Numerical Simulation Of Elastic Waves And Full Waveform Inversion Based On Meshless Generalized Finite Difference Method In Frequency Domain

With green and low-carbon development becoming the theme of the times,vigorously developing green geophysical technology is an important task faced by the geophysical industry.At present,the numerical simulation of elastic waves and full waveform inversion technology are constantly advancing,with a significant increase in computational and storage capacity,and an increasing energy consumption.From the perspective of green development,it is of great research significance to reduce the computational and storage costs of elastic wave numerical simulation and full waveform inversion,and achieve efficient and low energy consumption numerical calculations.The meshless generalized finite difference method is a new type of numerical method.It breaks the limitation of the traditional finite difference method that requires mesh generation,retains the advantage of localization in numerical algorithms,and improves the calculation efficiency while ensuring the calculation accuracy.In view of its unique advantages in numerical simulation,based on the generalized finite difference method,this paper systematically carried out the research work of frequency domain elastic wave numerical simulation and full waveform inversion.The main research results obtained in this article are as follows:(1)A meshless generalized finite difference method for elastic wave numerical simulation in frequency domain is proposed,which solves the problem of grid dispersion in grid method,improves the calculation efficiency of elastic wave numerical simulation in frequency domain,and reduces the storage capacity.Theoretical analysis shows that the generalized finite difference method needs about 5.6 nodes in a shear wavelength to suppress 1% dispersion error(regular node distribution),2.7 nodes less than the conventional finite difference method.The results of numerical examples show that the generalized finite difference method can accurately simulate the elastic waves in the frequency domain.Compared with the conventional finite difference method,the error between the analytical solution and the generalized finite difference method is smaller,and the computational efficiency is higher;The generalized finite difference method can improve the efficiency of elastic wave numerical simulation and reduce the storage requirements without affecting the simulation accuracy by generating node density that changes with model parameters and reducing the number of nodes involved in numerical simulation;Combining with the node generation algorithm proposed in this article,generating randomly uniformly distributed nodes that accurately describe known interfaces can effectively avoid grid dispersion in grid methods.(2)The block low rank multifrontal algorithm is studied to solve large-scale sparse linear equations,settled the problems of low computational efficiency and large storage capacity when using direct methods.The block low rank multifrontal method converts the dense frontal matrix in the LU decomposition process into a block low rank approximation format,which can not only retain the main characteristics of the original frontal matrix,but also reduce the storage capacity and computational complexity.At the same time,this algorithm has good parallel characteristics and can further improve the efficiency of solving linear equations through parallel computing.The numerical simulation experiment of elastic waves shows that compared to the conventional multi wavefront method,using the block low rank approximate multi wavefront method for solving linear equations can effectively improve computational efficiency and reduce memory requirements.(3)A full waveform inversion strategy combining generalized finite difference forward modeling,block low rank multifrontal method,combined orthogonal source coding and MPI two-stage parallel,is proposed,which effectively improves the calculation efficiency of full waveform inversion and reduces the storage capacity.The inversion results of the undulating model show that the generalized finite difference method combined with the variable density node distribution and MCPML boundary conditions is used for full waveform inversion.On the one hand,it can avoid the undulating interface jitter of the inversion results caused by grid method,on the other hand,the calculation efficiency is improved by about 24%,and the storage capacity is saved by about 42%;The inversion results of the Overthrust model indicate that,while ensuring inversion accuracy,block low rank multi wavefront full waveform inversion can effectively improve computational efficiency and reduce memory requirements;On this basis,combining orthogonal source codes can further improve the efficiency of full waveform inversion calculation.105 figures,14 tables,and 195 references...