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.     

A new approach to gradient geomagnetic sounding

A spherical model of the Earth including a heterogeneous upper mantle and excited by the magnetic field of a magnetospheric ring current is constructed. The obtained synthetic data are used for testing a new approach to gradient geomagnetic sounding ensuring the immunity of the sought impedance to distortions caused by lateral heterogeneity of the Earth. It is shown that this approach significantly increases the informativeness of deep electromagnetic sounding.     

Estimation of the correlation between magnetotelluric and geothermal data in the Bishkek geodynamic research area

The paper analyzes the correlation between the electrical conductivity and temperature in the upper crust of the Bishkek geodynamic research area (the Northern Tien Shan). Electrical conductivity profiles constructed from magnetotelluric data and thermograms from the boreholes near magnetotelluric sounding (MTS) points are used for estimations. The correlation analysis of conductivity and temperature profiles to depths of 3–4 km showed that, first, the correlation coefficients do not depend on the distance between the borehole and the nearest MTS point; second, the good correlation between the conductivity and temperature observed for the majority of borehole-MTS point pairs is accounted for by the fact that the study parameters vary with depth in a manner normal for laminated sedimentary rocks; and, third, a low correlation is due to specific features of the geological structure between the borehole and MTS point under consideration.     

Paleomagnetic correlation of sedimentary sequences: The use of secular geomagnetic variations for the differentiation and correlation of Holocene Aral Sea deposits

The paper presents results demonstrating the possibility of using data on paleosecular magnetic variations for correlation of young deposits. Using Holocene deposits of the Aral Sea as an example, it is shown that the combination of paleo-and petromagnetic data can be used to reliably correlate sections in presently isolated parts of a basin, as well as to correlate paleohydrologic events and estimate their age with regard for absolute radiocarbon datings. It is established that the most significant drop in the Aral Sea level occurred more than 2000–2500 yr ago and less significant drops that occurred later are dated at about 1500, 750–1050, and 270–500 yr ago.     

Interpretation of experimental data on HF propagation on the St. Petersburg-Spitsbergen path

The experimental ionograms of the oblique-incidence sounding of the ionosphere, obtained on the St. Petersburg-Spitsbergen high-latitude HF radio path during the magnetically quiet period December 14–15, 2001, are compared with the model calculations of radiowave trajectories. For this purpose, the corresponding oblique-incidence ionograms are numerically synthesized using the technique based on the shooting method and the computer program for constructing HF radiowave trajectories. The three-dimensional electron density distribution, calculated using the mathematical model of the high-latitude ionosphere previously developed at the Polar Geophysical Institute (PGI), is used to model radio propagation. The numerical calculations make it possible mainly to explain the specific features of the experimental data on the oblique-incidence sounding of the ionosphere.     

Field-aligned currents of zones 1 and 2 in the magnetosphere according to the experimental data

The discrepancy between the model and measured magnetic fields, which can be described by the contribution of field-aligned currents, has been determined. The division of the initial data array into the individual data sets with different IMF values makes it possible to estimate the dependence of field-aligned currents on IMF.     

Parameter identification of framed structures using an improved finite element model‐updating method—Part I: formulation and verification

In this study, we formulate an improved finite element model‐updating method to address the numerical difficulties associated with ill conditioning and rank deficiency. These complications are frequently encountered model‐updating problems, and occur when the identification of a larger number of physical parameters is attempted than that warranted by the information content of the experimental data. Based on the standard bounded variables least‐squares (BVLS) method, which incorporates the usual upper/lower‐bound constraints, the proposed method (henceforth referred to as BVLSrc) is equipped with novel sensitivity‐based relative constraints. The relative constraints are automatically constructed using the correlation coefficients between the sensitivity vectors of updating parameters. The veracity and effectiveness of BVLSrc is investigated through the simulated, yet realistic, forced‐vibration testing of a simple framed structure using its frequency response function as input data. By comparing the results of BVLSrc with those obtained via (the competing) pure BVLS and regularization methods, we show that BVLSrc and regularization methods yield approximate solutions with similar and sufficiently high accuracy, while pure BVLS method yields physically inadmissible solutions. We further demonstrate that BVLSrc is computationally more efficient, because, unlike regularization methods, it does not require the laborious a priori calculations to determine an optimal penalty parameter, and its results are far less sensitive to the initial estimates of the updating parameters. Copyright © 2006 John Wiley & Sons, Ltd.