| In exploration and earthquake seismology,waveform inversion method has been widely used,which requires a mount of seismic forward modeling calculation.Thus the computational efficiency of forward modeling method is very important.Meanwhile,waveform inversion methods usually require relatively uniform distribution of sources and receivers.The spatial distribution of earthquakes is nonuniform in many regions,which to some extent hinders the application of waveform inversion method in earthquake seismology.A feasible solution is to utilizing active source as a supplement.In recent years,large volume air-gun source has been widely concerned because of its high repeatability and large energy.However,it needs to be excited in water.The shape of natural reservoir is usually complex,so seismic forward modeling method for complex structure is the basis of using air-gun source in waveform inversion.This study mainly focuses on improving the efficiency of seismic forward modeling and seismic forward modeling for complex structures.Numerical simulation method in frequency-domain requires calculating multiple single-frequency wavefields.The amount of calculation is proportional to the number of single-frequency wavefields to be calculated.Deep learning has developed rapidly in recent years.In this study,we proposed a method based on U-Net to replace part of calculation with wavefield interpolation to accelerate numerical simulation in frequencydomain.The method could reduce the number of single-frequency wavefield to be calculated and improve forward modeling efficiency.We trained the U-Net by data obtained from 10 layered models.The predicted results are good in test data.Compared with the traditional fourth-order interpolation method,the results show that the traditional interpolation method is not suitable for this kind of problem.The predicted results in two-dimensional SEAM model are also good.We perform a series of tests on perturbation models with different scales and amplitudes.According to the results,the applicable cases are given quantitatively.Finally,the U-Net is applied directly to three-dimensional problems,and the results in complex layered model and Overthrust model are very close to the results obtained by calculation.To simulate the propagation of air gun source,the fluid-solid interface conditions need to be explicitly added to ensure the accuracy of simulation.The complex shape of fluid-solid interface can be better described only by tetrahedral mesh.High order schemes are required to reduce the memory requirements and ensure the accuracy of simulation in large scale computation.When using tetrahedral mesh and high-order scheme for 3D simulation,the traditional finite element method has the difficulty in parallel.Flux is introduced in the discontinuous Galerkin method,resulting in each cell become independent and easy to be solved in parallel.Therefore,it is very suitable for seismic forward modeling for complex structures.At present,many numerical fluxes have been applied to seismic forward modeling,and there are some differences among the numerical fluxes.In this study,by comparing different numerical fluxes in seismic forward modeling.We found that only RH-condition flux which based on RankineHugoniot jump condition does not have stability problem when strong wa ve impedance exists between adjacent elements,and the flux is more consistent with physical law.There may be a large difference of wave impedance at fluid-solid interface.RHcondition flux is very suitable for such cases.In this study,RH-condition flux is used to two-dimensional seismic forward modeling in fluid-solid media based on discontinuous Galerkin method with triangular mesh.The accuracy of the proposed method is verified by spectral element method in horizontal and sine-type layered fluid-solid media.The method is extended to three-dimensional with tetrahedral mesh,which provides a basis for waveform inversion using land air-gun source. |
