Body Wave Propagation Research Articles

Modeling the Dispersion of Waves in a Multilayered Inhomogeneous Membrane with Fractional-Order Infusion

The dispersion of elastic shear waves in multilayered bodies is a topic of extensive research due to its significance in contemporary science and engineering. Anti-plane shear motion, a two-dimensional mathematical model in solid mechanics, effectively captures shear wave propagation in elastic bodies with relative mathematical simplicity. This study models the vibration of elastic waves in a multilayered inhomogeneous circular membrane using the Helmholtz equation with fractional-order infusion, effectively leveraging the anti-plane shear motion equation to avoid the computational complexity of universal plane motion equations. The method of the separation of variables and the conformable Bessel equation are utilized for the analytical examination of the model’s resulting vibrational displacements, as well as the dispersion relation. Additionally, the influence of various wave phenomena, including the dependencies of the wavenumber on the frequency and the phase speed on the wavenumber, respectively, with the variational effect of the fractional order on wave dispersion is considered. Numerical simulations of prototypical cases validate the formulated model, illustrating its applicability and effectiveness. The study reveals that fractional-order infusion significantly impacts the dispersion of elastic waves in both single- and multilayer membranes. The effects vary depending on the membrane’s structure and the wave propagation regime (long-wave vs. short-wave). These findings underscore the potential of fractional-order parameters in tailoring wave behavior for diverse scientific and engineering applications.

Mechanical intelligence simplifies control in terrestrial limbless locomotion.

Limbless locomotors, from microscopic worms to macroscopic snakes, traverse complex, heterogeneous natural environments typically using undulatory body wave propagation. Theoretical and robophysical models typically emphasize body kinematics and active neural/electronic control. However, we contend that because such approaches often neglect the role of passive, mechanically controlled processes (those involving "mechanical intelligence"), they fail to reproduce the performance of even the simplest organisms. To uncover principles of how mechanical intelligence aids limbless locomotion in heterogeneous terradynamic regimes, here we conduct a comparative study of locomotion in a model of heterogeneous terrain (lattices of rigid posts). We used a model biological system, the highly studied nematode worm Caenorhabditis elegans, and a robophysical device whose bilateral actuator morphology models that of limbless organisms across scales. The robot's kinematics quantitatively reproduced the performance of the nematodes with purely open-loop control; mechanical intelligence simplified control of obstacle navigation and exploitation by reducing the need for active sensing and feedback. An active behavior observed in C. elegans, undulatory wave reversal upon head collisions, robustified locomotion via exploitation of the systems' mechanical intelligence. Our study provides insights into how neurally simple limbless organisms like nematodes can leverage mechanical intelligence via appropriately tuned bilateral actuation to locomote in complex environments. These principles likely apply to neurally more sophisticated organisms and also provide a design and control paradigm for limbless robots for applications like search and rescue and planetary exploration.

Analytical fragility relation for buried cast iron pipelines with lead-caulked joints based on machine learning algorithms

A new numerical-based fragility relation for cast iron (CI) pipelines with lead-caulked joints subjected to seismic body-wave propagation is proposed in this article. Two-dimensional 1600-m-length finite element models for pipelines buried in sand are developed in OpenSees. Parametric analysis is performed to investigate the influence of various parameters on the damage estimates of the buried pipelines. Numerical analyses are conducted to estimate the repair rates ( RR) for CI pipelines subjected to wave propagation. The predictive model for RR is thus developed based on the numerical results and the Gaussian Process Regression approach. The model developed employs four predictor variables, namely, the peak particle velocity and wave propagation velocity along axial direction, the maximum soil shear force per unit length, and the outer diameter of pipelines, exhibiting desirable performance in terms of predictive efficiency and generalization. The performance of the developed relation is compared to several existing fragility relations. The new fragility relation can be used to estimate RR for CI pipelines with lead-caulked joints with outer diameters ranging from 169 to 1554 mm subjected to seismic body-wave propagation.

