scholarly journals Rayleigh wave dispersion equation with real terms in a layered transversely isotropic half space

2017 ◽  
Vol 60 (6 Sup) ◽  
Author(s):  
Sankar Bhattacharya
Keyword(s):  
Rayleigh Wave ◽  
Dispersion Equation ◽  
Half Space ◽  
Transversely Isotropic ◽  
Wave Dispersion ◽  
Rayleigh Wave Dispersion

Study on the Dispersion Curves of Rayleigh Wave in Foundation of Obstacles

2011 ◽  
Vol 90-93 ◽  
pp. 2193-2199
Author(s):  
Fang Ding He ◽  
Guang Jun Guo ◽  
Zhi Gang Dou ◽  
Yang Yang
Keyword(s):  
Finite Element ◽  
Rayleigh Wave ◽  
Half Space ◽  
Time Domain ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Displacement Curve ◽  
Rayleigh Wave Dispersion ◽  
Water Drain

It is difficult to accurately identify dispersion curves of Rayleigh wave for the foundation with obstacles. Displacement curve of time-domain of half-space foundation have been obtained with the finite element in the paper. Then time-domain curve have been transformed Rayleigh wave dispersion curves. Rayleigh wave dispersion curves have been analysed in half-space foundation with water drain pipes. The results show that, there are reflection waves at the receiving signals in front of the obstacles, there are no reflection waves behind the obstacles basically. The location and spacing of the sensor have a greater impact on the results. The results provide the reference for the recognition of dispersion curves and disposition patterns of the sensors.

Surfa ce-wave dispersion computations: Knopoff's method

1970 ◽  
Vol 60 (5) ◽  
pp. 1491-1520 ◽  
Author(s):  
Fred Schwab
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Love Wave ◽  
Wave Dispersion ◽  
Dispersion Function ◽  
Matrix Representations ◽  
Surface Wave Dispersion ◽  
The Earth ◽  
Matrix Extension ◽  
Rayleigh Wave Dispersion

Abstract The optimization of Knopoff's method computer computation of surface-wave dispersion, and the comparison of this method with the Thomson-Haskell technic and its extensions are studied. Of the various versions of the Thomson-Haskell formulation for Rayleigh-wave dispersion computations, the reduced-δ-matrix extension is the most powerful, i.e., the fastest which contains the feature controlling the loss-of-precision problem occasionally encountered by the original formulation. It is shown that the results of the δ-matrix extensions are actually contained in Knopoff's work, which appeared earlier than these extensions, and that these results are obtainable directly from his formulation without recourse to δ-matrix theory. The flexibility of Knopoff's method is used to devise a new representation of the Rayleigh-wave dispersion function which is more powerful than the most powerful of the Thomson-Haskell versions, i.e., it contains the loss-of-precision control feature and is about 38 per cent faster than the reduced-δ-matrix extension; in fact, it is about 12 per cent faster than the fastest of the Thomson-Haskell versions. Explicit forms of the new representation are given for the layered-half-space analogs of continental and oceanic models of the Earth, which can be terminated by a homogeneous half-space beginning in the mantle, a liquid outer core, or a solid inner core. The representations for symmetric and antisymmetric modes of the symmetric-plate analog of the Earth are also given. The Rayleigh-wave dispersion functions for the product form of the original Thomson-Haskell formulation, the δ-matrix and reduced-δ-matrix extensions of this formulation, and the representations developed from Knopoff's method, are identical when written out fully. The various technics differ only in their matrix representations of the dispersion function, which, of course, govern the speeds of computation of the various methods. The Knopoff and Thomson-Haskell technics for computing Love-wave dispersion are compared. Although the matrix representations of the dispersion function differ for the two technics, the functions are identical, except for a possible sign reversal, when written out fully. The speeds of computation are also identical. The representations derived from Knopoff's method are given for the two possible flat-layer analogs of the Earth, which are applicable to Love-wave propagation.

