frequency and spatial sampling strategies for crosshole seismic waveform spectral inversion experiments analyses of synthetic frequency domain acoustic waveform data provide new insights into the design and imaging capability of crosshole surveys the full complex fourier spectral data offer significantly more information than other data representations such as the amplitude phase or hartley spectrum extensive eigenvalue analyses are used for further inspection of the information content offered by the seismic data the goodness of different experimental configurations is investigated by varying the choice of 1 the frequencies 2 the source and receiver spacings along the boreholes and 3 the borehole separation with only a few carefully chosen frequencies a similar amount of information can be extracted from the seismic data as can be extracted with a much larger suite of equally spaced frequencies optimized data sets should include at least one very low frequencycomponent the remaining frequencies should be chosen fromthe upper end of the spectrum available this strategy proved to be applica

laplace domain full waveform inversion of seismic data lacking low frequency information the lack of the low frequency information in field data prohibits the time or frequency domain waveform inversions from recovering large scale background velocity models on the other hand laplace domain waveform inversion is less sensitive to the lack of the low frequencies than conventional inversions in theory frequency filtering of the seismic signal in the time domain is equivalent to a constant multiplication of the wavefield in the laplace domain because the constant can be retrieved using the source estimation process the frequency content of the seismic data does not affect the gradient direction of the laplace domain waveform inversion we obtained inversion results of the frequency filtered field data acquired in the gulf of mexico and two synthetic data sets obtained using a first derivative gaussian source wavelet and a single frequency causal sine function they demonstrated that laplace domain inversion yielded consistent results regardless of the frequency content within the seismic data

quasinilpotent operators in operator lie algebras iii abstract in this paper we investigate some properties of algebras generated by essentially nilpotent lie algebras of operators especially we consider conditions on a lie algebra of operators that imply that the closed algebra generated by the lie algebra is commutative modulo the radical we also give an application to polynomially compact operators

new objective functions for waveform inversion inversion is an organized search for parameter values that maximize or minimize an objective function referred to here as a processor this note derives three new seismic processors that require neither prior deconvolution nor knowledge of the source receiver wavelet the most powerful of these is the fourwise processor as it is applicable to data sets from multiple shots and receivers even when each shot has a different unknown signature and each receiver has a different unknown impulse response somewhat less powerful than the fourwise processor is the pairwise processor which is applicable to a data set consisting of two or more traces with the same unknown wavelet but possibly different gains when only one seismogram exists the partition processor can be used the partition processor is also applicable when there is only one shot receiver and each receiver shot has a different signature in fourwise and pairwise inversions the unknown wavelets may be arbitrarily long in time and need not be mi

an enhanced russell measure in dea with interval data abstract traditional data envelopment analysis dea models do not deal with imprecise data and assume that the data for all inputs and outputs are known exactly in real world situations however this assumption may not always be true when some inputs and outputs are unknown decision variables such as interval data ordinal data and ratio bounded data the dea model is called imprecise dea idea in this paper we develop a new approach based upon the enhanced russell measure erm for dealing with interval data in dea

improvement of efficiency intervals based on dea by adjusting inputs and outputs we improve the efficiency interval of a dmu by adjusting its given inputs and outputs the interval dea model has been formulated to obtain an efficiency interval consisting of evaluations from both the optimistic and pessimistic viewpoints dmus which are not rated as efficient in the conventional sense are improved so that their lower bounds become as large as possible under the condition that their upper bounds attain the maximum value one the adjusted inputs and outputs keep each other balanced by improving the lower bound of efficiency interval since the lower bound becomes small if all the inputs and outputs are not proportioned in order to improve the lower bound of efficiency interval different target points are defined for different dmus the target point can be regarded as a kind of benchmark for the dmu first a new approach to improvement by adjusting only outputs or inputs is proposed then the combined approach to improvement by adjusting both inputs and outputs simultaneously is proposed lastly numerical examples are shown to illustrate our proposed approaches

fuzzy multiattribute grey related analysis using dea qualitative input is encountered in many real decision making domains often such domains include tradeoffs among multiple attributes and estimates of parameters are often expressed with some degree of uncertainty grey related analysis has been proposed as a means to use interval fuzzy representation of data when dealing with multiple criteria data model parameters that can involve uncertainty include both performances of alternatives on attributes as well as attribute weights dea is proposed as an objective way to derive weights this paper presents a grey related fuzzy set methodology incorporating data envelopment analysis as a way to more objectively rank alternatives the purpose is to demonstrate the method the focus is on identifying alternatives performing the most efficiently with respect to the decision maker s preference the method is demonstrated on a multiattribute siting problem simulation is applied to validate model efficiency

a taxonomy and review of the fuzzy data envelopment analysis literature two decades in the making data envelopment analysis dea is a methodology for measuring the relative efficiencies of a set of decision making units dmus that use multiple inputs to produce multiple outputs crisp input and output data are fundamentally indispensable in conventional dea however the observed values of the input and output data in real world problems are sometimes imprecise or vague many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in dea in this study we provide a taxonomy and review of the fuzzy dea methods we present a classification scheme with four primary categories namely the tolerance approach the a level based approach the fuzzy ranking approach and the possibility approach we discuss each classification scheme and group the fuzzy dea papers published in the literature over the past 20 years to the best of our knowledge this paper appears to be the only review and complete source of references on fuzzy dea

