Designing full waveform inverse problems: a combined data and model approach

SUMMARY Full waveform inversion has the potential to provide high-resolution insights into subsurface structures. However, its adoption, particularly in 3-D multiparameter applications, has been limited by high computational costs. This study addresses this challenge by introducing an optimized experimental design (OED) method that simultaneously optimizes source placement and model parametrization. The result is an optimized survey design and a compressed model representation that maximizes the information content. By reducing the source layout by approximately 50 per cent and compressing the model by approximately 90 per cent, this approach significantly reduces computational demands, allowing the use of fast convergence inversion algorithms such as the Gauss–Newton method. The OED calculation is reduced from a typical $\mathcal {O}(n^3)$ complexity, as in eigenvalue-based criteria, to $\mathcal {O}(n \log _2n)$ with the newly introduced wavelet transform-based criterion. Additionally, a post-acquisition source–receiver pair optimization method is developed, demonstrating that while random selection captures high information content, the proposed OED criterion effectively minimizes the number of required simulations. This approach further reduces computational cost and facilitates the efficient extraction of compact, high-value data sets from excessively large surveys.