Elastic Medium Research Articles

An Application of 3D Cross-Well Elastic Reverse Time Migration Imaging Based on the Multi-Wave and Multi-Component Technique in Coastal Engineering Exploration

Precise surveys are indispensable in coastal engineering projects. The extensive presence of sand in the coastal area leads to significant attenuation of seismic waves within unsaturated loose sediments. As a result, it becomes challenging for seismic waves to penetrate the weathered zone and reach the desired depth with significant amount of energy. In this study, the application of three-dimensional (3D) cross-well elastic reverse time migration (RTM) imaging based on multi-wave and multi-component techniques in coastal engineering exploration is explored. Accurate decomposition of vector compressional (P) and shear (S) waves is achieved through two wavefield decoupling algorithms without any amplitude and phase distortion. Additionally, compressional wave pressure components are obtained, which facilitates subsequent independent imaging. This study discusses and analyzes the imaging results of four imaging strategies under cross-correlation imaging conditions in RTM imaging. The analysis leads to the conclusion that scalarizing vector wavefields imaging yields superior imaging of P- and S-waves. Furthermore, the imaging results obtained through this approach are of great physical significance. In order to validate the efficacy of this method in 3D geological structure imaging in coastal areas, RTM imaging experiments were performed on two representative models. The results indicate that the proposed 3D elastic wave imaging method effectively generates accurate 3D cross-well imaging of P- and S-waves. This method utilizes the multi-wave and multi-component elastic wave RTM imaging technique to effectively leverage the Earth’s elastic medium without increasing costs. It provides valuable information about the distribution of subsurface rock layers, interfaces, and other structures in coastal engineering projects. Importantly, this can be achieved without resorting to extensive excavation or drilling operations. This method addresses the limitations of current cross-well imaging techniques, thereby providing abundant and accurate geological and geophysical information for the analysis and interpretation of 3D geological structures in coastal engineering projects. It has important theoretical and practical significance in real-world production, as well as for the study of geological structures in coastal engineering.

Improved numerical solution of anisotropic poroelastic wave equation in microseismicity: Graphic process unit acceleration and moment tensor implementation

AbstractThe accuracy and computational efficiency of full waveform forward modelling in poroelastic media are crucial for microseismic monitoring. It enables intuitive, precise and efficient simulation of subsurface responses, thereby improving the reliability of moment tensor inversion and seismic source mechanism interpretation. Additionally, it reflects the role of fluid effects in waveform evolution. In this paper, based on the Biot mechanism, we derived the first‐order velocity–stress equation of poroelastic media and discretized the model using a rotated staggered grid. The rotated staggered grid can well adapt to anisotropic media with high contrast parameters. We provide the finite difference formula based on graphic process unit–acceleration and moment tensor and also provide the graphic process unit workflow for forward modelling of anisotropic poroelastic media. First, two models with different grid sizes were run based on single graphic process unit, 1‐thread Central Processing Unit (CPU) and 16‐thread CPU. The results show that the speedup factors are approximately 14.3 and 3.7, respectively, compared with the running time of 1‐thread CPU and 16‐thread CPU. Then, we compare and evaluate the response of three basic source mechanisms (isotropic expansion, double couple and compensated linear vector dipole) in the model. The comparison of analytical and numerical results verifies the effectiveness of the method. Furthermore, wavefield snapshots of two typical anisotropic media (vertical transversely isotropic and horizontal transversely isotropic) are analysed to correspond to different moment tensor sources. The results showed that the source mechanism does not change the isotropic and anisotropic plane and the wave travel time, but it does change the polarization amplitude of the velocity component. The attenuation of slow qP‐wave increases along with the increase of the value of viscosity. The effect of permeability on wavefield appears with the opposite effect of viscosity. Finally, the seismic waveform differences between multi‐layer elastic media and poroelastic media are compared and analysed. The results showed that the seismic wavefield and waveform of poroelastic media are more complex, the propagation speed of seismic waves is faster, but the attenuation of seismic waves is stronger.

Seismic amplitude inversion based on a new PP-wave reflection coefficient approximation equation for vertical transversely isotropic media

We develop a method for the simultaneous amplitude-variation-with-offset or -angle inversion of anisotropic parameters for transversely isotropic media with vertical axis of symmetry (VTI media). First, we introduce a nonlinear PP-wave reflection coefficient approximation equation in terms of only P- and S-wave impedances for isotropic elastic media. Then, by replacing the isotropic part of Rüger’s equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called the ASI Rüger equation for VTI media. To invert the parameters for VTI media based on the ASI Rüger equation, we adopt the Bayesian generalized linear inversion (GLI) method, a combination of GLI and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero-mean Gaussian distribution. Compared with Rüger’s equation, the ASI Rüger equation decreases the trade-off between the parameters and reduces the ill-posedness of the inverse problem. The synthetic and field data tests demonstrate the feasibility of our method for inverting VTI media parameters (the vertical P-wave impedance, the vertical S-wave impedance, and Thomsen’s parameters [Formula: see text] and [Formula: see text]).