comparison of source independent methods of elastic waveform inversion in this paper we investigate several source independent methods of nonlinear full waveform inversion of multicomponent elastic wave data this includes iterative estimation of source signature ies standard trace normalization stn and average trace normalization atn inversion methods all are based on the finite element method in the frequency domain one synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature kss inversion method the numerical experiments show that the ies method is superior to both stn and atn methods in two component elastic wave inversion in the frequency domain when the source signature is unknown the stn and atn methods have limitations associated with near zero amplitudes or polarity reversals in traces from one of the components which destroy the energy balance in the normalized traces and cause a loss of frequency information but the atn method is somewhat superior to the stn method in suppressing random noise and improving stability as the developed formulas and the numerical experiments show we suggest the ies method as a practical procedure for multicomponent seismic inversion

solvable jordan algebras of compact operators it is proved that a jordan algebra of compact operators which is closed is either an engel jordan algebra or contains a nonzero finite rank operator moreover it is showed that any solvable jordan algebra of compact operators on an infinite dimensional banach space is triangularizable

source independent time domain waveform inversion using convolved wavefields application to the encoded multisource waveform inversion full waveform inversion requires a good estimation of the source wavelet to improve our chances of a successful inversion this is especially true for an encoded multisource time domain implementation which conventionally requires separate source modeling as well as the fourier transform of wavefields as an alternative we have developed the source independent time domain waveform inversion using convolved wavefields specifically the misfit function consists of the convolution of the observed wavefields with a reference trace from the modeled wavefield plus the convolution of the modeled wavefields with a reference trace from the observed wavefield in this case the source wavelet of the observed and the modeled wavefields are equally convolved with both terms in the misfit function and thus the effects of the source wavelets are eliminated furthermore because the modeled wavefields play a role of low pass filtering the observed wavefields in the misfit function the frequency selection stra

from local to global triangularization abstract it is shown that a semigroup of shatten p class operators is simultaneously triangularizable if each pair of operators in the semigroup is triangularizable several sufficient conditions for triangularizability of semigroups are obtained as corollaries a block triangularization theorem for algebras of compact operators is established consequences of which include a number of necessary and sufficient conditions for triangularization of such algebras

an improvement to the cost efficiency interval a dea based approach the purpose of this paper is to improve the cost efficiency interval of a decision making unit by adjusting its observed inputs and outputs we first propose a dea based model with an interval efficiency in which the lower bound and upper bound of this interval are respectively the efficiency obtained from optimistic and pessimistic viewpoints then units which are not prevail as cost efficient are improved so that their lower bounds of cost efficiency become as large as possible and their upper bound attain the maximum value 1 the particular application area investigated is that involving the gas companies of iran

robust source independent elastic full waveform inversion in the time domain abstractaccurate estimation of source wavelet is crucial in a successful full waveform inversion fwi however it cannot be guaranteed in the case of real seismic data we have developed time domain source independent elastic fwi using the convolution based objective function that was originally developed for acoustic fwi we have applied a new time window on the reference traces in the objective function to suppress the noises induced by the convolution and crosscorrelation operations also we have adopted l1 huber and hybrid norm objective functions to improve the antinoise ability of our algorithm we implemented a multiscale inversion strategy to conduct the tests with a quasi newton limited memory broyden fletcher goldfarb shanno l bfgs method to reduce the sensitivity to initial models and to improve the quality of inversion results synthetic tests verified that the new added time window can not only improve the inversion results but also accelerate the convergence rate our method can be

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

a new ranking method to fuzzy data envelopment analysis due to its wide practical use data envelopment analysis dea has been adapted to many fields to deal with problems that have occurred in practice one adaptation has been in the field of ranking decision making units dmus most methods of ranking dmus assume that all input and output data are exactly known but in real life the data cannot be precisely measured thus this paper will carry out some researches to dea under fuzzy environment a fuzzy comparison of fuzzy variables is defined and the ccr model is extended to be a fuzzy dea model based on credibility measure in order to rank all the dmus a full ranking method will be given since the ranking method involves a fuzzy function a fuzzy simulation is designed and embedded into the genetic algorithm to establish a hybrid intelligent algorithm however it is shown to be possible to avoid some of the need for dealing with these nonlinear problems by identifying conditions under which they can be replaced by linear problems finally we will provide a numerical example to illustrate the fuzzy dea model and the ranking method

dea efficiency assessment using ideal and anti ideal decision making units this paper introduces two virtual decision making units dmus called ideal dmu idmu and anti ideal dmu admu into the data envelopment analysis dea the resultant dea models are respectively referred to as the data envelopment analysis with ideal and anti ideal decision making units one evaluates dmus from the viewpoint of the best possible relative efficiency while the other evaluates them from the perspective of the worst possible relative efficiency the two distinctive efficiencies are combined to form a comprehensive index called the relative closeness rc to the idmu just like the well known topsis approach in multiple attribute decision making madm the rc index is then used as the evidence of overall assessment of each dmu based on which an overall ranking for all the dmus can be obtained two numerical examples are provided to illustrate the applications of the proposed dea models and the rc index