U-net-based pseudoseismic imaging for the short-offset transient electromagnetic method

AbstractShort-offset transient electromagnetic (SOTEM) is an innovation of the artificial-source electromagnetic method, and detection is conducted in the near-source area using an electromagnetic formation wave so that the signal has strong strength and large bandwidth. Inspired by the parallelism of the propagation of seismic body waves and EM formation waves, this paper intends to implement pseudoseismic imaging (PSI) on SOTEM data to give play to the high resolution of SOTEM. Traditionally, to perform the wave-field transform (WFT), a set of ill-posed linear equations needs to be solved and the solving process has strong ambiguity and instability. This paper presents a new method for performing WFT based on U-Net, and a nonlinear mapping from the EM diffusion field to the pseudoseismic wave field under the same velocity model is established by training the network. To eliminate the error that might result when the time‒depth transform is conducted for the wave-field record, another U-Net is used to transform the wave-field record into a depth-offset profile to accomplish the whole PSI process for SOTEM. Simulation and measured data are used to validate the effect of the networks, and the results indicate that this approach is highly feasible, thus providing a new strategy for using SOTEM to detect sedimentary strata.

PyRaysum: Software for Modeling Ray-theoretical Plane Body-wave Propagation in Dipping Anisotropic Media

This article introduces PyRaysum, a Python software for modeling ray-theoretical body-wave propagation in dipping and/or anisotropic layered media based on the popular Fortran code Raysum. We improve and expand upon Raysum in several ways: 1) we significantly reduce the overhead by avoiding I/O operations; 2) we implement automatic phase labeling to facilitate the interpretation of complex seismograms; 3) we provide the means to correct inaccuracies in the calculated amplitude of free surface reverberations. We take advantage of the modern, object-oriented Python environment to offer various classes and methods to perform receiver function calculation, filtering and plotting. PyRaysum also integrates well with NumPy and ObsPy, two standard libraries for numerical computing and seismology. PyRaysum is built in Python version 3 and requires a Fortran compiler, but otherwise runs on all platforms. The software offers a high-level, ease-of-use user interface and is equipped with complete documentation and testing as well as tutorials to reproduce published examples from the literature. Time-optimized post-processing functions allow for the straightforward and efficient incorporation of PyRaysum synthetic data into optimization or probabilistic parametric search approaches.

Wave propagation in a cylindrical body in the presence of surface forces depending on the relative displacement

Studies of wave propagation in extended bodies with external friction have a wide range of applications and are significant for various engineering and scientific fields. They contribute to the development of new technologies, improve the design and construction of structures, and expand our understanding of the physical processes occurring in various materials and media. In this article, axisymmetric two-dimensional problems of the propagation of longitudinal waves in a cylindrical body are numerically solved in the presence of surface friction forces of the Winkler and Kelvin-Voigt types. For the numerical solution, the Wilkins scheme of the finite difference method was used. The influence of friction forces on the wave parameters is revealed. It is determined that the results of the considered problems are between solutions using slippery contact without friction and with friction according to the Coulomb law. A 5-7% deviation of the hypothesis of flat sections is shown, which makes it possible to reduce such a problem to a one-dimensional formulation.

Determining In-situ Frequency Independent Attenuation and Complex Modulus of Pavement Materials using Wavelet Power Density of Vibration Method

The features of vibration sources, site characteristics, the propagation of surface and body waves in the ground, and the reaction of structures are all important to consider when analyzing vibration-related issues, including those caused by traffic loading. Pavement vibration analysis can be used to determine the impact of damaging vibrations on the road and surrounding buildings or structures. Furthermore, this vibration can be utilized to calculate the dynamic properties of road pavement materials, such as the attenuation factor and damping ratio of the material, as well as the complex modulus of the pavement material. To minimize vibration damage, an environmental zone that is effective in reducing ground vibration amplitude is frequently used. However, estimating the degree of decrease in vibration amplitude at a given distance is challenging. In general, vibration attenuation with distance is made up of two components: geometric damping and material damping. Geometric damping is related to the qualities of the ground and the magnitude of the vibration, while material damping is dependent on the nature of the source of the vibration. The majority of ground vibrations are now monitored mainly at the ground surface, rather than in deep layers, and propagation patterns are not properly considered. The wavelet power density of vibration technique was used in this study to quantify the frequency-dependent attenuation of geometric damping at a variety of pavement structures in Malaysia and Indonesia. At each location, the energy in a seismic wave signal was calculated as a function of the Gaussian of the derivative wavelet in signal amplitude. The vibration source's propagating waves were described by examining the recorded particle motions and significant energy components in the time-frequency domain. The complex modulus of pavement materials was then calculated using the frequency-dependent attenuation factors. The results reveal that the wavelet power density of vibration method can properly define the physical properties of the dynamic pavement material, such as attenuation frequency, damping ratio, and complex pavement modulus. This approach has the advantages of being quick, cost-effective, and nondestructive.

