surface integral equation method for the analysis of an obliquely stratified half space the radiation of a source in the presence of an obliquely stratified half space is studied using the surface integral equation method a generalized extinction theorem for the obliquely stratified half space problem is derived which gives eight surface integral equations for the fields the green s functions for the stratified media are found by a semianalytical method these surface integral equations can be used to solve the rather complicated two dimensional problem by the one dimensional finite element method fem which saves computer memory and computation time compared to the conventional two dimensional fem for some special cases the results obtained by this method are compared with those obtained by the numerical mode matching method and the fourier integral technique excellent agreement has been observed between them this method is general for any obliquely stratified half space with arbitrarily many layers in each region

a new integral equation method to solve highly nonlinear inverse scattering problems a family of new integral equations nie is proposed in this paper which are transformed from the original lippmann schwinger integral equation it can be shown that the nie can effectively reduce the nonlinearity of inverse scattering problems by reducing the global nonlinear effects introduced by the multiple scattering behaviors in estimating the contrast equipping the previously proposed twofold subspace based optimization method with such nie the new inversion method is able to solve inverse scattering problems with strong scatterers like with high contrast and or large dimensions in terms of wavelength ones furthermore such a family of nie could provide a convenient tool to appraise reconstructed results several representative numerical tests are carried out using both synthetic and experimental data to verify the efficacy of the new inversion method

on a nonlinear elliptic system with symmetric coupling abstract multiplicity results are proved for the nonlinear elliptic system u g v 0 v g u 0 in u v 0 on where r n is a bounded domain with smooth boundary and g r r is a nonlinear c 1 function which satisfies additional conditions no assumption of symmetry on g is imposed extensive use is made of a global version of the lyapunov schmidt reduction method due to castro and lazer and of symmetric versions of the mountain pass theorem

multiple solutions for asymptotically linear elliptic systems in this article we consider cooperative and noncooperative elliptic systems that are asymptotically linear at infinity we obtain infinitely many solutions with small energy if the potential is even if the noncooperative system is resonant both at zero and at infinity then the number of nontrivial solutions depends on the dimension of the eigenspaces between resonant values

three dimensional induction logging problems part i an integral equation solution and model comparisons a 3 d frequency domain solution based on a volume integral equation approach has been implemented to simulate induction log responses in our treatment of the problem we assume that the electrical properties of the bedding as well as the borehole and invasion zones can exhibit transverse anisotropy the solution process uses a krylov subspace iteration to solve the scattering equation which is based on the modified iterative dissipative method internal consistency checks and comparisons with mode matching and finite difference solutions for vertical borehole models demonstrate the accuracy of the solution there are no known analytical solutions for induction log responses arising from deviated boreholes intersecting horizontal bed boundaries to simulate such responses requires the numerical solution of maxwell s equations in three dimensions along with independent tests to validate the solution approach and its accuracy in this paper we compare two independent 3 d frequency domain solutions for the

new spectral lanczos decomposition method for induction modeling in arbitrary 3 d geometry traditional resistivity tools are designed to function in vertical wells in horizontal well environments the interpretation of resistivity logs becomes much more difficult because of the nature of 3 d effects such as highly deviated bed boundaries and invasion the ability to model these 3 d effects numerically can greatly facilitate the understanding of tool response in different formation geometries three dimensional modeling of induction tools requires solving maxwell s equations in a discrete setting either finite element or finite difference the solutions of resulting discretized equations are computationally expensive typically on the order of 30 to 60 minutes per log point on a workstation this is unacceptable if the 3 d modeling code is to be used in interpreting induction logs in this paper we propose a new approach for solutions to maxwell s equations the new method is based on the spectral lanczos decomposition method sldm with krylov subspaces generated from the inverse powers of th

gpbi cg generalized product type methods based on bi cg for solving nonsymmetric linear systems recently bi cgstab as a variant of bi cg has been proposed for solving nonsymmetric linear systems and its attractive convergence behavior has been confirmed in many numerical experiments bi cgstab can be characterized by its residual polynomial which consists of the product of the residual polynomial of bi cg with other polynomials generated from two term recurrence relations in this paper we propose a unified way to generalize a class of product type methods whose residual polynomials can be factored by the residual polynomial of bi cg and other polynomials with standard three term recurrence relations such product type methods which are based on bi cg can be regarded as generalizations of bi cgstab from the unified way the well known variants of the product type methods like cgs bi cgstab bi cgstab2 are reacquired again