nonlinear waveform tomography applied to crosshole seismic data the acoustic inverse problem of crosshole seismology is nonlinear in the medium velocities and ill posed because of the lack of complete data coverage surrounding the area of interest in light of these facts this paper develops a new nonlinear waveform tomography technique for imaging acoustic velocities from crosshole seismic data the technique based on tikhonov regularization defines solution models that minimize the normed misfit between observed and modeled data subject to a constraint on the spatial roughness of the model this type of regularization produces minimum structure velocity models which can vary in their degree of smoothness versus fit to the data we solve the tikhonov minimization condition numerically using a conjugate gradient algorithm to accurately calculate the components of the forward problem we use a frequency domain integral equation method with sinc basis functions the integral equation method discretizes the integral form of the acoustic wave equation over a 2 d area

on return to scale of fully efficient dmus in data envelopment analysis under interval data recently cooper et al manage sci 45 1999 597 proposed imprecise data envelopment analysis idea a situation in which some or all data are unknown the data in idea could be interval data ordinal data or data with bounded ratio usually in such cases the corresponding data envelopment analysis models becomes non linear when data assume to be interval decision making units dmus can divide to three classes as follows i efficient in any cases ii efficient in maximal sense iii always inefficient in this paper we investigate to the return to scale of dmus that are locate in first class also we introduce models that use exact data and present a combination if any which via that the dmu becomes a most productive scale size

on simultaneous triangularization of collections of compact operators abstract in this paper we consider collections of compact resp c p class operators on arbitrary banach resp hilbert spaces for a subring r of reals it is proved that an r algebra of compact operators with spectra in r on an arbitrary banach space is triangularizable if and only if every member of the algebra is triangularizable it is proved that every triangularizability result on certain collections e g semigroups of compact operators on a complex banach resp hilbert space gives rise to its counterpart on a real banach resp hilbert space we use our main results to present new proofs as well as extensions of certain classical theorems e g those due to kolchin mccoy and others on arbitrary banach resp hilbert spaces

efficient calculation of the steepest descent direction for source independent seismic waveform inversion an amplitude approach in seismic waveform inversion if we have no information on source signature we need to invert seismic data and source signature either simultaneously or successively in order to avoid the iterative update of the source signature in waveform inversion based on classical local optimization techniques we propose two source independent objective functions using amplitude spectra of fourier transformed wavefields one is constructed by normalizing the amplitude spectra of observed data and modeled data with respect to the respective reference amplitudes the other is achieved by cross multiplying the amplitude spectra of observed data and modeled data with the respective reference amplitudes in the computation of the steepest descent direction we circumvent explicitly computing the jacobian by employing a matrix formalism of the wave equation in the frequency domain through numerical examples for the marmousi model we demonstrate that our inversion algorithms can reproduce the subsurface velocity structure without estimating source signature

multifrequency viscoacoustic modeling and inversion modeling and inversion for seismic wavefields that include the attenuation and phase dispersion effects of q can be implemented in the space frequency domain the viscoacoustic wave equation is solved by the moment method absorbing boundary conditions are implemented by reducing q and adjusting the complex velocity to reduce q dependent reflectivity in a zone around the edges of the model grid nonlinear inversion is performed using iterative linearized inversions the residual wavefield at a single frequency is back projected using an anticausal green s function along the viscoacoustic wavepath in an estimate of the model to get updated velocity and q distributions the model obtained from data at one frequency becomes input to inversion at the next higher frequency velocity and q are inverted simultaneously as they are interdependent both modeling and inversion algorithms are successfully tested with synthetic examples data at two or three frequencies are sufficient to produce reliable images from noise free synthetic data

a comment on dea efficiency assessment using ideal and anti ideal decision making units abstract one of the main objectives of data envelopment analysis dea is the relative efficiency assessment for a set of decision making units dmus this paper concentrates on a previously reported dea efficiency assessment method developed by wang and luo y m wang y luo dea efficiency assessment using ideal and anti ideal decision making units applied mathematics and computation 173 2006 902 915 and later improved by wu d wu a note on dea efficiency assessment using ideal point an improvement of wang and luo s model applied mathematics and computation 183 2006 819 830 a discussion is made about wu s argument and improvement of wang and luo s model after a revisit to the previous two works a supplementary investigation of wang and luo s model is provided and a rescaled model is proposed to handle the problems involved in their model theoretical analysis and numerical illustrations demonstrate that it should be reassuring to apply wang and luo s model for overall dea efficiency assessment and ranking

on the computation of the frechet derivatives for seismic waveform inversion in 3d general anisotropic heterogeneous media we present a perturbation method and a matrix method for formulating the explicit frechet derivatives for seismic body wave waveform inversion in 3d general anisotropic heterogeneous media theoretically the two methods yield the same explicit formula valid for any class of anisotropy and are completely equivalent if the model parameterization in the inversion is the same as that used in the discretization scheme unstructured or structured mesh for forward modeling explicit formulas allow various model parameterization schemes that try to match the resolution capability of the data and possibly reduce the dimensions of the jacobian matrix based on the general expressions relevant formulas for isotropic and 2 5d and 3d tilted transversely isotropic tti media are derived two computational schemes constant point and constant block parameterization offer effective and efficient means of forming the jacobian matrix from the explicit frechet derivatives the sensitivity patterns of the displacement vector to the independent model parameters in a weakly anisotropic medium clearly convey the imaging capability possible with seismic waveform inversion in such an anisotropic medium

