Surface Waves in Dissipative Media: Forward and Inverse Modelling

This work is a continuation of our effort to develop a nondestructive technique for the detection and characterization of surface and near surface defects in ceramic bearing balls. We reported earlier on a method for detecting and sizing submicron surface depressions using a scanning acoustic microscope[1]. Our present work deals with the detection and sizing of surface cracks in the ceramic bearing balls, a problem which requires knowledge of the surface wave reflection coefficient of the crack, either at a single frequency in the long wavelength regime or as a function of frequency in the short wavelength regime. For this purpose, we need to learn the characteristics of surface wave propagation on spherical surfaces, the scattering of the surface waves from the cracks, and we need to develop a method for exciting the surface wave. We present a detailed theory of surface wave propagation on spheres. The results indicate that an arc source focuses the surface acoustic waved in a manner similar to bulk acoustic waves focusing by spherical transducers. We will present the details of this self focusing behavior. A spherical cap transducer structure similar to a planar wedge transducer is proposed to excite the spherical surface waves. We will present the details of the design of the spherical cap transducer for efficient surface wave excitation.

The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered.

Estimation of near-surface shear-wave velocities and quality factors using multichannel analysis of surface-wave methods

This study focuses on advancements in three broad aspects of active surface wave methods: modeling, testing, and inversion. Transfer matrix, global matrix, and stiffness matrix methods were employed to comprehensively model layered structures with half-space boundary conditions for soil structures with increasing/anomalous stiffness profiles, or pavement structures with decreasing stiffness profiles and leaky waves. All three methods were programmed in MATLAB as forward algorithms. The finite element method was adopted to simulate surface wave testing for various half-space site structures with absorbing layers using increasing damping technique. An improved experimental dispersion analysis scheme was developed by scanning phase-velocity and intercept-time followed by a power-spectrum analysis to minimize side lobes and increase sharpness of dispersion images. The multichannel simulation with one receiver (MSOR) method was applied to capture the dispersion characteristics of soil sites. The reciprocity principle for surface Rayleigh waves was verified by comparing dispersion images from MSOR and multichannel analysis of surface waves (MASW) testing at the same site with the same testing system. A multichannel surface wave acquisition system was developed to improve the accuracy of measuring high-frequency and high-velocity dispersion data on pavement sites. A minimally-invasive multimodal surface wave (MMSW) method was proposed to measure multi-mode dispersion data of Rayleigh waves by using either embedded receivers at various depths to record surface wave motions generated from moving impacts on the ground surface or using a multichannel seismograph with an array of geophones on the soil surface for measuring surface wave motions caused by Standard Penetration Test hammer blows at various depths in a borehole. Stiffness matrix and finite element simulations of the MMSW method were employed to identify the critical geophone depths for optimum measurement of higher-mode motions. A hybrid genetic-simulated-annealing (GSA) algorithm was applied to solve multiple minimization and non-linear optimization problems to match the theoretical dispersion curves against their experimental counterparts. Results from simulation and real-world studies demonstrate that the advancements made in the three aspects of surface wave methods can improve the accuracy of surface wave testing results with higher resolution of experimental dispersion data, more complete multi-modal dispersion data, and higher certainty of inversion.

The existence of exceptional bulk, quasi–bulk–surface and pseudo–surface waves in a crystal of arbitrary anisotropy coated with a solid layer of arbitrary anisotropy is considered. One–component exceptional bulk waves that exist on the mechanically free surface are shown to disappear on the plated surface. They give rise to quasi–bulk–surface and pseudo–surface waves. The connection between the appearance of quasi–bulk subsonic surface waves and the existence of subsonic ordinary (Rayleigh) surface waves is investigated. In the plated crystal, instead of one–component exceptional waves, there arise three–component exceptional waves which involve the limiting bulk wave and two inhomogeneous modes. It is shown that the presence of an overlay in a general manner provides the existence of high–velocity (supersonic) pure surface waves near the intermediate transonic state and the existence of leaky waves near the highest transonic state.

Comparative analysis of Rayleigh and Love waves detected propagating in the Nobi and Kanto basins during the 2004-, 2007- Chuetsu and 2011 Tohoku earthquakes

Multiple paired forward and inverse models for motor control

In this paper, the appropriate methods are presented to obtain the seismic rotational components caused by the arrival of the surface waves applying the theory of elastic wave propagation. The rocking component around a horizontal axis and the torsional component around a vertical axis are generated respectively by the Rayleigh and Love waves. At the same time, the calculation formulations of phase velocities about these waves with frequent dispersion are derived and introduced to the rotational components, which may be more suitable for engineering practice. A procedure is developed to compute the time histories. Finally, numerical results have shown that the rotational motions have more energy than the translatonal motions in high frequent range by using the given methods.

