Gaussian beams in inhomogeneous media: A review

The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method, which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are twins, though they differ by names. The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered medium.     

叠层橡胶垫基础隔震建筑结构设计方法与应用

简要概括了国内外叠层橡胶垫基础隔震技术的应用发展状况，介绍了隔震结构的各种反应分析模型，对隔震结构设计分析方法进行了讨论，提出了有益的建议，并指出了在《建筑抗震设计规范》（GB50011-2001）关于隔震结构的简化计算方法中存在的诸多不足。结合我国的隔震技术应用现状，引入了两阶段设计法的概念。此方法将有利于提高设计质量，减少设计周期。     

Interpretation of Gravity Anomalies with the Normalized Full Gradient (NFG) Method and an Example

The Normalized Full Gradient (NFG) method which was put forward about 50 years ago has been used for downward continuation of gravity potential data, especially in the former Union of Soviet Socialist Republics. This method nullifies perturbations due to the passage of mass depth during downward continuation. The method depends on the downwards analytical continuation of normalized full gradient values of gravity data. Analytical continuation discriminates certain structural anomalies which cannot be distinguished in the observed gravity field. This method has been used in various petroleum and tectonic studies. The Trapeze method was used for the determination of Fourier coefficients during the application of this method. No other techniques for calculating these coefficients have been used. However, the Filon method was used for the determination of Fourier coefficients during the application of the NFG method in this work. This method, rather than the Trapeze method, should be preferred for indicating abnormal mass resources at the lower harmonics. In this study, the NFG method using the Filon method has been applied the first time to theoretical models of gravity profiles as example field at the Hasankale-Horasan petroleum exploration province where successful results were achieved. Hydrocarbon presence was shown on the NFG sections by the application of NFG downward continuation operations on theoretical models. Important signs of hydrocarbon structure on the NFG section for field and model data at low harmonics are obtained more effectively using this method.     

EM Monitoring of Crustal Processes Including the Use of the Network-MT Observations

There are several kinds of coupling mechanisms which can convert mechanical, chemical or thermal energies due to seismic or volcanic activities into electromagnetic energies. As a result of concentrated efforts in laboratory and theoretical research, the basic relationship between the intensity of electromagnetic sources and changes in mechanical, chemical and thermal state is becoming established. Also with the progress of the electromagnetic simulation techniques, it has been possible to evaluate in situ sensitivity. Based on this progress and also due to extensive improvement in measuring techniques, many field experiments have been performed to elucidate subsurface geophysical processes underlying the preparation stage, onset, and subsequent healing stage of earthquakes and volcanic eruptions. In volcanic studies, many studies have reported the measurement of electromagnetic signals which were successfully interpreted in terms of various driving mechanisms. Although there have been numerous reports about the existence of precursory electromagnetic signals in seismic studies, only a few of them could be successfully explained by the proposed mechanisms, whereas coseismic phenomena are often consistent with those mechanisms including the absence of detectable signals. In many cases, one or two orders of higher sensitivity were required, especially for precursory signals. Generally, electromagnetic methods are more sensitive to near-surface phenomena. It will be necessary to discriminate electromagnetic signals due to these near-surface sources, which often possess no relationship with the crustal activities. Further efforts to enhance in situ sensitivity through improvements in observation techniques and in data processing techniques are recommended. At the same time, multi-disciplinary confirmation against the validity of electromagnetic phenomena will inevitably be necessary. A Network-MT observation technique has been developed to determine large-scale deep electrical conductivity structure. In the method, a telephone line network or purpose-built long baseline cables are utilized to measure voltage differences with long electrode separations. Because of the averaging effect of the electric fields, static shift problems due to small-scale, near-surface lateral heterogeneities can be alleviated. Several field experiments revealed regional scale deep electrical conductivity structures related to slab subduction or its stagnation, which enable us to elucidate underlying physical processes caused by the slab motion. The technique can also be applied to monitor the electric potential field related to crustal activities. The annual variation of the potential field and electrical conductivity in the French Alps were interpreted to be caused by the annual variation of lake water level. The method was also used to monitor the regional scale spatio-temporal variation of the SP field and electrical conductivity before and at the onset of earthquakes and volcanic eruptions.     

An adaptive capacity spectrum method for assessment of bridges subjected to earthquake action

Estimating seismic demands on structures, to predict their performance level with confidence, requires explicit consideration of the structural inelastic behaviour: to this end, the use of nonlinear static procedures is inevitably going to be favoured over complex nonlinear time-history methods. The currently available assessment procedures have been tested predominantly against building frames. A newly derived assessment procedure is proposed within the scope of bridge applications, based on an innovative displacement-based adaptive pushover technique. The procedure, which can be incorporated into a performance-based engineering philosophy, is applicable to MDOF continuous span bridges with flexible or rigid superstructures, and for varying degrees of abutment restraint. As a first application to determine the viability of the proposed procedure, a parametric study is conducted on a ensemble of bridges subjected to earthquake motion. It is shown that, compared to the seismic demand estimated by means of the more accurate nonlinear dynamic analysis tool, the novel static assessment method can lead to the attainment of satisfactory predictions, both in terms of displacement as well as moment demand on members.     

The numerical solution of the Advection-Dispersion Equation: A review of some basic principles

The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme.     

Entropy‐based equation to assess hillslope sediment production

A new equation to assess hillslope sediment production, based on physical and probabilistic approaches, is presented. The equation, which allows the computation of the delivery ratio for every event, considers the physical variables of travel distance, stream power, settling velocity and gross erosion. The probability density function that arises from the new formulation is solved using the principle of maximum entropy. Based on data from five watersheds in both tropical and temperate zones, the new delivery parameter K_v is calibrated and associated with vegetation cover and conservation practice. The proposed equation is rationally based in relation to parameter K_v. The entropy‐based equation was applied to assess sediment yield in two other experimental watersheds, showing good predictability for the set (mean absolute error of 20·8%). No systematic error was found in the analysed data. The entropy‐based equation showed good predictability for long‐term sets of data and for high‐erosivity events, but did not perform well for the low‐erosivity ones. Copyright © 2007 John Wiley & Sons, Ltd.     

Stability and accuracy analysis of outer loop dynamics in real‐time pseudodynamic testing of SDOF systems

Real‐time pseudodynamic (PSD) testing is an experimental technique for evaluating the dynamic behaviour of a complex structure. During the test, when the targeted command displacements are not achieved by the test structure, or a delay in the measured restoring forces from the test structure exists, the reliability of the testing method is impaired. The stability and accuracy of real‐time PSD testing in the presence of amplitude error and a time delay in the restoring force is presented. Systems consisting of an elastic single degree of freedom (SDOF) structure with load‐rate independent and dependent restoring forces are considered. Bode plots are used to assess the effects of amplitude error and a time delay on the steady‐state accuracy of the system. A method called the pseudodelay technique is used to derive the exact solution to the delay differential equation for the critical time delay that causes instability of the system. The solution is expressed in terms of the test structure parameters (mass, damping, stiffness). An error in the restoring force amplitude is shown to degrade the accuracy of a real‐time PSD test but not destabilize the system, while a time delay can lead to instability. Example calculations are performed for determining the critical time delay, and numerical simulations with both a constant delay and variable delay in the restoring force are shown to agree well with the stability limit for the system based on the critical time delay solution. The simulation models are also used to investigate the effects of a time delay in the PSD test of an inelastic SDOF system. The effect of energy dissipation in an inelastic structure increases the limit for the critical time delay, due to the energy removed from the system by the energy dissipation. Copyright © 2007 John Wiley & Sons, Ltd.