Propagator Matrix Method Research Articles

Experimental Study Of Anisotropic And Dispersion Signature Of Shale Reservoirs: Implications For Synthetic Seismic Well Tie

To investigate velocity anisotropy and dispersion in lacustrine shales, we conducted laboratory measurements of acoustic properties at seismic frequencies (2–100 Hz) and ultrasonic frequencies (1 MHz) under varying effective pressures. Our study reveals significant transverse isotropy, accompanied by notable velocity dispersion and attenuation, with anisotropy coefficients ranging from 0.45 to 0.74 for P-waves and 0.44 to 0.95 for S-waves. Attenuation exhibited weak dependence on frequency and pressure but showed a strong positive correlation with clay content. We interpreted the data by integrating geological and physical analyses. Using rock physics modeling and the propagation matrix method, we found that velocity dispersion primarily caused the mismatch between seismic data and synthetic seismograms, while anisotropy had minimal impact on near-offset seismic data. Our findings suggest that anisotropy and dispersion observed at the core scale persist at the seismic scale. Incorporating these effects into seismic workflows is crucial for improving data processing, inversion, and reservoir characterization. This study provides valuable insights for exploration and production strategies in the study area and similar settings.

Marginal stability analyses for thermochemical convection and its implications for the dynamics of continental lithosphere and core–mantle boundary regions

SUMMARY Significant compositional differences may exist in the lithospheric mantle and above the core–mantle boundary (CMB) relative to the ambient mantle. The intrinsic density differences may affect the development of thermal boundary layer (TBL) instabilities associated with lithospheric delamination and formation of thermochemical plumes. In this study, we explored the instability of two-layer thermochemical fluid using two different techniques: marginal stability analysis with a propagator-matrix method and finite element modelling. We investigated both the instabilities in lithospheric mantle (i.e. lithospheric instability) and the mantle above the CMB (i.e. plume-forming instability) using a background temperature Tbg(z) with the TBL. For lithospheric instability, we found that two-layer fluid with free-slip boundary conditions mainly undergoes the same three different convective modes (i.e. two oscillatory convection modes and one layered convection regime) as that with no-slip boundary conditions reported in Jaupart et al. However, with free-slip boundary conditions, the transitions between these convection modes occur at larger values of buoyancy number B. Free-slip boundary conditions lead to smaller critical Rayleigh number Rac, but larger convective wavelength and oscillation frequency ωc, compared with those with no-slip boundary conditions. Our numerical modelling results demonstrate that Rac and ωc predicted from the classical marginal stability analyses using Tbg(z) with TBL temperature may have significant errors when the oscillatory period is comparable with or larger than the timescale of lithospheric thermal diffusion that causes Tbg(z) to vary with time significantly. In this case, using a more gently sloped background temperature profile ignoring the TBL temperature, the stability analysis predicts more accurate stability conditions, thus presenting an effective remedy to the stability analysis. For plume-forming instability, because of the reduced viscosity in the hot and compositionally dense bottom layer, the transition to the layered convection occurs at significantly smaller B values, and in the oscillatory convection regime, Rac is larger but ωc is smaller, compared with those for lithospheric instability. Finally, our study provides a successful benchmark of numerical models of thermochemical convection by comparing Rac and ωc from numerical models with those from the marginal stability analysis.

Electromechanical coupling characteristics of multilayered piezoelectric quasicrystal plates in an elastic medium

AbstractQuasicrystals (QCs) have attracted tremendous attention of researchers for their unusual properties. In this paper, an exact electric‐elastic solution of the simply supported and multilayered three‐dimensional (3D) cubic piezoelectric quasicrystal (PQC) nanoplate with the nonlocal effect is derived. Based on the basic elasticity equation of 3D QCs, we construct the linear eigenvalue system in terms of the pseudo‐Stroh formalism, from which the general solutions of the extended displacements and stresses in any homogeneous layer can be obtained. The two‐parameter foundation model is utilized to simulate the interaction between the nanoplate and elastic medium. The propagator matrices are employed to connect the field variables at the upper interface to those at the lower interface of each layer. Based on the boundary conditions of the upper and lower surfaces of the laminate and foundation model, the solutions are employed to derive from the global propagator matrix. Compared with the conventional propagator matrix method, a new propagator method is reestablished to deal with numerical instabilities of the case of large aspect ratio and high‐order frequencies for QC laminates. Finally, typical numerical examples are presented to illustrate the influence of nonlocal parameters and elastic medium coefficients on phonon, phason, and electric variables of 3D PQC nanoplates.

