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

3 d numerical mode matching nmm method for resistivity well logging tools a three dimensional 3 d numerical mode matching nmm method is presented for poisson s equation in general inhomogeneons media it reduces the original 3 d problem into a series of two dimensional 2 d eigenvalue problems plus a one dimensional 1 d layered medium problem which can be modeled efficiently by a recursion procedure the algorithm is tested for several 3 d inhomogeneous media and an excellent agreement between the nmm and analytical solutions is obtained for all test cases we demonstrate some typical applications of the 3 d nmm algorithm in resistivity well logging including invasion zones of noncircular shape vertical and horizontal fractures and horizontal wells the solution procedure proposed is directly applicable to wave propagation in 3 d inhomogeneous media

fast computation of exact confidence limits for the common odds ratio in a series of 2 2 tables abstract the odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials we consider calculation of exact confidence limits for the common odds ratio in a series of independent 2 2 tables and propose three modifications of the network algorithm of mehta patel and gray 1 formulating and dealing with the problem in algebraic instead of graph theoretic terms 2 performing convolutions on the natural scale instead of the logarithmic scale and 3 using the secant method instead of binary search to compute roots of polynomial equations enhancement of computational efficiency exceeding an order of magnitude afforded by these modifications is empirically demonstrated we also compare the modified method with one based on the fast fourier transform fft further we show that the fft method can also result in considerable loss of numerical accuracy the modifications proposed in this article yield an algorithm that is not only fast and accurate but that combine

evaluation of exact and asymptotic interval estimators in logistic analysis of matched case control studies we compare six methods for constructing confidence intervals for a single parameter in stratified logistic regression three of these are based on inversion of standard asymptotic tests namely the wald the score and the likelihood ratio tests the other three are based on the exact distribution of the sufficient statistic for the parameter of interest these include the traditional exact method of constructing confidence intervals and two others the mid p and mean p methods which are modifications of this procedure that aim at reducing the conservative bias of the exact method using efficient algorithms the six methods are compared by determination of their exact coverage levels in a series of conditional sample spaces an incident case control study of lung cancer in women is used to further illustrate the differences among the various methods computation of coverage functions is seen as a useful graphical diagnostic tool for assessing the appropriateness of different methods the mid p and the score methods are seen to have better coverage properties than the other four

existence and properties of solutions of a control system with hysteresis effect abstract we consider a control system described by two ordinary nonlinear differential equations subject to a control constraint given by a multivalued mapping with closed nonconvex values which depends on the phase variables one of the equations contains the subdifferential of the indicator function of a closed convex set depending on the unknown phase variable the equation containing the subdifferential describes an input output relation of hysteresis type along with the original control constraint we also consider the convexified control constraint and the constraint consisting of the extremal points of the convexified control constraint we prove the existence of solutions of our control system with various control constraints and establish certain relationships between corresponding solution sets

solution of the fundamental problem in resistivity logging with a hybrid method the fundamental resistivity logging problem of a resistivity tool in the presence of both vertical and horizontal boundaries is solved with a hybrid method the hybrid method combines the mode concept in waveguide theory together with the finite element method in the mathematical formulation the horizontal boundaries are used to separate the geometry of the problem into different regions in each region the waveguide modes are obtained through the solution of an equivalent variational problem the solutions are calculated by a one dimensional finite element method the vertical boundaries are taken into account in these calculations the orthonormality of modes in each region allows a series representation of the potential in the regions boundary conditions at horizontal bed boundaries then couple the modes between different regions and enable the solutions for the potential to be expressed in terms of reflection and transmission matrices of modes the source excitation determines the amplitudes of th

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

improved confidence intervals for the difference between binomial proportions based on paired data existing methods for setting confidence intervals for the difference theta between binomial proportions based on paired data perform inadequately the asymptotic method can produce limits outside the range of validity the exact conditional method can yield an interval which is effectively only one sided both these methods also have poor coverage properties better methods are described based on the profile likelihood obtained by conditionally maximizing the proportion of discordant pairs a refinement methods 5 and 6 which aligns 1 alpha with an aggregate of tail areas produces appropriate coverage properties a computationally simpler method based on the score interval for the single proportion also performs well method 10