diffraction of axisymmetric waves in a borehole by bed boundary discontinuities this paper presents the calculation of the diffraction of axisymmetric borehole waves by bed boundary discontinuities the bed boundary is assumed to be horizontal and the inhomogeneities to be axially symmetric in such a geometry an axially symmetric source will produce only axially symmetric waves since the borehole is an open structure the mode spectrum consists of a discrete part as well as a continuum the scattering of a continuum of waves by bed boundaries is difficult to treat the approach used in the past in treating this class of problem has been approximate in nature or highly numerical such as the finite element method we present here a systematic way to approximate the continuum of modes by discrete modes after discretization the scattering problem can be treated simply since the approach is systematic it allows derivation of the solution to any desired degree of accuracy in theory but in practice it is limited by the computational resources available we also show that our appr

3d magnetotelluric inversion using a limited memory quasi newton optimization the limited memory quasi newton method with simple bounds is used to develop a novel fully 3d magnetotelluric mt inversion technique this nonlinear inversion is based oniterativeminimizationofaclassicaltikhonovregularized penalty function however instead of the usual model space of log resistivities the approach iterates in a model space with simple bounds imposed on the conductivities of the 3d target the method requires storage proportional to 2 ncp n wherenisthenumberofconductivitiestoberecovered and ncp is the number of correction pairs practically only a few these requirements are much less than those imposed byothernewtonmethods whichusuallyrequirestorageproportional ton m orn n where m is the number of data tobeinverted thederivativesofthepenaltyfunctionarecalculated using an adjoint method based on electromagnetic fieldreciprocity theinversioninvolvesallfourentriesofthe mt impedance matrix the x3d integral equation forwardmodeling code is used as an engine for this inversion convergence performance and accuracy of the inversion are demonstrated on synthetic numerical examples after investigating erratic resistivities in the upper part of the model obtainedforoneoftheexamples weconcludethatthestandard tikhonov regularization is not enough to provide consistently smooth underground structures an additional regularizationhelpstoovercometheproblem

a hybrid boundary element finite element approach to modeling plane wave 3d electromagnetic induction responses in the earth a novel hybrid boundary element finite element scheme which is accelerated by an adaptive multi level fast multipole algorithm is presented to simulate 3d plane wave electromagnetic induction responses in the earth the remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large scale complicated geo electromagnetic induction problems to achieve this goal first the galerkin edge based finite element method fem using unstructured meshes is adopted to solve the electric field differential equation in the heterogeneous earth where arbitrary distributions of conductivity magnetic permeability and dielectric permittivity are allowed for second the point collocation boundary element method bem is used to solve a surface integral formula in terms of the reduced electrical vector potential on the arbitrarily shaped air earth interface third to avoid explicit storage of the system matrix arising from large scale problems and to reduce the horrendous time complexity of the product of the system matrix with an initial vector of unknowns the adaptive multilevel fast multipole method is applied this leads to a matrix free form suitable for the application of iterative solvers furthermore a highly sparse problem dependent preconditioner is developed to significantly reduce the number of iterations used by the iterative solvers the efficacy of the presented hybrid scheme is verified on two synthetic examples against different numerical techniques such as goal oriented adaptive finite element methods numerical experiments show that at low frequencies where the quasi static approximation is applicable standard fem methods prove to be superior to our hybrid bem fem solutions in terms of computational time because the fem method requires only a coarse discretization of the air domain and offers an advantageous sparsity of the system matrix at radio magnetotelluric frequencies of a few hundred khz the hybrid bem fem scheme outperforms the fem method because it avoids explicit storage of the system matrices as well as dense volume discretization of the air domain required by fem methods at high frequencies in summary to the best of our knowledge this study is the first attempt at completely removing the air space for large scale complicated electromagnetic induction modeling in the earth