Studying the Interaction of Waves to Determine the Impact Response of a Layered Elastic Medium

When an impactor strikes a layered target, both the impactor and the target experience waves. The waves produced travel and engage in interactions with other waves as well as the interfaces in the impactor-target system. For the impact problems on a layered medium with periodic properties and layered elastic media of Goupillaud-type (each layer has the same wave travel time), researchers have presented an analytical solution for stress variation with position and time within the target. However, the solution for an elastic media not satisfying the above conditions is not available in the literature. The present study fills this gap and finds the behaviour of a generalized layered medium to an impact problem. The response of the material at any position inside the layered medium is found by solving the interaction between waves, interfaces, and boundaries. The mass, momentum balance and constitutive relationship are solved to get the exact analytical expressions for particle velocity and stress for each possible wave interaction happening in the impactor and the layered medium. The expressions are utilized in a computer program to study the impact behaviour of a layered media. The code tracks each wave as it travels through the system and identifies those interactions that occur in the shortest time, uses the stress and velocity expression for that interaction, and updates the state of the material. When stress produced at the impact surface is tensile in nature, the impactor and target can be separated. The work can be applied to both finite and semi-infinite impactors and targets, and the layered medium does not necessarily have to be a periodic layered media or a Goupillaud-type medium.

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023.

Heterogeneous elasticity drives ripening and controls bursting kinetics of transcriptional condensates

Many biomolecular condensates, including transcriptional condensates, are formed in elastic mediums. In this work, we study the nonequilibrium condensate dynamics in a chromatin-like environment modeled as a heterogeneous elastic medium. We demonstrate that the ripening process in such an elastic medium exhibits a temporal power-law scaling of the average condensate radius, depending on the local stiffness distribution and different from Ostwald ripening. Moreover, we incorporate an active process to model the dissolution of transcriptional condensates upon RNA accumulation. Intriguingly, three types of kinetics of condensate growth emerge, corresponding to constitutively expressed, transcriptional-bursting, and silenced genes. Furthermore, the simulated burst frequency decreases exponentially with the local stiffness, through which we infer a lognormal distribution of local stiffness in living cells using the transcriptome-wide distribution of burst frequency. Under the inferred stiffness distribution, the simulated distributions of bursting kinetic parameters agree reasonably well with the experimental data. Our findings reveal the interplay between biomolecular condensates and elastic mediums, yielding far-reaching implications for gene expression.

Thermal effects on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic medium

Nanotechnology has an impact on our lives in a many ways, from better medical treatments and more efficient energy sources to stronger and lighter materials and advanced electronics and this article presents the implementation of a perturbation method for the vibration analysis of simply supported and clamped–clamped Euler–Bernoulli nanobeams resting on nonlinear elastic foundations in thermal environment using nonlocal elasticity theory. Hamilton's principle is used to construct the differential equation of motion of a nanobeam in conjunction with appropriate boundary conditions. The equations of motion of the Euler–Bernoulli nanobeam are determined using nonlocal elasticity theory. It is shown how thermal loadings affect the vibration of the Euler–Bernoulli nanobeam. The multiple scale method, which is one of the perturbation method, is used to get an approximated solution for the presented system. The effects of temperature, Winkler, Pasternak and nonlinear foundation parameters on the vibration analysis of simply supported and clamped–clamped nanobeams are determined and results are given in tables and graphs.

Dynamic response of semi-cylindrical depression, cylindrical cavity and type-III crack to SH wave in half-space anisotropic media

In this study, the anti-plane dynamic response of an elastic half-space anisotropic medium containing surface semi-cylindrical depressions and internal cylindrical cavity and type-III crack is solved analytically. The wave function expansion method, the complex function method and the Green's function method can be used to effectively construct the free wave field equation and the scattered wave field equation in the case of SH wave incidence, in which the scattered wave field generated by the crack is constructed by the Green's function method and the "crack cut" method. For the scattered wave field generated by a circular cavity is constructed using the mirror method, where the positional offset coefficient in the mirror method of a half-space anisotropic medium is introduced, which well solves the problem of the asymmetry of the scattered wave field. Finally, the effects of anisotropic strength of the medium, SH wave incidence angle and dimensionless incident wave number on the surface displacement amplitude (|W|), dynamic stress concentration factor (DSCF) at the boundary of the circular cavity and dynamic stress intensity factor (DSIF) at the crack tip are investigated in both frequency and time domains under different working conditions, and conclusions different from those of isotropic medium are obtained, which provide some theoretical references for the earthquake-resistant design of the underground structure with canyon topography and the surface building.

