rayleigh marchenko redatuming for target oriented true amplitude imaging abstractmarchenko redatuming is a revolutionary technique to estimate green s functions from virtual sources in the subsurface using only data measured at the earth s surface without having to place either sources or receivers in the subsurface this goal is achieved by crafting special wavefields so called focusing functions that can focus energy at a chosen point in the subsurface despite its great potential strict requirements on the reflection response such as knowledge and accurate deconvolution of the source wavelet including absolute scaling factor and co location of sources and receivers have so far challenged the application of marchenko redatuming to real world scenarios i combine the coupled marchenko equations with a one way version of the rayleigh integral representation to obtain a new redatuming scheme that handles internal as well as free surface multiples using dual sensor band limited seismic data with an unknown source signature from any acquisition system that presents arbit

ordinal regression revisited multiple criteria ranking using a set of additive value functions abstract we present a new method called utagms for multiple criteria ranking of alternatives from set a using a set of additive value functions which result from an ordinal regression the preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives ar a called reference alternatives the preference model built via ordinal regression is the set of all additive value functions compatible with the preference information using this model one can define two relations in the set a the necessary weak preference relation which holds for any two alternatives a b from set a if and only if for all compatible value functions a is preferred to b and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b these relations establish a necessary and a possible ranking of alternatives from a being respectively a partial preorder and a strongly complete relation the utagms method is intended to be used interactively with an increasing subset ar and a progressive statement of pairwise comparisons when no preference information is provided the necessary weak preference relation is a weak dominance relation and the possible weak preference relation is a complete relation every new pairwise comparison of reference alternatives for which the dominance relation does not hold is enriching the necessary relation and it is impoverishing the possible relation so that they converge with the growth of the preference information distinguishing necessary and possible consequences of preference information on the complete set of actions utagms answers questions of robustness analysis moreover the method can support the decision maker when his her preference statements cannot be represented in terms of an additive value function the method is illustrated by an example solved using the utagms software some extensions of the method are also presented

tutorial on seismic interferometry part 2 underlying theory and new advances in the 1990s the method of time reversed acoustics was developed this method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal when ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers they focus at the position of the original source even when the medium is very complex in seismic interferometry the time reversed responses are not physically sent into the earth but they are convolved with other measured responses the effect is essentially the same the time reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers a mathematical derivation based on reciprocity theory formalizes this principle the crosscorrelation of responses at two receivers integrated over different sources gives the green s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver this green s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving recent developments circumventing these assumptions include interferometric representations for attenuating and or moving media as well as unified representations for waves and diffusion phenomena bending waves quantum mechanical scattering potential fields elastodynamic electromagnetic poroelastic and electroseismic waves significant improvements in the quality of the retrieved green s functions have been obtained with interferometry by deconvolution a trace by trace deconvolution process compensates for complex source functions and the attenuation of the medium interferometry by multidimensional deconvolution also compensates for the effects of one sided and or irregular illumination

some exact solutions for the bending of beams with spatially stochastic stiffness to the best of the knowledge of the authors there are no exact solutions available for the bending of beams with spatially stochastic stiffness investigators are therefore utilizing various approximate techniques in the present study a new method is developed to obtain exact solutions for first and second moments of displacements for statically determinate beams that have spatially random stiffness the method is based on the full probabilistic characterization of the random stiffness so that the solutions are valid for any value of the coefficient of variation of the stiffness the deterministic governing equations and boundary conditions derived for both first and second moments allow apparently for the first time in the literature the exact solutions for the mean and covariance functions of the displacements to be determined two governing equations are uncoupled from each other and can be solved separately several exact solutions for the mean and covariance functions are obtained to illustrate the application of the method it is hoped that the exact solutions determined will serve as benchmark solutions to enable the researchers to check the accuracy of various approximate analytical and numerical techniques on the test solutions presented in this study

