Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach.

摘要: In velocity and attenuation tomography, ray refraction leads to errors in time-of-arrival, as well due phase cancellation lateral beam displacement. Some authors have proposed iterative techniques based on numerical tracing correct for these effects. this paper, we consider an alternative approach using a perturbation analysis of refraction. This requires neither iteration nor integration the equation. Assuming that index deviates from its mean order small quantity e, derive expressions refracted path whose departure straight line is first e. Using result, obtain expansion integral refractive along time-delay correction e2 arising deviation line. The expression first-order also used explicit corrections phase-cancellation beam-displacement affect measurements when transducers finite extent are employed. addition, because refraction, large aperture susceptible arrival-time uncertainty time-of-flight measurement; maximum value derived. both two three dimensions, much simpler computationally than methods. Computer simulated reconstructions presented which clearly show improvement can be achieved with second-order time delay correction.