Irregular Interfaces Research Articles

Seismogram Synthesis for Multilayered Heterogeneous Media with Irregular Interfaces by the Global Generalized Reflection–Transmission Matrices Method

ABSTRACTWe present a semianalytical numerical method to simulate SH-wave propagation in heterogeneous multiple layers with smooth property variations. Wave propagation in such piecewise heterogeneous media will dominate the reflection and transmission at interfaces, whereas the scattered waves by volume heterogeneities inside each geological layer are superimposed on the boundary waves to cause fluctuations in amplitude and phase. The incident, boundary-scattering, and volume-scattering waves are accurately superposed through the generalized Lippmann–Schwinger integral (GLSI) equation. The multilayered heterogeneous media with irregular interfaces are sliced into horizontal and heterogeneous slabs, with each discretized into a series of volume elements. The traditional generalized reflection–transmission matrices (GRTMs) method is extended to solve the GLSI equation for each heterogeneous slab in the frequency–wavenumber domain by incorporating the boundary–volume integral equation numerical techniques. The global GRTM is obtained by integrating all the slab’s GRTMs in terms of the boundary condition across adjacent slabs. The wavefield at an arbitrary depth can be computed in a recursive relation from a source term. The accuracy of the method is tested by comparing it with other full-wave solutions to the SH problem. To show the applicability of the method, we calculate synthetic seismograms to demonstrate the significant impact of volume heterogeneities on seismic responses in layered heterogeneous media.

Surface Wave Analysis in Orthotropic Composite Structure with Irregular Interfaces

This paper intends to study the dispersion and attenuation characteristics of corrugation, reinforcement, heterogeneity and initial stress on propagation of Love type surface waves in a bedded structure with welded contact, subject to certain boundary conditions. Current composite model is consists of an initially stressed heterogeneous orthotropic layer bonded between fiber-reinforced upper half-space (under hydrostatic stress) and pre-stressed lower porous half-space separated by corrugated boundaries. Exponential variation in elastic parameters of the orthotropic medium is considered in the sandwiched layer. Dispersion equation has been obtained in closed form. Considerable effect of elastic parameters (reinforcement, heterogeneity and initial stress) on the phase velocity of Love type wave has been discussed graphically. Some particular cases have been discussed and it is found that dispersion equation is in well-agreement with the classical Love wave equation. The deduced equations coincide with the classical Love-wave condition for the uniform homogeneous isotropic structure. Numerical computations are carried out for involved parameters and demonstrated with the help of graphs.

On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM

We analyze the accuracy of two numerical methods for the variable coefficient Poisson equation with discontinuities at an irregular interface. Solving the Poisson equation with discontinuities at an irregular interface is an essential part of solving many physical phenomena such as multiphase flows with and without phase change, in heat transfer, in electrokinetics, and in the modeling of biomolecules’ electrostatics. The first method, considered for the problem, is the widely known Ghost-Fluid Method (GFM) and the second method is the recently introduced Voronoi Interface Method (VIM). The VIM method uses Voronoi partitions near the interface to construct local configurations that enable the use of the Ghost-Fluid philosophy in one dimension. Both methods lead to symmetric positive definite linear systems. The Ghost-Fluid Method is generally first-order accurate, except in the case of both a constant discontinuity in the solution and a constant diffusion coefficient, while the Voronoi Interface Method is second-order accurate in the L∞-norm. Therefore, the Voronoi Interface Method generally outweighs the Ghost-Fluid Method except in special case of both a constant discontinuity in the solution and a constant diffusion coefficient, where the Ghost-Fluid Method performs better than the Voronoi Interface Method. The paper includes numerical examples displaying this fact clearly and its findings can be used to determine which approach to choose based on the properties of the real life problem in hand.

