wave reflection coefficient normalized with respect to amplitude. The Kirchhoff integrals, however, are non reciprocal, so I propose to use new reciprocal integrals for modeling and angle migration. The new migration integral, which is much simpler than the Kirchhoff integral, gives an estimate of the plane-wave reflection coefficient normalized with respect to the energy flux normal to the reflector. A restricted inverse GRT has been proposed for migration-velocity analysis. By simplifying this, I derive an expression for amplitude-compensated migration that is the estimated reflection coefficient divided by the norm of the radiation pattern vector. This partly removes the effects of amplitude variations with scattering angle and azimuth.