binomial confidence intervals abstract for x with binomial n p distribution section 1 gives a one page table of 95 and 99 confidence intervals for p for n 1 2 30 this interval is equivariant under x n x and p 1 p has approximately equal probability tails is approximately unbiased has crow s property of minimizing the sum of the n 1 possible lengths and each of its ends is increasing in x and decreasing in n with about as regular steps as possible sections 2 and 3 consider the usual approximate confidence intervals calculations and asymptotic results show the need for the continuity correction in these even when n is large because of the nonuniformity of the binomial normal convergence as p 0 these intervals fail to have their stated asymptotic confidence coefficients simple corrections are given for this in the approximate interval x n c n x n 1 x n 1 2n it is shown that the factor c n should be replaced by c n c 2 2c n 1 n

bogolyubov type theorem with constraints induced by a control system with hysteresis effect abstract we consider the problem of minimization of an integral functional with nonconvex with respect to the control integrand we minimize our functional over the solution set of a control system described by two ordinary differential equations subject to a control constraint given by a multivalued mapping with closed nonconvex values the coefficients of the equations and the constraint depend on the phase variables one of the equations contains the subdifferential of the indicator function of a closed convex set depending on the unknown phase variable the equation containing the subdifferential describes an input output relation of hysteresis type along with the original problem we also consider the problem of minimizing the integral functional with the convexified with respect to the control integrand over the solution set of the same system with the convexified control constraint under sufficiently general assumptions we prove that this relaxed problem has an optimal solution which is the limit of a minimizing sequence of the original problem the convergence takes place simultaneously with respect to the trajectory the control and the functional and is uniform in appropriate topologies

a quasi exact test for comparing two binomial proportions the use of the fisher exact test for comparing two independent binomial proportions has spawned an extensive controversy in the statistical literature many critics have faulted this test for being highly conservative partly in response to such criticism some statisticians have suggested the use of a modified non randomized version of this test namely the mid p value test this paper examines the actual type i error rates of this test for both one sided and two sided tests and for a wide range of sample sizes we show that the actual levels of significance of the mid p test tend to be closer to the nominal level as compared with various classical tests the computational effort required for the mid p test is no more than that needed for the fisher exact test further the basis for its modification is a natural adjustment for discreteness thus the test easily generalizes to r c contingency tables and other discrete data problems

accurate calculation of green s function of the schrodinger equation in a block layered potential in this paper a new algorithm is presented for calculating the green s function of the schrodinger equation in the presence of block layered potentials such green s functions have various and practical applications in quantum modelling of electron transport within nano mosfet transistors the proposed method is based on expansions of the eigenfunctions of the subordinate sturm liouville problems and a collocation matching procedure along possibly curved interfaces of the potential blocks accurate numerical results are provided to validate the proposed algorithm

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

confidence intervals for the binomial parameter some new considerations several methods have been proposed to construct confidence intervals for the binomial parameter some recent papers introduced the mean coverage criterion to evaluate the performance of confidence intervals and suggested that exact methods because of their conservatism are less useful than asymptotic ones in these studies however exact intervals were always represented by the clopper pearson interval c p now we focus on sterne s interval which is also exact and known to be better than the c p in the two sided case introducing a computer intensive level adjustment procedure which allows constructing intervals that are exact in terms of mean coverage we demonstrate that sterne s interval performs better than the best asymptotic intervals even in the mean coverage context level adjustment improves the c p as well which with an appropriate level adjustment becomes equivalent to the mid p interval finally we show that the asymptotic behaviour of the mid p method is far poorer than is generally expected

confidence intervals for a binomial proportion thirteen methods for computing binomial confidence intervals are compared based on their coverage properties widths and errors relative to exact limits the use of the standard textbook method x n 1 96 square root of x n 1 x n n or its continuity corrected version is strongly discouraged a commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p is such that np and n 1 p both exceed 5 does not ensure adequate accuracy score limits are easily calculated from closed form solutions to quadratic equations and can be used at all times based on coverage functions the continuity corrected score method is recommended over exact methods its conservative nature should be kept in mind as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction

