Seismic Ray Theory

Introduction T he propagation of seismic body waves in complex, laterally varying 3-D layered structures is a complicated process. Analytical solutions of the elastodynamic equations for such types of media are not known. The most common approaches to the investigation of seismic wavefields in such complex structures are (a) methods based on direct numerical solutions of the elastodynamic equation, such as the finite-difference and finite-element methods, and (b) approximate high-frequency asymptotic methods. Both methods are very useful for solving certain types of seismic problems, have their own advantages and disadvantages, and supplement each other suitably. We will concentrate here mainly on high-frequency asymptotic methods, such as the ray method. The high-frequency asymptotic methods are based on an asymptotic solution of the elastodynamic equation. They can be applied to compute not only rays and travel times but also the ray-theory amplitudes, synthetic seismograms, and particle ground motions. These methods are well suited to the study of seismic wavefields in smoothly inhomogeneous 3-D media composed of thick layers separated by smoothly curved interfaces. The high-frequency asymptotic methods are very general; they are applicable both to isotropic and anisotropic structures, to arbitrary 3-D variations of elastic parameters and density, to curved interfaces arbitrarily situated in space, to an arbitrary source-receiver configuration, and to very general types of waves. High-frequency asymptotic methods are also appropriate to explain typical "wave" phenomena of seismic waves propagating in complex 3-D isotropic and anisotropic structures. The amplitudes of seismic waves calculated by asymptotic methods are only approximate, but their accuracy is sufficient to solve many 3-D problems of practical interest. Asymptotic high-frequency solutions of the elastodynamic equation can be sought in several alternative forms. In the ray method, they are usually sought in the form of the so-called ray series (see Babich 1956; Karal and Keller 1959). For this reason, the ray method is also often called the ray-series method, or the asymptotic ray theory (ART). The seismic ray method can be divided into two parts: kinematic and dynamic. The kinematic part consists of the computation of seismic rays, wavefronts, and travel times. The dynamic part consists of the evaluation of the vectorial complex-valued amplitudes of the displacement vector and the computation of synthetic seismograms and particle ground motion diagrams. The most strict approach to the investigation of both kinematic and dynamic parts of the ray method consists of applying asymptotic high-frequency methods to the elastodynamic equations. The kinematic part of the ray method, however, may also be attacked by some simpler approaches, for example, by variational principles (Fermat principle I N T R O D U C T I O N possible to develop the whole kinematic part of the seismic ray method using the well-known Snell's law. Such approaches have been used for a long time in seismology and have given a number of valuable results. There may be, however, certain methodological objections to their application. In the application of Snell's law, we must start from a model consisting of homogeneous layers with curved interfaces and pass from this model to a smoothly varying model by increasing the number of interfaces. Such a limiting process offers very useful seismological insights into the ray tracing equations and travel-time computations in inhomogeneous media, but it is more or less intuitive. The Fermat principle has been used in seismology as a rule independently for P and S waves propagating in inhomogeneous media. The elastic wavefield, however, can be separated into P and S waves only in homogeneous media (and perhaps in some other simple structures). In laterally varying media with curved interfaces, the wavefield is not generally separable into P and S waves; the seismic wave process is more complicated. Thus, we do not have any exact justification for applying the principle independently to P and S waves. In media with larger velocity gradients, the ray method fails due to the strong coupling of P and S waves. Only the approach based on the asymptotic solution of the elastodynamic equation gives the correct answer: the separation of the seismic wavefield in inhomogeneous media into two independent wave processes (P and S) is indeed possible, but it is only approximate, in that it is valid for high frequencies and sufficiently smooth media only. Similarly, certain properties of vectorial complex-valued amplitudes of seismic body waves can be derived using energy concepts, particularly using the expressions for the energy flux. Such an approach is again very useful for intuitive physical understanding of the amplitude behavior, but it does not give the complete answer. The amplitudes of seismic body waves have a vectorial complex-valued character. The waves may be elliptically polarized (S waves) and may include phase shifts. These phase shifts influence the waveforms. The energy principles do not yield a complete answer in such situations. Consequently, they cannot be applied to the computation of synthetic seismograms and particle ground motion diagrams. Recently, several new concepts and methods have been proposed to increase the possibilities and efficiency of the standard ray method; they include dynamic ray tracing, the ray propagator matrix, and paraxial ray approximations. In the standard ray method, the travel time and the displacement vector of seismic body waves are usually evaluated along rays. Thus, if we wish to evaluate the seismic wavefield at any point, we must find the ray that passes through this point (boundary value ray tracing). The search for such rays sometimes makes the application of the standard ray method algorithmically very involved, particularly in 3-D layered structures. The paraxial ray methods, however, allow one to compute the travel time and displacement vector not only along the ray but also in its paraxial vicinity. It is not necessary to evaluate the ray that passes exactly through the point. The knowledge of the ray propagator matrix makes it possible to solve analytically many complex wave propagation problems that must be solved numerically by iterations in the standard ray method. This capability greatly increases the efficiency of the ray method, particularly in 3-D complex structures. The final ray solution of the elastodynamic equation is composed of elementary waves corresponding to various rays connecting the source and receiver. Each of these elementary waves (reflected, refracted, multiply reflected, converted, and the like) is described by its own ray series. In practical seismological applications, the higher terms of the ray series have not yet been broadly used. In most cases, the numerical modeling of seismic wavefields and the interpretation of seismic data by the ray method have been based on the www.cambridge.or

