A fast and accurate method to compute dispersion spectra for layered media using a modified Kausel-Roësset stiffness matrix approach
TL;DR: In this paper, a simple modification to the widely-used Kausel-Roesset Stiffness Matrix Method (SMM) is presented, and in particular to its implementation in the context of the Thin-Layer Method (TLM).
About: This article is published in Soil Dynamics and Earthquake Engineering.The article was published on 2017-01-01. It has received 14 citations till now. The article focuses on the topics: Stiffness matrix & Finite element method.
Citations
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TL;DR: In this article, the authors used the dynamic stiffness matrix (DSM) approach to find the predominant mode in a dispersion plot and compared the results obtained with those reported in the literature.
Abstract: In case of irregular dispersive media, a proper analysis of higher modes existing in a dispersion plot becomes essential for predicting the shear wave velocity profile of ground on the basis of surface wave tests. In such cases, an establishment of the predominant mode becomes quite important. In the current investigation for Rayleigh wave propagation, the predominant modes have been evaluated by maximizing the normalized vertical displacements along the free surface. Eigenvectors computed from the dynamic stiffness matrix (DSM) approach are analyzed to find the predominant mode. The results obtained are then compared with those reported in the literature. By varying the displacement amplitude ratios of the predominant mode to the other modes, dispersion plots have also been generated from the multichannel analysis of surface waves (MASW) method. The establishment of the predominant mode becomes especially significant, where usually only two to six sensors are employed and the governing (predominant) modal dispersion curve is usually observed rather than several multiple modes, which can be otherwise identified by using around 24 to 48 sensors.
12 citations
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TL;DR: In this paper, the dispersion characteristics of guided waves in layered finite media, surface wave in layered semi-infinite spaces, and Stoneley wave in a layered infinite space were investigated using the Wittrick-Williams (W-W) algorithm.
Abstract: This paper studies the dispersion characteristics of guided waves in layered finite media, surface waves in layered semi-infinite spaces, and Stoneley waves in layered infinite spaces. Using the precise integration method (PIM) and the Wittrick–Williams (W-W) algorithm, three methods that are based on the dynamic stiffness matrix, symplectic transfer matrix, and mixed energy matrix are developed to compute the dispersion relations. The dispersion relations in layered media can be reduced to a standard eigenvalue problem of ordinary differential equations (ODEs) in the frequency-wavenumber domain. The PIM is used to accurately solve the ODEs with two-point boundary conditions, and all of the eigenvalues are determined by using the eigenvalue counting method. The proposed methods overcome the difficulty of seeking roots from nonlinear transcendental equations. In theory, the three proposed methods are interconnected and can be transformed into each other, but a numerical example indicates that the three methods have different levels of numerical stability and that the method based on the mixed energy matrix is more stable than the other two methods. Numerical examples show that the method based on the mixed energy matrix is accurate and effective for cases of waves in layered finite media, layered semi-infinite spaces, and layered infinite spaces.
9 citations
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TL;DR: In this article, a faster computational scheme is proposed to determine multimodal dispersion plots using the stiffness matrix method (SMM) for Rayleigh wave propagation in horizontally layered ground media.
8 citations
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TL;DR: In this paper , a set of codes have been developed in MATLAB for generating multimodal dispersion images by using three different transformation techniques, i.e., ω-c transform, ω − c transform and ω - c transform.
Abstract: A set of codes have been developed in MATLAB for generating multimodal dispersion images by using three different transformation techniques. While performing the multichannel analysis of surface waves (MASW), the field data obtained by using multiple geophones, in distance and time domain, become the required input data for these developed programs. The dispersion images have been examined by generating synthetic data, and performing field tests using a 20 lbs hammer at two different chosen sites with 48 geophones. The dispersion plots from the three different transformation techniques were found to match very closely with each other. The ω- c transform generally provides the best clarity. An increase in the spread length, however, without increasing the number of sensors often leads to development of aliased modes in the dispersion images.
7 citations
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TL;DR: In this paper, the authors synthesize the seismograms for the multiscale crustal model due to dislocations by a revised direct stiffness matrix method, extracting the exponential growth terms related to wavenumber and layer thickness, the fast and accurate wavefield modelling can be achieved for the multi-scale system with superficial fine layers (the layer thickness and velocity vary from metre level in the near surface to kilometre level in deep crustal zones).
Abstract:
The seismograms for the multiscale crustal model due to dislocations are synthesized by a revised direct stiffness matrix method. By extracting the exponential growth terms related to wavenumber and layer thickness, the fast and accurate wavefield modelling can be achieved for the multiscale system with superficial fine layers (the layer thickness and velocity vary from metre level in the near-surface to kilometre level in deep crustal zones). This method allows relatively high-frequency cases of engineering interest (about 10 Hz) to be tackled without extra computations, linking the geophysics to the geotechnical earthquake engineering. The simulations considering superficial fine layers (5–50 m) show that the horizontal peak ground velocities can be amplified twice with superficial velocity decreasing from 0.4 to 0.15 km s–1. A case study using a realistic fine model in Tokyo metropolis elucidates that the displacements are localized within the epicentre distance about 5 km, predicting the displacement responses by factors up to 6.7, 1.1 and 6.7 for radial, tangential and vertical directions in comparison to the simplified model without superficial fine structures.
5 citations
References
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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.
2,131 citations
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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 ...
1,378 citations
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TL;DR: In this article, the Haskell-Thompson transfer matrix method is used to derive layer stiffness matrices which may be interpreted and applied in the same way as stiffness matrix in conventional structural analysis, and the exact expressions are given for the matrices, as well as approximations for thin layers.
Abstract: The Haskell-Thompson transfer matrix method is used to derive layer stiffness matrices which may be interpreted and applied in the same way as stiffness matrices in conventional structural analysis These layer stiffness matrices have several advantages over the more usual transfer matrices: (1) they are symmetric; (2) fewer operations are required for analysis; (3) there is an easier treatment of multiple loadings; (4) substructuring techniques are readily applicable; and (5) asymptotic expressions follow naturally from the expressions (very thick layers; high frequencies, etc) While the technique presented is not more powerful than the original Haskell-Thompson scheme, it is nevertheless an elegant complement to it The exact expressions are given for the matrices, as well as approximations for thin layers Also, simple examples of application are presented to illustrate the use of the method
712 citations
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TL;DR: In this article, the effects of multiple modes on Rayleigh wave dispersion are discussed to reduce the ambiguity of uniqueness of shear wave velocity (Vs) profiles estimated by the surface wave method.
Abstract: The effects of multiple modes on Rayleigh wave dispersion are discussed to reduce the ambiguity of uniqueness of shear wave velocity (Vs) profiles estimated by the surface wave method. Based on a review of previous studies, dispersion curves of multiple‐mode Rayleigh waves induced by harmonic vertical point loading are derived for both vertical and horizontal particle motions. Also presented is the variation with frequency of the amplitude ratio between horizontal and vertical particle motions. Numerical studies indicate that a stiff soil layer overlying a softer soil layer induces a higher mode or multiple modes, leading to an inversely dispersive characteristic. Consideration of the effects of higher modes is strongly recommended in the inverse process when the observed data show an inversely dispersive trend. The ambiguity of uniqueness of the inverted soil profiles may be reduced by using either the dispersion data of horizontal motion or the amplitude ratio of particle motions in addition to the disp...
304 citations