advances in three dimensional magnetotelluric modeling using integral equations recent progress in integral equation modeling of three dimensional magnetotelluric responses includes the ability to simulate 3 d structures which outcrop excluding topography which transect layer interfaces and which extend indefinitely in one or more directions the most important factor in achieving this capability is an accurate treatment of the electric surface charge in particular a previous integro difference formulation for evaluating charges has been abandoned in favor of true surface integrations over the source cells with potential differencing across the field cells in the 3 d body the new procedure constitutes a good approximation to galerkin s method while preserving internal consistency in terms of pulse basis functions to verify outcropping structures juxtaposed conductive and resistive prisms at the surface are simulated and compared to 2 d results an elongate version of the 3 d model shows good agreement with both transverse electric and transverse magnetic modes of the 2 d res

response of a source on top of a vertically stratified half space the solution of the response of a source on top of a horizontally stratified half space is well known however when the half space is vertically stratified the problem can only be solved with numerical methods like the finite element method here a semi analytic approach to solve such a problem is presented the three dimensional variation of the problem is reduced to two dimensional variation by fourier transform in one coordinate variable the remaining two dimensional problem is solved by finding the eigensolution in each of the half spaces the eigensolutions of each region are found from the partial differential equation directly using the same basis set of expansion functions this makes the calculation of the reflection and transmission operators very efficient the reflection and transmission operators account for the mode conversion reflection and transmission of the waves with the reflection and transmission operators the field everywhere can be calculated the solution reduces to that of the sommerfeld s half space problem when the two half spaces are homogeneous

a finite difference frequency domain numerical scheme for the solution of the gust response problem abstract a numerical method is developed for solving subsonic flows with convected three dimensional vortical waves around lifting airfoils the first order method that is presented fully accounts for the distortion effects of the nonuniform mean flow on the convected vorticity the unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the lagrangian coordinates of the mean flow and an irrotational field whose potential satisfies a nonconstant coefficient inhomogeneous convective wave equation using an elliptic coordinate transformation the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the mach number and reduced frequency extensive comparisons are made with known solutions to unsteady vortical flow problems and it is seen that the agreement is in general very good for reduced frequencies ranging from zero to four

a spectral lanczos decomposition method for solving 3 d low frequency electromagnetic diffusion by the finite element method a very efficient three dimensional 3 d solver for the diffusion of the electromagnetic fields in an inhomogeneous medium is described the proposed method employs either the node based or the edge based finite element method fem to discretize maxwell s equations the resultant matrix equation is solved by the spectral lanczos decomposition method sldm which is based on the krylov subspace lanczos approximation of the solution in the frequency domain by analyzing some practical geophysical problems it is shown that the sldm is extremely fast and furthermore the electromagnetic fields at many frequencies can be evaluated by performing the sldm iteration only at the lowest frequency

3d time domain simulation of electromagnetic diffusion phenomena a finite element electric field approach we present a finite element time domain fetd approach for the simulation of 3d electromagnetic em diffusion phenomena the finite element algorithm efficiently simulates transient electric fields and the time derivatives of magneticfields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms to compute transient electromagnetic fields theelectricfielddiffusionequationistransformedinto asystemofdifferentialequationsviagalerkin smethodwith homogeneous dirichlet boundary conditions to ensure numerical stability and an efficient time step the system of the differential equations is discretized in time using an implicit backward euler scheme the resultant fetd matrix vector equation is solved using a sparse direct solver along with a fill inreducedorderingtechnique whenadvancingthesolution in time the fetd algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution to simulate a step off source waveform the 3d fetd algorithm also incorporates a 3d finite element direct current fedcalgorithmthatsolvespoisson sequationusingasecondarypotentialmethodforageneralanisotropicearthmodel examples of controlled source fetd simulations are compared with analytic and or 3d finite difference time domain solutions and are used to confirm the accuracy and efficiencyofthe3dfetdalgorithm

a finite element based domain decomposition approach for plane wave 3d electromagnetic modeling we developed a novel parallel domain decomposition approach for 3d large scale electromagnetic induction modeling in the earth we used the edge based finite element method and unstructured meshes unstructured meshes were divided into sets of nonoverlapping subdomains we used the curl curl electric field equation to carry out the analysis in each subdomain the electric field was discretized by first order vector shape functions along the edges of tetrahedral elements the tangential components of the magnetic field on the interfaces of the subdomains were defined as a set of lagrange multipliers the unknown lagrange multipliers were solved from an interface problem defined on the interfaces of the subdomains with the availability of the lagrange multipliers the electric field values in each subdomain were solved independently three synthetic examples were evaluated to verify our code excellent agreement with previously published solutions was obtained synthetic examples revealed that our domain decomposition technique is scalable with respect to the number of subdomains and robust with regard to frequency and the heterogeneous distribution of material parameters i e electric conductivity electric permittivity and magnetic permeability

