Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizin...

An interferometric form of Fermat’s principle is presented for redatuming PS transmission traveltimes to be those for sources lowered to the target body. The velocity model does not need to be known for redatuming, so the distorting effects of uninteresting parts of the velocity model and statics are eliminated by this target-oriented approach. Thus, traveltime tomography applied to the redatum...

The accuracy of computed traveltimes in a velocity model plays crucial role localization microseismic events. conventional approach usually utilizes robust fast sweeping or marching methods to solve the eikonal equation numerically with finite-difference scheme. These introduce traveltime errors that strongly depend on direction wave propagation. Such error results moveout changes and introduce...

We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with repsect to a hypothetical background medium is to be estimated. By a convincing heuristics a detection procedure for this perturbation was proposed based on optimization of ...

We present statistical and interval techniques for evaluating the uncertainties associated with geophysical tomographic inversion problems, including estimation of data errors, model errors, and total solution uncertainties. These techniques are applied to the inversion of traveltime data collected in a cross well seismic experiment. The inversion method uses the conjugate gradient technique, i...