the two loop sunrise graph in two space time dimensions with arbitrary masses in terms of elliptic dilogarithms we present the two loop sunrise integral with arbitrary non zero masses in two space time dimensions in terms of elliptic dilogarithms we find that the structure of the result is as simple and elegant as in the equal mass case only the arguments of the elliptic dilogarithms are modified these arguments have a nice geometric interpretation

the two loop sunrise integral around four space time dimensions and generalisations of the clausen and glaisher functions towards the elliptic case we present the result for the finite part of the two loop sunrise integral with unequal masses in four space time dimensions in terms of the o e0 part and the o e1 part of the sunrise integral around two space time dimensions the latter two integrals are given in terms of elliptic generalisations of clausen and glaisher functions interesting aspects of the result for the o e1 part of the sunrise integral around two space time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms

three dimensional modeling of ip effects in time domain electromagnetic data understanding the effects of induced polarization ip effects on time domain electromagnetic data requires the ability to simulate common survey techniques when taking chargeability into account most existing techniques preform this modeling in the frequency domain prior to transforming their results to the time domain even though this technique can allow for chargeable material to be easily incorporated its application for some problems can be computationally limiting we developed a new technique for forward modeling the time domain electromagnetic response of chargeable materials in three dimensions the frequency dependence of ohms law translates to an ordinary differential equation when considered in the time domain the system of ordinary partial differential equations was then discretized using an implicit time stepping algorithm that yielded absolute stability this approach allowed us to operate directly in the time domain and avoid frequency to time domain transformations although this approach can be applied directly to materials exhibiting debye dispersions other cole cole dispersions resulted in fractional derivatives in time to overcome this difficulty pade approximations were used to represent the frequency dependence as a rational series of integer order terms the resulting method was then simplified to generate a reduced time domain model that can be used to forward model the ip decay curves in the absence of any electromagnetic coupling we found numerical examples in which the method produced accurate results the potential application of the method was demonstrated by modeling the full time domain electromagnetic response of a gradient array ip survey and the occurrence of negative transients in airborne time domain electromagnetic data

relations between elliptic multiple zeta values and a special derivation algebra we investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length our method is based on representing elliptic multiple zeta values as iterated integrals over eisenstein series and exploiting the connection with a special derivation algebra its commutator relations give rise to constraints on the iterated integrals over eisenstein series relevant for elliptic multiple zeta values and thereby allow to count the indecomposable representatives conversely the above connection suggests apparently new relations in the derivation algebra under https tools aei mpg de emzv we provide relations for elliptic multiple zeta values over a wide range of weights and lengths ar x iv 1 50 7 02 25 4v 1 he pth 8 j ul 2 01 5

the complexity of some polynomial network consistency algorithms for constraint satisfaction problems abstract constraint satisfaction problems play a central role in artificial intelligence a class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described we analyze the time complexity of several node arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints the waltz filtering algorithm is a special case of the arc consistency algorithm in the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables

transient electromagnetic inversion a remedy for magnetotelluric static shifts surficial bodies can severely distort magnetotelluric mt apparent resistivity data to arbitrarily low frequencies this distortion known as the mt static shift is due to an electric field generated from boundary charges on surficial inhomogeneities and persists throughout the entire mt recording range static shifts are manifested in the data as vertical parallel shifts of log log apparent resistivity sounding curves the impedance phase being unaffected using a three dimensional 3 d numerical modeling algorithm simulated mt data with finite length electrode arrays are generated significant static shifts are produced in this simulation however for some geometries they are impossible to identify techniques such as spatial averaging and electromagnetic array profiling emap are effective in removing static shifts but they are expensive especially for correcting a previously collected mt data set parametric representation and use of a single invariant quantity such as the impedance tensor

exploiting functional dependencies in declarative problem specifications in this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications functional dependencies arise frequently in pure declarative specifications because of the intermediate results that need to be computed in order to express some of the constraints or due to precise modeling choices e g to provide multiple viewpoints of the search space in order to increase constraint propagation in either way the recognition of dependencies greatly helps solvers allowing them to avoid spending search on unfruitful branches while maintaining the highest degree of declarativeness by modeling constraint problem specifications as second order formulae we provide a characterization of functional dependencies in terms of semantic properties of first order ones and prove undecidability of the problem of their recognition despite such negative result we advocate the in many cases effective possibility of using automated tools to mechanize this task additionally we show how suitable search procedures can be automatically synthesized in order to exploit recognized dependencies we present opl examples of various problems taken from bio informatics planning and resource allocation and show how in many cases opl greatly benefits from the addition of such search procedures moreover we also give evidence that writing sophisticated ad hoc search procedures that handle dependencies exploiting the peculiarities of the particular problem is a very difficult and error prone task which in many cases does not seem to pay off