compact implicit maccormack type schemes with high accuracy in this work the maccormack methodology is extended to implicit compact differencing schemes a prefactorization method is developed which splits the implicit matrix into two independent upper and lower matrices which are easier to invert using this method a new class of high order accurate compact maccormack type schemes is derived two fourth order schemes are described and results are shown for three linear and nonlinear caa benchmark problems

an efficient finite difference scheme for electromagnetic logging in 3d anisotropic inhomogeneous media we consider a problem of computing the electromagnetic field in 3d anisotropic media for electromagnetic logging the proposed finite difference scheme for maxwell equations has the following new features based on some recent and not so recent developments in numerical analysis coercivity i e the complete discrete analogy of all continuous equations in every grid cell even for nondiagonal conductivity tensors a special conductivity averaging that does not require the grid to be small compared to layering or fractures and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity all of these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3d geometries without sacrificing accuracy

modeling of borehole resistivity measurements using infinite electrical grids an infinite electrical resistive grid generated by a finite difference approximation to poisson s equation in cylindrical coordinates with no azimuthal variation has been used to model borehole resistivity measurements the medium surrounding the borehole is infinite in extent and its resistivity varies only in the radial direction as a result the branch resistance values of the infinite grid also vary only in the radial direction a continued fraction of laurent operators determines the node voltages along the borehole s surface use of an operational calculus based upon the finite fourier transformation converts the continued fraction into a readily computed form this yields new formulas for apparent resistivity given various resistivity measuring arrays and a resistivity profile in the radial direction in contrast to classical methods the need to match boundary conditions at the interface of a cylindrically layered earth is eliminated so that the procedure is just as easily applied to a continuo

conservative modeling of 3 d electromagnetic fields part ii biconjugate gradient solution and an accelerator the preceding paper derives a staggered grid finite difference approximation applicable to electromagnetic induction in the earth the staggered grid finite difference approximation results in a linear system of equations ax b where a is symmetric but not hermitian this is solved using the biconjugate gradient method preconditioned with a modified partial cholesky decomposition of a this method takes advantage of the sparsity of a and converges much more quickly than methods used previously to solve the 3 d induction problem when simulating a conductivity model at a number of frequencies the rate of convergence slows as frequency approaches 0 the convergence rate at low frequencies can be improved by an order of magnitude by alternating the incomplete cholesky preconditioned biconjugate gradient method with a procedure designed to make the approximate solutions conserve current

3d integral equation modeling with a linear dependence on dimensions we have improved the integral equation method for modeling 3d electromagnetic fields by using the separability of its inherent 3 3 dyadic green s tensors conventional integral equation approaches exhibit a quadratic dependence on model size at least for the vertical dimension in contrast our approach has a linear dependence on all three dimensions we tested our method on an example of induction logging in deviated boreholes

fractional diffusion analysis of the electromagnetic field in fractured media part i 2d approach we address a 2d finite difference fd frequency domain modeling algorithm based on the theory of fractional diffusion of electromagnetic em fields which is generated by an infinite line source lying above a fractured geological medium the presence of fractures in the subsurface usually containing highly conductive pore fluids gives rise to spatially hierarchical flow paths of induced em eddy currents the diffusion of em eddy currents in such formations is anomalous generalizing the classical gaussian process described by the conventional maxwell equations based on the continuous time random walk ctrw theory the diffusion of em eddy currents in a rough medium is governed by the fractional maxwell equations here we model the em response of a 2d subsurface containing fractured zones based on the fractional maxwell equations the governing equation in the frequency domain is discretized using the fd approach the resulting equation system is solved by the multifrontal massively parallel solver mumps we find excellent agreement between the fd and analytic solutions for a rough half space model then fd solutions are calculated for a 2d fault zone model with variable conductivity and roughness we illustrate a case in which a rough fault zone would not be resolved by classical diffusion modeling even if its conductivity contrasts with the background

