An alternative method for accurately and efficiently modeling seismic wave fields using an optimal convolutional differentiator base on Shannon singular kernel theory is proposed. This approach uses optimization and truncation to form a localized operator, which can preserve the fine structure of the wave field in complex media. We verify this approach for wave field modeling in homogeneous and heterogeneous acoustic media. Our numerical results indicate that this method can suppress numerical dispersions and allow for the study of wave fields in arbitrarily heterogeneous structures. The results hold promise not only for future seismic studies, but also for any field that requires high-precision numerical solution.


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