A Green׳s function based procedure to account for non-quiescent past applied to numerical modeling of seismic offshore surveys

This work presents a strategy to initialize numerical methods applied to solve time-dependent wave propagation problems, e.g., transient acoustics. The strategy described here is dedicated to model wave propagating from air guns in offshore geophysical surveys applied to oil and gas industry. The model is formed by two distinct regions, i.e., a homogeneous (water) and a heterogeneous (sediment) one. For the geophysical applications considered here, the integrals of the BEM formulation can be simplified so that the final expressions allow one to calculate the wavefield in the homogeneous region, at any time, without needing to march on time through a time-stepping algorithm. Thus, this wavefield can be used to initialize any numerical method employed to propagate the pressure field throughout the model; in this work, the finite difference method (FDM) is the numerical method considered. The final integral equations for two- and three-dimensional problems are presented. An assessment of the accuracy of the results obtained by the strategy proposed here is provided at the end of this work, through the analysis of three examples.