Dual tomography for imaging complex structures

Abstract

The geophysical community admits that geotomography is a workable way to obtain accurate estimates of seismic velocity in complex structures. So‐called dual tomography improves the resolution of computed tomograms and thus can be applied to different geophysical and nongeophysical problems. Dual tomography emerges as a generalized approach to linearized constrained inversion. Dual inversion transforms a generalized constrained optimization problem being formulated in the physical space of seismic velocities to a dual unconstrained problem posed in the vector space of Lagrangian multipliers. It is a parametric optimization problem, with unknown solutions that are always perpendicular to the null‐space of a tomographic matrix. Imposed constraints improve the resolution and act as if the angular aperture coverage was extended. Thus dual tomography is able to quash image blurring associated with incomplete angular recording. Dual tomography does not require accurate knowledge of initial model. One starts with an arbitrary homogeneous medium and updates the medium in the course of iterations. Dual tomography does not require direct inversion of matrices and therefore it is relatively fast. Preliminary results indicate that dual tomography typically yields better images compared with algebraic reconstruction technique (ART), simultaneous reconstruction technique (SIRT), and other conventional techniques especially for limited angular aperture experiments typically used in seismic exploration.