response variability of stochastic frame structures using evolutionary field theory the integral form for the variance of the response of stochastic statically indeterminate structural systems involving the so called variability response function vrf and the spectral density function of the stochastic field modelling the uncertain system properties is established for the first time in this paper using evolutionary spectra theory the vrf is a function depending on deterministic parameters related to the geometry boundary conditions mean material properties and loading of the structural system no approximations are involved in the derivation of the integral form however a conjecture has to be made that is validated using monte carlo simulations the uncertain system property considered is the inverse of the elastic modulus flexibility closed form expressions can be derived in principle for the vrf of any statically determinate or indeterminate frame system using a flexibility based formulation alternatively a fast monte carlo simulation approach is provided to numerically evaluate the vrf it is shown in closed form and numerically that the vrf for statically indeterminate structures is a function of the standard deviation ff of the stochastic field modeling the inverse of the elastic modulus although the vrf depends on ff it appears to be independent of the functional form of the spectral density function of the stochastic field modeling the uncertain system properties for statically determinate structures the vrf is independent of ff the integral form can be used to compute the variance of the system response as well as its upper bound with minimal computational effort it also provides an excellent insight into the mechanisms controlling the response variability the upper bounds for the response variance are spectral and probability distribution free requiring knowledge of only the variance of the inverse of the elastic modulus the proposed bounds are realizable in the sense that it is possible to determine the probabilistic characteristics of the stochastic field that produces them several numerical examples are provided demonstrating the capabilities of the methodology

determination of weights of interacting criteria from a reference set abstract in this paper we present a model allowing to determine the weights related to interacting criteria this is done on the basis of the knowledge of a partial ranking over a reference set of alternatives prototypes a partial ranking over the set of criteria and a partial ranking over the set of interactions between pairs of criteria

multiattribute preference models with reference points in the context of multiple attribute decision making preference models making use of reference points in an ordinal way have recently been introduced in the literature this text proposes an axiomatic analysis of such models with a particular emphasis on the case in which there is only one reference point our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete models using reference points are shown to be a particular case of this general model the number of reference points is linked to the number of equivalence classes distinguished by the traces when there is only one reference point the induced traces are quite rough distinguishing at most two distinct equivalence classes we study the relation between the model using a single reference point and other preference models proposed in the literature most notably models based on concordance and models based on a discrete sugeno integral

imaging complex structures with semirecursive kirchhoff migration i present a semirecursive kirchhoff migration algorithm that is capable of obtaining accurate images of complex structures by combining wave equation datuming and kirchhoff migration the method is successful because breaking up the complex velocity structure into small depth regions allows traveltimes to be calculated in regions where the computation is well behaved and where the computation corresponds to energetic arrivals the traveltimes computed in such a region are used first for imaging and second for downward continuation of the entire survey shots and receivers to the boundary of the next region this process results in images comparable to those obtained by shot profile migration but at reduced computational cost because traveltimes are computed for small depth domains the adverse effects of caustics headwaves and multiple arrivals do not develop in principle this method requires only the same number of traveltime calculations as a standard migration tests on the marmousi data set produce excellent results

reference based preferences aggregation procedures in multi criteria decision making this paper aims at introducing and investigating a new family of merely qualitative models for multicriteria decision making such models do not require any numerical representation within this family we will focus on decision rules using reference levels in order to help comparing several alternatives we will investigate both the descriptive potential of such rules and their axiomatic foundations after recalling the descriptive and prescriptive limitations of merely ordinal rules that do not use reference points we will introduce a new axiom requiring that the decision maker s preference between two alternatives depends on the respective positions of their consequences relatively to reference levels under this assumption we will determine the only possible form for the decision rule and characterize some particular instances of this rule under transitivity constraints our results show that introducing reference points overcomes the usual limitations of purely ordinal aggregation methods by moving the application point of arrow s theorem

