Fréchet derivatives based approach for ROM bases update to improve FWI cost efficiency
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The reduction of energy carbon footprint justifies the recent major programs launched on CO2 storage in existing reservoirs known to geologists. Numerical simulation plays a key role in their implementation by providing a low-cost means of monitoring. The Full Waveform Inversion (FWI) method has demonstrated its ability in probing the subsurface accurately and, therefore, is considered to be a primary candidate for monitoring process. However, FWI is an iterative process that requires solving multiple large-scale forward problems, at each iteration, of about 108 cells [2]-[3]. On the other hand, Reduced Order Modeling (ROM) techniques have been proven to be efficient for fast and accurate computations of a large class of PDEs [1]. Hence, the idea of equipping FWI with a ROM procedure appears to be an attractive alternative for reducing the computational cost at a fixed parameter. Consequently, the main challenge of employing such an approach resides in the construction of the bases as the parameter is updated throughout the iterative process. Given that, we have designed an efficient strategy to update the ROM bases that utilizes the Fréchet derivatives as well as the Taylor expansion of the initial solution. Numerical results for three-dimensional configuration are presented to illustrate the performance efficiency of this new solution methodology.
