Full-waveform inversion uncertainty analysis with null-space shuttles

Scott Keating, Kristopher A. Innanen

Full-waveform inversion is an effective tool for recovering subsurface information, but quantification of confidence in this information can be very difficult. Uncertainty in a global sense is ever-present when using local optimization, preventing the calculation of an absolute uncertainty. Even when considering local uncertainty, the large dimensionality of the problem means that feasible, intelligible confidence metrics are generally limited to providing a scalar description of confidence for each variable, while a vector is required for completeness. Fortunately, complete characterization of uncertainty is seldom necessary from an applications perspective. More often, the uncertainty in a specific aspect of the inversion is important (for instance, confidence in a recovered anomaly). Here, we investigate the use of null-space shuttles to characterize the maximal change in a chosen metric that can be achieved without altering the inversion objective function. This provides a quantification of the uncertainty in this metric for the inversion result.