A vertebral artery aneurysm that elicited occipital pain, showed no abnormalities on imaging studies, but ruptured the next day: illustrative case.

The authors report the case of a patient with occipital headache whose imaging studies revealed no abnormalities but who died 1 day later due to vertebral artery (VA) aneurysm rupture. A male in his 40s with no relevant medical history had been taking over-the-counter medication for headache several times a month. One day before he visited our neurosurgery department, he experienced occipital headache, took the usual medicine, and applied a warm compress. Brain magnetic resonance imaging (MRI) and magnetic resonance angiography (MRA) studies returned no abnormal findings, and he went home. On the following day, his wife found his lifeless body in rigor mortis and requested a medicolegal autopsy. Preautopsy brain computed tomography showed diffuse subarachnoid hemorrhage (SAH). Histopathologically, there was no obvious VA dissection. The vascular wall at the rupture site lacked internal elastic lamina and media, it was covered only with thin fibrous connective tissue, and the adventitia was expanded. The cause of death was determined to be SAH due to rupture of a VA blister aneurysm. In our patient, brain MRI and MRA studies returned no abnormal findings. However, he died suddenly the next day. Autopsy identified SAH due to rupture of a blister-like VA aneurysm without dissection.

Bulk wave propagation analysis of imperfect FG bio-composite beams resting on variable elastic medium

Bio-composites are outstanding alternatives to prevalent biomaterials in medical instruments due to their supreme material properties. On the other hand, mechanical analyses of bio-systems should be carried out to optimize the designed biomedical applications such as medical implants. Therefore, bulk wave propagation analysis of functionally graded (FG) bio-composite beams could serve as design targets of biomedical structures. Some applications like medical implants have a layered structure and FG composites will be an appropriate choice for constitutive material of such structures. In the current study, the influence of imperfection on the propagation of bulk waves in FG bio-composite beams with biomedical applications lying on a variable elastic medium has been evaluated for the first time. The constitutive materials of FG bio-composite beams are hydroxyapatite and gold alloy which are common materials in the biomedical industry. To determine the effective material properties of the structure under study, the conventional porosity-dependent homogenization scheme has been implemented. Various distribution patterns have been accounted for variable elastic medium. Moreover, a refined higher-order shear deformation theory and Hamilton’s principle have been exerted to obtain the partial differential governing equations and the derived equations are analytically solved via a harmonic function. To check the accuracy of the used methodology, the obtained result has been validated firstly with former investigations. Eventually, the sensitivity of various considerable parameters has comprehensively been probed and discussed. It is found that some parameters including wave number, power law index, and elastic foundation have positive effects and some parameters including slenderness ratio, ξ parameter, and imperfection coefficient have negative effects on the propagated bulk waves. Also, the sinusoidal pattern possesses less increasing effect than other ones.

On seismic gradiometric wave equation inversion for density

SUMMARY Material density remains poorly constrained in seismic imaging problems, yet knowledge of density would provide important insight into physical material properties for the interpretation of subsurface structures. We test the sensitivity to subsurface density contrasts of spatial and temporal gradients of seismic ambient noise wavefields, using wave equation inversion (WEI), a form of seismic gradiometry. Synthetic results for 3-D acoustic media suggest that it is possible to estimate relative density structure with WEI by using a full acoustic formulation for wave propagation and gradiometry. We show that imposing a constant density assumption on the medium can be detrimental to subsurface seismic velocity images. By contrast, the full acoustic formulation allows us to estimate density as an additional material parameter, as well as to improve phase velocity estimates. In 3-D elastic media, severe approximations in the governing wave physics are necessary in order to invert for density using only an array of receivers on the Earth's free surface. It is then not straightforward to isolate the comparatively weak density signal from the influence of phase velocity using gradiometric WEI. However, by using receivers both at the surface and in the shallow subsurface we show that it is possible to estimate density using fully elastic volumetric WEI.

Inverse problem for Love waves in a layered, elastic half-space

In this paper we study Love waves in a layered, elastic half-space. We first address the direct problem and we characterize the existence of Love waves through the dispersion relation. We then address the inverse problem and we show how to recover the parameters of the elastic medium from the empirical knowledge of the frequency–wavenumber couples of the Love waves.