interval efficiency assessment using data envelopment analysis this paper studies how to conduct efficiency assessment using data envelopment analysis dea in interval and or fuzzy input output environments a new pair of interval dea models is constructed on the basis of interval arithmetic which differs from the existing dea models handling interval data in that the former is a linear ccr model without the need of extra variable alternations and uses a fixed and unified production frontier i e the same constraint set to measure the efficiencies of decision making units dmus with interval input and output data while the latter is usually a nonlinear optimization problem with the need of extra variable alternations or scale transformations and utilizes variable production frontiers i e different constraint sets to measure interval efficiencies ordinal preference information and fuzzy data are converted into interval data through the estimation of permissible intervals and a level sets respectively and are incorporated into the interval dea models the proposed interval dea models are developed for measuring the lower and upper bounds of the best relative efficiency of each dmu with interval input and output data which are different from the interval formed by the worst and the best relative efficiencies of each dmu a minimax regret based approach mra is introduced to compare and rank the efficiency intervals of dmus two numerical examples are provided to show the applications of the proposed interval dea models and the preference ranking approach

quasinilpotent banach lie algebras are baker campbell hausdorff abstract it is proved that for a banach lie algebra l the baker campbell hausdorff series converges for any pair a b l if and only if for each c l the adjoint operator a dc is quasi nilpotent

evaluating the performances of decision making units based on interval efficiencies efficiency could be not only the ratio of weighted sum of outputs to that of inputs but also that of weighted sum of inputs to that of outputs when the previous efficiency measures the best relative efficiency within the range of no more than one the decision making units dmus who get the optimum value of one perform best among all the dmus if the previous efficiency is measured within the range of no less than one the dmus who get the optimum value of one perform worst among all the dmus when the later efficiency is measured within the range of no more than one the dmus who get the optimum value of one perform worst among all the dmus if the later efficiency is measured within the range of no less than one the dmus who get the optimum value of one perform best among all the dmus this paper mainly studies an interval dea model with later efficiency in which efficiency is measured within the range of an interval whose upper bound is set to one and the lower bound is determined by introducing a virtual ideal dmu whose performance is definitely superior to any dmus the efficiencies obtained from interval dea model turn out to be all intervals and are referred to as interval efficiencies which combine the best and the worst relative efficiency in a reasonable manner to give an overall assessment of performances for all dmus assessor s preference information on input and output weights is also incorporated into interval dea model reasonably and conveniently through an example some differences are found from the ranking results obtained from interval dea model and bounded dea model using the hurwicz criterion approach to rank the interval efficiencies

crosshole seismic using vertical eigenstates this paper introduces the concept of vertical eigenstates to crosshole data analysis in surface seismics plane waves have played a fundamental role in many applications this paper points out that for crosshole seismics vertical eigenstates play a similar role the vertical eigenstates separate the wave equation and thus in terms of vertical eigenstate expansion the solution is a linear combination of modes each mode traveling sideways with a distinct phase velocity as a result the vertical eigenstates form a natural set of basis functions for solution and data expansion with potential applications to modeling migration and inversion

composite boundary valued solution of the 2 5 d green s function for arbitrary acoustic media theoretically the green s function can be used to calculate the wavefield response of a specified source and the frechet derivative with respect to the model parameters for crosshole seismic full waveform inversion in this paper we apply the finite element method to numerically compute the 2 5 d green s function for an arbitrary acoustic medium by solving a composite boundary valued problem in the wavenumber frequency domain the composite boundary condition consists of a 2 5 d absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling a numerical experiment performed for a uniform earth having a known exact solution shows the accuracy of the computation in the frequency and time domain an inhomogeneous medium test involving an embedded low velocity layer demonstrates that the permissible range of ky at each frequency can be determined rationally from the critical wavenumber value of the medium around the sou

finite dimensional solvable lie algebras generated by normal operators are commutative it is proved that any finite dimensional solvable lie algebra generated by normal operators is commutative and some other related results are given

application of the variable projection scheme for frequency domain full waveform inversion abstractwe found a data calibration scheme for frequency domain full waveform inversion fwi the scheme is based on the variable projection technique with this scheme the fwi algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters the calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data this process is directly included in the data misfit cost function therefore the inversion algorithm becomes source independent moreover because all the data points are considered in the calibration process this scheme increases the robustness of the algorithm numerical tests determined that the fwi algorithm can reconstruct velocity distributions accurately without the source waveform information

