Non‐linear traveltime inversion for 3‐D seismic tomography in strongly anisotropic media

SUMMARY We have developed two, new non‐linear traveltime inversion schemes for 3‐D seismic tomography in anisotropic media. They differ from the traditional linearized inversion approach and offer five significant improvements: (1) they are based on an alternative form of the first‐order traveltime perturbation equation, derived so as to simplify the inversion formulae and overcome the quasi shear wave singularity problem; (2) robust 3‐D ray tracing is employed which enables the simultaneous computation of the first‐arrival traveltimes and ray paths for the three body waves (qP, qS 1 and qS 2 ) in arbitrary anisotropic media; (3) the Jacobian matrix used in the update is based on an efficient computation for a 3‐D anisotropic model, so that the inversion is applicable to both weakly and strongly anisotropic situations, unlike most previous approaches which assume weak anisotropy; (4) a local‐search, constrained minimization is applied to the non‐linear inversion which makes anisotropic tomographic imaging an iterative procedure; (5) there is an option to invert for the elastic moduli directly or the Thomsen parameters directly in heterogenous, tilted transversely isotropic media, using any source–receiver recording geometry. We have examined the imaging capability of the non‐linear solver with individual body‐wave modes using a 3‐D synthetic anisotropic model incorporating two targets, a ‘high velocity’ and a ‘low velocity’ anomaly, embedded in a titled transversely isotropic medium. The model is illuminated by means of azimuthal VSP and crosshole measurements. The experimental results show that the two non‐linear inversion schemes successfully image the ‘targets’ and yield satisfactory 3‐D tomograms of the elastic moduli and the Thomsen parameters.