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

time domain modeling of electromagnetic diffusion with a frequency domain code we modeled time domain em measurements of induction currents for marine and land applications with a frequency domain code an analysis of the computational complexity of a number of numerical methods shows that frequency domain modeling followed by a fourier transform is an attractive choice if a sufficiently powerful solver is available a recently developed robust multigrid solver meets this requirement an interpolation criterion determined the automatic selection of frequencies the skin depth controlled the construction of the computational grid at each frequency tests of the method against exact solutions for some simple problems and a realistic marine example demonstrate that a limited number of frequencies suffice to provide time domain solutions after piecewise cubic hermite interpolation and a fast fourier transform

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

three dimensional magnetotelluric modeling using difference equations theory and comparisons to integral equation solutions we have developed an algorithm for computing the magnetotelluric response of three dimensional 3 d earth models it is a difference equation algorithm that is based on the integral forms of maxwell s equations rather than the differential forms this formulation does not require approximating derivatives of earth properties or electromagnetic fields as happens when using the second order vector diffusion equation rather one must determine how averages are to be computed side boundary values for the h fields are obtained from putting two dimensional 2 d slices of the model into a larger scale 2 d model and solving for the fields at the 3 d boundary positions to solve the 3 d system of equations we propagate an impedance matrix which relates all the horizontal e fields in a layer to all the horizontal h fields in that same layer up through the earth model applying a plane wave source condition and the side boundary h field values allows us to solve for the unknown fields within the model the r

a comparison of structural csp decomposition methods abstract we compare tractable classes of constraint satisfaction problems csps we first give a uniform presentation of the major structural csp decomposition methods we then introduce a new class of tractable csps based on the concept of hypertree decomposition recently developed in database theory and analyze the cost of solving csps having bounded hypertree width we provide a framework for comparing parametric decomposition based methods according to tractability criteria and compare the most relevant methods we show that the method of hypertree decomposition dominates the others in the case of general csps i e csps of unbounded arity we also make comparisons for the restricted case of binary csps finally we consider the application of decomposition methods to the dual graph of a hypergraph in fact this technique is often used to exploit binary decomposition methods for nonbinary csps however even in this case the hypertree decomposition method turns out to be the most general method

electromagnetic modeling of three dimensional bodies in layered earths using integral equations we have developed an algorithm based on the method of integral equations to simulate the electromagnetic responses of three dimensional bodies in layered earths the inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions a matrix equation is constructed using the electric tensor green s function appropriate to a layered earth and it is solved for the vector current in each cell subsequently scattered fields are found by integrating electric and magnetic tensor green s functions over the scattering currents efficient evaluation of the tensor green s functions is a major consideration in reducing computation time we find that tabulation and interpolation of the six electric and five magnetic hankel transforms defining the secondary green s functions is preferable to any direct hankel transform calculation using linear filters a comparison of responses over elongate three dimensional 3 d bodies with responses over two dimensional 2 d bodie

fixed parameter complexity in ai and nonmonotonic reasoning many relevant intractable problems become tractable if some problem parameter is fixed however various problems exhibit very different computational properties depending on how the runtime required for solving them is related to the fixed parameter chosen the theory of parameterized complexity deals with such issues and provides general techniques for identifying fixed parameter tractable and fixed parameter intractable problems we study the parameterized complexity of various problems in ai and nonmonotonic reasoning we show that a number of relevant parameterized problems in these areas are fixed parameter tractable among these problems are constraint satisfaction problems with bounded treewidth and fixed domain restricted forms of conjunctive database queries restricted satisfiability problems propositional logic programming under the stable model semantics where the parameter is the dimension of a feedback vertex set of the program s dependency graph and circumscriptive inference from a positive k cnf restricted to models of bounded size we also show that circumscriptive inference from a general propositional theory when the attention is restricted to models of bounded size is fixed parameter intractable and is actually complete for a novel fixed parameter complexity class

integral equation solution for the transient electromagnetic response of a three dimensional body in a conductive half space the time domain integral equation for the three dimensional vector electric field is formulated as a convolution of the scattering current with the tensor green s function the convolution integral is divided into a sum of integrals over successive time steps so that a numerical scheme can be formulated with a time stepping approximation of the convolution of past values of the solution with the system impulse response this together with spatial discretization leads to a matrix equation in which previous solution vectors are multiplied by a series of matrices and fed back into the system by adding to the primary field source vector the spatial discretization based on a modification of the usual pulse basis formulation in the frequency domain includes an additional subset of divergence free basis functions generated by integrating the green s function around concentric closed rectangular paths the inductive response of the body is more accurately modeled with these additional basis functions and a

