Pseudo-acoustic wavefield tomography with model constraints

Anisotropic wavefield tomography seeks to recover anisotropic parameters based on seismic wavefields. In terms of computational efficiency and degrees of freedom of the model parameters, the acoustic approximation to the anisotropic elastodynamics is more suitable than the full anisotropic elastic equations to the anisotropic tomography problem. We implement the wavefield tomography in VTI media based on the pseudo-acoustic coupled wave equations. Although three independent parameters are enough to describe acoustic VTI media, the choices of model parameterization remain case-dependent and ambiguous. To circumvent subjective choices and trade-offs in model parameterizations, we propose relating the model parameters using inequality constraints. Moreover, we show the potentials of using such inequality constraints to alleviate the acquisition signatures in anisotropic tomography. For example, one can mitigate the problem where, in VTI media, the data acquired from the cross-well acquisition geometry can hardly resolve phase velocities along the symmetry axis.