Reflection Transmission Coefficient Research Articles

Simultaneous Transmission and Reflection Beamforming Design for RIS-Aided MU-MISO

In this paper, we study the beamforming design for the simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS) assisted MU-MISO system, where the energy splitting (ES) mode is adopted for STAR-RIS. We aim to jointly design the beamforming strategy at the BS and the transmission-reflection coefficients (TRCs) at the STAR-RIS to minimize the total downlink transmit power of the base station (BS) subject to each user's SINR constraint. The formulated optimization problem is difficult to solve directly, and therefore we employ the iterative alternating optimization (AO) framework to obtain suboptimal solutions with promising performance. Specifically, we propose an AO-based solution to optimize each amplitude and phase of the TRCs at the STAR-RIS separately in a sequential manner, where two distinct approaches are introduced for the design of the amplitudes of STAR-RIS elements. Simulation results show that the proposed joint beamforming design at BS and passive design at STAR-RIS achieves a promising performance, and requires fewer iterations compared with the state-of-the-art.

Rapid construction of Rayleigh wave dispersion curve based on deep learning

Introduction:The dispersion curve of the Rayleigh-wave phase velocity (VR) is widely utilized to determine site shear-wave velocity (Vs) structures from a distance of a few metres to hundreds of metres, even on a ten-kilometre crustal scale. However, the traditional theoretical-analytical methods for calculating VRs of a wide frequency range are time-consuming because numerous extensive matrix multiplications, transfer matrix iterations and the root searching of the secular dispersion equation are involved. It is very difficult to model site structures with many layers and apply them to a population-based inversion algorithm for which many populations of multilayers forward modelling and many generations of iterations are essential.Method:In this study, we propose a deep learning method for constructing the VR dispersion curve in a horizontally layered site with great efficiency. A deep neural network (DNN) based on the fully connected dense neural network is designed and trained to directly learn the relationships between Vs structures and dispersion curves. First, the training and validation sets are generated randomly according to a truncated Gaussian distribution, in which the mean and variance of the Vs models are statistically analysed from different regions’ empirical relationships between soil Vs and its depth. To be the supervised dataset, the corresponding VRs are calculated by the generalized reflection-transmission (R/T) coefficient method. Then, the Bayesian optimization (BO) is designed and trained to seek the optimal architecture of the deep neural network, such as the number of neurons and hidden layers and their combinations. Once the network is trained, the dispersion curve of VR can be constructed instantaneously without building and solving the secular equation.Results and Discussion:The results show that the DNN-BO achieves a coefficient of determination (R2) and MAE for the training and validation sets of 0.98 and 8.30 and 0.97 and 8.94, respectively, which suggests that the rapid method has satisfactory generalizability and stability. The DNN-BO method accelerates the dispersion curve calculation by at least 400 times, and there is almost no increase in computation expense with an increase in soil layers.

Effect of mesoscopic-flow loss on seismic reflections in media with penny-shaped inclusions

Summary We obtain the amplitude and energy reflection coefficients of seismic waves in porous media with penny-shaped inclusions, based on the generalized Biot-Rayleigh model that takes into account the attenuation due to mesoscopic local fluid flow (LFF). We consider two cases, including a contact between two porous media having either different fluids (gas-water contact) or crack density/aspect ratio, as well as a water half-space overlying a porous medium, and study the frequency-dependent reflection-transmission (scattering) coefficients for open- and sealed-pore boundary conditions. Our examples show that the LFF mechanism mainly reduces the reflection coefficients (amplitude and energy) at the gas-water contact and at a water/porous-medium interface for frequencies less than 10 kHz, due to the fact that the velocity in the lower medium decreases. For the latter case, if the fluid is gas, the LFF effect becomes only important at frequencies between 0.0001 and 10 Hz for the open-pore case. This is due to the fact that the acoustic impedance contrast between water and gas is high. At frequencies less than 0.0001 Hz, the interface is equivalent to a water/elastic-medium one, and hence the results are the same as those of the sealed-pore case. Moreover, the crack density and aspect ratio affect the mesoscopic attenuation and relaxation frequency, and therefore the reflection coefficients.

Influence of boundary conditions on the reflection and transmission of qP-wave at an interface between two nonlocal transversely isotropic elastic half-spaces

This work is concerned with the reflection and transmission of quasi P wave incident at an imperfect interface between two nonlocal transversely isotropic elastic half-spaces. The linear spring model is used to describe the imperfection of bonding behavior at the interface. Reflection, transmission coefficients (RTC) have been derived analytically for when a longitudinal displacement wave strikes for both imperfect and perfect interface. Finally, numerical examples are provided to show the effect of the imperfect interface, nonlocal parameter and incident angle on the reflection and transmission coefficients.