comparison of integral equation and physical scale modeling of the electromagnetic responses of models with large conductivity contrasts acomparison is made between the results from two different approachestomodelinggeophysicalelectromagneticresponses anumericalapproachbasedupontheelectric fieldintegralequation and the physical scale modeling approach the particular implementation of the integral equation solution was developed recently and the comparison presented here is essentially a test of this new formulation the implementation approximates the regionofanomalousconductivitybyameshofuniformcuboidal cells and approximates the total electric field within a cell by a linear combination of bilinear edge element basis functions these basis functions give a representation of the electric field that is divergence free but not curl free within a cell and whose tangential component is continuous between cells the charge density which arises from the discontinuity of the normal component of the electric field across interfaces between cells of different conductivities and between cells and the background is incorporatedinasimilarmannertointegralequationsolutionsto dc resistivity modeling the scenarios considered for the comparisoncompriseagraphitecubeof6 3 10 4 s m conductivity and14 cmlengthinfreespaceandinbrine7 3 s m conductivity the transmitter and receiver were small horizontal loops measurements and computations were made for various fixed transmitter receiver separations and various heights of the transmitter receiver pair for frequencies ranging from 1 400 khz the agreement between the numerical results from the integralequation implementation and the measurements from the physicalscalemodelingwasverygood contributingtotheverification of this particular implementation of the integral equation solutiontoelectromagneticmodeling

geophysical application of a new surface integral equation method for em modeling we describe some 3 d electromagnetic em geophysical applications of a new frequency domain iterative surface integral equation sie method the new method is formulated by applying the scalar green s theorem to the three cartesian components of the magnetic field individually the boundary conditions are implemented through iterations the convergence behavior of the iteration is demonstrated explicitly through an example frequency domain results for a number of simple geophysical models are given the transient response of one model obtained via inverse fourier transform is shown to be consistent with previously published results the method is found to be stable for a wide range of conductivity contrasts and capable of giving reasonable descriptions of the em response from the resistive limit up to the inductive limit

a quasi 3d thin stratified medium fast multipole algorithm for microstrip structures an accurate and efficient full wave simulation method is proposed for general microstrip structures it is called the quasi 3d thin stratified medium fast multipole algorithm tsm fma different from the 2d tsm fma method it is constructed on a vector wave function based dyadic green s function for layered medium dglm instead of the symmetric form dglm this new form of dglm is represented in terms of only two sommerfeld integrals and is suitable for developing fast algorithm in quasi 3d cases similar to the 2d tsm fma the path deformation technique and the multipole based acceleration is used to transform the sommerfeld integral and expedite the matrix vector multiplication the computational time per iteration and the memory requirement is o nlogn in the quasi 3d tsm fma it is suitable to perform a full wave analysis of a large microstrip array with less computational resource

two dimensional transient electromagnetic responses the time domain electromagnetic tem modeling method of oristaglio and hohmann is reformulated here in terms of the secondary field this finite difference method gives a direct explicit time domain solution for a two dimensional body in a conductive earth by advancing the field in time with dufort frankel time differencing as a result solving for the secondary field defined as the difference between the total field and field of a half space is not only more efficient but is also simpler and eliminates several problems inherent in the solution for the total field for example because the secondary field varies slowly both in space and time it can be modeled on a coarse grid with large time steps in addition for a simple body the field is local therefore because the field can be assumed to satisfy a simple boundary condition in the earth computation is greatly simplified our tests show that for the same accuracy the secondary field solution is roughly five times faster than the total field so

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

decomposing constraint satisfaction problems using database techniques abstract there is a very close relationship between constraint satisfaction problems and the satisfaction of join dependencies in a relational database which is due to a common underlying structure namely a hypergraph by making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new results for constraint satisfaction problems in particular we prove that a constraint satisfaction problem may be decomposed into a number of subproblems precisely when the corresponding hypergraph satisfies a simple condition we show that combining this decomposition approach with existing algorithms can lead to a significant improvement in efficiency

solution of time convolutionary maxwell s equations using parameter dependent krylov subspace reduction we suggest a new algorithm for the solution of the time domain maxwell equations in dispersive media after spacial discretization we obtain a large system of time convolution equations then this system is projected onto a small subspace consisting of the laplace domain solutions for a preselected set of laplace parameters this approach is a generalization of the rational krylov subspace approach for the solution of non dispersive maxwell s systems we show that the projected system preserves such properties of the initial system as stability and passivity as an example we consider the 3d quasistationary induced polarization problem with the cole cole conductivity model important for geophysical oil exploration our numerical experiments show that the introduction of the induced polarization does not have significant effect on convergence