5a-J-4 量子細線、量子箱の電子状態における界面の不規則性の効果

5a-J-4 量子細線、量子箱の電子状態における界面の不規則性の効果

An efficient approach for simulating seismoacoustic scattering due to an irregular fluid-solid interface in multilayered media

SUMMARY The seismoacoustic scattering due to an irregular fluid–solid interface must be considered when we model the seismic wave propagation in oceanic regions or gulf areas. In this paper, an efficient approach will be presented to treat this kind of problem. The approach can be viewed as an extension of the method originally developed for seismogram synthesis in multilayered solid media with irregular interfaces. In this method, we use the traditional boundary element method to discretize the boundary integral equation in each layer; then define the global matrix propagators by the boundary and continuity conditions in such way that they propagate the information of the element displacements and tractions ‘downwards’ for layers above the source while ‘upwards’ for layers below the source, finally solve the problem in the source layer. The main idea of the method is to use the global matrix propagators to suppress the tremendous increase in the memory requirement appearing in the traditional boundary element method when modelling wave propagation in multilayered media. As for the fluid–solid interface, the direct application of the above method is difficult since the global matrix propagators in fluid layers are much different from those defined in solid layers. By using the pressure as the variable inside the fluid layer, we can treat the acoustic wave propagation as a Helmoltz problem. The global matrix propagators can then be extended into the same size as those defined for solid layers by using the standard boundary conditions at the fluid–solid interface (i.e. normal traction continuity, zero tangential traction and normal displacement continuity). By the extended global matrix propagators we can thus propagate the information of the acoustic wave into the elastic wavefield and further obtain the results of the elastic wave propagation in arbitrary solid layers. To demonstrate the validity and feasibility of our method, we should compare our numerical results with the existing solutions. For problems of irregularly layered structures, however, we do not have exact (analytic) solutions. Therefore, it is important to compare the results calculated by completely different numerical methods to ensure validity. For such purpose, we calculate the cases of a plane P wave vertically incident onto two basin-like fluid–solid structures and an SV wave source located below a basin-like fluid–solid interface, of which the synthetic seismograms are accessible from the existing publications. Our results show almost complete agreement with those calculated by the reflection/transmission matrix method and those calculated by the discrete wavenumber method. Second, we calculate the synthetic time domain waveforms for a model with and without a basin-like fluid layer. Comparison observation clearly shows the effects of the fluid layer on the seismic ground motion at land in which seismologists or geophysicists may be of great and practical interests. Furthermore, we take into account the case when an explosive source is located in a fluid layer and illustrate that the method can simulate the water reverberation in the sea. That makes significant sense to deep ocean acoustic experiments.

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity. However, the path that the rays travel along in media with irregular interfaces is not clear. Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements (SEMO) that can accurately evaluate waves traveling along an irregular interface. Consequently, the head waves are separated from interface waves by a time window. Thus, their energy and arrival time changes can be analyzed independently. These analyses demonstrate that, contrary to the case for head waves propagating along a flat interface, there are two mechanisms for head waves traveling along an irregular interface: a refraction mechanism and transmission mechanism. That is, the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media. Such knowledge will be helpful in constructing a more accurate inversion method, such as head wave travel-time tomography, and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas, such as the Tibetan Plateau.

An Efficient Approach for Simulating Wave Propagation with the Boundary Element Method in Multilayered Media with Irregular Interfaces

The boundary element method (BEM) is a useful method for seismic-wave simulation in a stratified medium with irregular interfaces. However, the central processing unit (CPU) time required for the traditional BEM method increases exponentially as the number of layers increases. Ge and Chen (2007) presented a BEM with global reflection/transmission matrix propagators that can prevent excessive requirement of both computer memory and CPU time. In this article, we present a more efficient approach for this method. In the new approach, the global matrix propagators can be calculated directly, which can further increase the efficiency by about 40%.