routine 2d inversion of magnetotelluric data using the determinant of the impedance tensor recent developments in the speed and quality of data acquisition using the radiomagnetotelluric rmt method whereby large amounts of broadband rmt data can be collected along profiles have prompted us to develop a strategy for routine inverse modeling using 2d models we build a rather complicated numerical model containing both 2d and 3d elements believed to be representative for shallow conductors in crystalline basement overlain by a thin sedimentary cover we then invert the corresponding synthetic data on selected profiles using both traditional mt approaches as well as the proposed approach which is based on the determinant of the mt impedance tensor we compare the estimated resistivity models with the true models along the selected profiles and find that the traditional approaches often lead to strongly biased models and bad data fit in contrast to those using the determinant in this case much of the bias is removed and the data fit is improved the determinant of the impedance tensor is independent of the chosen strike direction and once the a priori model is set the best fitting model is found to be practically independent of the starting model used we conclude that the determinant of the impedance tensor is a useful tool for routine inverse modeling

3d finite difference frequency domain modeling of controlled source electromagnetic data direct solution and optimization for high accuracy three dimensional modeling of marine controlled source electromagnetic csem data is vital to improve the understanding of electromagnetic em responses collected in increasingly complex geologic settings a modeling tool for simulating 3d marine csem surveys based on a finite difference discretization of the helmholtz equation for the electric fields has been developed optimizations for csem simulations include the use of a frequency domain technique a staggering scheme that reduces inaccuracies especially for horizontal electric dipole sources located near the seafloor and a new interpolation technique that provides highly accurate em field values for receivers located in the immediate vicinity of the seafloor source singularities are eliminated through a secondary field approach in which the primary fields are computed analytically for a homogeneous or a 1d layered background the secondary fields are computed using the finite difference technique exploiting recent advances in computer technology and algorithmic developments the system of finite difference equations is solved using the mumps direct matrix solver in combination with the other optimizations this allows accurate em field computations for moderately sized models on small computer clusters the explicit availability of matrix factorizations is advantageous for multisource modeling and makes the algorithm well suited for future use within an inversion scheme comparisons of simulated data for 1 1d models to data generated using a 1d reflectivity technique and 2 3d models to published 3d data demonstrate the accuracy and benefits of the approach

electromagnetic induction in a generalized 3d anisotropic earth part 2 the lin preconditioner a practical limitation in the use of generalized 3d forward modeling algorithms for inversion of electromagnetic data is the high computational cost of solving large ill conditioned systems of linear equations arising from the discretization of the governing maxwell equations to address this problem a new class of preconditioners has recently been proposed which is based on a helmholtz decomposition of the electric field in the low induction number lin regime this paper further develops that idea and introduces a lin preconditioner which can be applied to problems characterized by a fully generalized anisotropic medium included are sample calculations demonstrating a reduction by two orders of magnitude in the number of quasi minimal residual iterates and a speedup by a factor of approximately four in the solution time for one forward calculation also included are results previously unobtainable by standard jacobi preconditioning for simulating multicomponent induction sonde response in a horizo

finite element analysis of controlled source electromagnetic induction using coulomb gauged potentials a 3 d finite element solution has been used to solve controlled source electromagnetic em induction problems in heterogeneous electrically conducting media the solution is based on a weak formulation of the governing maxwell equations using coulomb gauged em potentials the resulting sparse system of linear algebraic equations is solved efficiently using the quasi minimal residual method with simple jacobi scaling as a preconditioner the main aspects of this work include the implementation of a 3 d cylindrical mesh generator with high quality local mesh refinement and a formulation in terms of secondary em potentials that eliminates singularities introduced by the source these new aspects provide quantitative induction log interpretation for petroleum exploration applications examples are given for 1 d 2 d and 3 d problems and favorable comparisons are presented against other previously published multidimensional em induction codes the method is general and can also be adapted for controlled so