an adaptive spectral galerkin stochastic finite element method using variability response functions a methodology is proposed in this paper to construct an adaptive sparse polynomial chaos pc expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields the proposed methodology utilizes the concept of variability response function vrf in order to compute an a priori low cost estimate of the spatial distribution of the second order error of the response as a function of the number of terms used in the truncated karhunen lo eve kl expansion this way the influence of the response variance to the spectral content correlation structure of the random input is taken into account through a spatial variation of the truncated kl terms the criterion for selecting the number of kl terms at different parts of the structure is the uniformity of the spatial distribution of the second order error this way a significantly reduced number of pc coefficients with respect to classical pc expansion is required in order to reach a uniformly distributed target second order error this results in an increase of sparsity of the coefficient matrix of the corresponding linear system of equations leading to an enhancement of the computational efficiency of the spectral stochastic finite element method ssfem copyright c 2014 john wiley sons ltd

axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough set decision rules abstract utility or value functions play an important role of preference models in multiple criteria decision making we investigate the relationships between these models and the decision rule preference model obtained from the dominance based rough set approach the relationships are established by means of special cancellation properties used in conjoint measurement as axioms for representation of aggregation procedures we are considering a general utility function and three of its important special cases associative operator sugeno integral and ordered weighted maximum for each of these aggregation functions we give a representation theorem establishing equivalence between a very weak cancellation property the specific utility function and a set of rough set decision rules each result is illustrated by a simple example of multiple criteria decision making the results show that the decision rule model we propose has clear advantages over a general utility function and its particular cases

receiver side near surface corrections in the τ p domain a raypath consistent solution for converted wave processing abstractremoving near surface effects in the processing of 3c data is key to exploiting the information provided by converted waves particularly for the case of the ps mode converted energy travels back to the surface as s waves therefore s wave static corrections are needed for the receiver side this is often done under the assumption of surface consistency this implies a constant correction for all the traces recorded at a fixed receiver location however if the velocity change between the near surface layer and the medium underneath is gradual the vertical raypath assumption that supports the surface consistent approach is no longer valid this property results in a nonstationary change of the near surface traveltimes that need to be addressed to properly solve the problem we have determined how the delays introduced by the presence of very low s wave velocities in the near surface can introduce raypath dependent effects the magnitudes of these delays can be larger than what can be considered

wave equation datuming before stack this note describes the extension to unstacked seismic data of a computationally efficient form of the kirchhoff integral published several years ago in the previous paper berryhill 1979 a wave equation procedure was developed to change the datum of a collection of zero offset seismic traces from one surface of arbitrary shape to another even when the velocity for wave propagation is not constant this procedure was designated wave equation datuming and its applications to zero offset data were shown to include velocity replacement datum corrections and multilayer forward modeling extending this procedure to unstacked data requires no change in the mathematical algorithm it is necessary only to recognize that operating on a common source group of seismic traces has the effect of extrapolating the receivers from one datum to another and that because of reciprocity operating on a common receiver group changes the datum of the sources two passes through the data common source computations th

near surface attenuation estimation using wave propagation modeling the effect of the near surface on seismic land data can be so severe that static corrections are insufficient full waveform inversion followed by redatuming may be an alternative but inversion will work only if the starting model is sufficiently close to the true model as a first step toward determining a viscoelastic near surface model we assume that existing methods can provide a horizontally layered velocity and density model because near surface attenuation is strongest we propose a method to estimate the p wave attenuation based on viscoacoustic finite difference modeling we compare energy decay along traveltime curves of reflection and refraction events in the modeled and observed seismic data for a range of attenuation parameters the best match provides an estimate of the attenuation first we estimate only the attenuation of the top layer and study the sensitivity to depth and velocity perturbations then we consider multiple layers we apply the method to synthetic and real data and investigate the effect of source wavelet and topography the method is robust against depth and velocity perturbations smaller than 10 the results are sensitive to the source wavelet incorporating the surface topography in the computed traveltimes reduces the uncertainty of the attenuation estimates especially for deeper layers

further results on concordance relations the purpose of this note is to sharpen the results in an earlier paper bouyssou d pirlot m 2005 a characterization of concordance relations european journal of operational research 167 2 427 443 giving an axiomatic characterization of concordance relations we show how the conditions used in this earlier paper can be weakened so as to become independent from the conditions needed to characterize a general conjoint measurement model tolerating intransitive and or incomplete relations this leads to a clearer characterization of concordance relations within this general model