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

approximate interval estimation of the difference in binomial parameters correction for skewness and extension to multiple tables recently beal 1987 biometrics 43 941 950 found mee s modification of anbar s approximate interval estimation for the difference in binomial parameters to be a good choice in small sample sizes as this method can be derived from the score theory of bartlett it is easily corrected for skewness exact numerical evaluation shows that this correction is not as important for this case as for the ratio of binomial parameters gart and nam 1988 biometrics 44 323 338 the score theory is also used to extend this method to the stratified or multiple table case thus good approximate interval estimates for differences ratios and odds ratios of binomial parameters can all be derived from the same general theory

approximate binomial confidence limits abstract this article examines the accuracy of normal approximations to confidence limits for the binomial n p parameter p the method of getting exact values from an f table is too slow for practical use and useless for large n the two usual approximations have unsatisfactory accuracy both for small n and asymptotically and the simpler one lacks an invariance property of the confidence limit hall s 1982 approximation also lacks invariance and even when symmetrized has unsatisfactory accuracy pratt s 1968 approximation has excellent accuracy for all n inversion of a molenaar 1973 normal approximation to the binomial gives better asymptotic accuracy than pratt s approximation but poor values for observations close to n

confidence intervals for the mean of a variable taking the values 0 1 and 2 the problem of setting a confidence interval for the mean of a variable on 0 1 2 arises in three contexts paired organ procedure rates estimation of gene frequency and three point likert scales an effective approach to its estimation may be based on a good interval for a paired difference of proportions four good methods due to newcombe and tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications

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

estimation of aquifer scale proportion using equal area grids assessment of regional scale groundwater quality 1 the proportion of an aquifer with constituent concentrations above a specified threshold high concentrations is taken as a nondimensional measure of regional scale water quality if computed on the basis of area it can be referred to as the aquifer scale proportion a spatially unbiased estimate of aquifer scale proportion and a confidence interval for that estimate are obtained through the use of equal area grids and the binomial distribution traditionally the confidence interval for a binomial proportion is computed using either the standard interval or the exact interval research from the statistics literature has shown that the standard interval should not be used and that the exact interval is overly conservative on the basis of coverage probability and interval width the jeffreys interval is preferred if more than one sample per cell is available cell declustering is used to estimate the aquifer scale proportion and kish s design effect may be useful for estimating an effective number of samples the binomial distribution is also used to quantify the adequacy of a grid with a given number of cells for identifying a small target defined as a constituent that is present at high concentrations in a small proportion of the aquifer case studies illustrate a consistency between approaches that use one well per grid cell and many wells per cell the methods presented in this paper provide a quantitative basis for designing a sampling program and for utilizing existing data

frequency domain and time domain finite element solution of maxwell s equations using spectral lanczos decomposition method an efficient solver is described for the solution of the electromagnetic fields in both time and frequency domains the proposed method employs the node based and 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 first a new explicit axisymmetric solver for the diffusion of electromagnetic fields in an inhomogeneous medium is introduced the procedure is then extended to treat the three dimensional problems in the low frequency regime finally maxwell s equations in their general form are solved in frequency and time domains depending on the application our method requires the implementation of the lanczos process only at the largest or smallest time or frequency of interest consequently a multiple time and frequency domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time the efficiency and effectiveness of this new technique are illustrated by using various practical numerical examples

gaussian windowed frame based method of moments formulation of surface integral equation for extended apertures scattering or coupling of electromagnetic beam field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation which are solved by the method of moments with the aid of the gabor based gaussian window frame set of basis and testing functions the application of the gaussian window frame provides i a mathematically exact and robust tool for spatial spectral phase space formulation and analysis of the problem ii a system of linear equations in a transmission line like form relating mode like wave objects of one medium with mode like wave objects of the second medium iii furthermore an appropriate setting of the frame parameters yields mode like wave objects that blend plane wave properties as if solving in the spectral domain with green s function properties as if solving in the spatial domain and iv a representation of the scattered field with gaussian beam propagators that may be used in many large in terms of wavelengths systems

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

image solution for the 3 d static green s function of a vertically stratified two layer half space the general form of 3 d static green s function for a general structure consisting of n arbitrary adjacent dielectric wedges is derived using the kontorovich lebedev and fourier transforms it consists of several point sources in physical space and a line image source in complex space for each region of the problem geometry while the point sources can be treated conventionally the line image distributions are obtained by extracting a proper asymptotic behavior of the solution which can be numerically computed as an example the case of a vertically stratified two layer half space is investigated and the respective point and line image sources are obtained the efficiency of the proposed solution method is demonstrated by comparing the computational time for a given structure with that required by a commercially available numerical code using the finite integration technique