Simulation of thermoelastic wave propagation in 3-D multilayered half-space media

SUMMARY Thermal phenomena are common in both the generation and propagation of seismic waves. To investigate the propagation characteristics of thermoelastic waves generated by point sources in a 3-D multilayered half-space, herein, we develop a method that can solve problems involving coupled mechanical and thermal motions. The method first transforms the governing equations into two sets of first-order ordinary differential equations with a unified form in the frequency–wavenumber domain and then solves them by a generalized reflection and transmission coefficient method. To verify the correctness of our method and the corresponding computer program, we compare our solutions with analytical solutions. We further apply the method to different multilayered models, and the numerical results clearly demonstrate the reflection and transmission phenomena of thermoelastic waves within the interlayer. Furthermore, the generated thermal and seismic signals are synchronous, and the two P waves predicted by generalized thermoelastic theory can be converted into each other. The records on the ground show that thermal motions influence our observation of direct waves, especially in the presence of high thermal conductivity subsurface media, it can significantly impact the propagation of both body and surface waves, making surface seismic observations more complex than those predicted by elastic theory.

Study of wave propagation in discontinuous and heterogeneous media with the dynamic lattice method

The development of a new dynamic lattice element method (dynamicLEM) as well as its application in the simulation of the propagation of body waves in discontinuous and heterogeneous media is the focus of this research paper. The conventional static lattice models are efficient numerical methods to simulate crack initiation and propagation in cemented geomaterials. The advantages of the LEM and the developed dynamic solution, such as simulation of arbitrary crack initiation and propagation, illustration and simulation of existing inherent material heterogeneity as well as stress redistribution upon crack opening, opens a new engineering field and tool for material analysis. To realize the time dependency of the dynamic LEM, the equation of motion of forced vibration is solved while using the Newmark-beta method and implementing the non-linear Newton–Raphson Jacobian method. The method validation is done according to the results of a boundary element method (BEM) in the plane P-SV-wave propagation within a plane strain domain. Further tests comparing the generated wave types, simulation and study of crack discontinuities as well as inherent heterogeneities in the geomaterials are conducted to illustrate the accurate applicability of the new dynamic lattice method. The results indicate that with increasing heterogeneity within the material, the wave field becomes significantly scattered and further analysis of wave fields according to the wavelength/heterogeneity ratio become indispensable. Therefore, in a heterogeneous medium, the application of continuum methods in relation to structural health monitoring should be precisely investigated and improved. The developed dynamic lattice element method is an ideal simulation tool to consider particle scale irregularities, crack distributions and inherent material heterogeneities and can be easily implemented in various engineering applications.

Assessment of the Lattice Discrete Element Method in the simulation of wave propagation in inhomogeneous linearly elastic geologic materials

Attenuation equations for seismic peak ground acceleration, ground velocity or seismic response spectra, in terms of distance to the source and magnitude of the causative event are typically based on results of the theory of linearly elastic wave propagation in homogenous solids. The latter also furnishes the fundaments for both the study of vibrations induced by surface loadings on the ground and for the design of isolation systems. In engineering applications, the propagation of seismic waves through inhomogeneous materials acquires unquestionable relevance. At the same time, analytical solutions impose increasing difficulties, requiring resort to numerical approaches. In the paper, a version of the Discrete Element Method, herein designated as Lattice Element Method (LDEM), is employed to study propagation of body waves in linearly elastic homogeneous and inhomogeneous media, with or without viscous linear material damping, with the objective of assessing bounds for solutions based on the assumption of linear elastic material models.