a fuzzy mathematical programming approach to the assessment of efficiency with dea models in many real applications the data of production processes cannot be precisely measured this is particularly worrying when assessing efficiency with frontier type models such as data envelopment analysis dea models since they are very sensitive to possible data errors for this reason the possibility of having available a methodology that allows the analyst to deal with imprecise data becomes an issue of great interest in these contexts to that end we develop some fuzzy versions of the classical dea models in particular the bcc model by using some ranking methods based on the comparison of cuts the resulting auxiliary crisp problems can be solved by the usual dea software we show in a numerical example how our models become specially useful for detecting sensitive decision making units our approaches can be seen as an extension of the dea methodology that provides users and practitioners with models which represent some real life processes more appropriately

the orthogonal lie algebra of operators ideals and derivations abstract we study in this paper the infinite dimensional orthogonal lie algebra o c which consists of all bounded linear operators t on a separable infinite dimensional complex hilbert space h satisfying c t c t where c is a conjugation on h by employing results from the theory of complex symmetric operators and skew symmetric operators we determine the lie ideals of o c and their dual spaces we study derivations of o c and determine their spectra these results complete some results of p de la harpe and provide interesting contrasts between o c and the algebra b h of all bounded linear operators on h

interval efficiency measures in data envelopment analysis with imprecise data the conventional data envelopment analysis dea measures the relative efficiencies of a set of decision making units dmus with exact values of inputs and outputs for imprecise data i e mixtures of interval data and ordinal data some methods have been developed to calculate the upper bound of the efficiency scores this paper constructs a pair of two level mathematical programming models whose objective values represent the lower bound and upper bound of the efficiency scores respectively based on the concept of productive efficiency and the application of a variable substitution technique the pair of two level nonlinear programs is transformed to a pair of ordinary one level linear programs solving the associated pairs of linear programs produces the efficiency intervals of all dmus an illustrative example verifies the idea of this paper a real case is also provided to give some interpretation of the interval efficiency interval efficiency not only describes the real situation in better detail psychologically it also eases the tension of the dmus being evaluated as well as the persons conducting the evaluation

an inverse dea model for inputs outputs estimate abstract in this paper we discuss such problems if among a group of decision making units we increase certain inputs to a particular unit and assume that the dmu maintains its current efficiency level with respect to other units how much more outputs could the unit produce or if the outputs need to be increased to a certain level and the efficiency of the unit remains unchanged how much more inputs should be provided to the unit we treat them as inverse data envelopment analysis dea problems and propose a method to solve such problems the problem is transformed into a multi objective programming problem to solve though in some special cases it can be answered by solving just one single object lp problem we use two examples to illustrate our computation method

fuzzy efficiency without convexity in this paper we develop a fuzzy version of the crisp free disposal hull fdh method for measuring technical efficiency for samples of similar production units the fdh method is basically data envelopment analysis dea without the underlying assumption of convexity of the technology set our approach builds directly upon the definition of farrell s indexes of technical efficiency used in crisp fdh therefore we do not require the use of fuzzy programming techniques but only utilize ranking probabilities of intervals as well as a related definition of dominance between pairs of intervals we illustrate the approach using a data set of 200 lithuanian family farms for the period of 2004 2009 2014 elsevier b v all rights reserved

a simple approximation of productivity scores of fuzzy production plans this paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans the procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational

finite element formulation of acoustic scattering phenomena with absorbing boundary condition in the frequency domain this paper discusses a finite element formulation with an absorbing boundary condition to simulate acoustic scattering phenomena in a general situation that is including density as well as sound velocity variations of single and multi scatterers of arbitrary two dimensional cross sections in this model a galerkin finite element formulation is incorporated with an absorbing boundary operator that explicitly accounts for the open field problem by mapping the sommerfeld radiation condition from the far field to the near field by applying the absorbing boundary operator on the artificial boundary of the finite domain the truncation errors as well as the artificial reflected power is minimized without compromising the sparsity of the finite element matrix performance analysis indicates that the absorbing boundary operator increases the accuracy from o 1 r3 2 to o 1 r9 2 the numerical results are compared with analytical solutions of cylindrical scatterers of different sizes and at different frequenci

seismic waveform inversion in the frequency domain part 1 theory and verification in a physical scale model seismic waveforms contain much information that is ignored under standard processing schemes seismic waveform inversion seeks to use the full information content of the recorded wavefield in this paper i present apply and evaluate a frequency space domain approach to waveform inversion the method is a local descent algorithm that proceeds from a starting model to refine the model in order to reduce the waveform misfit between observed and model data the model data are computed using a full wave equation viscoacoustic frequency domain finite difference method ray asymptotics are avoided and higher order effects such as diffractions and multiple scattering are accounted for automatically the theory of frequency domain waveform wavefield inversion can be expressed compactly using a matrix formalism that uses finite difference finite element frequency domain modeling equations expressions for fast local descent inversion using back propagation techniques then follow naturally implementation of

a critical appraisal of asymptotic 3d to 2d data transformation in full waveform seismic crosshole tomography abstractseismic full waveform inversion fwi is often based on forward modeling in the computationally attractive 2d domain this implies the assumption of a line source extended in the out of plane medium invariant direction with far field amplitudes decaying inversely with the square root of distance realistic point sources however generate amplitudes that decay approximately with the inverse of distance conventionally practitioners correct for this amplitude difference and the associated phase shift by transforming the recorded 3d field data to the approximate 2d equivalent by using simplistic asymptotic filter algorithms such filters assume straight raypaths a constant velocity medium and far field recordings we have assessed the validity of 3d to 2d data transformation in the context of crosshole seismic full waveform tomography by propagating 3d and 2d wavefields through 2d media and comparing 2d reference synthetics with their filtered 3d equivalent the filter performs well in simple si