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

fast simulation of triaxial borehole induction measurements acquired in axially symmetrical and transversely isotropic media we introduce and successfully test an efficient method to simulate triaxial borehole electromagnetic em induction measurements acquired in axially symmetrical and transversely isotropic ti media the method uses a fourier series expansion to express the azimuthal dependence of em fields and the source term whereby the essentially 3d problem collapses to a series of independent 2d problems each 2d problem is solved with a semianalytic method that uses normalized bessel functions and normalized hankel functions to express the radial dependence of em fields thereby improving numerical stability in addition use is made of amplitude and slope basis functions to describe the longitudinal dependence of em fields to avoid grid refinement in the vicinity of horizontal formation boundaries for validation we compare the new simulation method to two 1d analytic methods in horizontally and radially layered formations and to one 3d finite difference method 3dfd in multilayered formations that include borehole and invasion zones numerical results indicate that the method is accurate in formations with high conductivity contrasts compared to 1d methods and is more than ten times more efficient than the 3dfd method in multilayer formations

delta method and bootstrap in linear mixed models to estimate a proportion when no event is observed application to intralesional resection in bone tumor surgery resecting bone tumors requires good cutting accuracy to reduce the occurrence of local recurrence this issue is considerably reduced with a navigated technology the estimation of extreme proportions is challenging especially with small or moderate sample sizes when no success is observed the commonly used binomial proportion confidence interval is not suitable while the rule of three provides a simple solution unfortunately these approaches are unable to differentiate between different unobserved events different delta methods and bootstrap procedures are compared in univariate and linear mixed models with simulations and real data by assuming the normality the delta method on the z score and parametric bootstrap provide similar results but the delta method requires the estimation of the covariance matrix of the estimates in mixed models the observed fisher information matrix with unbounded variance components should be preferred the parametric bootstrap easier to apply outperforms the delta method for larger sample sizes but it may be time costly copyright 2016 john wiley sons ltd

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

a relaxation result for unbounded control system with hysteresis abstract we consider a control system of two odes describing a hysteresis effect the term unbounded in the title refers to the fact that the multivalued mapping giving the control constraints may admit unbounded values being at the same time nonconvex valued we convexify the constraint and we approximate solutions of thus obtained relaxed problem by those of the given system the property of lipschitz continuity of the multivalued mapping traditionally employed for such kind of relaxation problems is weakened to a more appropriate in the context of unbounded valued multifunctions truncated version of it

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

indexes of contrast and quantitative significance for comparisons of two groups although boundaries for large and small differences are needed to plan research and interpret results the diverse indexes of descriptive contrast for the central indexes a and b of two groups have not received intensive attention for two means the increment of mid r a bmid r reflects the slope of a line showing the effect but is altered by different units of measurement division of mid r a bmid r by the common standard deviation produces the standardized increment si which is sometimes called the effect size despite many advant ages it does not contrast the relative magnitudes of a and b for the latter contrast the relative change or proportionate increment mid r a bmid r b is particularly easy to understand and the relative translocation mid r a bmid r a b produces a bounded range from 1 to 1 nevertheless all indexes of relative magnitude ablate the scales of measurement thereby increasing difficulty in interpretation although seldom applied proportionate reduction in overall system variance can be highly useful its square root leads to eta the analogue of a correlation coefficient which corresponds to a standardized slope for the direct increment the values of eta usually approximate si 2 although arbitrary levels have been proposed for quantitative significance of the si the proportionate reduction in overall system variance is often regarded as ineffectual unless 10 per cent with this belief minimum boundaries for quantitative significance can often be set at eta 0 3 and si 0 6 in indexes of relative magnitude for two proportions or rates p a and p b confusion is produced if q a and q b are alternatively chosen for the denominators the odds ratio p a q b p b q a avoids these choices but is often difficult to interpret for easy understanding and communication the preferred index is nne the number needed to produce one excess effect calculated as the inverse of the direct increment that is 1 mid r p a p b mid r the standardized increment mid r p a p b mid r radical pq where p is the average of p a and p b and q 1 p could offer a single index applicable to both dimensional and binary data but when p becomes quite small that is 0 01 radical pq requires special calculations and also approaches the value of radicalp boundaries of quantitative significance are particularly difficult to establish for comparisons of two rates because of additional consequences in populational extrapolations and clinical implications nevertheless the principles of quantitative significance can aid the ad hoc construction of boundaries that must be set for medical importance when sample sizes are calculated and when results are interpreted for studies of either efficacy or equivalence