transient electromagnetic response of a three dimensional body in a layered earth the three dimensional 3 d electromagnetic scattering problem is first formulated in the frequency domain in terms of an electric field volume integral equation three dimensional responses are then fourier transformed with sine and cosine digital filters or with the decay spectrum the digital filter technique is applied to a sparsely sampled frequency sounding which is replaced by a cubic spline interpolating function prior to convolution with the digital filters typically 20 to 40 frequencies at five to eight points per decade are required for an accurate solution a calculated transient is usually in error after it has decayed more than six orders in magnitude from early to late time the decay spectrum usually requires ten frequencies for a satisfactory solution however the solution using the decay spectrum appears to be less accurate than the solution using the digital filters particularly after early times checks on the 3 d solution include reciprocity and convergence checks in the frequenc

two dimensional induction log modeling using a coupled mode multiple reflection series method in induction logging both vertical and radial conductivity variations exist in the logged medium elementary separation of variables cannot be applied directly to the partial differential equation describing the electromagnetic field in such a medium a modal expansion method of solution can be designed using modes defined with respect to the vertical coordinate this method breaks the original two dimensional 2 d problem into a set of independent one dimensional 1 d problems the receiver signal is decomposed into a direct signal traveling within the borehole and a reflection signal bearing information about the conductivity distribution outside the borehole the solution is obtained as a coupled mode multiple reflection series accounting for repeated mode reflections at the vertical boundaries in the medium each term in the series represents the next higher order reflection in a sequence of multiple reflections results show two terms are sufficient to reach accuracy acceptable for log modeling

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

a generalized haskell matrix method for borehole electromagnetics theory and applications in borehole electromagnetics both cylindrical and planar interfaces are present leading to nonseparable field equations the problem is two dimensional 2 d and the finite element method is usually employed for solution in this paper the generalized haskell matrix layer eigenstate propagator method is introduced to this class of problems in the method the solution problem is decomposed into a set of one dimensional 1 d problems and then the 1 d solutions are combined to form the final solution the method employs no approximation other than discretization of a continuous system as in all computer methods induction logs are calculated for the 6ff40 tool and a number of models results agree well with those of the finite element method an important case in induction log interpretation is studied namely a three layer formation traversed by a borehole the center layer being an oil bearing resistive layer sandwiched between two conductive shoulder layers simulation shows that conventional c

three dimensional induction logging problems part 2 a finite difference solution a 3 d finite difference solution is implemented for simulating induction log responses in the quasi static limit that include the wellbore and bedding that exhibits transverse anisotropy the finite difference code uses a staggered grid to approximate a vector equation for the electric field the resulting linear system of equations is solved to a predetermined error level using iterative krylov subspace methods to accelerate the solution at low induction numbers lins a new preconditioner is developed this new preconditioner splits the electric field into curl free and divergence free projections which allows for the construction of an approximate inverse operator test examples show up to an order of magnitude increase in speed compared to a simple jacobi preconditioner comparisons with analytical and mode matching solutions demonstrate the accuracy of the algorithm

fourier series expansion in a non orthogonal system of coordinates for the simulation of 3d dc borehole resistivity measurements abstract we describe a new method to simulate 3d borehole resistivity measurements at zero frequency dc the method combines the use of a fourier series expansion in a non orthogonal system of coordinates with an existing 2d goal oriented higher order self adaptive hp finite element algorithm the new method is suitable for simulating measurements acquired with borehole logging instruments in deviated wells it delivers high accuracy simulations and it enables a considerable reduction of the computational complexity with respect to available 3d simulators since the number of fourier modes basis functions needed to solve practical applications is limited typically below 10 furthermore numerical results indicate that the optimal 2d grid based on the 0th fourier mode also called central fourier mode can be employed to efficiently solve the final 3d problem thereby avoiding the expensive construction of optimal 3d grids specifically for a challenging through casing resistivity application we reduce the computational time from several days using a 3d simulator to just 2 h with the new method while gaining accuracy the new simulation method can be easily extended to different physical phenomena with similar geometries as those arising in the simulation of 3d borehole electrodynamics and sonic acoustics coupled with elasticity measurements in addition the method is especially suited for inversion since we demonstrate that the number of fourier modes needed for the exact representation of the materials is limited to only one the central mode for the case of borehole measurements acquired in deviated wells

