Optimizing Full Waveform Inverse Problems: A Combined Data and Model approach

Full Waveform Inversion (FWI) has emerged as a groundbreaking tool in geophysics, offering unprecedented resolution in subsurface imaging. However, its broader application is often limited by substantial computational demands, especially in 3D elastic applications. This research addresses this critical barrier by introducing a novel approach that optimizes both data (source-receiver layout) and model (model parameterization) spaces, thereby reducing computational overhead and extending FWI's applicability. The interdependence between data and model spaces is a key factor to optimize FWI. We believe that both spaces must be simultaneously optimized to enhance the efficiency of FWI. This optimization is particularly crucial for intensive FWI problems but is also expected to make FWI accessible to a broader range of users, including those with limited computational resources.

We combine principles from Optimal Experimental Design (OED) and Compact Full Waveform Inversion (CFWI). Selecting only the most relevant source-receiver pair ensures a minimal, yet informative data set. By using a wavelet representation of the model, it is possible to easily tune the compression of the model based on the local resolution. The outcome of our data-model approach is a source-receiver layout that maximize the resolution of a compressed representation of the model.

Initial results with applications focused on synthetic 2D acoustic problems shows that the data-model approach allow for a significant reduction in both source-receiver pairs (≈ 50%) and model parameters (≈ 90%), whilst retaining 90% of the information content. Compare to classical OED criterion, our approach posses a lower time complexity by about 2 order of magnitude (O (m) vs O (mn²)). The significant speed up enables optimizing for sources and receivers independently, leading to further optimized layouts.

The data and model compression enables the use of Gauss-Newton optimization algorithm, leveraging faster convergence and greater flexibility. Benefits of this algorithm includes the possibility to optimize source-receiver layouts not only prior to fieldwork, but also during the inversion. At each stage of the inversion process, the most relevant data points are effectively identified and retained. This selection significantly reduces both computational and memory requirements. An additional benefit of this approach is the straightforward implementation of targeted OED, enabling optimization of the source-receiver layout for specific subsurface targets.

Key aspects to ensure a reliable and efficient data-model approach include evaluating the prior model's influence, examining the effects of compression ratio, resolving ambiguities in survey layout and model parametrization, and refining source and receiver positioning. We will present initial results and  highlight its potential benefits to significantly reduce the computational load of FWI.