Nonlocal free vibration of magneto-electro-elastic nanoplates with imperfect contacts

We study the wave propagation phenomenon in magneto-electro-elastic (MEE) nanoplates with extended linear spring-type imperfect contacts in the framework of nonlocal theory. The extended pseudo-Stroh approach, propagator-matrix method, imperfect interface model, and Eringen’s nonlocal theory method are employed to investigate the wave features of the MEE nanoplates. In particular, a BaTiO 3 / CoFe2O 4 / BaTiO3 sandwich plate is considered in a numerical example and the natural frequency and mode shape are computed. Numerical results show that the nonlocal effect and interfacial imperfection could allow the tuning of the dispersion curves and mode shapes for the given layup. In addition, compared with the nonlocal effect, the interfacial imperfections have more pronounced effects on the mode shapes.

Sound propagation modeling in forests using the transmission line matrix method: Comparison with experimental in situ measurements

We present efforts to adapt the time-domain Transmission Line Matrix (TLM) method for modeling sound propagation in forests. It is relevant to professionals and researchers in environmental acoustics and to those interested in studying sound propagation in outdoor environments using numerical modeling techniques. The study aims to demonstrate the applicability of the method in complex media where sound waves undergo multiple reflections combined with ground effects during their propagation from a sound source to a receiver point. The TLM method is used to numerically model sound propagation in a 3D forest geometry generated based on a real tree distribution case. Data from an experimental campaign conducted in the rainforest of French Guyana are used as a reference. The results show an encouraging comparison between them and the in situ measurements, even if the hypotheses made to adapt the input data in the model were strong. We find that more measurement points and more specifications (ground impedance measurements, canopy density, etc.) about the experimental site are needed for further simulations, even if obtaining them presents technical difficulties.

Plunger gate effects on magneto transport in double-top gate spin-orbit devices

A propagation matrix method is used to investigate the quantum conductance of an n-type double-top gate device under a strong Rashba-Zeeman coupling interaction. The effects of a plunger gate potential and the total top gate length on the magneto conduction properties are investigated. Transcendental equations and analytical formulas are derived to accurately predict the resonance state and hole-like bound state structures. Furthermore, the effect of the distance of the two top gates from the plunger gate is examined for both symmetric and asymmetric structures. The analytical technique employed in this study provides an accurate and reliable approach for calculating the conductance of the quantum transport and is therefore beneficial for the design of n-type semiconductor devices.

Three-dimensional unsteady state solution of multilayered saturated anisotropic finite media subjected to point source

The three-dimensional (3D) unsteady state solution of a saturated anisotropic finite porous medium due to a point source is presented in this paper. First, Laplace transform is introduced to address the governing equations of anisotropic poroelasticity. Next, the eigen equation method and the modified pseudo-Stroh formalism are used to obtain the transient solution for homogeneous saturated finite media. Then, the propagation matrix method is used to address the corresponding multilayered porous elastic media, and the 3D unsteady state solution of the layered porous medium subjected to a point source is obtained. The solution for a finite porous foundation is presented to demonstrate the use of the closed form solution. The numerical results of a homogeneous foundation due to an internal time-dependent point source are given. Two different point sources are used to show the transient responses of the proposed method. By comparing with those obtained by the finite element method, the accuracy of the proposed method has been proved. Meanwhile, the influence of the depth of the point source on the hydromechanical responses of the homogeneous foundation is discussed. Finally, the transient response of an anisotropic sandwich foundation due to a point source at different depths is investigated. These numerical examples prove the feasibility of the transient 3D solution. The closed form solution presented in this paper can provide help for 3D transient fluid-deforming coupling analysis of laminated porous media.