Seismic characterization of reservoirs with variable fracture spacing by double focusing Gaussian beams

Fractured reservoirs account for a majority of the oil production worldwide and often have low recovery rate. Fracture characterization is important in building reservoir flow models for enhanced oil recovery. Information about fracture orientation, fracture spacing, and fracture compliances is essential. When a fracture network consisting of multiple sets of fractures with variable fracture spacing/orientation is present, we have to determine the spatial information about them as this may represent important connectivity information for fluid flow. We present a seismic method that can achieve the above goals in the context of seismic scattering, when the fracture spacing is on the order of half of the wavelength. The method is based measuring the beam interference pattern for two Gaussian beams focused on a fractured reservoir location, one beam from the sources and the other from the receivers. Numerical examples show that our method can provide spatially dependent information on fracture parameters.Massachusetts Institute of Technology. Earth Resources Laboratory (Founding Members Program

Rpgrip1 is required for rod outer segment development and ciliary protein trafficking in zebrafish

The authors would like to thank the Royal Society of London, the National Eye Research Centre, the Visual Research Trust, Fight for Sight, the W.H. Ross Foundation, the Rosetrees Trust, and the Glasgow Children’s Hospital Charity for supporting this work. This work was also supported by the Deanship of Scientific Research at King Saud University for funding this research (Research Project) grant number ‘RGP – VPP – 219’.Mutations in the RPGR-interacting protein 1 (RPGRIP1) gene cause recessive Leber congenital amaurosis (LCA), juvenile retinitis pigmentosa (RP) and cone-rod dystrophy. RPGRIP1 interacts with other retinal disease-causing proteins and has been proposed to have a role in ciliary protein transport; however, its function remains elusive. Here, we describe a new zebrafish model carrying a nonsense mutation in the rpgrip1 gene. Rpgrip1homozygous mutants do not form rod outer segments and display mislocalization of rhodopsin, suggesting a role for RPGRIP1 in rhodopsin-bearing vesicle trafficking. Furthermore, Rab8, the key regulator of rhodopsin ciliary trafficking, was mislocalized in photoreceptor cells of rpgrip1 mutants. The degeneration of rod cells is early onset, followed by the death of cone cells. These phenotypes are similar to that observed in LCA and juvenile RP patients. Our data indicate RPGRIP1 is necessary for rod outer segment development through regulating ciliary protein trafficking. The rpgrip1 mutant zebrafish may provide a platform for developing therapeutic treatments for RP patients.Publisher PDFPeer reviewe

Spillover Effects of Studying with Immigrant Students; A Quantile Regression Approach

Abstract: We analyze how the share of immigrant children in the classroom aects the educational attainment of native Dutch children in terms of their language and math performance at the end of primary school. Our paper studies the spill-over effects at different parts of the test score distribution of native Dutch students using a quantile regression approach. We fi nd no evidence of negative spillover effects of the classroom presence of immigrant children at the median of the test score distribution. In addition, there is no indication that these spill-over effects are present at other parts of the distribution.

Histone deacetylase inhibitors valproate and trichostatin A are toxic to neuroblastoma cells and modulate cytochrome P450 1A1, 1B1 and 3A4 expression in these cells