On the Directivity and Spectra of Noise from Unheated and Heated Jets

The present paper considers the transmission of sound from a source distribution inside a jet to a receiver or observer outside; the source can be represented by a combination of multipoles moving relative to the jet. The shear layer has a random shape with a plane mean position, and entrains a region of turbulence. The transmission across the plane shear layer involves: (i) scattering by the convected, irregular and unsteady interface across which occurs the transition from the jet to the ambient medium; (ii) refraction in the region of low Mach number turbulence entrained by the shear layer. If the jet Mach number does not exceed two the local turbulence can be taken as incompressible. The transmission involves: (i) a deterministic amplitude factor due to the difference in sound speed, mass density and velocity between the jet and ambient medium; (ii) a random phase shift due to the scattering of sound by the irregular interface and the convection of sound by the turbulence entrained with the shear layer. Since there is a random phase shift for the acoustic pressure, the acoustic power, which is quadratic in the acoustic pressure, involves the statistics of interference between two waves. The latter specify the spectral directivity, defined as the acoustic power radiated per unit solid angle and unit frequency band, i.e. either the spectrum received in each direction or the directivity of sound received outside the jet at each frequency. The statistics of sound scattering by irregular interfaces and convection by turbulence are subject to assumptions and constraints which affect critically the directivity and spectra. The evaluation of radiation integrals without low- or high-frequency approximations is also essential to reproduce experimental results on the noise of cold or hot jets. An accuracy of 3 dB can be expected for directivities and 6 dB for spectra, for directions not too far away from the vertical, (i.e perpendicular to the jet).

An efficient second-order accurate cut-cell method for solving the variable coefficient Poisson equation with jump conditions on irregular domains

A numerical method is presented for solving the variable coefficient Poisson equation on a two-dimensional domain in the presence of irregular interfaces across which both the variable coefficients and the solution itself may be discontinuous. The approach involves using piecewise cubic splines to represent the irregular interface, and applying this representation to calculate the volume and area of each cut cell. The fluxes across the cut-cell faces and the interface faces are evaluated using a second-order accurate scheme. The deferred correction approach is used, resulting in a computational stencil for the discretized Poisson equation on an irregular (complex) domain that is identical to that obtained on a regular (simple) domain. In consequence, a highly efficient multigrid solver based on the additive correction multigrid (ACM) method can be applied to solve the current discretized equation system. Several test cases (for which exact solutions to the variable coefficient Poisson equation with and without jump conditions are known) have been used to evaluate the new methodology for discretization on an irregular domain. The numerical solutions show that the new algorithm is second-order accurate as claimed, even in the presence of jump conditions across an interface. Copyright © 2006 John Wiley & Sons, Ltd.

A Comparative Study on Seismic Wave Methods for Multilayered Media with Irregular Interfaces: Irregular Topography Problem

AbstractBy studying the scattering from various topographies due to an incident SH wave, three methods of seismogram synthesis (Aki‐Larner method, Bouchon‐Campillo method, and global generalized R/T matrices method) are evaluated in terms of the accuracy of the results, numerical stability and computational efficiency. Using the FFT algorithm, the Aki‐Larner method is the most efficient of the three methods, but is least accurate because of the limitation of Rayleigh ansatz. The Bouchon‐Campillo method is quite accurate and stable, but has the lowest efficiency; moreover it cannot treat very steep topography precisely. The global generalized R/T matrices method not only is very accurate, stable and with a modest computational efficiency, but also can treat the very steep topography well. Therefore, the global generalized R/T matrices method is the best method among the three, and provides a very effective tool to synthesize seismograms for complex media.

Reflection and transmission operator for irregular interfaces derived from the indirect boundary element method

SUMMARY A method is presented to turn into reality the idea of the reflection and transmission operators in the space–frequency domain for infinitely spread irregular interface in terms of the indirect boundary element method (abbreviated to I-BEM), and to apply them to the wavefield in irregularly stratified media. This method is a hybrid between the strategy of the reflection and transmission matrices method (abbreviated to R /T-MM) developed in seismology and that of I-BEM developing in the engineering community. The I-BEM is one of the ways to disassemble the wavefield into up and down going waves in layers sandwiched between irregular interfaces. Green’s function matrices of I-BEM play the role of the wave function of R /T-MM, and the imaginary forces distributed along both faces of interfaces that of the coefficients vectors. The usage of the reference solution, that is the wavefield in the corresponding horizontally stratified media, gives us a good approximation to handle infinitely spread interfaces. This method of calculation can stack the effect of reflection and transmission at irregular interfaces on the wavefield as the wave goes by. Therefore, for example, the waves coming directly from the seismic source can be extracted from latter phases. The test case for a 2-D homogeneous basin shows the incident wave and reflected waves that bounce up and down in the basin. It is expected that the formulation shown here can make consideration of the wavefield in complex velocity structures and the search for appropriate and efficient approximations easier.