Three-dimensional thermoelastic analysis of orthotropic laminated cylindrical shells subjected to uniformly localized thermal boundary conditions

Accurate evaluation of three-dimensional (3D) thermal-elastic analysis of laminated cylindrical shells under different loads has a significant impact on their safety design. In this study, we present a 3D thermoelastic solution of laminated orthotropic cylindrical shells subjected to uniformly localized thermal boundary conditions. For a homogeneous orthotropic layer, a thinning layer approach is introduced to deal with the heat conduction equation and the elastic equation. Based on the eigenequation method and pseudo-Stroh formalism, general solutions for physical quantities of a homogeneous layer are derived. The propagator matrix method is used to deal with multilayered media. A closed form solution for the laminated cylindrical shells is obtained. A numerical example of a 3-layered cylindrical shell subjected to convective heat transfer boundary conditions is presented to verify the solutions’ correctness. An excellent convergence of the current approach is found and the physical quantities predicted by the current method agree well with the numerical results by the finite element method. Finally, the numerical solutions of a 3-layered orthotropic cylindrical shell subjected to uniformly localized thermal boundary conditions are obtained by the current method. The closed form solution presented in this article can be used for 3D thermoelastic analysis of laminated cylindrical shells under complex boundary conditions.

Calculating InN/GaN Transmission Coefficient from Single Barrier to Five Barriers with Propagation Matrix and Transfer Matrix Methods

In this study, the value of transmission coefficient on InN/GaN semiconductor from a single barrier to five barriers was determined by using the propagation matrix method and the transfer matrix method. This study aims to see the effect of adding a barrier to the number of resonance tunneling that occurs, to see the difference in transmission coefficient values which was obtained with the two methods, and to determine the effectiveness of the program execution process time from the propagation matrix and transfer matrix methods using Matlab programming. The results obtained indicated that the value of the transmission coefficient obtained from the two methods was the same. As the number of barriers increases, the number of resonance tunneling that occurs will increase. These two matrix methods had differences in terms of the effectiveness of the program execution process time and calculation process. The propagation matrix method was considered more effective than the transfer matrix method.

A novel method for calculating dislocation Green's functions and deformation in a transversely isotropic and layered elastic half-space

A novel and comprehensive method is proposed for calculating the dislocation Love numbers (DLNs), Green's functions (GFs), and the corresponding deformation in a transversely isotropic and layered elastic half-space. It is based on the newly introduced Fourier-Bessel series system of vector functions, along with the dual variable and position method. Two important features associated with this new system are: (1) it is much faster than the conventional cylindrical system of vector functions; (2) we can even pre-calculate the DLNs which are only possible in terms of this new system. This is due to the fact that the variables to be solved in the new system are functions of the simple discrete zero points of the Bessel functions, instead of the numerical integration of continuous Bessel functions between the neighboring zero points as in the conventional system. The introduced dual variable and position method is unconditionally stable as compared to the traditional propagator matrix method in dealing with layering. Exact asymptotic expressions of the DLNs for large wavenumber are further derived, which makes the Kummer's transformation applicable in accelerating the convergence of the corresponding GFs. For the reduced case of homogeneous and isotropic half-space, the present solutions amazingly reduce to the existing exact closed-form solutions. These new features are further seamlessly combined for calculating the deformation due to a finite dislocation (or a finite fault in geophysics) in the layered structure, which are demonstrated to be accurate and efficient.

Ballistic spin transport in DC-bias single top gate p-type narrow channel device with Zeeman–Rashba effects

The ballistic transport of holes in a p-type quasi-one-dimensional channel system is investigated without considering the coupling effect of the light and heavy holes. A top gate (TG) is used to form a potential barrier in the quantum channel with Zeeman–Rashba (ZR) effects. The Luttinger Hamiltonian and propagation matrix method are used to examine the relationship between the conductance and the incident hole energy. The results show that when the gate width L is large, an electron-like bound state (E-BS) structure is formed at the inflection point of the spin-down branch. When a positive gate potential energy is applied (U0>0), the light and heavy hole spins form an electron-like quasi-bound state (E-QBS) at the top of the branch under the hole spin. Conversely, when a negative gate potential energy (U0<0) is applied, the light and heavy hole spins form a hole-like quasi-bound state (H-QBS) structure at the bottom of the branch.

Semi-analytical solution for mixed supported and multilayered two-dimensional thermo-elastic quasicrystal plates with interfacial imperfections

The tremendous attention of researchers has been attracted to the unusual properties of quasicrystals (QCs). In this article, the thermo-elastic problems of imperfectly bonded, multilayered, two-dimensional decagonal QC plates with mixed boundary conditions are investigated based on the QC linear elasticity theory. The temperature, heat flux, displacement, and stress components are expressed in terms of differential quadrature regional discrete point expansions in any rectangular plate, from which the state equations with thermomechanical coupling effects in a concise and compact matrix form is obtained. The different imperfect interface conditions are introduced to characterize specific structural and thermal contact properties at the interfaces and are further converted into the interface propagator matrix. Different from the conventional propagator matrix method, the new global propagator relation for the composite laminate with the presence of perfect/imperfect interfaces is recursively obtained by means of the reduced propagator distance and the exponential term between the layer to layer propagator matrix. The numerical examples indicate that numerical results are stability and precision, different boundary conditions have hardly influenced temperature and heat fluxes, and interlaminar thermal stresses strengthen with increasing interface coefficients. The methods and results can also serve as a reference for verifying existing or future QC laminate theories.

