Rayleigh Wave Numerical Simulation Base On FCT Finite-difference Method

As a new geophysical prospecting method, Rayleigh wave has been developing rapidly in recent years, its economic, fast and efficient features are gradually recognized by engineers, and it is widely used in engineering geological investigation and engineering non-destructive testing fields. At present, the Rayleigh wave of theoretical research focuses on the dispersion curves of forward and inversion terms. In order to have a more accurate and comprehensive understanding of the characteristics of Rayleigh wave propagation, some scholars have done a numerical significant research on simulation of Rayleigh wave.Finite difference method based on elastic wave equation is a powerful tool for Rayleigh wave numerical simulation, but the phenomenon of the numerical dispersion appears when there are fewer samples in unit wavelength, which impairs the accuracy and resolution of wave-field simulation. To seek a fast and effective method for wave-field simulation, this dissertation has combined the flux-corrected transport method which is commonly used in fluid dynamics and the staggered-grid finite difference method. We have completed the simulation for the whole wave field, including Rayleigh surface wave and body wave by FCT finite difference method. The simulation results show that this method is effective to suppress the numerical frequency dispersion phenomenon by thick grids as well as to retain the real wave oscillation, especially to highlight the dispersion characteristics of Rayleigh surface wave in the layered mediums. The result points out that it improves the computing efficiency by 1.3 times compared with the thinning grids method with the same level of accuracy.The dissertation firstly reviews the Rayleigh wave exploration, seismic wave simulation and FCT finite difference method of the status quo; and then introduces the basic theory of Rayleigh wave; thirdly, discusses the two-dimensional first-order stress-velocity elastic wave equation in staggered difference schemes, boundary conditions, source functions, differential format compatibility, and convergence and stability, and gives flow charts of the whole procedure; fourthly, describes the dispersion of wave phenomena, wave equation derived from dispersion relations, the distinction between dispersion phenomena in the physical dispersion and dispersion, and explains the causes of numerical dispersion and eliminating method; fifthly, describes the basic theory and the FCT method calculation steps; finally selects 11 examples to calculate and analyze, then gives conclusions on the study and directions for further work.