Research On Rayleigh-wave Data Processing Technique With High Horizontal Resolution

Rayleigh (1885) firstly described the theory of the motion of Rayleigh waves in a homogeneous elastic half-space, which opened a new page to study the structure and composition of the Earth using Rayleigh waves. Haskel (1953) used matrix method to carry out dispersion computation on a solid layered half-space, which provided the foundation for Earth interior and near-surface geophysics study using earthquake and seismic surface-wave signal. Many scientists have widely investigated on Rayleigh-wave propagation in varies materials over the last half century.Rayleigh waves are surface waves that travel along a 'free' surface, such as the earth-air interface and are the result of interfering P- and S-waves. Particle motion is constrained to the vertical plane consistent with the direction of wave propagation. Different wavelengths carry geotechnical information at different depths. S-wave velocities of near-surface materials (soil, rocks, and pavement) and their effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Because of the S-wave velocity being the dominant property of the fundamental mode of Rayleigh wave phase velocities, S-wave velocities can be estimated quickly from inversion of Rayleigh-wave data.Multichannel analysis of surface waves (MASW) proposed by Kansas Geological Survey (KGS) tries to overcome the few weaknesses (such as low precision of dispersion curves, multimode data mixture, body wave energy contamination, and so on) of the Spectral Analysis of Surface Waves (SASW) method. This technique consists of: acquisition of wide band (2~200Hz), high frequency ground roll using portable, repeatable, seismic source; utilization of wave-field analysis algorithm to extract and analyze 1D Rayleigh wave dispersion curves; inversion of dispersion curves to obtain S-wave velocity profiles; and generation of a 2D shear-velocity section by aligning 1D models at the midpoint of each spread with a spatial interpolation scheme. Because the MASW can acquire data at a lower cost and estimate S-wave velocities with relatively high precision and high efficiency, it has been one of the research hotspot in Rayleigh-wave investigation in recent years, including field repeatability, artifacts of data process, affects of model parameters, and others.Although the MASW has undergone significant development in recent years that has greatly enhanced its capabilities, great effort should be spent on increasing horizontal resolution of Rayleigh-wave data. One of the most effective ways improving the horizontal resolution of the MASW is to extract accurate dispersion curves from a record with a short geophone spread. The fundamental-mode Rayleigh waves, however, are easily contaminated by high modes or body wave energy in the real-world data, so it is most important to use proper seismic processing technique to separate the fundamental-mode Rayleigh waves from raw surface-wave data. The main aspects include: (1) because different high-frequency (≥5Hz) Rayleigh-wave modes and body waves interfere and overlap with each other in the t-x domain, it is necessary to apply advanced techniques to carry out shot-gather data transform and to separate different mode of Rayleigh waves and body waves in a corresponding domain. In other words, the data after transform should possess high resolution so that different-mode Rayleigh waves can be easily distinguished; (2) an algorithm should have the ability to preserve amplitude and phase, so mode separation could be feasible; and (3) the data processing technique should be efficient to real-world data.Based on the summary of main facts affecting on the horizontal resolution of the MASW, I studied the characteristics of Rayleigh waves in different field domains, used wavefield separation technique to carry out Rayleigh-wave mode separation, and proposed and accomplished a Rayleigh-wave data processing technique with high horizontal resolution. In developing the technique, I focused following subjects.(1) I investigated the horizontal resolution of dispersion curves of the MASW, which is the basic research for 2D Rayleigh-wave exploration.(2) I analyzed the accuracy of Rayleigh-wave dispersion curves calculated by a pair of traces in a Poisson's solid homogenous half-space and propose to use a pair of traces to calculate dispersion curves constrained by the MASW.(3) I analyzed the advantages and disadvantages of current four algorithms in calculating image of high-frequency Rayleigh-wave dispersive energy, I proposed to image Rayleigh-wave dispersive energy and carry out mode separation by high-resolution linear Radon transform (LRT) and used a pair of consecutive traces within the shot gather after mode separation to calculate a dispersion curve.