A note on fast computation of Rayleigh wave dispersion in the multilayered elastic half-space

1970 ◽  
Vol 60 (1) ◽  
pp. 161-166 ◽  
Author(s):  
T. H. Watson
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Computing Time ◽  
Wave Dispersion ◽  
Elastic Half Space ◽  
Fast Computation ◽  
Machine Computation ◽  
High Frequencies ◽  
Rayleigh Wave Dispersion

abstract Matrix formulas for modal solutions in the layered, elastic half-space are modified to give faster machine computation. Accuracy at high frequencies is also included. Computing time is reduced by 30 per cent from the fastest program previously reported.

Inversion of Rayleigh wave dispersion curves via adaptive GA and nested DLS

2019 ◽  
Vol 218 (1) ◽  
pp. 547-559 ◽  
Author(s):  
Yuhang Lei ◽  
Hongyan Shen ◽  
Xinxin Li ◽  
Xin Wang ◽  
Qingchun Li
Keyword(s):  
Rayleigh Wave ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Rayleigh Wave Dispersion

Third Order Elastic Constants and Rayleigh Wave Dispersion of Shot Peened Aero-Engine Materials

2013 ◽  
Vol 768-769 ◽  
pp. 201-208 ◽  
Author(s):  
Marek Rjelka ◽  
Martin Barth ◽  
Sven Reinert ◽  
Bernd Koehler ◽  
Joachim Bamberg ◽  
...  
Keyword(s):  
Residual Stress ◽  
Rayleigh Wave ◽  
Elastic Constants ◽  
Cold Work ◽  
High Strength ◽  
Wave Dispersion ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Aero Engine ◽  
Rayleigh Wave Dispersion

Aero-engine components exposed to high mechanical stresses are made of high-strength alloys and additionally, they are surface treated by shot peening. This process introduces compressive residual stress into the material making it less sensitive to stress corrosion cracking and fatigue and therefore benefits the components performance and lifetime. Moreover cold work is induced in an amount depending on the peening parameters. To approximate the remaining lifetime, a quantitative, non-destructive method for stress assessment is required. It was shown that surface treatment of such alloys can be characterized by broadband Rayleigh wave dispersion measurements. However, the relative contributions of residual stress and cold work, respectively, remained an open point. This paper presents the determination of third order elastic constants (TOEC) for IN718 and Ti6246, providing, together with a model for the inversion of dispersion data, a quantitative access to the acoustoelastic effect. Finally, some measurements of differently treated samples are given.

Rayleigh Wave Dispersion Curve Inversion with the Artificial Bee Colony Algorithm

2021 ◽  
Vol 26 (2) ◽  
pp. 99-110
Author(s):  
Xin Wang ◽  
Hongyan Shen ◽  
Xinxin Li ◽  
Qin Li ◽  
Daoyuan Wang
Keyword(s):  
Rayleigh Wave ◽  
Dispersion Curve ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Wave Dispersion ◽  
Velocity Model ◽  
S Wave ◽  
Bee Colony ◽  
Search Optimization ◽  
Rayleigh Wave Dispersion

Rayleigh wave dispersion curve inversion is a non-linear iterative optimization process with multi-parameter and multi-extrema. It is difficult to carry out inversion and reconstruction of stratigraphic parameters quickly and accurately with a single linear or non-linear inversion for the data processing of Rayleigh waves with complex seismic geological conditions. We proposed a new method that combines artificial bee colony algorithm (ABC) and damped least squares algorithm (DLS) to invert Rayleigh wave dispersion curve. First, food sources are initialized in a large scale of the model based on the prior geological information. Then, after three kinds of bee operators (employed bees, onlooker bees and scout bees) transform each other and perform search optimization with several iterations, the targets are converged near the optimal solution to obtain an initial S-wave velocity model. Finally, the final S-wave velocity model is obtained by local optimization of DLS inversion with fast convergence and strong stability. The correctness of the method has been verified by one high-velocity interlayer model, and it was further applied to a real Rayleigh wave dataset. The results show that our method not only absorbs the advantages of ABC global search optimization and strong adaptability, but also makes full use of the advantages of DLS inversion, such as high accuracy and fast convergence speed. The inversion strategy can effectively suppress the inversion falling into local extrema, get rid of the dependence on an initial model, enhance the inversion stability, further improve the convergence speed and inversion accuracy, while has good anti-noise ability.

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