Study On The Sensitivity Analysis And Inversion Method Of High-frequency Surface Waves

Rayleigh and Love waves are two types of surface waves that travel along a free surface, such as the earth-air interface, or along the earth-water interface. Rayleigh waves are the results of interfering P and SV waves, while Love waves are formed by the constructive interference of multiple reflections of SH waves in a shallow subsurface. Multi-channel analysis of surface-wave (MASW) has been widely applied in solving near-surface geological and geophysical problems because they are non-destructive, non-invasive, low cost, and relatively highly accurate. Compared with Rayleigh waves, there is less attention focused on utilizing Love waves in the near-surface community. That may be due to the fact that activating SH-wave data was not as easy as P-wave in past. However, with the development of science and technology, seismographs now can be used to record Love-wave signals from 1 Hz to 1000 Hz. Recent studies on high-frequency Love-wave method have obtained more and more attention from the near-surface geophysicists.Based on the assumption of horizontal layered homogenous media, Rayleigh-wave phase velocity can be defined as a function of frequency and four groups of earth parameters:P-wave velocity, SV-wave velocity, density and thickness of each layer. Unlike Rayleigh waves, Love-wave phase velocities of a layered homogenous earth model could be calculated using frequency and three groups of earth properties: SH-wave velocity, density, and thickness of each layer. Because the dispersion of Love waves is independent of P-wave velocities, high-frequency Love-wave method possesses several attractive advantages, such as (1) Love-wave dispersion curves are much simpler than Rayleigh wave; (2) dispersion images of Love-wave energy possess a higher signal to noise than those generated from Rayleigh waves; and (3) inversion of Love-wave dispersion curves is less dependent on initial models and more stable than Rayleigh waves. Due to the particular characteristics of Rayleigh and Love waves, the research of high-frequency surface-wave methods in the shallow geophysical exploration is necessary, which includes the study on the sensitivity analysis of Rayleigh and Love waves, joint inversion methods of their dispersion curves, and improvement of horizontal resolution in subsurface mapping.This dissertation adopts the combinations of theoretical analysis and practical applications. A series of appropriate theoretical models are used in research, in which the propagation properties of Rayleigh and Love waves in these models are investigated. According to applications of practical examples, the applicability of high-frequency surface-wave (Rayleigh and Love waves) method can be verified. This dissertation uses several typical geological models to analyze the sensitivities of Rayleigh-wave and Love-wave dispersive phase velocities. Sensitivity analysis is basic in understanding the ability of estimating accurate S-wave velocities. Previous studies indicate that each inverted 1D S-wave velocity model genetated from the MASW method reflects an averaged vertical S-wave velocity variation under each geophone spread, therefore the horizontal resolution of S-wave velocity is low. Hence, travel-time tomography of surface waves (Rayleigh and Love waves) is implemented to improve the horizontal resolution of an S-wave velocity model. In the study, this dissertation focus on the following issues.(1) Three typical geological models (a normal layered model, a high-velocity-layer model, and a low-velocity-layer model) are designed to analyze their characteristics of multimode surface-wae dispersion curves.(2) It is essential to analyze the sensitivity of each mode of surface-wave (Rayleigh and Love waves) phase velocities to S-wave velocity in different layer. Systematical study of sensitivities due to irregular models that contain a low-velocity layer or a high-velocity layer may provide whole picture of the MASW method and expand our knowledge on high-accuracy inversion results.(3) With the comparisons of the penetrating depths between Rayleigh and Love waves for the same mode, we can systematically study the differences of penetrating depths between Rayleigh and Love waves.(4) In both lateral homogenous media and radial anisotropic media, joint inversion approaches of Rayleigh and Love waves are proposed to improve the accuracy of S-wave velocities. I discuss on inversion results from lack of surface-wave (Rayleigh and Love waves) dispersion data and influences of inversion results of irregular models which contain an anomalous layer. It is indispensable to investigate advantages of the joint inversion approaches of Rayleigh and Love waves. A real-world example is applied to verify the accuracy and stability of the proposed joint inversion method.(5) Surface-wave travel-time tomography method is specifically applied for enhancing the horizontal resolution of 2D S-wave velocity sections. The synthetic and real-world data are used to test the practicability of this method.This dissertation takes Rayleigh and Love waves as subjects. By the systematic study of surface-wave dispersive characteristics, penetrating depth, inversion methods and horizontal resolution of surface-wave method, I achieve the following conclusions:(1) This dissertation first extracts the multi-mode surface-wave dispersion curves of three typical geological models (a normal layered model, a low-velocity-layer model, a high-velocity-layer model). Numerical studies of each parameter’s contribution to the fundamental and higher mode surface waves have confirmed that S-wave velocity is the dominant parameter influencing changes in surface-wave phase velocities. Based on the sensitivity analysis of different