Histone deacetylase inhibitors such as valproic acid (VPA) and trichostatin A (TSA) were shown to exert antitumor activity. Here, the toxicity of both drugs to human neuroblastoma cell lines was investigated using MTT test, and IC50 values for both compounds were determined. Another target of this work was to evaluate the effects of both drugs on expression of cytochrome P450 (CYP) 1A1, 1B1 and 3A4 enzymes, which are known to be expressed in neuroblastoma cells. A malignant subset of neuroblastoma cells, so-called N-type cells (UKF-NB-3 cells) and the more benign S-type neuroblastoma cells (UKF-NB-4 and SK-N-AS cell lines) were studied from both two points of view. VPA and TSA inhibited the growth of neuroblastoma cells in a dose-dependent manner. The IC50 values ranging from 1.0 to 2.8 mM and from 69.8 to 129.4 nM were found for VPA and TSA, respectively. Of the neuroblastoma tested here, the N-type UKF-NB-3 cell line was the most sensitive to both drugs. The different effects of VPA and TSA were found on expression of CYP1A1, 1B1 and 3A4 enzymes in individual neuroblastoma cells tested in the study. Protein expression of all these CYP enzymes in the S-type SK-N-AS cell line was not influenced by either of studied drugs. On the contrary, in another S-type cell line, UKF-NB-4, VPA and TSA induced expression of CYP1A1, depressed levels of CYP1B1 and had no effect on expression levels of CYP3A4 enzyme. In the N-type UKF-NB-3 cell line, the expression of CYP1A1 was strongly induced, while that of CYP1B1 depressed by VPA and TSA. VPA also induced the expression of CYP3A4 in this neuroblastoma cell line

Intervenção psicológica em terminalidade e morte: relato de experiência

O presente artigo objetivou analisar e refletir sobre a atuação do psicólogo em situações de morte no contexto hospitalar, bem como sobre o processo de terminalidade e despedida para as pessoas enfermas e seus familiares. Utilizou-se relato de experiência profissional através de estudo de caso. Os resultados evidenciaram reconfiguração das relações familiares nos diferentes papéis e funções, na perspectiva de maior autonomia. O ritual de despedida constitui-se em vivência possibilitadora de mudanças e resgates das relações familiares, bem como de elaboração do processo de luto, tanto para o sujeito doente e família quanto para a equipe de saúde

Mitochondrial Fragmentation Is Involved in Methamphetamine-Induced Cell Death in Rat Hippocampal Neural Progenitor Cells

Methamphetamine (METH) induces neurodegeneration through damage and apoptosis of dopaminergic nerve terminals and striatal cells, presumably via cross-talk between the endoplasmic reticulum and mitochondria-dependent death cascades. However, the effects of METH on neural progenitor cells (NPC), an important reservoir for replacing neurons and glia during development and injury, remain elusive. Using a rat hippocampal NPC (rhNPC) culture, we characterized the METH-induced mitochondrial fragmentation, apoptosis, and its related signaling mechanism through immunocytochemistry, flow cytometry, and Western blotting. We observed that METH induced rhNPC mitochondrial fragmentation, apoptosis, and inhibited cell proliferation. The mitochondrial fission protein dynamin-related protein 1 (Drp1) and reactive oxygen species (ROS), but not calcium (Ca2+) influx, were involved in the regulation of METH-induced mitochondrial fragmentation. Furthermore, our results indicated that dysregulation of ROS contributed to the oligomerization and translocation of Drp1, resulting in mitochondrial fragmentation in rhNPC. Taken together, our data demonstrate that METH-mediated ROS generation results in the dysregulation of Drp1, which leads to mitochondrial fragmentation and subsequent apoptosis in rhNPC. This provides a potential mechanism for METH-related neurodegenerative disorders, and also provides insight into therapeutic strategies for the neurodegenerative effects of METH

Evidence of coexistence of change of caged dynamics at Tg and the dynamic transition at Td in solvated proteins

Mossbauer spectroscopy and neutron scattering measurements on proteins embedded in solvents including water and aqueous mixtures have emphasized the observation of the distinctive temperature dependence of the atomic mean square displacements, , commonly referred to as the dynamic transition at some temperature Td. At low temperatures, increases slowly, but it assume stronger temperature dependence after crossing Td, which depends on the time/frequency resolution of the spectrometer. Various authors have made connection of the dynamics of solvated proteins including the dynamic transition to that of glass-forming substances. Notwithstanding, no connection is made to the similar change of temperature dependence of obtained by quasielastic neutron scattering when crossing the glass transition temperature Tg, generally observed in inorganic, organic and polymeric glass-formers. Evidences are presented to show that such change of the temperature dependence of from neutron scattering at Tg is present in hydrated or solvated proteins, as well as in the solvents used unsurprisingly since the latter is just another organic glass-formers. The obtained by neutron scattering at not so low temperatures has contributions from the dissipation of molecules while caged by the anharmonic intermolecular potential at times before dissolution of cages by the onset of the Johari-Goldstein beta-relaxation. The universal change of at Tg of glass-formers had been rationalized by sensitivity to change in volume and entropy of the beta-relaxation, which is passed onto the dissipation of the caged molecules and its contribution to . The same rationalization applies to hydrated and solvated proteins for the observed change of at Tg.Comment: 28 pages, 10 figures, 1 Tabl