asymptotically linear system of three equations near resonance abstract this paper deals with the asymptotically linear system u 1 1 u 3 f 1 x u 1 u 2 u 3 in u 2 2 u 2 f 2 x u 1 u 2 u 3 in u 3 3 u 1 f 3 x u 1 u 2 u 3 in u 1 u 2 u 3 0 on where i 0 for i 1 2 3 with 2 1 3 is a real parameter and r n is a bounded domain with smooth boundary the linear part of the system has two simple eigenvalues with nonnegative eigenfunctions each with at least one zero component we provide sufficient conditions which guarantee bifurcation from infinity of positive solutions from both one or none of the two simple eigenvalues under additional assumptions on the nonlinear perturbations we determine the direction of bifurcation as well we use bifurcation theory to establish our results

aerodynamics and interaction noise of streamlined bodies in nonuniform flows abstract the unsteady aerodynamics and interaction noise of streamlined bodies are modeled in terms of the euler equations linearized about a nonuniform flow the validity of the inviscid approach is supported by recent les simulations of an airfoil in a gust indicating that for not too small impinging excitations the interaction process is dominated by inertia forces results in the present paper are focused on the aerodynamics and interaction noise of a turbofan modeled as an annular cascade the model accounts for the inflow fan duct coupling and the high frequency of the interaction process two high order numerical algorithms are developed with body fitted coordinate system one algorithm uses a primitive variable formulation the other uses an efficient velocity splitting algorithm and is suitable for broadband computations analytical and numerical analysis of disturbances in rotational flows is developed and exact inflow outflow boundary conditions are derived yielding directly the radiated acoustics the upstream disturbances evolve in rotational flows and as a result the aerodynamic aeroacoustic response of the annular cascade depends on the initial conditions location computational results show that the three dimensional geometry of the annular cascade the mean flow swirl and the blade geometry have strong influence on the blade sectional lift and the radiated sound these results also show the inadequacy of using the popular linear cascade model particularly for realistic fan geometry and inflow conditions

residual smoothing techniques for iterative methods an iterative method for solving a linear system ax b produces iterates x k with associated residual norms that in general need not decrease smoothly to zero residual smoothing techniques are considered that generate a second sequence y k via a simple relation y k 1 eta k y k 1 eta k x k the authors first review and comment on a technique of this form introduced by schonauer and weiss that results in y k with monotone decreasing residual norms this is referred to as minimal residual smoothing certain relationships between the residuals and residual norms of the biconjugate gradient bcg and quasi minimal residual qmr methods are then noted from which it follows that qmr can be obtained from bcg by a technique of this form this technique is extended to generally applicable quasi minimal residual smoothing the practical performance of these techniques is illustrated in a number of numerical experiments

an asymptotically linear non cooperative elliptic system with lack of compactness in this paper we consider an asymptotically linear non cooperative elliptic system at resonance the functional associated to the system is strongly indefinite and so the morse index of each critical point is infinite to overcome this difficulty we will use morse theory for strongly indefinite functionals developed by abbondandolo we shall prove that if the system has a non resonant solution the morse index of which is different from the morse index at infinity then there exists another solution

3d vector finite element electromagnetic forward modeling for large loop sources using a total field algorithm and unstructured tetrahedral grids abstractunstructured tetrahedral grids with local refinement facilitate the use of total field solution approaches to geophysical electromagnetic em forward problems these approaches when combined with the vector finite element fe method and with refinement near transmitters and receivers can give accurate solutions and can easily handle realistic models with complex geometry and topography we have applied this approach to 3d forward modeling for fixed and moving loop configurations mumps a direct solver was used to solve the linear system of equations generated by fe analysis a direct solver is particularly suited to the moving loop configuration for which the right side is different for every transmitter loop but for which the coefficient matrix is unchanged therefore the coefficient matrix need only be factorized once and then the system can be solved efficiently for all different right sides we compared our results with several typical scenarios from the literature a conductive bric