Scattering of shear horizontal waves by the piezomagnetic material cylinder embedded in an elastic medium

Scattering of shear horizontal waves by the piezomagnetic material cylinder embedded in an elastic medium

Buried object localization by spectral analysis of surface wave reflections

A proposed method of buried object localization, based upon spectral analysis of surface wave reflections, is investigated numerically. This arises from a hypothesis to the effect that reflectivity would be maximized at some intermediate wavelength, shorter ones associated with disturbances too shallow to substantially excite the object as a secondary (reflecting) source, and longer ones with disturbances involving such volumes of earth in motion that the object become insignificant as a reflector. Discernment of that intermediate wavelength of maximum reflectivity might, thereby, provide an index of the object’s depth. Horizontal distance from echo return time, and azimuth from phase array techniques, could complete a localization methodology. Presented, accordingly, are 2D FEA simulations, in which narrow-banded surface wave trains are excited by a point source on the surface of an elastic medium, a void provided at some horizontal distance and depth, the strength of reflected surface motions thereafter examined in relation to frequency. These bear out the hypothesis, finding maximal reflectivity for a surface wavelength about two-thirds of the object depth. Proposed is that this could serve as the basis for a horizontal stand-off detection method, especially for applications like landmines, for which it may be undesirable to scan from above.

Reconstructing the source condition for focused shear wave beams in soft elastic media

Shear waves are employed in medical ultrasound imaging because they reveal variations in viscoelastic properties of soft tissue. Focused shear waves produced by a longitudinally vibrating piston at several hundred hertz are investigated here experimentally in soft tissue phantoms and using an analytical model for shear wave beam generation and propagation. Experiments employed a spherically concave piston shaped to focus the shear wave beam at a depth of 4 cm in a soft tissue phantom. Analytical modeling of this data provided a good fit, but required treating the focal length and piston diameter as adjustable parameters. The largest source of error in the modeling is suspected to be that the source condition is assumed to exhibit zero displacement surrounding the piston, whereas the actual condition in the source plane is a traction-free surface surrounding the piston. Here, in order to elucidate the actual source condition, numerical back propagation of field measurements is employed. Simulations show that the shear source condition can be accurately recovered with information related only to the shear wave, i.e., without compressional wave information. Back propagation of measured beams is discussed in the context of more accurately modeling the source condition for future device optimization.

Wavefield simulation and reverse time migration for acoustic TTI media

Seismic imaging necessitates precisely separating P and S waves to mitigate undesirable crosstalk between them. Failure to properly handle this crosstalk can lead to distorted or misinterpreted images. In an elastic anisotropic medium, the polarization of a P wave is not necessarily parallel to its propagating direction, making the separation of P and S waves more difficult than in the case of an elastic isotropic medium. A pure acoustic transversely isotropic (TI) wave equation involves a mixed-domain problem. This usually means the space dependencies and wavenumbers are coupled in the wavefield extrapolator. An efficient solution to the wavefield requires a separation between the space dependencies and wavenumbers in the extrapolator. There are two primary approaches: (1) an analytical separation of the mixed-domain term; and (2) a numerical solution to the mixed-domain term, such as low-rank and Poynting vector methods. In this study, the acoustic approximation is derived by setting the S-wave phase velocity to zero in all phase directions. An analytical separation is developed in this study by employing a Taylor series to linearize the anellipticity term, thereby decoupling the space-dependent and wavenumber-dependent variables within the wavefield extrapolator. The kinematics analysis demonstrates that our method has competitive phase velocity accuracy compared with existing methods. Moreover, the corresponding TI acoustic wave equation can be efficiently solved by the hybrid finite-difference/pseudospectral method. In a 2D case, it only requires one fast Fourier transform, two inverse Fourier transforms, and a few additional spatial differentiations at each time step. Remarkably, our wavefield solution remains independent of the wavefield heterogeneity (as observed in the low-rank approach) and is immune to wavefield interference (as encountered in the Poynting vector method). The developed acoustic approximation ensures the absence of any S-wave artifacts with relatively cheap computation. Numerical examples indicate our acoustic tilted transversely isotropic wave equation is reliable for accurate wavefield modeling and reverse time migration.

Method of automated extracting dispersion curves based on time-frequency distribution of seismic data

This paper discusses examples of testing a new implementation of the method of multi-channel surface wave analysis on synthetic data computed for elastic media with complex boundary geometry. The new implementation of the method includes developed algorithms for noise-resistant spectral analysis based on time-frequency domain filtering of seismograms and inversion of dispersion curves of phase velocities based on determination of ranges of possible transverse wave velocity models and application of artificial neural networks. Based on the results of synthetic data processing, the accuracy, lateral resolution limitations and applicability limits of the method under consideration are evaluated.