a finite difference time domain solution for three dimensional electromagnetic modeling we have developed a finite difference solution for three dimensional 3 d transient electromagnetic problems the solution steps maxwell s equations in time using a staggered grid technique the time stepping uses a modified version of the du fort frankel method which is explicit and always stable both conductivity and magnetic permeability can be functions of space and the model geometry can be arbitrarily complicated the solution provides both electric and magnetic field responses throughout the earth because it solves the coupled first order maxwell s equations the solution avoids approximating spatial derivatives of physical properties and thus overcomes many related numerical difficulties moreover since the divergence free condition for the magnetic field is incorporated explicitly the solution provides accurate results for the magnetic field at late times an inhomogeneous dirichlet boundary condition is imposed at the surface of the earth while a homogeneous dirichlet condition is employed along the subsurface boundaries numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth order difference method at early times and a second order method at other times numerical checks against analytical integral equation and spectral differential difference solutions show that the solution provides accurate results execution time for a typical model is about 3 5 hours on an ibm 3090 600s computer for computing the field to 10 ms that model contains 100 x 100 x 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry with the smallest grid spacing at 10 m and the highest resistivity at 100 omega m the execution time indicates that the solution is computer intensive but it is valuable in providing much needed insight about tem responses in complicated 3 d situations

constraint propogation techniques for the disjunctive scheduling problem abstract constraint propagation is an elementary method for reducing the search space of combinatorial search and optimization problems which has become more and more important in the last decades the basic idea of constraint propagation is to detect and remove inconsistent variable assignments that cannot participate in any feasible solution through the repeated analysis and evaluation of the variables domains and constraints describing a specific problem instance the contribution of this paper is twofold the first contribution is a description of efficient constraint propagation methods also known as consistency tests for the disjunctive scheduling problem dsp which is a generalization of the classical job shop scheduling problem jsp applying an elementary constraint based approach involving a limited number of search variables we will derive consistency tests that ensure 3 b consistency we will further present and analyze both new and classical consistency tests which to some extent are generalizations of the aforementioned consistency tests involving a higher number of variables but still can be implemented efficiently with a polynomial time complexity further the concepts of energetic reasoning and shaving are analyzed and discussed the other contribution is a classification of the consistency tests derived according to the domain reduction achieved the particular strength of using consistency tests is based on their repeated application so that the knowledge derived is propagated i e reused for acquiring additional knowledge the deduction of this knowledge can be described as the computation of a fixed point since this fixed point depends upon the order of the application of the tests we first derive a necessary condition for its uniqueness we then develop a concept of dominance which enables the comparison of different consistency tests as well as a simple method for proving dominance an extensive comparison of all consistency tests is given quite surprisingly we will find out that some apparently stronger consistency tests are subsumed by apparently weaker ones at the same time an open question regarding the effectiveness of energetic reasoning is answered

mixed tate motives over z we prove that the category of mixed tate motives over z is spanned by the motivic fundamental group of p 1 minus three points we prove a conjecture by m hoffman which states that every multiple zeta value is a q linear combination of n 1 n r where n i 2 3

identification of three dimensional electric conductivity changes from time lapse electromagnetic observations we present a novel solution algorithm for 3d parameter identification based on low frequency electromagnetic data with focus on large scale applications such as monitoring of subsea oil production co 2 sequestration and geothermal systems the proposed solution algorithm is designed to meet challenges related to low parameter sensitivity nonuniqueness of the inverse solutions nonlinearity in the mapping from the data to the parameter space and costly numerical simulations motivated by earlier investigations on the relation between sensitivity nonlinearity and scale the proposed solution approach is based on a reduced composite parameter representation though a reduced representation restricts the solution space flexibility with respect to which parameter functions that can be represented is obtained by facilitating the estimation of the structure and smoothness of the representation itself moreover the resolution of the parameter function is detached from the computational grid and determined as part of the estimation the performance of the proposed solution algorithm is illustrated through numerical examples for identification of underground electric conductivity changes from time lapse electromagnetic observations

is the fast hankel transform faster than quadrature the fast hankel transform fht implemented with digital filters has been the algorithm of choice in em geophysics for a few decades however other disciplines have predominantly relied on methods that break up the hankel transform integral into a sum of partial integrals that are each evaluated with quadrature the convergence of the partial sums is then accelerated through a nonlinear sequence transformation while such a method was proposed for geophysics nearly three decades ago it was demonstrated to be much slower than the fht this work revisits this problem by presenting a new algorithm named quadrature with extrapolation qwe the qwe method recasts the quadrature sum into a form conceptually similar to the fhtapproach by using a fixed point quadrature rule the sum of partial integrals is efficiently accelerated using the shanks transformation computed with wynn s algorithm a matlab implementation of the qwe algorithm is compared with the fht method for accuracy and speed on a suite of relevant modeling problems including frequency domain controlledsource em time domain em and a large loop magnetic source problem surprisingly the qwe method is faster than the fht for all three problems however when the integral needs to be evaluated at many offsets and the lagged convolution variant of the fht is applicable the fht is significantly faster than the qwe method for divergent integrals such as those encountered in the large loop problem the qwe method can provide an accurate answer when the fht method fails