fast 2d inversion of large borehole em induction data sets with an efficient frechet derivative approximation in addition to reliability and stability the efficiency and expediencyofinversionmethodshavelongbeenastrongconcernfor their routine applications by well log interpreters we have developedandsuccessfullyvalidatedanewinversionmethodtoestimate2dparametricspatialdistributionsofelectricalresistivity from array induction measurements acquired in a vertical well the central component of the method is an efficient approximation to frechet derivatives where both the incident and adjoint fields are precomputed and kept unchanged during inversion to further enhance the overall efficiency of the inversion we combined the new approximation with both the improved numerical mode matching method and domain decomposition examples of application with synthetic data sets show that the new method iscomputerefficientandcapableofretrievingoriginalmodelresistivities even in the presence of noise performing equally well in both high and low contrasts of formation resistivity in thin resistive beds the new inversion method estimates more accurate resistivities than standard commercial deconvolution software we also considered examples of application with field data sets that confirm the new method can successfully process a large data set that includes 200 beds in approximately 40 minutes of cpu time on a desktop computer in addition to 2d parametric spatial distributions of electrical resistivity the new inversion methodprovidesaqualitativeindicatoroftheuncertaintyofestimated parameters based on the estimator s covariance matrix the uncertainty estimator provides a qualitative measure of the nonuniqueness of estimated resistivity parameters when the data misfitlieswithinthemeasurementerrornoise

hybridizing semianalytical and conventional finite element schemes for simulations of electromagnetic borehole resistivity measurement abstracta semianalytical finite element method fem has been developed to simulate electromagnetic borehole resistivity measurements in a layered underground formation a piecewise homogeneous structure is divided into several layers each layer is uniform in the longitudinal direction and the distributions of geometry and material can be arbitrary on the transverse plane or cross section of the layer to develop this semianalytical finite element scheme the standard functional corresponding to the vector wave equation is cast to a new form in the hamiltonian system based on dual variables that are the transverse components of electric and magnetic fields on the cross section of the layer the 2d finite elements are used to discretize the cross section and a high precision integration scheme based on the riccati equations is used to exploit the longitudinal homogeneity in the layer by transforming a 3d layered problem into a series of 2d problems this semianalytical fem can save a great amount of

efficient computation of electromagnetic waves in anisotropic orthogonal plano cylindrically layered media using the improved numerical mode matching nmm method an orthogonal plano cylindrically layered opcl medium consists of materials stratified planarly and layered concentrically in the orthogonal directions the numerical mode matching nmm method has previously been shown to be a fast and robust semianalytical solver to investigate the propagation of electromagnetic em waves in such a complex but isotropic or transversely isotropic medium in this paper several important improvements have been made to extend applications of this efficient solver to the anisotropic ocpl medium the formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application the perfectly matched layer pml is incorporated along the radial direction as an absorbing boundary condition abc to make the nmm method more accurate and efficient for unbounded low conductivity media and applicable to lossless media we manipulate the weak form of maxwell s equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem finally we also offer formulas for computing em fields excited by a magnetic dipole located at any position with an arbitrary orientation numerical results have demonstrated the efficiency and accuracy of this method

an efficient rescaled formulation for tensor green s function computation in cylindrical multilayered media a robust formulation is presented to eliminate overflow underflow and convergence problems that arise the computation of tensor green s functions in cylindrical multilayered media under finite precision arithmetic this is done by first introducing a set of rescaled functions associated to the canonical cylindrical bessel and hankel functions representing standing waves and outgoing waves along the radial direction the rescaled cylindrical functions are designed to avoid the poor scaling inherent to the canonical cylindrical functions for very small or very large arguments in addition a parabolic sommerfeld integration path is constructed in the spectral complex plane to yield a numerical integration with good convergence properties for a wide range of parameter values

a hybrid regularization scheme for the inversion of magnetotelluric data from natural and controlled sources to layer and distortion parameters magnetotelluric mt radiomagnetotelluric rmt and in particular controlled source audiomagnetotelluric csamt data are often heavily distorted by near surface inhomogeneities we developed a

acoustic vorticity waves in swirling flows the propagation of small disturbances in an annular duct with a mean vortical swirling flow is studied the disturbance velocity is split into a nearly convected part and a nearly sonic part obeying weakly coupled equations a normal mode analysis shows that the eigenvalues are segregated into a finite number of propagating pressure dominated nearly sonic waves and a cluster of infinite number of vorticity dominated nearly convected modes a generalized gust can then be identified with the vorticity dominated nearly convected eigensolutions the nearly convected eigenvalues form two branches on either side of a critical layer which corresponds to purely convected modes an asymptotic analysis is used to investigate the stability of the nearly convected eigensolutions in the vicinity of the critical layer