Catalytic effectiveness of irregular interfaces and rough pores: the “land surveyor approximation”

We apply the concept of active zone in Laplacian transport to investigate the steady state mass transfer of a diffusive species towards an arbitrarily irregular catalytic interface. By means of a recently proposed coarse-graining technique, it is possible to compute the reactive flux on the catalytic interface from its geometry alone, without solving the general Laplace problem. As a result, we demonstrate by direct numerical simulation of molecular diffusion and first-order reaction that this method allows one to predict the catalytic effectiveness of a slit-shaped pore with an arbitrary rough geometry and over a wide range of diffusion–reaction conditions. It is found that, contrary to the traditional pseudo-homogeneous approach, the effect of the irregular morphology at the mesoscopic pore level is to modify the reaction rate and not the effective diffusion coefficient. We show that, for all practical situations where the reactant penetration in the pore is significant, a simplified picture of a smooth pore with an effective reactivity K eff can be used to describe the efficiency of a rough pore. Remarkably, K eff is the product of the intrinsic reactivity by a screening factor S, which has an elementary geometrical meaning, namely, the ratio between the real and the apparent surface area.

Can one hear the shape of an electrode? I. Numerical study of the active zone in Laplacian transfer

The concept of active zone in the Laplacian transport to and across irregular interfaces is rigorously introduced. It applies to arbitrary geometries and uses the coarse-graining method proposed by Sapoval to compute the flux across an irregular interface from its geometry without solving the general Laplace problem. Such transport play a dominant role in electrochemistry, heterogeneous catalysis and physiological diffusion processes. In the field of electrochemistry, the method permits one to predict the impedance of an electrode of arbitrary geometry for any value of the frequency. It shows that, for systems with aspect ratios of the order of a few times unity or less, impedance spectroscopy yields in principle a reliable approximate measure of the length of the chord corresponding to a perimeter length inversely proportional to the interface capacitance and frequency. For these cases, impedance spectroscopy can determine the shape of an electrode to the extent that the knowledge of the average chord length as a function of the perimeter determines the shape. For systems of arbitrary geometry, it is shown that impedance spectroscopy permits a measure of the size of the active zone. These results can be transposed to several problems related to Laplacian transfer, such as etching of irregular solids and catalysis in the Eley-Rideal regime.

A Simple Method to Compute the Response of Non-Homogeneous and Irregular Interfaces: Electrodes and Membranes

We present a detailed numerical test of the coarse-graining method proposed by Sapoval to compute the flux through an irregular interface in the case where the local response is inhomogeneously distributed. It is shown, through comparison with detailed finite elements simulations, that this method permits to deduce the flux across an irregular interface from its topography only, as for example in the case of non-uniform polarizability in electrochemistry. The interest of the method lies in its computational simplicity. It then constitutes an essential step towards the understanding of the flux across irregular interfaces in non-linear regimes.

Analysis of mass transfer in composite materials with irregular interfaces

We present a theoretical analysis of permeation through composite bi-layer materials with an irregular interface. The conservation of mass equation for the permeating species is solved using both approximate analytic and numerical techniques. The approximate analytic solution is valid for small deviations of the interface from planarity. To assess the accuracy of the analytic solution, the analytic solution is compared to numerical approximations for a wide range of composite geometries and relative material permeabilities. The analytic solution proves to be accurate and easy to use. The analysis demonstrates that a composite material with an irregular interface possesses a higher permeability and slightly lower selectivity than an equivalent composite with a flat interface. Furthermore, the changes in permeability depend strongly on the magnitude of the interface irregularity but are relatively insensitive to the relative thickness of the two layers.

Crustal reflections and the nature of regional P coda

Abstract F-K spectra for regional P coda are presented for events recorded at the Scandinavian NORESS, FINESA, and ARCESS arrays and the New England NYNEX array. The spectra are dominated by on-azimuth energy with apparent velocities between Pn (or faster) and Lg . Following this analysis, reflection coefficients calculated with an efficient boundary integral scheme are used to study the role irregular interfaces play in the creation of regional P coda. We find that observed crustal scattering in these regions is strikingly consistent with P-P and P-SV scattering from the two-dimensional (2D) irregular Moho and even more consistent with scattering from a 2D irregular near-surface interface.

