Numerical and analogue modelling of induction effects in laterally non-uniform conductors

Modelling of electromagnetic fields in laterally non-uniform geoelectric structures is briefly reviewed. Attention is paid to progress achieved specifically during the last three years in numerical and analogue techniques of solving two- and three-dimensional problems. Some new important results are also mentioned.     

Surface waves in isotropic,laterally inhomogeneous media

Summary Two different viewpoints of the phase velocities of the elastic surface waves in isotropic, laterally inhomogeneous media have led to inconsistent results. Arguments in terms of surface wave modes give the conclusion that the phase velocity is independent of the propagation direction, while the outcome of calculations based on a constructive interference of body waves in a surface layer is that the phase velocity is dependent on the propagation direction. Both arguments are summarized and an error in the calculations giving dependence is pointed out. The calculations and observations of surface wave amplitude changes in laterally inhomogeneous media are also summarized.     

Seismic response of weakly laterally inhomogeneous structure

Summary The seismic response (the transfer properties) of a model consisting of two layers above a homogeneous halfspace, with curved interfaces and continuously laterally varying velocity within the layers is investigated assuming vertical plane SH-wave incidence from below. The frequency response and the synthetic seismograms are computed by the ray and matrix methods. The dependence of the seismic response on the prevailing frequencies of the incident wave, the role of the individual layers in forming the seismic response, as well as the effect of causal absorption are studied.

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Wavefield features of teleseismic receiver function in laterally inhomogeneous media

IntroductionSince1980(s,theteleseismicreceiverfunctionhasbeenbroadlyappliedtoexploringthecrustalanduppermantlestructure.Thatthismethoddrawssomanyattentionsisnotonlybecauseitscheapercostandhighverticalresolution,butalsobecauseitcanbeusedforexploringthelateralvariationofthecrustalstructure.IntheUSnationalresearchprogramofthecontinentaldynamicsmuchemphasiswasgiventothereceiverfunctionmethod(Phinney,1989).Uptonow,the1-Dreceiverfunctioninversiontechniquehasbecomesophisticatedandmanypracticalresul…     

Spectral theory of electromagnetic induction in a radially and laterally inhomogeneous earth

Summary The partial differential equations of electromagnetic induction in a 3-D Earth of inhomogeneous conductivity are reduced to a system of ordinary differential equations of the 2nd order for the spectral coefficients of the field.

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横向非均匀介质多道瑞雷波频散曲线正演

作为近地表横波速度结构成像的主要手段之一,面波多道分析法的正问题研究对现场观测系统设计及后续反演计算具有重要意义.目前面波频散曲线的正演主要分为两类:一是对水平层状介质中面波的本征值问题进行求解,该类方法计算效率高但较难考虑地下介质在横向上的不均匀性;二是基于波动方程的全波场模拟,该类方法在理论上可考虑任意复杂的地质模...     

Seismic response analysis of laterally inhomogeneous ground with emphasis on strains

The objective of this paper is to make it clear how strain behaviors are affected by the lateral inhomogeneity of ground based on both theoretical simulation and array observation of earthquake motions. We use a two-dimensional pseudo-spectral method to numerically obtain strain motions as well as acceleration motions. We applied the method to some model grounds, which have typical inhomogeneity in the horizontal direction, to estimate general features of strains and accelerations. In addition, the technique was also applied to a site where subsurface irregularity is typically found and an array observation system of earthquake motions was densely deployed. In the latter application of the method, we placed emphasis on comparisons between the observed and simulated motions.     

Point source radiation in inhomogeneous anisotropic structures

The ray formulae for the radiation from point sources in unbounded inhomogeneous isotropic as well as anisotropic media consist of two factors. The first one depends fully on the type and orientation of the source and on the parameters of the medium at the source. We call this factor the directivity function. The second factor depends on the parameters of the medium surrounding the source and this factor is the well-known geometrical spreading. The displacement vector and the radiation pattern defined as a modulus of the amplitude of the displacement vector measured on a unit sphere around the source are both proportional to the ratio of the directivity function and the geometrical spreading.For several reasons it is desirable to separate the two mentioned factors. For example, there are methods in exploration seismics, which separate the effects of the geometrical spreading from the observed wave field (so-called true amplitude concept) and thus require the proposed separation. The separation also has an important impact on computer time savings in modeling seismic wave fields generated by point sources by the ray method. For a given position in a given model, it is sufficient to calculate the geometrical spreading only once. A multitude of various types of point sources with a different orientation can then be calculated at negligible additional cost.In numerical examples we show the effects of anisotropy on the geometrical spreading, the directivity and the radiation pattern. Ray synthetic seismograms due to a point source positioned in an anisotropic medium are also presented and compared with seismograms for an isotropic medium.     

Numerical modelling of geoelectric structures using the galerkin and finite elements methods

Summary The Galerkin and finite elements methods are used to model numerically H- and E-polarized electromagnetic fields in inhomogeneous media. The error of approximation is studied and an example of numerical results is given.     

