Tomographic string inversion

When square pixels are used to parameterize the slowness field in traveltime tomography, the problems of discretization for inversion purposes and discretization for display purposes are inextricably mixed. A “high resolution” result demands many pixels or model parameters, thus burdening tomography with the inversion of a large and sparse projection matrix though simplifying the display problem by using regions of constant slowness. In this paper, we present a method of separating the tomography problem into two distinct steps first inversion, then imaging. To reduce the complexity of the inversion step, we select a more natural set of pixels which are derived from the raypaths used to model the process of creating the traveltime data. The support of the string function is the raypath itself, thus the strings and raypaths are orthogonal (except when both equal the same line) and the projection matrix is diagonal and invertable in closed form. We are then left to image, i.e., synthesize the inversion result for display purposes. The method is tested on cross-well synthetic and field data requiring iterative curved raytracing. It is demonstrated to be a fast and robust technique of traveltime tomography.