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SPECFEM2D-DG, an open-source software modelling mechanical waves in coupled solid–fluid systems: the linearized Navier–Stokes approach

SUMMARYWe introduce SPECFEM2D-DG, an open-source, time-domain, hybrid Galerkin software modelling the propagation of seismic and acoustic waves in coupled solid–fluid systems. For the solid part, the visco-elastic system from the routinely used SPECFEM2D software is used to simulate linear seismic waves subject to attenuation. For the fluid part, SPECFEM2D-DG includes two extensions to the acoustic part of SPECFEM2D, both relying on the Navier–Stokes equations to model high-frequency acoustics, infrasound and gravity waves in complex atmospheres. The first fluid extension, SPECFEM2D-DG-FNS, was introduced in 2017 by Brissaud, Martin, Garcia, and Komatitsch; it features a nonlinear Full Navier–Stokes (FNS) approach discretized with a discontinuous Galerkin numerical scheme. In this contribution, we focus only on introducing a second fluid extension, SPECFEM2D-DG-LNS, based on the same numerical method but rather relying on the Linear Navier–Stokes (LNS) equations. The three main modules of SPECFEM2D-DG all use the spectral element method (SEM). For both fluid extensions (FNS and LNS), two-way mechanical coupling conditions preserve the Riemann problem solution at the fluid–solid interface. Absorbing outer boundary conditions (ABCs) derived from the perfectly matched layers’ approach is proposed for the LNS extension. The SEM approach supports complex topographies and unstructured meshes. The LNS equations allow the use of range-dependent atmospheric models, known to be crucial for the propagation of infrasound at regional scales. The LNS extension is verified using the method of manufactured solutions, and convergence is numerically characterized. The mechanical coupling conditions at the fluid–solid interface (between the LNS and elastodynamics systems of equations) are verified against theoretical reflection-transmission coefficients. The ABCs in the LNS extension are tested and prove to yield satisfactory energy dissipation. In an example case study, we model infrasonic waves caused by quakes occurring under various topographies; we characterize the acoustic scattering conditions as well as the apparent acoustic radiation pattern. Finally, we discuss the example case and conclude by describing the capabilities of this software. SPECFEM2D-DG is open-source and is freely available online on GitHub.

Retrieving S-wave velocity from surface wave multimode dispersion curves with DispINet

We present a data-driven dispersion curve inversion network (DispINet) that directly maps the multimode dispersion curves to the S-wave velocity model. DispINet is trained with synthetic samples that consist of multimode dispersion curve data and the corresponding S-wave velocity models. The S-wave velocity models are generated according to prior information in a specific study area. Multimode dispersion curves are calculated by the generalized reflection-transmission coefficient method for each model. The well-trained DispINet could be used to predict the S-wave velocity model for other dispersion curve data never seen by DispINet. Testing data and Qademah field data results show that DispINet has the ability to retrieve a reasonable underground S-wave velocity structure in real time.

A Novel Magnetosphere–Ionosphere Coupling Model for the Onset of Substrom Expansion Phase

A novel magnetosphere–ionosphere (M-I) coupling model is proposed to simulate the brightening of the onset auroral arc of a magnetospheric substorm event. The new M-I coupling model is modified from the M-I coupling model proposed by the Alaska research team in 1988. We adjust the magnetospheric boundary conditions by including the Hall effects in the thin current sheet and allowing the spatial distributions of the reflection–transmission coefficient to vary with time. As a result, brightening and poleward drifting of multiple auroral arcs appear for the first time in an M-I coupling model. The new results indicate that the coupled Hall effects in the near-Earth plasma sheet and the E-region ionosphere play a vital role in triggering the onset of a magnetospheric substorm.

Calculation method and characteristic analysis of dispersion curves of Rayleigh channel waves in transversely isotropic media

Coal seams have beddings and fissures and are typically anisotropic media. Current channel wave theories are mainly based on isotropic media, and few studies exist on the dispersion characteristics of Rayleigh channel waves in anisotropic models, such as transversely isotropic (TI) media. We chose the generalized reflection-transmission coefficient method to solve the dispersion curves of Rayleigh channel waves in TI media. However, it is difficult to solve the associated dispersion equations of Rayleigh channel waves using this method directly. Therefore, we have extended the generalized reflection-transmission coefficient method and determined the improved accuracy through numerical simulation. We analyzed the dispersion characteristics of Rayleigh channel waves of several typical coal seam models in TI media. The results showed that in the three-layer model, the difference in fundamental-mode dispersion curves between vertically transversely isotropic (VTI) media and isotropic media was relatively small; however, the differences in the higher order dispersion curves were slightly larger. The difference in the Airy phase velocity between horizontal transversely isotropic (HTI) and isotropic media was relatively large. When the coefficient of variation in the qP waves ([Formula: see text]) was greater than 0, the fundamental-mode and first-order phase velocity curves of HTI media exhibited an evident intersection at the head end. In the dirt-band-containing coal seam model, within the 350 and 550 Hz band, the high-frequency velocity of fundamental-mode phase velocity curve of isotropy and HTI media was slightly higher than the low-frequency velocity, which is a notable phenomenon.