an axiomatic approach to noncompensatory sorting methods in mcdm i the case of two categories in the literature on mcdm many methods have been proposed in order to sort alternatives evaluated on several attributes into ordered categories most of them were proposed on an ad hoc basis the purpose of this paper is to contribute to a recent trend of research aiming at giving these methods sound theoretical foundations using tools from conjoint measurement we provide an axiomatic analysis of the partitions of alternatives into two categories that can be obtained using what we call noncompensatory sorting models these models have strong links with the pessimistic version of electre tri our analysis allows to pinpoint what appears to be the main distinctive features of electre tri when compared to other sorting methods it also gives hints on the various methods that have been proposed to assess the parameters of electre tri on the basis of assignment examples

flexibility based upper bounds on the response variability of simple beams spectral and probability distribution free upper bounds on the response variability of both statically determinate and indeterminate beams are established in the present paper based on exact closed form analytic expressions derived for the variance of the response displacement a conjecture has to be made in the case of statically indeterminate beams in order to establish these bounds the conjecture is supported through an argument postulating the existence of an integral form for the variance of the response displacement and through a brute force optimization procedure providing numerical validation such bounds require knowledge of only the variance of the stochastic field modeling the inverse of the elastic modulus and are realizable in the sense that it is possible to fully determine the probabilistic characteristics of the stochastic field modeling the inverse of the elastic modulus that produces them furthermore it is possible to fully determine also the corresponding stochastic field modeling the elastic modulus that produces these bounds these spectral and probability distribution free bounds can also be computed numerically using a so called fast monte carlo simulation procedure that does not require a closed form analytic expression for the response displacement making this approach much more general numerical examples are provided involving a statically determinate and a statically indeterminate beam

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

elastic full waveform inversion for surface topography abstractelastic full waveform inversion efwi attempts to find high resolution model parameters that are able to match observed data exactly by minimizing residuals between the observed and predicted data however irregular surface topography can generate problematic efwi results to resolve this issue an efwi method in the curvilinear system is presented to invert velocities for areas with surface topography this method meshes the regions near the surface topography into body fitted grids and areas off surface regions into rectangular grids we derived the gradient formulas with respect to multiple parameters in the curvilinear system and developed a step search method to calculate the corresponding step lengths wiener filtering is performed on a multiscale decomposition method to invert the velocity from a low to a high wavenumber error analysis using a homogeneous model with a surface topography demonstrates the accuracy and validity of our methods numerical experiments with an elastic hill g

higher order weighted integral stochastic finite element method and simplified first order application it is well known that expansion based stochastic methods are approximate schemes as they are based on a first or at most second order series expansion on the basic variable e g displacement therefore expansion based stochastic analysis schemes are bound to show small response variability when compared with monte carlo simulation mcs results and application of these schemes is limited to stochastic problems with relatively small variability in order to overcome these general drawbacks of the expansion methods we suggest a higher order stochastic field function that can be employed in the expansion based stochastic analysis scheme of the weighted integral method we then propose a new weighted integral formulation using the higher order stochastic field function the new formulation is not only applicable to stochastic problems with a high degree of uncertainty but also can reproduce the phenomenon of accelerated increase in the response variability when the coefficient of variation of the stochastic field increases as observed in the mcs in order to show the validity of the proposed formulation we provide two numerical examples and the results are discussed in detail

