The Research Of Seismic Modeling With Finite-element Method And Full Waveform Inversion Method

Two main research contents in this paper are seismic modeling with finite-element method and full waveform inversion method.Numerical seismic modeling is an important process in seismic inversion and migration.The irregular topography must be considered in the case of land seismic exploration.However conventional finite difference method often uses a stepped approximation which will cause unwanted diffraction.The finite element method is one of the ways to solve this problem,and the unstructured grids composed of triangles can adapt to any irregular surface.Therefore,it is necessary to study the numerical simulation of seismic waves in the unstructured grids.In addition,seismic exploration is aiming at deeper reservoirs and higher resolution.Full waveform inversion can make full use of the kinematic and kinetic information of seismic waves and get high resolution inversion results.So,it has a strong ability of recovering underground information.Aiming at the dispersion and stability of triangular meshes,we do the research about the seismic modeling with finite-element method based on acoustic wave equation.From the theoretical results and simulation results,the mesh composed of equilateral triangle elements has the highest accuracy.The effect of the finite element method is dependent on the results of meshing.It is necessary to control the size of transition zone during generating grids.We figure out the relationship between the aspect ratio of transition zone and the change rate of grid.For the artificial boundary reflections,we use PML boundary condition for second-order equations.The PML boundary condition combined with unstructured grids preserves its conventional stable effect of absorption.Full waveform inversion is an iterative local optimization process,which involves a large number of numerical simulations,so it is a computationally intensive task.The L-BFGS optimization algorithm has higher convergence speed,better deep-information recovery effect,fewer step-search times,and no increase in computation and storage.The source-encoding technique can greatly improve the inversion efficiency,and the random coding can suppress the crosstalk.In this paper,the L-BFGS algorithm are combined with the source-encoding method by secant equation to solve the instability problem,and the fast inversion of the 3D SEG/EAGE Overthrust model is achieved.