(4) I primarily researched on the joint inversion of high-frequency Rayleigh waves with fundamental and higher modes. I discussed the sensitivity of dispersion curves with different modes in different frequency ranges for a six-layer earth model and used the theoretical model and a real-world example to demonstrate the advantages of joint inversion of multimodes to estimate S-wave velocities using a damped least-square method and the singular value decomposition (SVD) technique.I conclude that:(1) Under the assumption of plane-wave propagation, the horizontal resolution of the extracted dispersion curve by the MASW is mainly determined by the geophone spread length, the inverted 1D S-wave velocity is an averaged geophysical model under the geophone spread, and the horizontal resolution of the inverted 2D section is most influenced by the receiver spread length and the acquisition interval. So, one of the most direct ways to improve the horizontal resolution of inverted S-wave velocity is to extract accurate dispersion curves from a record with a short geophone spread;(2) Results of the calculated dispersion curve by a pair of traces and receiver spacing (horizontal resolution) in a Poisson's solid homogenous half-space show that: a pair of traces with a smaller receiver spacing achieve higher horizontal resolution but result in a larger relative error; the relative error of the phase velocity at a high frequency is smaller than at a low frequency, and the relative error of the phase velocity is strongly affected by the S/N ratio of data. For real-world applications, one should choose a trade-off between horizontal resolution and accuracy of the calculated dispersion curves. Results of both synthetic and real-world data demonstrate that, after choosing a proper receiver interval, inverting high-frequency surface-wave dispersion curves—by a pair of traces through cross-correlation with the phase shift scanning method developed in my study and with the damped least-square method and the singular-value decomposition technique—can feasibly achieve a reliable pseudo-2D S-wave velocity section with relatively high horizontal resolution;(3) Results of imaging Rayleigh-wave dispersive energy by the high-resolution LRT show that, compared with the slant stacking algorithm, high-resolution LRT can improve the overall resolution of images of dispersion energy by more than 50% and dispersion energy of different modes generated by the high-resolution LRT can be easily distinguished, which are important in picking multi-mode data for joint inversion and mode separation;(4) Because the high-resolution LRT effectively preserves amplitude and phase information and improves overall resolution of images of dispersion energy with high efficiency, it is successfully used in mode separation. Results of mode separation show that, images of dispersion energy of different modes generated by the high-resolution LRT possess distinguished trends, which are the foundation for mode separation. Further more, higher mode dispersive energy extends its frequency range at the low frequency end so it can not only 'see' deeper and possess higher resolution but also cut-off frequencies can be determined more accurately;(5) I image Rayleigh-wave dispersive energy and carry out mode separation by the high-resolution LRT and use a pair of consecutive traces within the shot gather after mode separation to calculate a dispersion curve. Results show that: compared with the MASW, the Rayleigh-wave data processing technique with high horizontal resolution greatly improves the horizontal resolution of dispersion curves. In addition, synthetic and real-world examples suggested, the number of shots required in data acquisition can be dramatically reduced with the process technique. For example, I may only need maximum three shots, one at each end and one at the middle of a geophone spread for a real-world application where 24 shots are normally required for the MASW method to map a portion of bedrock.(6) Sensitivity analysis of the six-layered model shows that fundamental mode data are more sensitive to the S-wave velocities of shallow layers and are concentrated on a very narrow frequency band, while higher mode data are more sensitive to the parameters of relatively deeper layers and are distributed over a wider frequency band. These properties provide a foundation of using a multimode joint inversion to define S-wave velocities. Inversion results of both synthetic data and a real-world example demonstrate that joint inversion with the damped least-square method and the singular-value decomposition technique to invert high-frequency surface waves with fundamental and higher mode data simultaneously can effectively reduce the ambiguity and improve the accuracy of S-wave velocities.