simultaneous joint inversion of amplitude versus offset and controlled source electromagnetic data by implicit representation of common parameter structure abstracti evaluated a simultaneous joint inversion of seismic amplitude versus offset avo and controlled source electromagnetic csem data for fluid flow monitoring a new approach for structure coupled joint inversion was presented in which the coupling of the two data types was obtained by allowing for the direct identification of parameter structure that is shared by the different geophysical model parameters the main idea was to use a composite parameter representation which enables inversion with respect to the parameter magnitude and parameter structure in the current application parameter structure refers to transitions between dominating property values and is represented by the position and shape of the flooding front hence with this approach the position and shape of the flooding front are inverted for directly and the coupling between the different data sets is obtained without the inclusion of an additional penalizing term in the objective function regularization of the inverse pr

the logic of constraint satisfaction the constraint satisfaction problem csp formalization has been a productive tool within artificial intelligence and related areas the finite csp fcsp framework is presented here as a restricted logical calculus within a space of logical representation and reasoning systems fcsp is formulated in a variety of logical settings theorem proving in first order predicate calculus propositional theorem proving and hence sat the prolog and datalog approaches constraint network algorithms a logical interpreter for networks of constraints the constraint logic programming clp paradigm and propositional model finding and hence sat again several standard and some not so standard logical methods can therefore be used to solve these problems by doing this we obtain a specification of the semantics of the common approaches this synthetic treatment also allows algorithms and results from these disparate areas to be imported and specialized to fcsp the special properties of fcsp are exploited to achieve for example completeness and to improve efficiency it also allows export to the related areas by casting csp both as a generalization of fcsp and as a specialization of clp it is observed that some but not all fcsp techniques lift to csp and perhaps thereby to clp various new connections are uncovered in particular between the proof finding approaches and the alternative model finding approaches that have arisen in depiction and diagnosis applications

a logical framework for depiction and image interpretation we propose a logical framework for depiction and interpretation that formalizes image domain knowledge scene domain knowledge and the depiction mapping between the image and scene domains this framework requires three sets of axioms image axioms scene axioms and depiction axioms an interpretation of an image is defined to be a logical model of these axioms n the approach is illustrated by a case study a reconstruction in first order logic of a simplified map understanding program mapsee the reconstruction starts with a description of the map and a specification of general knowledge of maps geographic objects and their depiction relationships for the simple map world we show how the task level specification may be refined to a provably correct implementation by applying model preserving transformations to the initial logical representation to produce a set of propositional formulas the implementation may use known constraint satisfaction techniques to find the set of models of these propositional formulas in addition we sketch preliminary logical treatments for image queries contingent scene knowledge ambiguity in image description occlusion complex objects preferred interpretations and image synthesis n this approach provides a formal framework for analyzing and going beyond existing systems such as mapsee and for understanding the use of constraint satisfaction techniques it can be used as a foundation for the specification design and implementation of vision and graphics systems that are correct with respect to the task and algorithm levels

transforming a time domain electromagnetic signal to a frequency domain electromagnetic response using regularization inversion abstractwide applications of time domain electromagnetic tem data require 3d inversion a possible strategy is to use the developed 3d inversion algorithms in frequency domain fd electromagnetic em methods thus the key of the strategy is how to transform the time domain t d em signal into the fd an inversion algorithm has been developed to transform the t d signal into a corresponding fd response in this method a step off current is presumed under this assumption the fourier transform relating the em fd response to the t d signal becomes a sine or cosine transformation using the polynomial approximation method the transformation turns into a linear equation from a set of t d signals fd responses could be obtained by solving these linear equations in the least squares sense to reduce the nonuniqueness of the solution and enhance the solution stability an additional smoothness constraint on the fd response is imposed thus converting the minimization problem into a regularization inver

transient electromagnetic inversion based on an approximate solution to the forward problem a rapid algorithm for forward one dimensional modeling is based on the graphical construction of a multi layered apparent resistivity curve using an appropriate combination of two layered curves a collection of two layered curves is calculated only once for fixed geoelectrical parameters and saved for future use an arbitrary two layered curve within the wide range of the geoelectrical parameters is then obtained by simple interpolation this method reduces computation time over other fast algorithms by at least one order of magnitude in addition it does not produce any significant computation errors in the late stage as do most other methods a maximum relative error of about 10 to 15 percent may occur at a few points usually two to three in the vicinity of the intersection of the two layered curves in most cases however this error does not affect the inversion since the relative contributions of these points to an objective function are small the application of such a rapid forward algorithm al