analysis of mean and mean square response of general linear stochastic finite element systems a general finite element based formulation is presented for the analysis of the mean and mean square response of stochastic structural systems whose material properties are described by random fields a flexibility based formulation is followed that does not involve any approximations closed formed integral expressions for the mean and mean square value of the response displacement of statically indeterminate stochastic structures are introduced in this paper these integral expressions involve the spectral density function of a stochastic field modeling the uncertain material properties and two new quantities named the mean response function mrf and the variability response function for the mean square response vrf1 the mrf and the vrf1 have many similarities with the classical variability response function vrf used to estimate the variance of the response displacement the existence of the mrf and the vrf1 depends on a conjecture that is validated numerically using a brute force monte carlo simulation approach a so called finite element method based fast monte carlo simulation procedure fem fmcs is introduced for the accurate and efficient numerical evaluation of the mrf and the vrf1 this methodology is established for the analysis of stochastic beam frame structures as well as for more general stochastic finite element systems i e plane stress and shell problems numerical examples are provided including a statically indeterminate beam a plane stress problem and a shell structure the mrf and vrf1 are used to perform sensitivity parametric analyses with respect to various probabilistic characteristics involved in the problem i e correlation distance standard deviation and to establish realizable upper bounds on the mean value of the response displacement throughout this paper the vrf is computed in parallel to the mrf and the vrf1 it should be noted that although the concept of the vrf has been introduced in an earlier work this is the first time that a flexibility based approach has been used to estimate the vrf for two dimensional problems

straight rays redatuming a fast and robust alternative to wave equation based datuming wave equation based redatuming is expensive and requires a detailed knowledge of the shallow velocity field we derive the analytical expression of a new prestack wavefield extrapolation operator the topographic datuming operator tdo which applies redatuming based on straight rays approximation above and below a chosen datum this redatuming operator is directly applied to common source gathers to downward continue the source and the receivers simultaneously to the datum level without resorting to common receiver gathers as a result the method is far more efficient and robust than the conventional wave equation based redatuming and does not require an accurate depth domain interval velocity model in addition tdo unlike wave equation based redatuming requires effective velocities above datum and thus can be applied using attributes valid for static correction methods effective velocities beneath the datum permit us to replace the surface integral which is needed for wave equation redatuming

wave field reciprocity and optimization in remote sensing a unified approach to local optimization techniques and wave field reciprocity as applied to constructing solutions to remote sensing imaging and inversion problems in acoustic elastic and electromagnetic wave theory is presented the starting point is a system of linear first order partial differential equations in space time of the class to which the indicated wave phenomena gives rise for this system three types of remote sensing problems the inverse source the inverse scattering and the inverse transducted wave field problems are formulated and the construction of their solutions via local optimization techniques is discussed emphasis is placed on iterative algorithms that are based on a guaranteed decrease in the mismatch between modelled and observed data at each update of the medium subsequently the wave field reciprocity theorems of the time convolution and the time correlation types are derived and their occurrence in the optimization procedures is discussed also attention is paid to approximate methods in particular to the rayleigh gans born approximation approximations of this sort provide the means to invoke the method of preconditioning in the process of inverting the operator equations exotic media for example chiral media in electromagnetics are included in the analysis

unified double and single sided homogeneous green s function representations in wave theory the homogeneous green s function consists of the impulse response to a point source minus its time reversal it can be represented by a closed boundary integral in many practical situations the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only the inherent approximations are acceptable as long as the effects of multiple scattering are negligible however in case of strongly inhomogeneous media the effects of multiple scattering can be severe we derive double and single sided homogeneous green s function representations the single sided representation applies to situations where the medium can be accessed from one side only it correctly handles multiple scattering it employs a focusing function instead of the backward propagating green s function in the classical double sided representation when reflection measurements are available at the accessible boundary of the medium the focusing function can be retrieved from these measurements throughout the paper we use a unified notation which applies to acoustic quantum mechanical electromagnetic and elastodynamic waves we foresee many interesting applications of the unified single sided homogeneous green s function representation in holographic imaging and inverse scattering time reversed wave field propagation and interferometric green s function retrieval

qualitative decision theory with preference relations and comparative uncertainty an axiomatic approach this paper investigates a purely qualitative approach to decision making under uncertainty since the pioneering work of savage most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate giving up this tradition we relax this assumption and introduce an axiom of ordinal invariance requiring that the decision maker s preference between two acts only depends on the relative position of their consequences for each state within this qualitative framework we determine the only possible form of the corresponding decision rule then assuming the transitivity of the strict preference the underlying partial confidence relations are those at work in non monotonic inference and thus satisfy one of the main properties of possibility theory the satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure unique up to a monotonic transformation for encoding the relative likelihood of events