Analysis of source location errors for a magnetic dipole buried in a laterally inhomogeneous conducting earth

Summary A numerical model is used to simulate a vertical magnetic dipole (VMD), with time harmonic excitation, buried under a segmented overburden. Results are presented in terms of readily measured field quantities. Of special interest are the ellipticities of the magnetic field in the vertical and horizontal planes. These turn out to be very sensitive to the lateral variation of the conductivity structure. Other parameters, such as the vertical magnetic field on the surface, are much less influenced. It is suggested that the combination of such measurements should lead to an optimum system for source location in application to mine rescue operations.     

Magnetovariation and magnetotelluric parameters of longitudinally inhomogeneous structures

The analysis of magnetovariation (MV) and magnetotelluric (MT) parameters is performed for the models of elongated structures whose electric conduction varies along the length. The common feature of models with a different ratio of conduction is that MV parameters substantially differ from their two-dimensional counterparts. The same situation is also observed for longitudinal curves of impedance.     

Geometrical spreading of seismic body waves in laterally inhomogeneous media with curved interfaces of the second order

Summary Seismic rays and geometrical spreading in laterally inhomogeneous media are described by a system of ordinary differential equations of the first order. When the ray crosses an interface of the second order, certain quantities in the system change discontinuously. The initial conditions for the system at the point of intersection of the ray with the interface are presented.     

Self-organization of IGW structures in an inhomogeneous ionosphere: 2. Nonlinear vortex structures

The generation and further nonlinear dynamics of internal gravity wave (IGW) structures in a dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) have been studied. The effectiveness of the IGW amplification mechanism during the interaction with an inhomogeneous zonal wind is analyzed based on the corresponding model system of nonlinear dynamic equations constructed in (Aburjania et al., 2013). It has been indicated that IGWs effectively obtain the shear flow energy at the initial linear evolution stage and substantially (by an order of magnitude) increase their amplitude and, correspondingly, energy. The nonlinear self-localization mechanism starts operating with increasing amplitude, and the process terminates with the self-organization of nonlinear solitary strongly localized vortex structures. A new degree of system freedom and the disturbance evolution trend in a medium with a shear flow appear in such a way. Nonlinear IGW structures can be a purely monopoly vortex, a transverse vortex chain, and/or a longitudinal vortex path against the background of an inhomogeneous zonal wind, depending on the shear flow velocity profile. The accumulation of such vortices in the ionospheric medium can generate a strongly turbulent state.     

Electromagnetic fields of a vertical magnetic dipole above a laterally inhomogeneous thin layer of conductive overburden

An analytical formulation is developed for the resultant electromagnetic field of an oscillating vertical magnetic dipole located over a thin conductive sheet of infinite extent. The sheet is characterized by a conductivity-thickness product or conductance d that may be a function of the horizontal coordinates. The system of integral equations arising in the general formulation is simplified greatly when azimuthal symmetry prevails. Numerical results for a Gaussian variation of d in the radial direction are presented for the case of a symmetrically located source. These results are for the fields at the level of the source dipole over the conductive sheet. It is shown that the quadrature response of the sheet is enhanced when there is rapid variation of the conductance. The null in the resultant wave tilt is also found to be shifted toward the direction of increasing conductance.     

Numerical modelling of suspended sediments

The turbulent advection-diffusion mathematical model in three-dimensional space is solved by a mixed finite element finite difference method. Linear finite elements in the vertical direction and central finite differences in the horizontal directions are used coupled with the Galerkin error minimization procedure. The integration in time is performed in fractional steps (one explicit one implicit) by splitting the differential operator. The method is illustrated by application to the three-dimensional movement of suspended sediment. Its accuracy is checked by comparison to analytical solutions and its efficiency is gauged relative to finite elements and implicit finite difference solutions for two-dimensional suspended sediment transport over a dredged channel.     

Comparison between two methods of modelling the flow in a mantle with laterally variable viscosity

Summary Two different spectral methods have recently been used to model the flow driven by harmonic loads in a Newtonian mantle with laterally variable viscosity. The first method, by Zhang and Christensen (1993), transforms the problem with a general three-dimensional viscosity into a series of standard spherically symmetric problems. A different approach has been chosen by Martinec et al. (1993). Their method is based on integral formulation of the problem. The solution, which corresponds to a minimum of the dissipative energy, is found by means of the gradient search. We have tested the efficiency and numerical behaviour of both methods. The results of our tests favour the former method which is found more accurate and significantly faster than the gradient algorithm.     

Numerical modelling of time-harmonic seismic wave fields in simple structures by the gaussian beam method. part I

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Numerical modelling of time-harmonic seismic wave fields in simple structures by the Gaussian beam method. Part II

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Numerical modelling of strain in lava tubes

Received: 5 November 1998 / Accepted: 17 November 1999