The postmortem detection of coronary artery lesions using coronary arteriography

Postmortem coronary angiography was undertaken in 230 hospital deaths from all causes. X-rays before and after decalcification of the intact coronary arterial tree were assessed with regard to the degree and morphology of arterial lesions and extent of calcification. These angiographic appearances were correlated with histological sections following routine paraffin embedding and serial sectioning where appropriate. Stable but patent lesions, characterized histologically by an intact plaque cap and no intraluminal thrombus formation, angiographically revealed a smooth interface between the barium and vessel wall with no filling defect and often an hour-glass configuration. In contrast, patent unstable lesions, characterized histologically by plaque fissuring and intra-intimal or intraluminal thrombus formation, showed an irregular interface angiographically, often with irregular filling defects. Similarly, distinction between an old stable occlusion and a recent thrombotic occlusion could be made angiographically on the basis of smooth or irregular interfaces between barium and vessel wall. Various angiographic appearances are interpreted in the light of the histological morphology encountered and it is concluded that postmortem coronary angiography is an accurate, rapid and invaluable technique in the autopsy investigation of ischemic heart disease and sudden death.

A solution of multiple scattering problem by method of spatial stochastic systems. I. Discrete scatterers with arbitrary shape. II. Discrete scatterers and random interface. III. Two random irregular interfaces

This paper is an application of the “Spatial stochastic system theory” [K. C. Liu, J. Sound Vib. 79(3), 321–339 (1979); 80(4), 473–498 (1982)] to the problem of multiple scattering. It consists of three parts: (1) multiple scattering of randomly distributed discrete scatterers with arbitrary shape, (2) multiple scattering between discrete scatterers and a random irregular interface, and (3) multiple scattering between two random irregular interfaces. For these cases, a general expression for the space correlation function and intensity of the multiple scattered field is derived under very weak constraints. By means of these expressions, the space correlation functions and intensities of the multiple scattered fields caused by any kind (plane or spherical or others) of monochromatic incident wave can be calculated as long as the scattering property of each scatterer (for the first case) or each scatterer and the random interface (for the second case) under plane monochromatic incident wave and the density function and the probability distribution of orientation of the scatterers are given. This calculation consists of only a single integration, a single summation, and some convolution operation. Some examples are considered and results will be presented for a uniform distribution of spherical particles in the presence of random irregular interfaces.

A finite‐difference treatment of irregular interfaces for the parabolic wave equation

A finite‐difference approach, introduced to handle the horizontal interface condition, is extended to treat the irregular interface condition for the parabolic wave equation. The irregular interface condition is developed to preserve the continuity of pressure as well as continuity of vertical particle velocity. The formulation of irregular interfaces is by means of a finite‐difference scheme in conjunction with the Taylor series expansion while the handling of the irregular interfaces is by a line segmentation. The complete mathematical development will be outlined. The method is designed to be implicit and is conditionally stable. This treatment is extended further to handle the irregular boundary. The validity of this approach is clearly shown by the theory, however, a test example is presented as a supporting evidence. [Work supported by NAVSEA.]

Emission from an inhomogeneous layer with irregular interfaces

A theoretical model for microwave emission from an inhomogeneous layer has been developed using the radiative transfer method. The top and bottom boundaries of the layer are assumed to be randomly rough surfaces, and the scatter characteristics are assumed to be describable by the Kirchhoff scatter model. The presence of an irregular top boundary is found to cause a slower angular trend than the case of a plane layer and causes, in addition, a rise in temperature if the layer permittivity is large. On the other hand, if only the bottom boundary of the layer is rough, a rise in emission is observed relative to the plane layer. When both the top and the bottom boundaries are rough, the emissions at small nadir angles are closer to those of a layer with a rough bottom boundary, and the emissions at large nadir angles are closer to those of a layer with a rough top boundary. A comparison of the layer model with reported angular measurements from a snow layer at three different frequencies and polarizations shows promise for such a model. An additional comparison of emission versus the depth of a snow pile indicates that an irregular snow ground interface causes higher emissions at small depths. This fact is necessary to explain the observed measurements.