Image-guided ray tracing and its applications

Abstract

Eikonal solvers have found important applications in seismic data processing and in-version, the so-called image-guided methods. To this day in image-guided applications, thesolution of the eikonal equation is implemented using partial-differential-equationsolvers, such as fast-marching or fast-sweeping methods. We show that alternatively, onecan numerically integrate the dynamic Hamiltonian system defined by the image-guidedeikonal equation and reconstruct the solution with image-guided rays. We present interest-ing applications of image-guided raytracing to seismic data processing, demonstrating theuse of the resulting rays in image-guided interpolation and smoothing, well-log interpola-tion, image flattening, and residual-moveout picking. Some of these applications make useof properties of the raytracing system that are not directly obtained by eikonal solvers, suchas ray position, ray density, wavefront curvature, and ray curvature. These ray propertiesopen space for a different set of applications of the image-guided eikonal equation, beyondthe original motivation of accelerating the construction of minimum distance tables. Westress that image-guided raytracing is an embarrassingly parallel problem, which makes itsimplementation highly efficient on massively parallel platforms. Image-guided raytracing isadvantageous for most applications involving the tracking of seismic events and imaging-guided interpolation. Our numerical experiments using synthetic and real data sets showthe efficiency and robustness of image-guided rays for the selected applications.