Equivalent Medium Parameterization For Complex Heterogeneous Model And Two-Dimensional Finite-difference Global Seismic Waveform Simulation

In the past few decades,space satellite technology and material science have developed rapidly.Since the successful deployment of a seismometer on the lunar surface by the Apollo 11 spacecraft in 1969,humans have deployed seismometers on the Moon,Venus,and Mars several times and successfully received "seismic" records.This has greatly developed the potential of seismic methods in the study of the internal structure and evolution of extraterrestrial bodies.Flexible and accurate global seismic wave simulation methods are important tools for studying the internal structure of celestial bodies.The finite-difference method(FDM)has been widely used in seismic wave simulation due to its simple implementation,high efficiency,and ease of parallelization.In order to reduce the number of computational grids and improve computational efficiency,many high-order and optimized FD schemes have been developed in recent years.The goal of high-order and optimized schemes is to reduce the error generated by traditional finite difference Taylor series expansion,namely dispersion error.By adopting high-order and optimized schemes,the dispersion error can be reduced to an acceptable range when there are 3-4 grid points per wavelength,greatly reducing computation.The use of coarse grids in the finite-difference(FD)seismic waveform simulation of models with strong interfaces leads to large interface errors and the generation of artificial diffraction from stair-step interfaces.To suppress the interface errors in finitedifference simulation,we propose a TTI equivalent medium parameterization method.The derivation of the TTI equivalent medium parameterization is inspired by the longwavelength equivalent theory.In the long-wavelength equivalent theory,when the scale of the heterogeneity is much smaller than the wavelength of the seismic wave,the heterogeneity can be equivalent to a homogeneous anisotropic medium.In finite-difference simulation,usually three or more grid points per wavelength are required,while the medium heterogeneity within a grid cell is much smaller than the wavelength.Based on this idea,we used a similar derivation to the long-wavelength equivalent theory to obtain the equivalent medium parameters at the grid points.Numerical tests demonstrate that the proposed TTI equivalent medium parametrization can be used with higher-order and optimized schemes at three points per wavelength and produce satisfactory results.In addition,we also develop an efficient algorithm of equivalent medium parameterization implementation for finite-difference seismic wave simulation methods.Since the accuracy of the equivalent medium is closely related to the interface input method or characterization method,we present a representation method for complex interfaces,in which each layer of the medium with an interface discontinuity can have lateral and vertical changes.In our implementation,considering that most of the previous equivalent medium parameterization methods require the computation of volume averaging of the medium within the grid cells,this thesis separates the algorithm for fast calculating the volume averaging and the calculation method for the angle required for calculating the TTI equivalent.Different from the previous code that encrypts all grid cells for volume averaging,we use an auxiliary grid comprised of half-grid cells to locate grid points that ensure that we only compute numerical integration on the cells crossed by the interfaces,which significantly improves computational efficiency.In the calculation of the interface inclination and the intersection point of the interface and the auxiliary grid required for the TTI equivalent medium method,we adopt the lookup table of Marching Cube method in computer graphics to construct the intersection table by using the topological relationship between the auxiliary grid labels and the intersecting edges,thereby reducing the calculation amount required for finding intersection points.Combining the TTI equivalent medium parameterization proposed in this study and the curvilinear-grid finite-difference method,we implement a finite-difference global simulation method.We discuss the feasibilities and advantages of using curvilineargrid finite-difference method in global seismic wave simulation from the aspects of FD scheme selection,grid generation and finite-difference value processing,discontinuous grid,and medium discretization.To reduce the number of grids required for each wavelength and consider the stability of the one-sided format,we used the eighth-order center SBP(Summation-by-Parts)difference scheme.Considering the particularity of the calculation area,the grid partitioning in this article uses vertically stretched grids relative to the center,and special processing methods for difference value of the center and horizontal period are given.The correctness of the grid generation and the special treatment of finite difference values is also tested.Due to the flexibility of the curved grid finite difference method,we can easily simulate wave propagation of models with surface undulations and elliptical regions through grid partitioning.To avoid the problem of excessively small spatial grids near the center caused by a unified stretched grid and excessively small time steps determined by the CFL condition,we discuss the application of discontinuous grids in this problem.We also present implementation schemes for medium discretization and equivalent medium parameterization methods for global seismic wave simulation problems.When calculating layered media or media with velocity anomalies,accurate simulation results can be obtained by using equivalent medium parameterization methods without dividing the grid at the medium interface,avoiding dependence on third-party grid generation software.Finally,we discuss details of component rotation of sources and seismogram records.This work has implemented a complete set of C/C++code.This code encompasses functionalities such as reading input files,grid generation,medium discretization,source and station positioning,finite-difference calculations,discontinuous grid implementation,wavefield and seismogram output,and visualization.Combining the curvilinear grid finite difference method and the equivalent medium parameterization method,the global seismic wave simulation scheme and code framework proposed in this work have the advantages of being flexible and independent of third-party grid generation.It can provide reliable tools for the study of the internal structure of celestial bodies such as the Moon and Mars in the future.