Multimode Characteristics Of Rayleigh Waves In Multilayered Media And Their Applications In Forword-Deduction And Inversion

Rayleigh-wave-method is a new method in geophysical prospecting. Rayleigh wave usually has more energy and higher signal to noise ratio than body waves, so there are more and more applications of Rayleigh wave in geophysical prospecting, seismology and ultrasonic nondestructive testing and so on recent years. It involves three aspects: data collection, forward-deduction and inversion. Till now, the study on the formation and the vibration characteristics corresponding to the dispersion curves is not enough. And the study will be meaningful for the forward-deduction and inversion of Rayleigh waves. In this dissertation, the formation and the vibration characteristics corresponding to the dispersion curves are studied, and the results are applied in Rayleigh wave forward-deduction and inversion. The main contribution are as follows:The secular function family is applied into the computation of eigenfunctions. Then the eigenfunctions are used to study the vibration characteristics of the three basic modes of Rayleigh wave (R-mode,R-period-mode,S-period-mode). Firstly, the secular function family is applied into the computation of eigenfunctions with generalized R/T coefficients method. Through this, the numerical instability in computing eigenfunctions with generalized R/T coefficients method can be avoided. Then the vertical eigendisplacement curves corresponding to the dispersion points can be obtained. By analyzing the eigendisplacements corresponding to different modes of Rayleigh wave in three models, the vibration characteristics of the three basic modes of Rayleigh wave are studied. It is found that the vibration of R mode is mainly near the surface and attenuates with depth rapidly, and the penetrate depth is about half of the wave length, the vibration of R-period-mode is in the first several layers, and the penetrate depth is independent of the wave length, the vibration of S-period-mode is in the low velocity layers, and the penetrate depth is independent of the wave length. Normally, the eigendisplacement curve corresponding to R mode has only one extreme, while the amounts of extremes of eigendisplacement curves corresponding to R-period-mode or S-period-mode approximately equals the mode order. The reason of root lost during computing dispersion curves with generalized R/T coefficients method is studied more deeply from the formula. It is found that when the energy gap is too large, the computation of generalized R/T coefficients will be instable, which causes the root lost. Based on the vibration characteristics of the basic modes, it is demonstrated clearly that the secular function family can be reduced into the secular functions corresponding to surface and low velocity layers.The modes of Rayleigh waves near the'cross point'of dispersion curves and the relationship between the frequencies of the cross points and the parameters are studied. The variation of Rayleigh waves near the'cross'points is analyzed with vertical eigendisplacement curves. It is found that the'cross'phenomenon is usually related to the existence of two different modes of Rayleigh wave in the same velocity zone. If the two dispersion curves are not cross, the transformation between two different modes via coupled mode happens to the mode on each curve. And if the two dispersion curves are cross, the mode corresponding to the same dispersion curve remains unchanged, though there may be some coupled mode very close to the cross point. With approximation in high frequencies andδmatrix method, the formula to the position of cross points is deduced and the error is analyzed. With this formula, the relationship between the frequencies of the cross points and the parameters is studied. It is found that the more obvious the low velocity layer is, the lower the frequency of each the cross point is.The sensitivity of dispersion curves to the S-wave velocities is explained with horizontal eigendisplacement curves, and an inversion method concerning the sensitivity is presented based on it. Two examples are used to study the relationship between the sensitivity and the eigendisplacements. It is found that usually the sensitivity is related to the eigendisplacements of the Rayleigh wave in each layer, especially the horizontal eigendisplacements. Normally, if the horizontal eigendisplacement corresponding to one dispersion point is larger in one layer than another layer, the Rayleigh wave velocity will be more sensitive to the S-wave velocity in this layer, and vice versa. This characteristic is more obvious in high frequencies. The result shows the relationship between sensitivity with the basic modes of Rayleigh waves. Based on this, a kind of inversion method concerning about sensitivity is presented. Inversion simulation is conducted and the results are compared with that obtained from multimode inversion method. It is found that the method sometimes avoids the problem of local minimum in normal local optimizations. However, the method often needs more dispersion points, and the stability also needs to be improved.The'zigzag'phenomenon of dispersion curves when there is low velocity layer is studied. The parameters of a given medium are changed under three different sources to study the influence of the parameters on the'jump point'frequencies. The frequencies showed little relationship with the offset. It is found that although the'jump point'frequencies depend on the source style, there are the same rules under each source: the S-wave velocities of the low velocity layer and the layer above it are the dominant parameters that influence the'jump point'frequencies, and followed by their thickness, the other parameters have less effect on the'jump point'frequencies, the more obvious the low velocity layer is, the lower the'jump point'frequency is. The result can be used as a qualitative analysis of low velocity layer in the cases like compaction test of subgrade. Rayleigh wave dispersion curves in two layer media can be approximately seen to be linear corresponding with S-wave velocities. Based on this, a quick inversion method of Rayleigh wave fundamental mode dispersion curves for two layer media is presented. All the formulas of the Rayleigh wave velocity in isotropic half space before contain complex computation. In this paper, a new formula without complex computation is presented. It makes the computation of Rayleigh wave velocities more convenient.