A Domain Decomposition Approach for Fast Reduced Order Solutions in Geophysical Exploration

Summary Model order reduction (MOR) is a powerful technique that enables the possibility of real-time computation of parametric solutions for multitude of engineering applications. Here we focus on wave propagation problems driving forward modeling for geophysical applications. Usual algorithms, for instance time migration or full waveform inversion, impose repetitive forward modeling evaluations to iterate over the model solution and compute the required sensibilities to any desired parameter. Thus, the use of MOR methods on these geophysical models can generate fast online solutions providing an invaluable framework to accelerate the overall execution of the process. In order to find solutions for those cases where the MOR approach fails and, in particular, drastically speed up the computation of its offline phase for geophysical problems, we explore in this work the application of domain decomposition methods (DDM). This approach is based on using DDM for the high dimensional domain (i.e. partitioning along space and parameter dimensions) and then reduce the local models with the proper generalized decomposition MOR method.