Study on transmitted channel wave-based, horizontal multilayer 3-D velocity model inversion and quantitative coalbed thickness detection method

Most methods using transmitted channel wave (TCW) prospecting to quantitatively detect the thickness of coal seams based on the statistic relationship of group velocity in certain wave bands to the thickness of coal seams cannot be applied universally. To establish a universal applicable method, we first obtained the theoretical dispersion curve of TCW using the generalized reflection–transmission coefficient method and the 1-D horizontal multilayer velocity model, performed iteratively match calculation using the inversion model and the genetic algorithm and analyzed the distributive characteristics of shear wave velocity of coal and rock formations at a certain depth. We then obtained the 3-D velocity images of the coal seam working face based on TCW data using the 3-D back-projection technology. According to the changes of shear wave velocity at the coal–rock interface and the rate of inversion velocity change, we further proposed the quantitative discriminant model for coalbed thickness. Based on the model, we quantitatively interpreted the thickness of the coal seam by computing the depths corresponding to the extremes of the positive and negative rate of the shear wave velocity change and obtained the distribution characteristics of the coal thickness in the working surface. To verify the feasibility and validity of the proposed model for coalbed thickness, we conducted a 3-D physical similarity model experiment and subjected the collected two-component TCW data to inversion calculation and compared the obtained coal seam thickness with the known model parameters. Overall, our study achieved the universal 3-D quantitative detection of coalbed thickness and provided technical supports for intelligentized coalbed mining.

Characteristics of dispersion curves for Love channel waves in transversely isotropic media

Coal seams have a pronounced bedding structure with developed cracks and exhibit significant anisotropy. However, few studies have examined the frequency dispersion properties of channel waves in anisotropic coal seams. In this study, numerical solutions are calculated using the generalized reflection-transmission coefficient method for the dispersion curves of Love channel waves in vertical transversely isotropic (VTI) and horizontal transversely isotropic (HTI) medium models. Moreover, the frequency dispersion characteristics of Love channel waves in several typical transversely isotropic models are analyzed. We find that the dispersion curves for isotropic and VTI media differ significantly. In addition, the phase and Airy-phase velocities in VTI media are higher than those in isotropic media. Thus, neglecting this difference in practical channel wave detection will result in large detection errors. The dispersion curves for the isotropic and HTI media do not differ significantly, and the Airy-phase velocities of various modes are similar. The group-velocity curve for a coal seam model containing a dirt band is found to be extremely irregular. The fundamental-mode Airy phase is not pronounced, but the first-mode Airy phase can be clearly observed. Hence, first-mode channel waves are suitable for detecting dirt bands.

The Forward Problem for Surface Wave Dispersion in Layered Media

We examine a new method for the calculation of the traveling wave characteristic in a layered medium. The seismic impedance tensor method is improved by introducing the notion of a potential function and new iterative relationships are obtained for isotropic layered media. Comparison of the dispersion equation roots between the generalized reflection-transmission coefficient method (GR/TC) and the seismic impedance tensor method (SIT) has detected some roots that do not exist in SIT. To check the accuracy of the roots in both methods, we have compared the experimental results between the classical transition matrix method (Thomson-Haskell) and our new method (SIT) for the same layered medium model. The experimental results show that the roots obtained by the impedance method coincide with the classical transition matrix method. This also shows that some roots obtained from the dispersion equation in GR/TC cannot be accurately determined.

Calculation of the Characteristics of Traveling Waves in Layered Media

A new method is considered for the calculation of traveling-wave characteristics in a layered medium. It is mainly based on the transfer-matrix method [2–10] and the generalized reflection-transmission coefficient (GRTC) method [11–14] for the calculation of characteristics. Introducing an impedance tensor of rank 2, Ẑ (z), in the boundary-value stress problem and utilizing in this way the boundary conditions and the Lame equation, we obtain a system of differential equations which is solved by the fourth-order Runge-Kutta method. Specifying a model of the layered medium in terms of known constants, we find the traveling-wave characteristic γ as a function of frequency ω . Given γ, we easily calculate the dispersion curves, which closely fit the GRTC method. Compared with the GRTC method, the impedance-tensor method fully solves the dispersion curve of the normal-mode traveling waves, and it is applicable to both a homogeneous planar Earth model and a model with a slow layer.

