Model building for tilted transversely isotropic media has commonly been performed by a single parameter tomography that updates the velocity in the symmetry direction, while the orientation of the symmetry axis and Thomsen parameters ε and δ are typically estimated from the migration stack and well data. Unfortunately, well data are often not available. In addition, when they are available, their lateral sampling is typically very sparse and their vertical sampling usually spans only a limited range of depths. In order to obtain spatially varying anisotropic models, with or without well data, we developed a multiparameter joint tomographic approach that simultaneously inverts for the velocity in the symmetry axis direction, ε and δ. We derived a set of reflection tomography equations for slowness in the symmetry axis direction and Thomsen parameters ε and δ. In order to address the nonuniqueness of the tomography, we developed a regularization strategy that uses an independent regularization operator and regularization factor for each individual anisotropy parameter. Synthetic tests found that ambiguity exists between the anisotropy parameters and that velocity has a better resolution than ε and δ. They also confirmed that joint tomography provides a better data fit than single parameter tomography. The field example was used to test a way to incorporate the sonic data in the model building process and limit the tomographic updates on certain anisotropy parameters by adjusting the regularization.

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