treatment of singularity in the method of boundary integral equations for 2 5d electromagnetic modeling abstractfast and accurate simulation of responses of electromagnetic logging while drilling tools in 2d and 3d formations is important for further development of the proactive geosteering service which is currently based on the 1d layered model inversion in search of an optimal method of forward simulation we have developed boundary integral equations in a 2d formation model with planar boundaries a peculiarity of the method is that the number of grid nodes required for reaching a certain accuracy and hence the computation time increases as the transmitter approaches the boundary to retain efficiency in the case of transmitter boundary proximity we use the following modification of the method the main term of the calculated electromagnetic field namely the solution for the two layered model corresponding to the closest boundary is calculated by the well known explicit formulas whereas the anomalous field is found from the system of integral equations the modified method is implemented and tes

iterative forward and inverse algorithms based on domain integral equations for three dimensional electric and magnetic objects an iterative approach to full vector three dimensional inverse scattering problems where the unknown objects can have conductivity permittivity and permeability different from the known background medium is discussed since this problem involves a large number of unknowns it has to be solved effectively and efficiently so that the results can be obtained in timely manner the forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations and hence it is also of significant importance in the optimization process of the inverse problem the inverse scattering problem is attacked using the multiplicative regularized contrast source inversion method as known in the literature the complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type furthermore this inverse method has been armed with a weighted l2 norm regularizer which has been included as a multiplicative constraint some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms

inversion of slingram electromagnetic induction data using a born approximation abstractwe present an efficient approximate inversion scheme for near surface loop loop em induction data slingram that can be applied to obtain 2d or 3d models on a normal desktop computer our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half space as a background model the measurements are not required to fulfill the low induction number condition low frequency and conductivity the high efficiency of the method is achieved by invoking the born approximation around a half space background the born approximation renders the forward operator linear the choice of a homogeneous half space yields closed form expressions for the required electromagnetic normal fields it also yields a translationally invariant forward operator i e a highly redundant jacobian in connection with the application of a matrix free conjugate gradient method this allows for very low memory requirements during the inversion even in three dimensions as a cons

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

solution of 3d time domain electromagnetic problems using optimal subspace projection abstracttime domain problems for controlled source electromagnetic exploration require accurate discretization of the solution for multiple spacial and temporal scales therefore forward simulation using conventional computational methods becomes computationally expensive even without accounting for induced polarization ip effects these effects create another complication caused by the presence of a convolution integral in the time domain maxwell system we suggested a novel fast and robust algorithm to solve the 3d time domain electromagnetic em problems that can be considered as a generalization of the spectral lanczos decomposition method the new method also allowed us to incorporate the ip effects without significant cost increase the discretized large scale maxwell system was projected onto a small subspace consisting of the laplace domain solutions the so called parameter dependent krylov subspace for an optimally chosen set of laplace parameters the projected system preserved stabilit

a hybrid fast hankel transform algorithm for electromagnetic modeling a hybrid fast hankel transform algorithm has been developed that uses several complementary features of two existing algorithms anderson s digital filtering or fast hankel transform fht algorithm and chave s quadrature and continued fraction algorithm a hybrid fht subprogram called hybfht written in standard fortran 77 provides a simple user interface to call either subalgorithm the hybrid approach is an attempt to combine the best features of the two subalgorithms in order to minimize the user s coding requirements and to provide fast execution and good accuracy for a large class of electromagnetic problems involving various related hankel transform sets with multiple arguments special cases of hankel transforms of double order and double argument are discussed where use of hybfht is shown to be advantageous for oscillatory kernel functions

efficient 2 5d electromagnetic modeling using boundary integral equations abstractfast and accurate simulation of responses of logging while drilling lwd electromagnetic em tools in complex 2d and 3d formations is very important for reconstruction of the resistivity distribution in proactive geosteering currently real time interpretation is based on the 1d parametric inversion advances in fast simulation beyond the 1d model would open a way for real time 2d inversion we developed implemented numerically and tested an efficient method for simulation of lwd em tools in complex 2d formations with an arbitrary 3d position of the tool the method is based on the boundary integral equations for the tangential components of the field and the fourier transform which reduces the problem to a series of 1d integral equations computations are carried out simultaneously for the whole set of measurement points with the same matrix which provides a short computation time per point we verified the method by comparing our results with those obtained by the well known explicit 1d m