How Negative Energy and Kelvin–Helmholtz Instabilities Grow by Longitudinal Waves in Solar Atmospheric Jets

Abstract We model the propagation of slow magnetoacoustic body waves in solar jets in the course of negative energy wave excitation in the context of magnetohydrodynamic theory. Explicit approximate expressions are provided for the dispersion relation of slow body waves, providing insight into the influence of the steady flow speed, radiative cooling, and plasma-β at a glance. Analytic expressions are provided regarding critical speeds in the presence of backward waves, negative energy wave speeds, and instabilities. The buildup of the Kelvin–Helmholtz instability above the negative energy wave instability is expressed through analytic expressions that provide insight into the interplay of equilibrium conditions and dispersive effects as they affect the instability growth rate of slow body waves at various altitudes. As slow magnetoacoustic waves propagate with the same speed in the long-wavelength limit, slow body kink waves experience stronger dispersion than sausage waves. Backward waves are also probable at lower steady flow speeds for medium wavelengths when the jet hosts slow body kink waves that provide greater domains for dissipative processes. Slow body sausage waves grow faster while nearing the long-wavelength limit, while the internal plasma-β decreases the instability growth rate. The seismological aspect is that energy transfer to the external medium is observed on various timescales. The observational aspect is that slow body kink waves may exist at higher altitudes as energy has already been extracted to the external medium due to negative energy unstable slow body sausage waves in earlier stages contributing toward coronal heating.

Revisiting Piezoelectric Sensor Calibration Methods Using Elastodynamic Body Waves

The application of absolutely calibrated piezoelectric (PZT) sensors is increasingly used to help interpret the information carried by radiated elastic waves of laboratory/in situs acoustic emissions (AEs) in nondestructive evaluation. In this paper, we present the methodology based on the finite element method (FEM) to characterize PZT sensors. The FEM-based modelling tool is used to numerically compute the true Green’s function between a ball impact source and an array of PZT sensors to map active source to theoretical ground motion. Physical-based boundary conditions are adopted to better constrain the problem of body wave propagation, reflection and transmission in/on the elastic medium. The modelling methodology is first validated against the reference approach (generalized ray theory) and is then extended down to 1 kHz where body wave reflection and transmission along different types of boundaries are explored. We find the Green’s functions calculated using physical-based boundaries have distinct differences between commonly employed idealized boundary conditions, especially around the anti-resonant and resonant frequencies. Unlike traditional methods that use singular ball drops, we find that each ball drop is only partially reliable over specific frequency bands. We demonstrate, by adding spectral constraints, that the individual instrumental responses are accurately cropped and linked together over 1 kHz to 1 MHz after which they overlap with little amplitude shift. This study finds that ball impacts with a broad range of diameters as well as the corresponding valid frequency bandwidth, are necessary to characterize broadband PZT sensors from 1 kHz to 1 MHz.

Beam propagation of the 15‐degree equation and prestack depth migration in tilted transversely isotropic media using a ray‐centred coordinate system

ABSTRACTSeismic wave imaging in complex media requires an accurate wavefield simulation method that can accurately describethe wave propagation in realistic media. Reverse time‐depth migration is the preferred method for seismic wave imaging in complex media. Although it is relatively expensive, its imaging accuracy is usually better than migrations based on the ray method. Migration of primary reflection data requires a wave propagation simulation method that can accurately describe primary reflected/scattered wave energy and incorporate anisotropy. Accordingly, we propose the simulation of wave propagation in tilted transversely isotropic media using a 15° one‐way wave equation in a ray‐centred coordinate system, combining the flexibility of ray theory and the accuracy of wave theory. We use this equation to describe the propagation of body waves in a single ray tube, a ‘beam’. The wavefield along the beam, guided by its central raypath, has an angle limit defined only by the ray angle; therefore, wave propagation in complex and steeply dipping media can be simulated with a 15° one‐way wave equation. Numerical experiments show that the simulation results for beam propagation using the 15° equation in the ray‐centred coordinate system have good accuracy. For prestack depth migration in tilted transversely isotropic media, we built a beam imaging method using this propagator, and this migration method yielded accurate images with greater efficiency than reverse time‐depth migration.

