Research On Finite Difference Algorithm For Three-dimensional Viscous Acoustic Wave Equation

As the basis of the inversion,forward modeling is always the vital point of Computational Mathematics and Geoscience researchers.Every geoscience researcher hopes to use an accurate,efficient and low frequency dispersion algorithm for numerical simulation under the condition of conforming to the actual formation complexity as much as possible.We have studied the propagation of seismic waves in three-dimensional viscoelastic medium with this expectation in this thesis.We extend the ONADM method to the viscoelastic media.Based on this,we use the nonlinear optimization theory,Fourier analysis method and Monte-Carlo method to study the stability and dispersion properties of the ONADM method.The research results show that the ONADM method can suppress the numerical dispersion better than the central difference method,the LWC method and the SG method.This means that the ONADM method needs less grid in a wavelength,that is,the ONADM method can effectively suppress the numerical dispersion in the larger space step condition with the lower memory requirement and higher computational efficiency.In this paper,the parallelized ONADM method is proposed,and parallel computing is used to solve the problem that the common computer cannot bear the computing resources needed for large-scale three-dimensional forward problems.For the numerical examples given in this thesis,we find that the acceleration ratio and parallel efficiency of the ONADM method are approximately 1.8 times that of the SG method through analysis of the speedup ratio and parallel efficiency.Numerical examples show that(1)In viscoelastic media,the ONADM method is used for numerical simulation based on different velocity models and the obtained wave-field snapshots are clear and without dispersion.(2)In the process of equal time simulation in the same area,the storage of ONADM method is only 8.08%of the SG method,and the calculation speed is about 6.26 times of SG.It shows that the ONADM method has the characteristics of low storage and high computing efficiency compared with the SG method.(3)When the seismic wave propagates in the viscoelastic medium,the energy(amplitude)is obvious attenuation,which is consistent with the propagation law of seismic waves in the viscoelastic medium.