Bayesian survey design to optimize resolution in waveform inversion

We describe a Bayesian methodology for designing seismic experiments that optimally maximize model-parameter resolution for imaging purposes. The proposed optimal experiment design algorithm finds the measurements that are likely to optimally reduce the expected uncertainty on the model parameters. This Bayesian D-optimality-based algorithm minimizes the volume of the expected confidence ellipsoid and leads to the maximization of the expected resolution of the model parameters. Computational efficiency is achieved by a greedy algorithm in which the design is sequentially improved. In contrast to minimizing the uncertainty volume over the entire subsurface simultaneously, a refinement of the algorithm minimizes the marginal uncertainties in a region of interest. Minimizing marginal uncertainties simultaneously accounts for quantitative prior model uncertainties while honoring a qualitative focus on particular regions of interest. The benefits of the proposed method over traditional non-Bayesian ones are demonstrated with several geophysical examples. These include reducing large seismic data volumes for real-time imaging and solving the problem of designing seismic surveys that account for source bandwidth, signal-to-noise ratio, and attenuation.