irreducible compact operators the purpose of the present paper is to show that a positive compact ideal irreducible operator t in a banach lattice of dimension greater than one has spectral radius r t 0 i e t is not quasi nilpotent it was shown in 6 that there exist positive irreducible operators which are quasi nilpotent and the question under what conditions a positive irreducible operator t satisfies r t 0 has been studied extensively see e g 6 and 7 sect v 6 in particular we mention the ando krieger theorem see e g 9 theorem 136 9 which states that a positive irreducible kernel operator t in a banach function space has r t 0 recently in 8 some special situations are discussed in which a compact positive irreducible operator has a strictly positive spectral radius let l be a real or complex banach lattice by 2 we denote the banach space of all bounded linear operators in l as usual we write s t in l whenever su tu for all o uel given 0 t l the closed ideal j in l is called t invariant if t j j and t is called ideal irreducible if the only closed t invariant ideals are 0 and l see 7 iii 8 for the general theory of banach lattices and positive operators we refer to the books 7 and 9 in the proof of the main result of the paper we will use some properties of the center of a banach lattice we recall some elementary facts let l be a real banach lattice the center z l of l is the subspace of 5 l consisting of all operators z for which there exists 0 2 ir such that f l 2 f for all f l the center has the structure of a vector lattice with nl v n2 u n l u v n2u and ozla zz u lu a nzu for all o u l and all l n2ez l moreover z l is a commutative algebra with respect to composition as multiplication and the identity operator i in l is a strong unit i e for any rc z l there exists 0 2eir such that zi 2i see 9 chap 20 note that if l c k for some compact hausdorff space k then z l can be identified with c k acting on itself by multiplication if l is a dedekind complete banach lattice and 0 u v in l then it is an easy consequence of the freudenthal spectral theorem 4 theorem 40 2 that there exists n z l such that zcv u and o n i however in an arbitrary banach lattice such a 7z need not exist as is shown by the banach lattice l c 0 1 the next lemma shows that under rather mild conditions we can

the berger wang formula for the markovian joint spectral radius abstract the berger wang formula establishes equality between the joint and generalized spectral radii of a set of matrices for matrix products whose multipliers are applied not arbitrarily but in accordance with some markovian law there are also known analogs of the joint and generalized spectral radii however the known proofs of the berger wang formula hardly can be directly applied in the case of markovian products of matrices since they essentially rely on the arbitrariness of appearance of different matrices in the related matrix products nevertheless as has been shown by x dai 1 the berger wang formula is valid for the case of markovian analogs of the joint and the generalized spectral radii too although the proof in this case heavily exploits the more involved techniques of multiplicative ergodic theory in the paper we propose a matrix theory construction allowing to deduce the markovian analog of the berger wang formula from the classical berger wang formula

irreducible representations of infinite dimensional lie algebras abstract some results concerning the operatorially irreducible topologically irreducible operatorially and topologically irreducible representations of a class of infinite dimensional lie algebras by bounded operators in a complex banach space are obtained

measuring the performances of decision making units using interval efficiencies efficiency is a relative measure because it can be measured within different ranges the traditional data envelopment analysis dea measures the efficiencies of decision making units dmus within the range of less than or equal to one the corresponding efficiencies are referred to as the best relative efficiencies which measure the best performances of dmus and determine an efficiency frontier if the efficiencies are measured within the range of greater than or equal to one then the worst relative efficiencies can be used to measure the worst performances of dmus and determine an inefficiency frontier in this paper the efficiencies of dmus are measured within the range of an interval whose upper bound is set to one and the lower bound is determined through introducing a virtual anti ideal dmu whose performance is definitely inferior to any dmus the efficiencies turn out to be all intervals and are thus referred to as interval efficiencies which combine the best and the worst relative efficiencies in a reasonable manner to give an overall measurement and assessment of the performances of dmus the new dea model with the upper and lower bounds on efficiencies is referred to as bounded dea model which can incorporate decision maker dm or assessor s preference information on input and output weights a hurwicz criterion approach is introduced and utilized to compare and rank the interval efficiencies of dmus and a numerical example is examined using the proposed bounded dea model to show its potential application and validity

wave equation tomography the relation between ray trace and diffraction tomography is usually obscured by formulation of the two methods in different domains the former in space the latter in wavenumber here diffraction tomography is reformulated in the space domain under the title of wave equation tomography with this transformation wave equation tomography projects monochromatic scattered wavefields back over source receiver wavepaths just as ray trace tomography projects traveltime delays back over source receiver raypaths derived under the born approximation these wavepaths are wave theoretic back projection patterns for reflected energy derived under the rytov approximation they are wave theoretic back projection patterns for transmitted energy differences between ray trace and wave equation tomography are examined through comparison of wavepaths and raypaths followed by their application to a transmission geometry synthetic data set rytov wave equation tomography proves superior to ray trace tomography in de

