Efficient Full-Waveform Inversion via QR-Based Data Selection

Arnaud Mercier , Hansruedi Maurer, Christian Boehm

Full-waveform inversion (FWI) is computationally intensive due to the large number of data points, forward simulations, and model parameters. However, realistic acquisition geometries often produce highly redundant linearized systems. In this work, we reformulate post-acquisition data selection as a matrix row-subset selection problem acting directly on the Jacobian of the linearized inverse problem. Using rank-revealing QR factorization, we introduce two complementary strategies: (i) row-wise selection to reduce the size of the linear system while preserving conditioning, and (ii) cost-aware selection to minimize the number of unique forward and adjoint simulations. In addition, we incorporate wavelet-based model compression derived from the Hessian diagonal to reduce the dimension of the update space. The methods are evaluated on synthetic elastic FWI experiments for crosshole and surface acquisition geometries. Row-wise QR selection consistently outperforms random subsampling and achieves accurate reconstructions using a fraction of the original data points. Cost-aware selection significantly reduces simulation cost with limited degradation of inversion quality. Model compression further decreases the number of active parameters, with compressibility strongly dependent on acquisition illumination. These results demonstrate that computational complexity in FWI can be controlled strategically by identifying the dominant bottleneck, memory, simulation cost, or model dimension, and applying the corresponding algebraic reduction mechanism. Although illustrated for seismic FWI, the proposed framework extends to inverse problems where the Gauss–Newton system is explicitly constructed or approximated, enabling algebraic manipulation of the Jacobian for data selection.