Computation of synthetic seismogram in real earth model by eigen function expansion

The method of eigen function expansion has been used in the present study to compute synthetic or theoretical seismogram in layered elastic half-space of real earth model. Simple dislocation source model has been considered. The transverse (SH) or radial and vertical (P-SV) components of displacement field have been computed as summed modes and compared by using both exact and numerical techniques. The methods used in the study, include exact evaluation by propagator matrix approach using Reflection-Transmission coefficients as well as numerical computations using Runge-Kutta method of order 4. The specialty of the present study is to evaluate approximate displacement field for the earth models with homogeneous and / or inhomogeneous layers. The normalization technique has been used in the study to control the overflow errors. The study has an advantage to get an idea of earth structure or source model by an inverse iterative technique.

Scattering, bound, and quasi-bound states of the generalized symmetric Woods-Saxon potential

The exact analytical solutions of the Schrödinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound, and quasi-bound states in one dimension. The reflection and transmission coefficients are analytically obtained. Then, the correlations between the potential parameters and the reflection-transmission coefficients are investigated, and a transmission resonance condition is derived. Occurrence of the transmission resonance has been shown when incident energy of the particle is equal to one of the resonance energies of the quasi-bound states.

Transmission–Reflection Coefficient in the Lattice Boltzmann Method

We consider the permeable bounce-back scheme in the lattice Boltzmann (LB) method for incompressible flows, in which a fraction of the distribution function is bounced back and the remainder travels to the neighboring lattice points. An asymptotic analysis of the scheme is carried out in order to show that the fractional coefficient, referred to as the transmission–reflection coefficient, relates the pressure drop to the flow velocity. The derived relation, which clarifies the role played by the transmission–reflection coefficient in the macroscopic description, is helpful in using the scheme to simulate flows involving a pressure drop or gradient. The scheme is compared with the existing methods in which the transmission–reflection coefficient is employed, and the difference is clarified. As an application of the permeable bounce-back scheme, we perform an LB simulation for flows through porous media described by the Brinkman model.

Energy flow model for thin plate considering fluid loading with mean flow

Energy Flow Analysis (EFA) has been developed to predict the vibration energy density of system structures in the high frequency range. This paper develops the energy flow model for the thin plate in contact with mean flow. The pressure generated by mean flow affects energy governing equation and power reflection–transmission coefficients between plates. The fluid pressure is evaluated by using velocity potential and Bernoulli's equation, and energy governing equations are derived by considering the flexural wavenumbers of a plate, which are different along the direction of flexural wave and mean flow. The derived energy governing equation is composed of two kinds of group velocities. To verify the developed energy flow model, various numerical analyses are performed for a simple plate and a coupled plate for several excitation frequencies. The EFA results are compared with the analytical solutions, and correlations between the EFA results and the analytical solutions are verified.

Resolution of prestack depth migration

The resolution of a general 3-D common-shot elastic prestack depth migration in a heterogeneous anisotropic medium is studied approximately, using the ray theory. It is demonstrated that the migrated section can approximately be represented by the convolution of the reflectivity function with the corresponding local resolution function. Alternatively, it can also be approximately represented by the convolution of the spatial distribution of the weak-contrast displacement reflection-transmission coefficient with the corresponding local resolution function. The derived explicit approximate equations enable us to predict the migration resolution approximately without doing the whole and expensive migration. The equations are applicable to 3-D elastic migrations in 3-D isotropic or anisotropic, heterogeneous velocity models.

A note on the equivalence of three major propagator algorithms for computational stability and efficiency

It is shown in this note that the three methods, the orthonormalization method, the minor matrix method and the recursive reflection-transmission matrix method are closely related and solve the numerical instability in the original Thomson-Haskell propagator matrix method equally well. Another stable and efficient method based on the orthonormalization and the Langer block-diagonal decomposition is presented to calculate the response of a horizontal stratified model to a plane, spectral wave. It is a numerically robust Thomson-Haskell matrix method for high frequencies, large layer thicknesses and horizontal slownesses. The technique is applied to calculate reflection-transmission coefficients, body wave receiver functions and Rayleigh wave dispersion.

傾斜異方性多層構造の地震記象の計算式

We present mathematical expressions to compute body-wave response function for dipping anisotropic multi-layer structure. The expression is derived on the basis of ray theory incorporating reflection-transmission coefficients on velocity boundary interfaces. By using the expression, synthetic seismograms are computed for some seismic structures consisting of dipping anisotropic layers. The resultant seismograms are transformed into receiver functions. We verify that the receiver functions are approximately in agreement with those synthesized by the layer-matrix method based on wave theory. As an example, we show receiver functions calculated for an anisotropic velocity structure of the subduction zone where the oceanic plate is obliquely descending.