High Signal to Noise Ratio Piezoelectric Thin Film Sensor Based on Elastomer Amplification for Ambulatory Blood Pressure Monitoring.

Continuous pulse wave detection can be used for monitoring and diagnosing cardiovascular diseases, and research on pulse sensing based on piezoelectric thin films is one of the hot spots. Usually, piezoelectric thin films do not come into direct contact with the skin and need to be connected through a layer of an elastic medium. Most views think that the main function of this layer of elastic medium is to increase the adhesion between the sensor component and the skin, but there is little discussion about the impact of the elastic medium on pulse vibration transmission. Here, we conducted a detailed study on the effects of Young's modulus and the thickness of elastic media on pulse sensing signals. The results show that the waveform amplitude of the piezoelectric sensing signal decreases with the increase of Young's modulus and thickness of the elastic medium. Then, we constructed a theoretical model of the influence of elastic media on pulse wave propagation. The amplitude of the pulse wave signal detected by the optimized sensor was increased to 480%. Our research shows that by regulating Young's modulus and thickness of elastic media, pulse wave signals can undergo a similar amplification effect, which has an important theoretical reference value for achieving ambulatory blood pressure monitoring based on high-quality pulse waves.

Propagation Behavior of P1-Wave Passing through Fluid-Saturated Porous Continuous Barrier in Layered Saturated Soil

The fluid-saturated porous continuous barrier has a better vibration isolation effect than the single-phase solid continuous barrier, and layer-forming saturated soils will have an impact on the vibration isolation effect of the barriers due to their irregular layer-forming distribution. Based on Biot’s theory of saturated porous media and Snell’s law, a dynamic model of a fluid-saturated porous continuous barrier in layered saturated soil is established in this study. By introducing the potential function and using the continuous boundary condition of the interface between the saturated soil and the barrier, the analytical solution of the inverse transmission amplitude ratio of a P1-wave passing through the fluid-saturated porous continuous barrier in stratified saturated soil is obtained. The rationality of the proposed method is verified by comparing the solution of the P-wave model at the interface between the elastic medium and the saturated coarse particle interlayer. The differences in the propagation characteristics of fluid-saturated porous continuous barriers in layered saturated soils, homogeneous saturated soils, and layered single-phase soils are analyzed via numerical examples, and the influence of changes in the physical and mechanical parameters of the fluid-saturated porous continuous barriers on the reflectance amplitude ratios under the conditions of a layered saturated soil foundation are also analyzed. The results show that the presence of fluid in the stratified saturated soil model changes the trend of the reflection amplitude ratio with the incidence angle. The reflection amplitude ratio of the P2-wave and the SV-wave increases first and then decreases with the increase in the incident angle, while the reflection amplitude ratio of P1-wave decreases first and then increases. Barrier thickness and porosity change the energy distribution relationship at the interface; a relatively thicker barrier thickness and a higher porosity would result in a higher amplitude of barrier reflections.

Torsional vibration behavior of a restrained non-circular nanowire in an elastic matrix

This study introduces an approach to analyze torsional vibration in non-circular nanowires within magnetic fields, considering various boundary conditions on an elastic foundation. Analytical formulas for natural angular frequencies are obtained using nonlocal strain gradient theory. The analysis covers three non-circular cross-sections, incorporating the warping effect. Elastic springs at the wire ends simulate support conditions, restricting rotation around the wire’s axis. The torsion function around the axis is represented by a Fourier series, discretized at the spring points and linked using the Stokes’ transform alongside the boundary values. This leads to an eigenvalue problem that includes higher-order material size parameters (strain gradient, nonlocal), spring parameters, and the warping function. The study’s novelty lies in effectively solving torsional vibration for non-circular sections, addressing warping function, elastic medium, and size effects under both deformable and non-deformable boundary conditions. The presented solution is capable of determining vibration frequencies for both rigid and deformable boundary conditions. This is accomplished by specifying the torsional spring stiffness values, thereby obviating the necessity for additional recalculations. In order to verify the obtained results and compare them with the existing literature, nanowires with free and clamped boundary conditions are solved numerically by changing the spring parameters in the eigenvalue problem. In the formulation of natural angular frequency; length scale parameters, warping, magnetic field, elastic medium effects are included. In addition, since the support conditions are modeled with elastic springs, the resulting formulas are quite general and can be used to solve different types of torsional vibration problems.