Elastic Ray-Born L₂-Migration/Inversion

Summary

The approximate ray Green's tensor in 3-D heterogeneous elastic media combined with the first-order Born approximation lead to new explicit equations for solving, modelling and inverse scattering problems. Individual wave scattering contributions (PP, PS, SP, SS) are represented for four different linear approximations (i.e. parameter linearizations). the first-order Born appoximation yields a scattered wavefield which is linearly related to medium parameter perturbations. the linearized inverse scattering problem is solved in the space-time domain and consists of minimizing a cost function within the l₂ norm with a one-step conditioned gradient procedure. From uni- or multicomponent data and a reference heterogeneous background model representing adequately either the long spatial wavelengths of the medium (i.e. the smooth model), and/or its principal features (i.e. the macro-model), this operation reduces to: (1) pre-stack depth-migrating the scattered data yielding three intermediate images; and (2) deconvolving these images by an elastic Hessian correction which produces final high-resolution images representing the medium's short spatial wavelength variations convolved with the source function (e.g. P and S impedances and density maps). If the reference model and data are satisfactory, typical artefacts are due to limited aperture or insufficient coverage. Use of high-frequency and Born approximations require certain constraints. For example, the dominant wavelength must always be smaller than the characteristic length of the reference medium, but larger than the scatterer characteristic length. to increase computational efficiency, the high-frequency approximate Green's tensor is calculated by the paraxial ray method. 2-D elastic synthetic examples for surface reflection and cross-hole experiments show the ability of such a technique to delineate subsurface structure and to recover local changes in elastic properties. However, density variations are more difficult to resolve than P and S impedance or velocity changes.