dual models of interval dea and its extension to interval data abstract the purpose of this paper is to develop a new dea with an interval efficiency an original dea model is to evaluate each dmu optimistically there is another model called inverted dea to evaluate each dmu pessimistically but there are no relations essentially between dea and inverted dea thus we formulate a dea model with an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints thus two end points can construct an interval efficiency with the same idea we deal with the interval inefficiency model which is inverse to interval efficiency finally we extend the proposed dea model to interval data and fuzzy data

spectral conditions on lie and jordan algebras of compact operators abstract we investigate the properties of bounded operators which satisfy a certain spectral additivity condition and use our results to study lie and jordan algebras of compact operators we prove that these algebras have nontrivial invariant subspaces when their elements have sublinear or submultiplicative spectrum and when they satisfy simple trace conditions in certain cases we show that these conditions imply that the algebra is simultaneously triangularizable

fuzzy data envelopment analysis dea model and ranking method data envelopment analysis dea is a very effective method to evaluate the relative efficiency of decision making units dmus since the data of production processes cannot be precisely measured in some cases the uncertain theory has played an important role in dea this paper attempts to extend the traditional dea models to a fuzzy framework thus producing a fuzzy dea model based on credibility measure following is a method of ranking all the dmus in order to solve the fuzzy model we have designed the hybrid algorithm combined with fuzzy simulation and genetic algorithm when the inputs and outputs are all trapezoidal or triangular fuzzy variables the model can be transformed to linear programming finally a numerical example is presented to illustrate the fuzzy dea model and the method of ranking all the dmus

cost efficiency measures in data envelopment analysis with data uncertainty this paper extends the classical cost efficiency ce models to include data uncertainty we believe that many research situations are best described by the intermediate case where some uncertain input and output data are available in such cases the classical cost efficiency models cannot be used because input and output data appear in the form of ranges when the data are imprecise in the form of ranges the cost efficiency measure calculated from the data should be uncertain as well so in the current paper we develop a method for the estimation of upper and lower bounds for the cost efficiency measure in situations of uncertain input and output data also we develop the theory of efficiency measurement so as to accommodate incomplete price information by deriving upper and lower bounds for the cost efficiency measure the practical application of these bounds is illustrated by a numerical example

crosshole seismic inversion with normalized full waveform amplitude data we investigate a simple scheme for full waveform amplitude spectrum inversion of crosshole seismic data with an unknown source wavelet the method is based on our 2d 2 5d finite element method of acoustic wave modeling the normalized amplitude data defined as the spectral ratio of the original trace amplitude to the average amplitude for the entire common shot gather are used for full waveform inversion in the frequency domain in essence the normalization of amplitudes removes the source wavelet and is easily carried out in the time domain or frequency domain from crosshole seismic surveying two synthetic models simulating respectively a dipping fracture model and a complicated sedimentary structure are examined with the inversion scheme the numerical results show that clear images of the targets can be obtained by using the single and multiple frequency data for comparison two other amplitude inversion schemes in which the source signatures are known and estimated with an iterative procedure were carried out for the same models the results show that the iteratively source estimated procedure also produces satisfactory images of the velocity structure and yields an approximate amplitude of the source wavelet with the multifrequency data three such schemes yield very competitive results

volterra semigroups have invariant subspaces abstract it is proved that any multiplicative semigroup consisting of compact quasinilpotent operators on a banach space is triangularizable the consequences are discussed

the generalized spectral radius theorem an analytic geometric proof abstract let be a bounded set of complex matrices m a 1 a m a i the generalized spectral radius theorem states that where and are defined as follows lim sup m 1 m where m sup a a m with a the spectral radius lim sup m 1 m where m sup a a m with any matrix norm we give an elementary proof based on analytic and geometric tools which is in some ways simpler than the first proof by berger and wang

invariant subspaces of operator lie algebras and lie algebras with compact adjoint action it is proved that a lie algebra of compact operators with a non zero volterra ideal is reducible has a nontrivial invariant subspace a number of other criteria of reducibility for collections of operators is obtained the results are applied to the structure theory of lie algebras of compact operators and normed lie algebras with compact adjoint action

joint spectral radius operator semigroups and a problem of w wojtynski abstract we investigate the connections between the invariant subspace problem for operator semigroups and the joint spectral radius as a consequence it is proved that any quasinilpotent lie algebra of compact operators on a banach space is triangularizable we extend the berger wang formula to precompact sets of essentially scalar operators and prove the continuity of the joint spectral radius on them

the generalised berger wang formula and the spectral radius of linear cocycles using ergodic theory we prove two formulae describing the relationships between different notions of joint spectral radius for sets of bounded linear operators acting on a banach space the first formula was previously obtained by v s shulman and yu v turovski using operator theoretic ideas the second formula shows that the joint spectral radii corresponding to several standard measures of noncompactness share a common value when applied to a given precompact set of operators this result may be seen as an extension of classical formulae for the essential spectral radius given by r nussbaum a lebow and m schechter both results are obtained as a consequence of a more general theorem concerned with continuous operator cocycles defined over a compact dynamical system as a byproduct of our method we answer a question of j e cohen on the limiting behaviour of the spectral radius of a measurable matrix cocycle

