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 [Formula: see text] and [Formula: see text] 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, [Formula: see text] and [Formula: see text]. We derived a set of reflection tomography equations for slowness in the symmetry axis direction and Thomsen parameters [Formula: see text] and [Formula: see text]. 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 [Formula: see text] and [Formula: see text]. 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.
Over the last few years, migration‐velocity analysis methods have been developed for 2‐D and 3‐D models by extending the assumptions and approximations used for rms velocity models. Computational requirements for these analyses have increased dramatically because top‐down layer‐stripping migration is needed to derive interval velocities directly instead of using rms velocities and then converting into interval velocities. We establish exact equations for 1‐D and 2‐D residual velocity analysis in the depth‐plane‐wave domain and use these in an iterative and interactive migration velocity analysis program. The new method updates interval velocities directly in a top‐down residual‐difference correction for all layers after prestack depth migration instead of top‐down layer‐stripping migration followed by residual analysis. This makes the new method a suitable tool for migration velocity analysis, especially for 3‐D surveys. We test the method on synthetic and field data. The field data results show that a reasonable velocity model is obtained and most common image gathers are correctly imaged using no more than four iterations.
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