Abstract
We consider the conjugate gradient method for the normal equations in the solution of discrete ill-posed problems arising from seismic tomography. We use a linear approach of traveltime tomography that is characterized by an ill-conditioned linear system whose unknowns are the slownesses in each block of the computational domain. The algorithms considered in this work regularize the linear system by stopping the conjugate gradient method in an early iteration. They do not depend on the singular-value decomposition and represent an attractive and economic alternative for large-scale problems. We review two recently proposed stopping criteria and propose a modified stopping criterion that takes into account the oscillations in the approximate solution.
Highlights
Exploration seismology, or seismics, is the field of geophysics that is most employed for subsurface imaging in the oil industry, and uses an ensemble of techniques based upon the theory of propagation of elastic and acoustic waves
We considered the solution of an ill-conditioned least-squares problem arising from the discretization of a model for linear seismic tomography, which is a tool with wide application in reservoir geophysics
The discrete problem was presented as a system of linear equations, which we solved by the standard conjugate gradient method regularized by stopping in an early stage
Summary
Exploration seismology, or seismics, is the field of geophysics that is most employed for subsurface imaging in the oil industry, and uses an ensemble of techniques based upon the theory of propagation of elastic and acoustic waves.
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