Reflection characteristics of thin-beds with aligned fractures

Fractures are ubiquitous in rock and therefore considerably affect the overall mechanical properties of rock. In this study, effective medium theory is used to analyze the reflection characteristics of elastic waves in thin-beds containing aligned fractures. First, elastic parameters are obtained for a single thin bed containing discrete vertical fractures. Then, an exact solution is derived for the reflection coefficient of elastic waves in horizontally transverse isotropic (HTI) thin-beds using the propagation matrix method. Next, the effects of the fracture density and fillings on the reflection pattern are analyzed. Thin-beds without fractures are equivalent to a vertically transverse isotropic (VTI) medium in the long-wavelength limit. The introduction of vertical fractures makes thin-beds equivalent to a single thin bed in an orthorhombic anisotropic (ORT) medium (where the thickness of ORT thin bed is the total thickness of the original thin-beds). The ORT model of fractured thin-beds is presented by the equivalent medium theory. The results obtained using the HTI thin-beds and ORT models are compared, and the influences of the ORT model accuracy and formation parameters (such as thickness-to-wavelength ratio of a single thin bed, total thickness of thin-beds, etc.) on the ORT approximation results are analyzed. The response characteristics of elastic waves in complex thin-beds with fractures determined in this study can give an important guidance to real applications in geophysics and rock mechanics.

Spin quantum transport in double top-gate system

The quantum transport in an n-type two-dimensional electron gas (2DEG) with a double top gate system is investigated. A propagation matrix method is used to derive the band structure and obtain the conductance of the considered system. The results show that in the presence of the Rashba and the Zeeman interactions, resonance peaks and hole-like bound state structure are formed in the conductance spectra influenced by the gate potential and gate distance. While, under the influence of the Rashba–Dresselhaus and the Zeeman interactions, resonance peaks and inner-mode resonance conductance peaks are formed reflecting the gate potential and the gate distance. Notably, when the Dresselhaus interaction reaches a certain strength, the partial conductance of the spin-preservation internal mode becomes significant. Finally, a simple transcendental equation is found to estimate the energy of a bound state.

Shear elastic waves in bi-material multi-layered waveguide

This analytical study demonstrates shear elastic wave propagation in stratified waveguide with emphasis on wave localisation effects using the propagator matrix method. The stratified waveguide consists of two-phase piecewise homogeneous periodically arranged finite number sub-layers along waveguide thickness. Analytical solutions are carried out for traction free waveguide. The existence of two modal types of guided waves is established: i) a localised surface mode occurring in “stopband” and ii) normal modes arising in a “passband” of frequencies.

A multi-scale model to predict the electromagetic interference shielding performance of (Fe/Cu)@CNT/SA/PDMS flexible composite

(Fe/Cu)@CNT/SA/PDMS flexible composites are prepared by vacuum infiltrating PDMS into CNT/SA aerogel with Fe and Cu bimetallic nanoparticles coated on tubes. The dielectric loss and magnetic loss capacity of the composite are effectively improved by the coated Fe and Cu bimetallic nanoparticles. In addition, CNTs in the aerogel skeleton connected to each other to form a stable conductive network, leading to a nice conductivity and shielding stability under certain strain. More importantly, a multi-scale model based on propagation matrix method are developed. Based on the introduced model, the EMI-SE values of the composite are calculated and the internal mechanisms are analyzed. Results shown that the EMI-SE values of the composite can be further improved more than 90 dB. These light-weight composites with good flexibility and stable EMI-SE have a wide range of application prospects.