two and one half dimensional born inversion with an arbitrary reference multidimensional inversion algorithms are presented for both prestack and poststack data gathered on a single line these algorithms both image the subsurface i e give a migrated section and given relative true amplitude data estimate reflection strength or impedance on each reflector the algorithms are two and one half dimensional 2 5 d in that they incorporate three dimensional 3 d wave propagation in a medium which varies in only two dimensions the use of 3 d sources does not entail any computational penalty and it avoids the serious degradation of amplitude incurred by using the 2 d wave equation our methods are based on the linearized inversion theory associated with the born inversion thus we assume that the sound speed profile is well approximated by a given background velocity plus a perturbation it is this perturbation that we seek to reconstruct we are able to treat the case of an arbitrary continuous background profile however the cost of implementation increases as one

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

topologically irreducible representations and radicals in banach algebras it is shown that the topologically irreducible representations of a normed algebra define a certain topological radical in the same way that the strictly irreducible representations define the jacobson radical and that this radical can be strictly smaller than the jacobson radical an abstract theory of topological radicals in topological algebras is developed and used to relate this radical to the baer radical prime radical the relations with topologically transitive representations and standard representations in the sense of meyer are also explored 1991 mathematics subject classification 46h15 46h25 16nxx

banach lie algebras with lie subalgebras of finite codimension their invariant subspaces and lie ideals the paper studies the existence of closed invariant subspaces for a lie algebra l of bounded operators on an infinite dimensional banach space x it is assumed that l contains a lie subalgebra l0 that has a non trivial closed invariant subspace in x of finite codimension or dimension it is proved that l itself has a non trivial closed invariant subspace in the following two cases 1 l0 has finite codimension in l and there are lie subalgebras l0 l0 l1 lp l such that li 1 li li li 1 for all i 2 l0 is a lie ideal of l and dim l0 these results are applied to the problem of the existence of non trivial closed lie ideals and closed characteristic lie ideals in an infinite dimensional banach lie algebra l that contains a non trivial closed lie subalgebra of finite codimension

an asymptotic formula for the commutators in what follows we shall describe some asymptotic formulas for the commutators defined by the values of the analytic functional calculus of some commutingn tuple of bounded operators in a complex banach space

lie algebras generated by bounded linear operators on hilbert spaces abstract it is proved that the operator lie algebra e t t generated by a bounded linear operator t on hilbert space h is finite dimensional if and only if t n q n is a normal operator n q 0 and dim a q q where e t t denotes the smallest lie algebra containing t t and a q q denotes the associative subalgebra of b h generated by q q moreover we also give a sufficient and necessary condition for operators to generate finite dimensional semi simple lie algebras finally we prove that if e t t is an ad compact e solvable lie algebra then t is a normal operator

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

nonlinear diffractive inverse scattering for multiple scattering in inhomogeneous acoustic background media this paper discusses a nonlinear diffractive inversion of the helmholtz equation for multiscattering configurations where the scatterers are embedded in an inhomogeneous background medium using the finite element model to iteratively compute the scattered field in conjunction with a novel discrete cosine transform dct representation of the object function permits the development of an efficient nonlinear inversion algorithm the object function expansion is obtained by applying the dct to sampling points which are chosen at the zeros of the chebyshev polynomials and achieves an accuracy comparable to the more popular sinc basis with far fewer expansion terms after the inverse scattering formulation is converted into a nonlinear parameter estimation problem the final matrix equation is linearized and solved by a standard least squares algorithm several examples of two dimensional single and multiple scattering configurations for both homogeneous and inhomogeneous acoustic backgrounds will illustra

generalized spectral radius and its max algebra version abstract let c n n and r n n be bounded subsets and let and denote the generalized spectral radius of and the max algebra version of the generalized spectral radius of respectively we apply a single matrix description of to give a new elementary and straightforward proof of the berger wang formula in max algebra and consequently a new short proof of the original berger wang formula in the case of bounded subsets of n n non negative matrices we also obtain a new description of in terms of the schur hadamard product and prove new trace and max trace descriptions of and in particular we show that limsup m sup a m tr a 1 m limsup m sup a m tr a 1 m and limsup m sup b m tr b 1 m limsup m sup b m tr b 1 m where tr a max i 1 n a ii and b b ij

frequency domain acoustic wave modeling and inversion of crosshole data part 1 2 5 d modeling method crosshole experiments usually have sources and receivers confined to a plane and it is assumed that there is negligible variation in the properties of the medium normal to this plane therefore the problem appears two dimensional except for the sources which are 3 d points rather than lines this configuration is denoted as two and one half dimensional we present a frequency domain approach to modeling acoustic wave propagation in such situations which allows correct treatment of point sources but takes advantage of the assumed 2 d nature of the medium to avoid full 3 d simulations the approach uses a fourier transform with respect to the out of plane coordinate to reduce the problem of modeling in 3 d to repeatedly solving a 2 d equation which we accomplish using finite differences the discrete inverse fourier transform from the out of plane wavenumber implies the existence of an infinite number of spurious ghost sources spaced periodically in the out of plane direction these sources generate s