The characterization of the embankment can be done by constructing the shear wave velocity in subsurface. The investigation of near surface wave velocity using Rayleigh wave dispersion analysis is popular. This method is very fast and effective to construct the vertical wave velocity, but has no unique solution. As a result, the inverse modelling is often trapped in local optimums. Therefore, we used Quantum-behaved PSO to get the best solution (global optimum). Inversion method using Quantum-behaved PSO was performed on synthetic and field measurement data. Field data acquisition was executed at P80-81 using both active and passive surface waves methods. The inversion result of Rayleigh wave dispersion is shear wave velocity structure. Shear wave velocity imaging resulted by this method was used to characterize the embankment of mud flow dam in Sidoarjo (LUSI) and be compared to the resistivity measurement data. The subsurface structure which is constructed from the inversion of Rayleigh wave gives the same result as the resistivity.

SUMMARY A 2-D orthogonal distributed acoustic sensing (DAS) array designed for seismic experiments was buried horizontally beneath the Kafadar Commons Geophysical Laboratory on the Colorado School of Mines campus at Golden, Colorado. The DAS system using straight fibre-optic cables is a cost-efficient technology that enables dense seismic array deployment for long-term seismic monitoring, favouring both earthquake-based and ambient-noise-based surface wave analysis for subsurface characterization. In our study, the horizontally orthogonal DAS array records ambient noise data for a period of about two months from November 2018 to January 2019. During this time, the array also detected seismic signals from an ML3.6 earthquake at Glenwood Springs, Colorado, which exhibit opposite signal polarities in the orthogonal DAS section recordings. We derive the transformation matrix for DAS strain measurements in horizontally orthogonal cables to retrieve both Rayleigh and Love wave dispersion information from the single-component DAS signals using the 2-D multichannel analysis of surface waves method. In addition, ambient noise interferometry is applied to long-term DAS noise recordings. Our theoretical derivation demonstrates that Rayleigh and Love wave Green's functions are coupled in the noise cross-correlation functions (NCFs) of DAS receiver pairs. Stacking NCFs over the horizontally orthogonal DAS array can constructively recover the radial Rayleigh wave component but destructively suppress the Love wave component. The multimodal Monte Carlo inversion of the earthquake-based Rayleigh wave and Love wave dispersion measurements and the noise-based Rayleigh wave measurement reveals a 1-D layered structure that agrees qualitatively with geological surveys of the site. Our study demonstrates that although straight fibre-optic cables lack broadside sensitivity, using appropriate DAS array configuration and seismic array methods can extend the seismic acquisition ability of DAS and enable its application to a broad range of scenarios.

Propagation and attenuation of seismic body waves in dissipative medium under initial and couple stresses

Making use of the transformation of constitutive relations for electromagnetic waves and the transformation of the wave vector in Minkowski space, we have worked out the theory of wave propagation along a waveguide filled with moving magnetized plasma (MMPW). The dispersion equations of the wave propagation in a circular MMPW are given in this paper, along with a detailed discussion of their behaviors. Numerical calculations show that there are many interesting and important features of the wave propagation along an MMPW compared with that in a stationary magnetized plasma-filled waveguide (MPW).

The method of the parabolic equation and its application in the theory of wave propagation is discussed. Examples of solutions of various physical problems are presented, and the role played by the proposed method in the description of the wave beams and the wave packets in nonlinear and inhomogeneous media is shown. Different ways of moving from the initial equations to the approximate equations of parabolic type are shown, and methods for generalization and improvement are discussed.

The dispersion curves of surface waves have been widely used for the retrieval of subsurface structures. Because the surface-wave dispersion is not sensitive to Vp, classical dispersion inversion can only retrieve Vs structures. To retrieve Vp, the dispersion of guided-P waves, which belong to leaky waves, should be considered. Due to the difficulty in forward modeling, the quantitative analysis of the leaky-wave dispersion curves has been rarely reported. In this study, we first derive the sensitivity analysis method of the leaky-wave dispersion based on previously proposed the semi-analytical spectral element method. Then the quantitative sensitivity analysis of leaky-wave dispersion curves is carried out, which confirms the ability of guided-P wave dispersion to constrain the velocity structures. With the theoretical analysis, we propose a joint inversion method based on surface and guided-P wave dispersion curves, which can simultaneously retrieve Vp and Vs. To verify the effectiveness, the proposed joint inversion has been applied to different kinds of field data including ocean bottom seismometer data with active sources and the seismic data of Nevada in the United States in 2008. Both of the inversion tests show that the joint inversion of surface- and leaky-wave dispersion can effectively constrain the velocity structure of Vp and Vs at the same time, which helps to obtain more complete and accurate models than the traditional surface wave dispersion inversion.

In this paper, we investigated the propagation of surface waves in a nonhomogeneous rotating fibre-reinforced viscoelastic anisotropic media of higher order of nth order including time rate of strain. The general surface wave speed is derived to study the effect of rotation on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. Also results for homogeneous media can be deduced from this investigation. For order zero our results are well agreed to fibre-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to well known isotropic medium. It is also observed that, surface waves cannot propagate in a fast rotating medium. Comparison was made with the results obtained in the presence and absence of rotation and parameters for fibre-reinforced of the material medium Numerical results are given and illustrated graphically. The results indicate that the effect of rotation and parameters for fibre-reinforced of the material are very pronounced.