Investigation of Effects of Near‐Surface Complexities on Measurement of Mantle Discontinuity Using SS and Its Precursors

AbstractSeismic observations of the mantle discontinuities at depths of 410 and 660 km provide crucial information to constrain the thermal and compositional states and further shape our understanding of mantle dynamics. The topography and impedance contrast of the mantle discontinuities, at both global and regional scales, have been imaged through differential travel times and amplitude ratios between SS and its precursors. However, a relatively simple reference phase (SS) is often assumed, which may overlook potential bias caused by near‐surface complexities. To assess these effects, we developed an algorithm to simulate the waveforms of SS and its precursors efficiently based on the propagation matrix method. We found that the crustal thickening increases the differential travel times but does not change the amplitude ratios much, while the sedimentary layer significantly affects both the differential travel times and amplitude ratios. The global anomalies of differential travel times and amplitude ratios are mapped incorporating earth models from CRUST1.0 and PREM. The time shift can reach ∼9 s, which will bring a depth bias of mantle discontinuity of more than 20 km, while the amplitude ratio anomaly is up to ∼40%, which will make the impedance contrast of the mantle discontinuity overestimated. The near‐surface complexities cannot be ignored in the investigation of mantle discontinuities with SS precursors, especially when the bounce points located in the regions with sediment.

Dynamic response of the periodic pile-reinforced composite foundation to harmonic seismic waves

The dynamic analysis of the pile-reinforced composite foundation (PCF) under seismic waves is important for the design of the PCF and corresponding upper structures. Owing to huge number of degrees of freedom (DOFs) in the modeling, it is still difficult to simulate the dynamic response of the PCF to seismic waves directly by means of traditional numerical methods. To overcome this difficulty, the PCF is simplified as the periodic pile-reinforced composite foundation (PPCF) in this study, and the harmonic wave finite element (HWFE) model for the PPCF under seismic waves is proposed. To establish the HWFE model, the response of the PPCF is decomposed into a series of horizontally propagating harmonic waves with amplitudes varying with the depth. Based on the principle of virtual work (PVW), the finite element method (FEM) equations for each harmonic wave are established. To impose the boundary conditions and input seismic waves at the bottom of the PPCF, the traction-displacement relation at the surface of the underlying half-space bedrock is derived. Solving the FEM equations for the PPCF and synthesizing the resulting solutions for the harmonic waves via the DFT method, dynamic responses of the PPCF to plane harmonic seismic waves are obtained. To verify the developed HWFE model, results obtained by the proposed HWFE model are compared with those by the propagator matrix method (PMM). The numerical results show that the resonance frequency of the PPCF increases with decreasing pile spacing; also, the presence of the stiffer soil layers will enhance the resonance frequency of the PPCF.

Periyodik yığılı kütleli kirişlerde eğilme dalgalarının yayılımı

In this study, dispersion analysis is carried out in the Euler-Bernoulli beam with periodic lumped mass, and periodicity effects are investigated. First, the dispersion relation is derived using the propagator matrix method for an infinitely long periodic beam with lumped mass. The banded frequency spectrum is given depending on the mass ratio. Then, in the case of a finite number of periodic lumped masses, the effect on wave propagation was investigated and the transmission function was obtained. Finally, the displacement mode shapes of the barrier consisting of these lumped masses were obtained for the pass and stop band frequency values. The results show that it is possible to use designs made with periodic lumped masses as wave barriers.

Photonic cavity mode tuning in porous silicon-based microcavities by He+ and H+ ion irradiation

The present investigation reports the optical characteristics of the porous Si (PSi) based microcavities before and after energetic He+ and H+ ion irradiations. These PSi microcavities were fabricated by the galvanostatic electrochemical etching process and irradiated with 35 keV He+ and H+ ions with three different ion fluences: 1 × 1015, 5 × 1015, and 1 × 1016 ions/cm2. Significant color contrast is evident in the reflection images after ion irradiation. These reflection spectra of the optical microcavities are systematically investigated before and after ion irradiations. The dominant resonant cavity peak of the microcavity shows a notable shift of ∼28–48 and ∼17–26 nm toward the higher wavelength region with He+ and H+ ion irradiations at various ion fluences, respectively. The relative changes in the cavity wavelengths are about ∼5%–10% and ∼3%–5% for He+ and H+ ion irradiations, respectively. The redshift in the reflectance spectra is attributed to modification in the refractive index of microcavities induced by He+ and H+ ions. These experimental results compare well with the ion propagation and transfer matrix method simulations. The observed changes in the optical properties arise due to surface modification of the Si–Si and Si–O bonds and thereby refractive index modification of individual PSi layers of the microcavity. This study establishes that low-energetic ions produce broadly optically tunable and photonic structures suitable for optoelectronic applications.