Mathematical simulation of elastoplastic deformation in cubic materials with an account of anisotropic bulk compressibility

It was shown for the first time that when modelling the deformation of materials with cubic symmetry (at full stress), the rotation of the computational axes leads to the identification of anisotropic volumetric compressibility. Loading of the materials with cubic symmetry of properties in the directions not coincided with the main directions (for example, 011) allows one to detect 75% cases of the auxetic single crystals (i.e. with negative Poisson’s ratio). In these cases, the negative volumetric compressibility has anisotropy, in contrast to the volumetric compressibility calculated along the crystallographic axes for cubic materials. Anisotropy of the volumetric compressibility leads to anisotropy of velocities of propagation of body waves. This paper considers several elastoplastic problems for a cubic material with different orientations of a coordinate system about its crystallographic axes. The behaviour of such a material under dynamic loads is modelled with an account of anisotropic bulk compressibility to provide the same anisotropy of bulk wave velocities in the elastic and plastic ranges and a uniform pressure function at the elastic-to-plastic strain transition. For each orientation of the coordinate system and respective planes, different values at the indicatrices of elastic constants are specified, and this specifies different deformation processes in cubic materials. Such an effect is demonstrated by solving three problems in three-dimensional (3D) statements approximating the following processes: (1) one-dimensional elastoplastic deformation in a thin target impacted by a thin plate; (2) uniform compression in a spherical body under pulsed hydrostatic pressure; and (3) 3D elastoplastic deformation in a cylindrical body striking a rigid target in view of anisotropic bulk compressibility. The problems were solved numerically using original programs based on the finite element method modified by GR Johnson for impact problems. Solving problems in a 3D formulation makes it possible to take into account the dependences of the direction of the elastic and plastic characteristics of the material, as well as the velocities of propagation of elastic and plastic waves from that direction. The simulation results suggest that for cubic materials, changing the orientation of two coordinate axes in a plane changes the strains along all three axes, including those perpendicular to this plane. It is concluded that anisotropic bulk compressibility in cubic materials should be allowed for by mathematical models of their elastic and plastic deformation. We demonstrate that the orientation of a computational coordinate system for cubic materials should be in those directions in which their deformation is analysed in each particular case.

Case-wise investigation of body-wave propagation in a cross-anisotropic soil with multiple inhomogeneity coefficients

The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material. The material properties such as Young’s moduli, shear modulus, and density have been assumed to vary as a function of depth. These functions have been considered as the possible combinations of a polynomial function, exponential function, and trigonometric function. A suitable mathematical formulation of the physical problem has been developed (an eigenvalue problem) with displacement components as fundamental variables. With the help of separation of variables, appropriate substitution, and applicable mathematical treatment, displacement components have been deduced. Furthermore, employing intrinsic boundary conditions, the closed-form expressions for quasi-wave velocities have been derived. Numerical examples have been investigated, and the dependency of phase velocity on phase angle and inhomogeneity coefficients have been shown graphically. It has been observed that the increment and decrement in the degree of material anisotropy disturb the magnitude of phase velocity to a great extent.

Ion acoustic solitary and shock waves in strongly coupled degenerate plasma with relativistic effects

The ion acoustic solitary and shock waves are studied in strongly coupled nonrelativistic and relativistic plasma. The wave profile has been discussed for the kinetic and hydrodynamic regimes. The ions are considered to be strongly coupled, and electrons as degenerated and relativistic to deal with nonlinear waves using continuity and Poisson’s equations together with generalized hydrodynamical (GH) and quantum hydrodynamical (QH) models. The reductive perturbation method is used to formulate Korteweg–de Vries (KdV) and Korteweg–de Vries Burgers (KdVB) equations in both nondegenerate and degenerated cases. The effects of relativistic, degeneracy parameter and longitudinal viscosity coefficient on the profile of nonlinear waves are discussed. The amplitude and width of a shock in both nonrelativistic and ultrarelativistic cases increase with an increase in the viscosity coefficient, while with an increase in the electron diffraction parameter, the amplitude and width of the shock wave increase, and for a solitary wave decreases in both the nonrelativistic and ultra-relativistic cases. It is also shown that solitary ion acoustic wave propagates with more energy in nonrelativistic plasma than ultrarelativistic. The results of the work will be useful, for example, for astrophysics to understand the process of wave propagation in dense astrophysical bodies.

