Optimized experimental design for seismic full waveform inversion: A computationally efficient method including a flexible implementation of acquisition costs

Optimized experimental design aims at reducing the cost of a seismic survey by identifying the optimal locations and amounts of sources and receivers. While the acquisition design in the context of seismic imaging applies criteria like fold, offset and spatial sampling, different attributes such as the sensitivity kernels are more relevant for seismic full waveform inversion. An ideal measure to quantify the goodness of an acquisition design relies on the eigenvalue spectrum of the approximate Hessian matrix, but this technique is computationally too expensive for practical use. A more affordable goodness measure has been proposed in the past, but we demonstrate that this measure is inappropriate for target‐oriented optimized experimental design. To address those issues, we derived a sequential receiver‐based procedure using a goodness measure based on the determinant of the approximate Hessian matrix. We show with numerical tests that it efficiently provides an optimized design for target‐oriented as well as for extensive full waveform inversion. This design allows a better reconstruction of the subsurface than an evenly spaced acquisition geometry. Furthermore, the optimization algorithm itself can easily be parallelized, therefore making it attractive for applications to large‐scale three‐dimensional surveys. In addition, our algorithm is able to incorporate variable costs, representing any kind of acquisition‐related costs, for every individual source location. The combined optimization with respect to the information content of sources and to the true cost will allow a more comprehensive and realistic survey planning and has a high potential for further applications.