Assessing estimated velocity-depth models: Finding error bars in tomographic inversion

Abstract

In conventional migration velocity analysis methods, a velocity model is estimated that results in flattened events in common-image gathers. However, after this process, no information is available on the accuracy of this velocity model. A statistical analysis of velocity-model parameters is very difficult because of the integrated nature of the process. In common-focus-point technology, velocity estimation is split into two processes: a first step to estimate one-way focusing operators from the seismic data and a second step to translate these one-way propagation operators into a velocity-depth model. Because the second step does not involve seismic data and uses a hands-off model parameterization, a statistical analysis of the inversion result becomes rather straightforward. We developed a methodology for obtaining a suite of possible solutions, from which statistical measures can be extracted. By varying initial settings, the inversion of one-way traveltimes provides a space of solutions. Rather than having a single estimated model, we can obtain an ensemble of models. By performing statistical analysis of this ensemble, the error bars of the estimated velocity model can be retrieved. The procedure was tested for a 2D synthetic and field data set, for which the latter compares favorably to a conventional two-way traveltime tomography approach. The information provided by such an analysis is important because it shows the reliability of the final estimated model and could provide feedback for acquisition geometry design. More or better data might be needed to obtain a model to which a smaller degree of ambiguity is associated.