effect of multiple uncertain material properties on the response variability of in plane and plate structures abstract in the majority of research works on stochastic finite element analysis the main concern is put on the effect of uncertain elastic modulus on the response variability this is mainly due to the importance of this parameter in the stochastic response of structures but also to the difficulties in introducing other material and or geometrical uncertain parameters in the stochastic formulation in this paper a formulation is suggested in order to determine the response variability of in plane and plate structures with multiple uncertain material parameters i e elastic modulus and poisson s ratio to accomplish this use is made of the general equation for n th joint moment and a polynomial expansion on the coefficients of constitutive matrix for computational purposes the infinite series of stochastic sub stiffness matrices is truncated preserving sufficient accuracy to demonstrate the validity of the proposed formulation some numerical examples are provided and the results are compared with those obtained by means of classical monte carlo simulation combined with the local average scheme

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

inverse extrapolation of primary seismic waves forward wave field extrapolation operators simulate propagation effects from one depth level to another inverse wave field extrapolation operators eliminate those propagation effects since forward wave field extrapolation can be described in terms of spatial convolution inverse wave field extrapolation can be described in terms of spatial deconvolution a simple approximation to a stable spatially band limited deconvolution operator is obtained by taking the complex conjugate of the convolution operator a one way version of the kirchhoff integral that contains the conjugate complex green s function is derived unlike the situation with respect to the forward problem the modification of the closed surface integral into an open boundary integral involves an approximation that is identical to the approximation in the conjugate complex deconvolution approach this approximation neglects the evanescent field and causes a second order amplitude error for a plane acquisition surface the one way kirchhoff

following the traces an introduction to conjoint measurement without transitivity and additivity this paper presents a self contained introduction to a general conjoint measurement framework for the analysis of nontransitive and or incomplete binary relations on product sets it is based on the use of several kinds of marginal traces on coordinates induced by the binary relation this framework leads to defining three general families of models depending on the kind of trace that they use contrary to most conjoint measurement models these models do not involve an addition operation this allows for a simple axiomatic analysis at the cost of very weak uniqueness results

adaptive overburden elimination with the multidimensional marchenko equation abstractiterative substitution of the multidimensional marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process in so called marchenko imaging a macro velocity model of the subsurface is required to meet this objective the model is used to back propagate the data during the first iteration and to truncate integrals in time during all successive iterations in case of an erroneous model the image will be blurred akin to conventional imaging and artifacts may arise from inaccurate integral truncations however the scheme is still successful in removing artifacts from internal multiple reflections inspired by these observations we rewrote the marchenko equation such that it can be applied early in a processing flow without the need of a macro velocity model instead we have required an estimate of the two way traveltime surface of a selected horizon in the subsurface we have introduced an approximation such that adaptive subtracti

a characterization of concordance relations abstract the notion of concordance is central to many multiple criteria techniques relying on ordinal information e g outranking methods it leads to compare alternatives by pairs on the basis of a comparison of coalitions of attributes in terms of importance this paper proposes a characterization of the binary relations that can be obtained using such comparisons within a general framework for conjoint measurement that allows for intransitive preferences we show that such relations are mainly characterized by the very rough differentiation of preference differences that they induce on each attribute

response variability due to randomness in poisson s ratio for plane strain and plane stress states summary in the ordinary structural materials one of the parameters that can be assumed to have spatial uncertainty is poisson s ratio therefore the independent evaluation of the effects of this parameter on the response variability is of importance the difficulties in obtaining the response variability due to randomness in poisson s ratio lie in the fact that the poisson s ratio enters the stiffness matrix as a non linear parameter in this paper a formulation to determine the response variability in plane strain and plane stress states due to the randomness in the poisson s ratio is given the formulation is accomplished by means of the stochastic decomposition of the constitutive matrix into several sub matrices taking into consideration of the polynomial expansion on the coefficients of constitutive relation to demonstrate the validity of the proposed formulation some example structures are chosen and the results are compared with those obtained by means of monte carlo simulation through the formulation proposed in this study it becomes possible for the weighted integral stochastic finite element analysis to consider all the uncertain material parameters in its application