two sided confidence intervals for the single proportion comparison of seven methods simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals criteria appropriate to the evaluation of various proposed methods include closeness of the achieved coverage probability to its nominal value whether intervals are located too close to or too distant from the middle of the scale expected interval width avoidance of aberrations such as limits outside 0 1 or zero width intervals and ease of use whether by tables software or formulae seven methods for the single proportion are evaluated on 96 000 parameter space points intervals based on tail areas and the simpler score methods are recommended for use in each case methods are available that aim to align either the minimum or the mean coverage with the nominal 1 alpha

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

numerical mode matching method for the multiregion vertically stratified media em wave propagation the response of a source in the presence of an n region vertically stratified media is solved using the numerical mode matching method by treating the fields propagating in the direction parallel to the subboundaries of the stratified media in terms of the propagators and by introducing the concepts of reflection operators transmission operators and generalized reflection operators the two dimensional problem is reduced to several one dimensional problems which are solved by the one dimensional finite element method fem the one dimensional method saves computer storage and computation time compared to the two dimensional version a formulation valid for a general n region vertically stratified medium is derived when there are only three regions the results compare well with those in the literature some typical numerical results for n 3 are also shown

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

approximate interval estimation of the ratio of binomial parameters a review and corrections for skewness various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically it is found that the method based on likelihood scores koopman 1984 biometrics 40 513 517 miettinen and nurminen 1985 statistics in medicine 4 213 226 performs best in achieving the nominal confidence coefficient but it may distribute the tail probabilities quite disparately using general theory of bartlett 1953 biometrika 40 306 317 1955 biometrika 42 201 203 we correct this method for asymptotic skewness following gart 1985 biometrika 72 673 677 we extend this correction to the case of estimating the common ratio in a series of two by two tables computing algorithms are given and applied to numerical examples parallel methods for the odds ratio and the ratio of poisson parameters are noted

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

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

optimal stopping for interval estimation in bernoulli trials we propose an optimal sequential methodology for obtaining confidence intervals for a binomial proportion theta assuming that an independent and identically distributed sequence of bernoulli theta trials is observed sequentially we are interested in designing 1 a stopping time t that will decide the best time to stop sampling the process and 2 an optimum estimator hat theta t that will provide the optimum center of the interval estimate of theta we follow a semi bayesian approach where we assume that there exists a prior distribution for theta and our goal is to minimize the average number of samples while we guarantee a minimal specified coverage probability level the solution is obtained by applying standard optimal stopping theory and computing the optimum pair t hat theta t numerically regarding the optimum stopping time component t we demonstrate that it enjoys certain very interesting characteristics not commonly encountered in solutions of other classical optimal stopping problems in particular we prove that for a particular prior beta density the optimum stopping time is always bounded from above and below it needs to first accumulate a sufficient amount of information before deciding whether or not to stop and it will always terminate before some finite deterministic time we also conjecture that these properties are present with any prior finally we compare our method with the optimum fixed sample size procedure as well as with existing alternative sequential schemes

a new technique for the derivation of closed form electromagnetic green s functions for unbounded planar layered media a closed form electromagnetic green s function for unbounded planar layered media is derived in terms of a finite sum of hankel functions the derivation is based on the direct inverse hankel transform of a pole residue representation of the spectral domain form of the green s function such a pole residue form is obtained through the solution of the spectral domain form of the governing green s function equation numerically through a finite difference approximation rather than analytically the proposed methodology can handle any number of layers including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction the numerical implementation of the proposed methodology is straightforward and robust and does not require any preprocessing of the spectrum of the green s function for the extraction of surface wave poles or its quasi static part the number of terms in the derived closed form expression is chosen adaptively with the distance between source and observation point as parameter the development of the closed form green s function is presented for both vertical and horizontal dipoles its accuracy is verified through a series of numerical examples and comparisons with results from other established methods

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

quantitative stability of variational systems i the epigraphical distance this paper proposes a global measure for the distance between the elements of a variational system parametrized families of optimization problems

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