three effective inverse laplace transform algorithms for computing time domain electromagnetic responses abstractthe inverse laplace transform is one of the methods used to obtain time domain electromagnetic em responses in geophysics the gaver stehfest algorithm has so far been the most popular technique to compute the laplace transform in the context of transient electromagnetics however the accuracy of the gaver stehfest algorithm even when using double precision arithmetic is relatively low at late times due to round off errors to overcome this issue we have applied variable precision arithmetic in the matlab computing environment to an implementation of the gaver stehfest algorithm this approach has proved to be effective in terms of improving accuracy but it is computationally expensive in addition the gaver stehfest algorithm is significantly problem dependent therefore we have turned our attention to two other algorithms for computing inverse laplace transforms namely the euler and talbot algorithms using as examples the responses for central loop fixed loop and horizontal electri

variational bayesian inversion of synthetic 3d controlled source electromagnetic geophysical data abstractinversion of controlled source electromagnetic data is dealt with for a geophysical application the goal is to retrieve a map of conductivity of an unknown body embedded in a layered underground from measurements of the scattered electric field that results from its interaction with a known interrogating wave this constitutes an inverse scattering problem whose associated forward problem is described by means of electric field domain integral equations the inverse problem is solved in a bayesian framework in which prior information is introduced via a gauss markov potts model this model describes the body as being composed of a finite number of different materials distributed into compact homogeneous regions the posterior distribution of the unknowns is approached by means of the variational bayesian approximation as a separable distribution that minimizes the kullback leibler divergence with respect to the posterior law thus we get a parametric model for the distributions of the induced cu

crosswell electromagnetic inversion using integral and differential equations the crosswell electromagnetic em inverse problem is solved with an integral equation ie formulation using successive born approximations in the frequency domain because the inverse problem is nonlinear the predicted fields and green s functions are continually updated updating the fields and green s functions relates small changes in the predicted data to small changes in the model parameters through frechet kernels these fields and green functions are calculated with an efficient 3 d finite difference solver since the resistivity is invariant along strike the 3 d fields are integrated along strike so the 2 d kernels can be assembled at the early stages of the inversion smoothing of the electrical conductivity stabilizes the inverse solution when it is far from convergence as the solution converges this smoothing is relaxed and more effort is made to reduce the data misfit bounds on the conductivity are included in the solution to eliminate unrealistic estimates the robustness of the inver

conjugate direction relaxation solutions for 3 d magnetotelluric modeling in recent years there has been a tremendous amount of progress made in three dimensional 3 d magnetotelluric modeling algorithms much of this work has been devoted to the integral equation technique e g hohmann 1975 weidelt 1975 wannamaker et al 1984 wannamaker 1991 this method has contributed significantly to our understanding of electromagnetic field behavior in 3 d models however some of the very earliest work in 3 d modeling concentrated on differential methods e g jones and pascoe 1972 reddy et al 1977 it is generally recognized that differential methods are better suited than integral equation methods to model arbitrarily complex geometries and consequently this area has recently been receiving a great deal of attention e g madden and mackie 1989 xinghua et al 1991 mackie et al 1993 smith 1992 personnal communication differential methods lead to large sparse systems of equations to be solved for the unknown field values it is possible to use relaxation al

constraint satisfaction from a deductive viewpoint research note abstract this paper reports the result of testing the author s proof techniques on the class of constraint satisfaction problems csps this experiment has been successful in the sense that a completely general proof technique turns out to behave well also for this special class of problems which itself has received considerable attention in the community so at the same time the paper happens to present a new deductive mechanism for solving constraint satisfaction problems that is of interest in its own right this mechanism may be characterized as a bottom up lazy evaluation technique which reduces any such problem to the problem of evaluating a database expression typically involving a number of joins a way of computing such an expression is proposed

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

quasi analytical method for frequency to time conversion in csem applications frequency to time transformations are of interest to controlled source electromagnetic methods when time domain data are inverted for a subsurface resistivity model by numerical frequency domain modeling at a selected small number of frequencies whereas the data misfit is determined in the time domain we propose an efficient prony type method using frequency domain diffusive field basis functions for which the time domain equivalents are known diffusive fields are characterized by an exponential part whose argument is proportional to the square root of frequency and a part that is polynomial in integer powers of the square root of frequency data at a limited number of frequencies suffice for the transformation back to the time in the exponential part several diffusion time values must be chosen once a suitable range of diffusion time values are found the method is quite robust in the number of values used the highest power in the polynomial part can be determined from the source and receiver type when the frequency domain data are accurately approximated by the basis functions the timedomain result is also accurate this method is accurate over a wider time range than other methods and has the correct late time asymptotic behavior the method works well for data computed for layered and 3d subsurface models