Surface wave investigation and phenomenological analysis: Application on in vivo human cutaneous tissue

The wave phenomenon in free surface media stems from the propagation of mode grouping. Due to the nature of propagation in a given medium, this phenomenon expresses different types of dependence on the medium's properties and represents its mechanical admittance. In contrast with body wave propagation, dependencies related to surface propagation in a medium can be described by spatial-temporal characteristics. These characteristics can be obtained by performing appropriate experiments and do not require prior knowledge of the physical properties of the medium. In this study, we propose an original surface wave investigation and a phenomenological analysis approach adapted to the mechano-bio-structural states evaluation of in vivo human skin. Two objectives are sought with the method proposed: the first concerns the development of a non-invasive device for generating and tracking surface waves in human skin called Free-Skin-Surface-Wave (FSSW); the second concerns the adaptation of the Multi-Chanel Analysis of Surface Waves (MASW) method to evaluate the mechano-bio-structural states of human cutaneous tissue in vivo on the basis of the propagating phenomena observed. As an illustration of the proposed method application, we have done an in vivo evaluation, on intern-forearm of female volunteers population. In addition, we proposed a study of the aging effect and a comparison with ultrasound B-Mode technique, to validate the method sensitivity to follow the mechano-morphological properties of the in vivo human skin. In this study, our medium of application was human skin in vivo, but it is conceivable to extend this application to other soft biological media.

Body waves propagation in a fluid-saturated transversely isotropic poroelastic solid with a potential method

This study is focused on the propagation of plane harmonic body waves in a transversely isotropic linear poroelastic fluid-saturated medium, where the material symmetry axes for both solid and fluid are coincide. Simplified formulation is considered as the framework. A set of two scalar potential functions is employed to decouple the coupled fluid continuity equation and equations of motion. The velocities and corresponding attenuation coefficients of both longitudinal and transverse waves are extracted from the presented acoustic equations for the body waves. To show the validity of the analytical solution given in this paper, degeneration to the case of a single phase transversely isotropic and consequently isotropic solid is presented to provide interesting comparisons with the solutions reported in the literatures. The incompressible solid and fluid are degenerated from the general slowness obtained in this study for some special cases. In addition, the effects of mechanical and hydraulic parameters of materials on the velocity of propagation and attenuation coefficient of the waves are investigated in more detail. To this end, various synthetic poroelastic transversely isotropic materials are defined and the dependency of wave motion to these parameters is illustrated by plotting the graphs.

The 2018 Geothermal Reservoir Stimulation in Espoo/Helsinki, Southern Finland: Seismic Network Anatomy and Data Features

AbstractA seismic network was installed in Helsinki, Finland to monitor the response to an ∼6-kilometer-deep geothermal stimulation experiment in 2018. We present initial results of multiple induced earthquake seismogram and ambient wavefield analyses. The used data are from parts of the borehole network deployed by the operating St1 Deep Heat Company, from surface broadband sensors and 100 geophones installed by the Institute of Seismology, University of Helsinki, and from Finnish National Seismic Network stations. Records collected in the urban environment contain many signals associated with anthropogenic activity. This results in time- and frequency-dependent variations of the signal-to-noise ratio of earthquake records from a 260-meter-deep borehole sensor compared to the combined signals of 24 collocated surface array sensors. Manual relocations of ∼500 events indicate three distinct zones of induced earthquake activity that are consistent with the three clusters of seismicity identified by the company. The fault-plane solutions of 14 selected ML 0.6–1.8 events indicate a dominant reverse-faulting style, and the associated SH radiation patterns appear to control the first-order features of the macroseismic report distribution. Beamforming of earthquake data from six arrays suggests heterogeneous medium properties, in particular between the injection site and two arrays to the west and southwest. Ambient-noise cross-correlation functions reconstruct regional surface-wave propagation and path-dependent body-wave propagation. A 1D inversion of the weakly dispersive surface waves reveals average shear-wave velocities around 3.3 km/s below 20 m depth. Consistent features observed in relative velocity change time series and in temporal variations of a proxy for wavefield partitioning likely reflect the medium response to the stimulation. The resolution properties of the obtained data can inform future monitoring strategies and network designs around natural laboratories.

Effect of inertial mass on elastic waveguide characteristics

When studying the process of wave propagation in elastic bodies the choice of boundary conditions is important. In this paper we propose a simple model to study the effect of the inertial mass distributed over the plane of the elastic layer on the characteristics of the elastic waveguide.