mode surface-wave phase velocity with respect to the variation of S-wave velocity of particular layer in three typical geological models, the sensitivity results indicate that: A certain mode of surface waves is sensitive to a certain depth range. For both Rayleigh and Love waves, sensitive band for the surface layer spreads over the high frequency range and its width is broad. And with increases of depth, a frequency range of sensitive bands for layers that located deeper will get narrower. ②In a normal layered model, the sensitivities of higher mode surface waves are more higher than that of the fundamental mode in the same depth (the second-higher mode> the first-higher mode> the fundamental mode). Inversion stability can be improved if including higher modes data, because higher modes possess a wider frequency sensitive band for S-wave velocity. ③In a low-velocity layer model, sensitivity of the low-velocity layer is higher since most energy are absorbed by and transformed to guide wave in the low-velocity layer. And little energy will penetrate into layers beneath the low-velocity layer, resulting in the low sensitivity for layers beneath the low-velocity layer. ④In a high-velocity layer model, Rayleigh and Love waves are insensitive to those of layers beneath the high-velocity layer and the high-velocity layer itself. This is because that when surface waves propagate to the top boundary of the high-velocity layer, more energy will reflect from the high-velocity layer rather than penetrate through. ⑤Sensitivities of the same mode of Rayleigh and Love waves are concentrated in different frequency bands. So joint inversion of Rayleigh and Love-wave phase velocities could increase the accuracy in calculating S-wave velocity.(2) Normalized row vectors of the Jacobian matrix are used to investigate the relationship between wavelength and penetrating depth. The results show that different modes of surface waves (Rayleigh and Love waves) are sensitive to different frequency bands. Longer wavelength components are sensitive to deeper layers while shorter wavelength components are sensitive to shallower layers. No matter for Rayleigh and Love waves, higher mode waves can penetrate deeper than fundamental mode waves do for a given wavelength. For a normal layered model and given the same wavelength, we compare the penetrating depth between multimode Rayleigh and Love waves. Analyzing results indicate that the fundamental Rayleigh-wave data can "see" deeper than the fundamental Love-wave data. The higher-mode components of the two waves, however, penetrate the same depth. We quantitatively sort out the differences in penetrating depth between Rayleigh and Love waves. Except for the effect of abnormal layer, the penetrating depth ratios of Rayleigh waves to Love waves are around 1.3-1.4 for the same wavelength.(3) In the lateral homogenous media, the effectiveness of the joint inversion method of Rayleigh and Love waves is tested through a two-layered earth model and a multilayered earth model. A 10% random white noise and a 20% random white noise are added to the synthetic dispersion curves to check out anti-noise ability of the proposed joint inversion method. The lack of surface-wave (Rayleigh or Love waves) dispersion data may lead to inaccuracy S-wave velocities through the single inversion of Rayleigh or Love waves, so this dissertation presents the joint inversion method of Rayleigh and Love waves which will improve the accuracy of S-wave velocities. Considering the influences of the anomalous layer, Rayleigh and Love waves are insensitive to those layers beneath the high-velocity layer or low-velocity layer and the high-velocity layer itself. Low sensitivities will give rise to high degree of uncertainties of the inverted S-wave velocities of these layers. Considering that sensitivity peaks of Rayleigh and Love waves separate at different frequency ranges, the theoretical analyses have demonstrated that joint inversion of these two types of waves would probably ameliorate the inverted model.(4) Compared with the joint inversion method in the lateral homogenous media, we add the constraint item of model differences to the joint inversion method in the radial anisotropic media. A six layered earth model which contains the vertical S-wave velocity (vsv) and the horizontal S-wave velocity (vsh) are defined in testing the validity of joint inversion method. And a real-world example is used to verify the effectiveness of the joint inversion method.(5) This article applies the surface-wave travel-time tomography method in improving the horizontal resolution of high-frequency surface-wave method. Firstly, the dispersion curves between any two traces are calculated by the combined method of cross-correlation and phase-shift scanning from a shot gather that only contains the fundamental-mode surface-wave; Secondly, I determine measured surface-wave travel-time between any two adjacent traces based on the relations among travel-time, distance, and surface-wave phase velocity (for each frequency). Taking the measured surface-wave travel-time as an input data, each grid’s phase-velocity distribution at different frequencies can be achieved by the inversion of surface-wave travel-time. Finally, each grid’s 1D S-wave velocity is obtained by inverting its pure-path dispersion curves. A pseudo-2D S-wave velocity section is then generated by aligning all the 1D models. The proposed surface-wave tomography method increases the accuracy of determined dispersion curves from consecutive two traces. Meanwhile, surface-wave tomography method can effectively enhance the ability of random noise immunity. Results of synthetic models and real-world examples demonstrate that travel-time tomography method can improve the horizontal resolution of surface-wave methods.