a parallel finite difference approach for 3d transient electromagnetic modeling with galvanic sources a parallel finite difference algorithm for the solution of diffusive three dimensional 3d transient electromagnetic field simulations is presented the purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources grounded wires over arbitrarily complicated distributions of conductivity and magnetic permeability using a staggered grid and a modified dufort frankel method the scheme steps maxwell s equations in time electric field initialization is done by a conjugate gradient solution of a 3d poisson problem as is common in 3d resistivity modeling instead of calculating the initial magnetic field directly its time derivative and curl are employed in order to advance the electric field in time a divergence free condition is enforced for both the magnetic field time derivative and the total conduction current density providing accurate results at late times in order to simulate large realistic earth models the algorithm has been designed to run on parallel computer platforms the upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two dimensional parallel fast fourier transform example simulations are compared with analytical integral equation and spectral lanczos decomposition solutions and demonstrate the accuracy of the scheme

a finite element solution for the transient electromagnetic response of an arbitrary two dimensional resistivity distribution we present a numerical method for solving maxwell s equations in the case of an arbitrary two dimensional resistivity distribution excited by an infinite current line the electric field is computed directly in the time domain the computations are carried out in the lower half space only because exact boundary conditions are used on the free surface the algorithm follows the finite element approach which leads after space discretization to an equation system with a sparse matrix time stepping is done with an implicit time scheme at each time step the solution of the equation system is provided by the fast system iccg 0 the resulting algorithm produces good results even when large resistivity contrasts are involved we present a test of the algorithm s performance in the case of a homogeneous earth with a reasonable grid the relative error with respect to the analytical solution does not exceed 1 percent even 2 s after the source is turned off

motivic multiple zeta values and superstring amplitudes the structure of tree level open and closed superstring amplitudes is analyzed for the open superstring amplitude we find a striking and elegant form which allows one to disentangle its expansion into several contributions accounting for different classes of multiple zeta values this form is bolstered by the decomposition of motivic multiple zeta values i e the latter encapsulate the expansion of the superstring amplitude moreover a morphism induced by the coproduct maps the expansion onto a non commutative hopf algebra this map represents a generalization of the symbol of a transcendental function in terms of elements of this hopf algebra the expansion assumes a very simple and symmetric form which carries all the relevant information equipped with these results we can also cast the closed superstring amplitude into a very elegant form

on the parallel complexity of discrete relaxation in constraint satisfaction networks abstract constraint satisfaction networks have been shown to be a very useful tool for knowledge representation in artificial intelligence applications these networks often utilize local constraint propagation techniques to achieve local consistency consistent labeling in vision such methods have been used extensively in the context of image understanding and interpretation as well as planning natural language analysis and truth maintenance systems in this paper we study the parallel complexity of discrete relaxation one of the most commonly used constraint propagation techniques since the constraint propagation procedures such as discrete relaxation appear to operate locally it has been previously believed that the relaxation approach for achieving local consistency has a natural parallel solution our analysis suggests that a parallel solution is unlikely to improve the known sequential solutions by much specifically we prove that the problem solved by discrete relaxation arc consistency is log space complete for p the class of polynomial time deterministic sequential algorithms intuitively this implies that discrete relaxation is inherently sequential and it is unlikely that we can solve the polynomial time version of the consistent labeling problem in logarithmic time by using only a polynomial number of processors some practical implications of our result are discussed we also provide a two way transformation between and or graphs propositional horn satisfiability and local consistency in constraint networks that allows us to develop optimal linear time algorithms for local consistency in constraint networks

3d interpretation of electromagnetic data using a modified extended born approximation we present a new method dubbed the modified extended born approximation meba for efficient three dimensional 3d simulation and inversion of geophysical frequency domain electromagnetic em data for a targeted object lodged in a layered half space based on the integral equation method and modified from an extended born approximation technique the meba method calculates the total electric field in an electrical conductivity inhomogeneity without any need for solving a huge matrix equation this is done by multiplying the background electric field by a depolarization tensor the fourier transform and the convolution theorem are used to dramatically increase the computational efficiency comparisons of meba generated numerical data for tabular targets with data generated by other means are used to verify the scheme and check its range of validity the results indicate that the meba technique yields better accuracy when current channeling in the conductivity anomaly dominates over the induction process the meba algorithm has been incorporated into a least squares inversion scheme which is used to interpret borehole to surface em tomography field data the survey served to monitor the subsurface conductivity change associated with the extraction of a volume of saltwater previously injected into a known aquifer

locating all the modes of green s function for a three layered medium based on the path tracking algorithm through a mathematical analysis on the relationship between the characteristic equations of the microstrip geometry and a configuration with a three layered medium a method based on the path tracking algorithm is proposed for precisely locating all the modes for a three layered medium with moderate thickness including surface wave modes leaky wave modes and improper real modes with this method the difficulty caused by branch points and cuts in the contour integral method could be avoided this method can be applied not only in the discrete complex image method dcim but also in the steepest descent path sdp method the proposed method can be extended to more complicated configurations