Full-waveform inversion is an effective tool for recovering subsurface information, but many factors make this recovery subject to uncertainty. In particular, unwanted noise in measurements can bias results toward models which are not representative of the true subsurface, and numerical optimization techniques used in the inversion allow for only approximate minimization of the inversion objective function. Assessing the uncertainty these factors introduce can be difficult, due to the large dimensionality of the inversion problem. Fortunately, complete characterization of inversion uncertainty is seldom necessary for applications employing an inversion result, meaning the entire dimensionality of the problem may not be relevant for practical uncertainty quantification. Typically, it is only the uncertainty in a few specific aspects of the inversion that is important (for instance, confidence in a recovered anomaly). A targeted uncertainty quantification, characterizing only the confidence in a specific feature of the subsurface model, can greatly reduce the dimensionality of the uncertainty characterization problem, potentially making it tractable. We propose an approach for quantifying the confidence of the inversion in a chosen hypothesis about the recovered subsurface model. We test these hypotheses through numerical optimization on the set of equal-objective model-space steps, called null-space shuttles. By approximating the null-space shuttles which maximally violate a given hypothesis about the inversion, this method establishes an effective approximation of the uncertainty in that hypothesis at relatively small computational cost.

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