TL;DR: In this article, a multichannel shot gather is decomposed into a swept-frequency record, allowing the fast generation of an accurate dispersion curve, which can then be examined and its effects appraised in both frequency and offset space.
Abstract: The frequency-dependent properties of Rayleigh-type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface-wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental-mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source-generated noise inhibits the reliability of shear-wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental-mode Rayleigh waves (noise) are body waves, scattered and nonsource-generated surface waves, and higher-mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear-wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive traceto-trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable-frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real-time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface-wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single-measurement surveying of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing random or nonlinear noise introduced during recording. A multichannel shot gather decomposed into a sweptfrequency record allows the fast generation of an accurate dispersion curve. The accuracy of dispersion curves determined using this method is proven through field comparisons of the inverted shear-wave velocity (vs) profile with a downholevs profile.
TL;DR: In this paper, a matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media.
Abstract: A matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media. The method is used to compute phase and group velocities of Rayleigh waves for two assumed three-layer models and one two-layer model of the earth9s crust in the continents. The computed group velocity curves are compared with published values of the group velocities at various frequencies of Rayleigh waves over continental paths. The scatter of the observed values is larger than the difference between the three computed curves. It is believed that not all of this scatter is due to observational errors, but probably represents a real horizontal heterogeneity of the continental crusts.
TL;DR: In this paper, an iterative solution technique to the weighted equation proved very effective in the high frequency range when using the Levenberg-Marquardt and singular value decomposition techniques.
Abstract: The shear‐wave (S-wave) velocity of near‐surface materials (soil, rocks, pavement) and its effect on seismic‐wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh‐wave phase velocity of a layered‐earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion‐curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high‐frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high‐frequency range when using the Levenberg‐Marquardt and singular‐value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg‐Marquardt method. Synthetic examples demonstrated calculation efficiency and stability ...
TL;DR: In this paper, a tool using the neighbourhood algorithm was developed to invert the one-dimensional V s profile from passive or active source experiments, with and without a priori information.
Abstract: Passive recordings of seismic noise are increasingly used in earthquake engineering to measure in situ the shear-wave velocity profile at a given site Ambient vibrations, which are assumed to be mainly composed of surface waves, can be used to determine the Rayleigh-wave dispersion curve, with the advantage of not requiring artificial sources Due to the data uncertainties and the non-linearity of the problem itself, the solution of the dispersion-curve inversion is generally non-unique Stochastic search methods such as the neighbourhood algorithm allow searches for minima of them is fit function by investigating the whole parameter space Due to the limited number of parameters in surface-wave inversion, they constitute an attractive alternative to linearized methods An efficient tool using the neighbourhood algorithm was developed to invert the one-dimensional V s profile from passive or active source experiments As the number of generated models is usually high in stochastic techniques, special attention was paid to the optimization of the forward computations Also, the possibility of inserting a priori information into the parametrization was introduced in the code This new numerical tool was successfully tested on synthetic data, with and without a priori information We also present an application to real-array data measured at a site in Brussels (Belgium), the geology of which consists of about 115 m of sand and clay layers overlying a Palaeozoic basement On this site, active and passive source data proved to be complementary and the method allowed the retrieval of a V s profile consistent with borehole data available at the same location
TL;DR: A survey of surface wave methods can be found in this article, where surface wave propagation in vertically inhomogeneous, inelastic continua measurements of surface waves are performed using a combination of velocity and dispersion analysis.
Abstract: Overview of surface wave methods Seismic waves Test methodology Historical perspective Challenges of surface wave methods Typical applications Advantages and limitations Linear wave propagation in verticallyinhomogeneous continua Basic notions of wave propagation Rayleigh waves in homogeneous elastic half-spaces Existence of Love waves Surface waves in vertically inhomogeneouselastic continua Surface waves in vertically inhomogeneous, inelastic continua Measurement of surface waves Seismic data acquisition The wave field as a signal in time and space Acquisition of digital seismic signals Acquisition of surface waves Equipment Dispersion analysis Phase and group velocity Steady-state method Spectral analysis of surface waves Multi-offset phase analysis Spatial autocorrelation Transform-based methods Group velocity analysis Errors and uncertainties in dispersion analyses Attenuation analysis Attenuation of surface waves Univariate regression of amplitude versus offset data Transfer function technique and complex wavenumbers Multichannel multimode complex wavenumber estimation Other simplified approaches Uncertainty in the attenuation measurement Inversion Conceptual issues Forward modeling Surface wave inversion by empirical methods Surface wave inversion by analytical methods Uncertainty Case histories Comparison among processing techniques with active-source methods Comparison among inversion strategies Examples for determining Vs and Ds profiles Dealing with higher modes Surface wave inversion of seismic reflection data Advanced surface wave methods Love waves Offshore and nearshore surface wave testing Joint inversion with other geophysical data Passive seismic interferometry Multicomponent surface wave analysis, polarization studies, and horizontal-to-vertical spectral ratio References Index