accelerating hessian free gauss newton full waveform inversion via l bfgs preconditioned conjugate gradient algorithm abstractfull waveform inversion fwi has emerged as a powerful strategy for estimating subsurface model parameters by iteratively minimizing the difference between synthetic data and observed data the hessian free hf optimization method represents an attractive alternative to newton type and gradient based optimization methods at each iteration the hf approach obtains the search direction by approximately solving the newton linear system using a matrix free conjugate gradient cg algorithm the main drawback with hf optimization is that the cg algorithm requires many iterations in our research we develop and compare different preconditioning schemes for the cg algorithm to accelerate the hf gauss newton gn method traditionally preconditioners are designed as diagonal hessian approximations we additionally use a new pseudo diagonal gn hessian as a preconditioner making use of the reciprocal property of green s function furthermore we have developed an l bfgs inverse hessian preconditioning

structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

a new asymptotically optimal code for the positive integers a new universal binary code for the positive integers is proposed as a modified version of m wang s see ibid vol 34 p 324 6 mar 1988 flag encoding scheme the codeword length of the new scheme is shorter than wang s on an average for large initial segments of the positive integers the performance of the new scheme is also compared with that of other universal schemes furthermore it is shown that an asymptotically optimal code can be achieved by modifying the new flag scheme such that the flag length varies dynamically

approximate linearized inversion by optimal scaling of prestack depth migration linearized inversion provides one possible sense of image amplitude correctness an image or bandlimited model perturbation has correct amplitudes if it is an approximate inversion that is if linearized modeling demigration with the image as input reproduces the data approximately the theory of linearized acoustic inverse scattering with slowly varying background or macromodel shows that an approximate inversion may be recovered from the output of prestack depth migration by a combination of scaling and filtering the necessary filter is completely specified by the theory and the scale factor may be estimated via filtering linearized modeling a second migration and the solution of a small auxiliary inverse problem

applications of high resolution time frequency transforms to attenuation estimation abstractattenuation estimates quantify the loss of energy of propagating seismic waves due to anelastic processes it is often carried out in the frequency domain the most well known methods for attenuation estimation such as the spectral ratio and frequency shift methods compare spectral shapes of waveforms along a given raypath they require broad spectra such as those obtained with the fourier transform and the continuous wavelet transform these methods are incompatible with high resolution time frequency transforms which drastically localize time frequency information on the other hand these transforms indicate stronger resistance to noise and can be used in combination with the peak frequency method to estimate attenuation we have applied high resolution transforms namely the synchrosqueezing transform basis pursuit and complete ensemble empirical mode decomposition to a synthetic wedge example and two seismic data set examples a seismic reflection profile and a vertical seismic profile

meta fibonacci codes efficient universal coding of natural numbers in this paper we address the problem of the universal coding of natural numbers a new numeration system is introduced which is based on variable r meta fibonacci sequences and it is a generalization of the zeckendorf numeration system this new numeration system is used to construct binary prefix free uniquely decodable universal codes called meta fibonacci codes the main advantage of these codes is that they are parametrized by a sequence of numbers the sequence o by controlling the growth of the values of this sequence we can control the length of the code word this means that we can provide a general framework for building efficient universal coders for natural numbers such framework is applied to the upper bounds of the code word length defined by leung yan cheong and cover 1978 levenshtein 1968 and ahlswede 1997 there is no other code meeting these bounds in each case we build meta fibonacci codes and demonstrate that the upper bound of their code word length is satisfied up to an additive constant thereby solving these open problems the framework may be applied to other upper bounds that satisfy kraft inequality

preconditioning of full waveform inversion in viscoacoustic media intrinsic absorption in the earth affects the amplitude and phase spectra of the seismic wavefields and records and may degrade significantly the results of acoustic full waveform inversion amplitude distortion affects the strength of the scatterers and decreases the resolution phase distortion may result in mislocated interfaces we show that viscoacoustic gradient based inversion algorithms e g steepest descent or conjugate gradients compensate for the effects of phase distortion but not for the effects of amplitude distortion to solve this problem at a reasonable numerical cost we have designed two new forms of preconditioning derived from an analysis of the inverse hessian operator the first type of preconditioning is a frequency dependent compensation for dispersion and attenuation which involves two extra modeling steps with inverse absorption amplification at each iteration the second type only corrects the strength of the recovered scatterers and requires two extra modeling steps at the first iteration only the new preconditioning methods have been incorporated into a finite difference inversion scheme for viscoacoustic media numerical tests on noise free synthetic data illustrate and support the theory

compensating q effects in viscoelastic media by adjoint based least squares reverse time migration low values of p and s wave quality factors qp and qs result in strong intrinsic seismic attenuation in both seismic modeling and imaging we use a linearized waveform inversion approach by generalizing least squares reverse time migration lsrtm for viscoelastic media q lsrtm to compensate the attenuation loss for both p and s images we use the first order particle velocity stress and memory variable equations with explicit q in the formulations based on the generalized standard linear solid gsls as the forward modeling operator the linearized two way viscoelastic modeling operator is obtained with modulus perturbations introduced for the relaxed p and s moduli the viscoelastic adjoint operator and the p and s imaging conditions for modulus perturbations are derived using the adjoint state method and an augmented lagrangian functional q lsrtm solves the viscoelastic linearized modeling operator for generating synthetic data and the adjoint operator is used for back propagating the data re

amplitude and kinematic corrections of migrated images for nonunitary imaging operators obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary one possible solution to this problem is iterative inversion however inversion is an expensive process that can be rather difficult to apply especially with 3d data in this paper i propose estimating migrated images similar to the least squares inverse images by approximating the inverse hessian thus avoiding the need for iterative inversion the inverse hessian is approximated with a bank of nonstationary matching filters these filters are not exact impulse responses and are limited in their ability to mimic the full effects of least squares inversion tests on two data sets show that this filtering approach gives results similar to iterative least squares inversion at a lower cost this technique is flexible enough to be applied to images migrated from zero offset or angle domain common image point gathers

quick and accurate q parameterization in viscoelastic wave modeling we introduce a procedure for including the attenuation factor q in a consistent manner in seismic modeling and show 3d examples the q fitting over a chosen frequency band involves two algorithms the first creates starting values of relaxation times and the second does nonlinear inversion using the results of the first as initial values the resulting q function gives a good approximation to a constant q over the chosen frequency band the algorithm is combined with a finite difference f d code that includes topographies in 3d seismic media the velocity stress formulation for viscoelastic wave modeling is used with an arbitrary number of relaxation mechanisms to model a desired q behavior these equations are discretized by high order f ds in the interior of the medium and we gradually reduce the f d order to two at the stress free surface where we implement our free surface boundary conditions the seismic f d algorithm is applied to a marine seismic experiment with and without viscoelasticity to emphasize the importance of including physical attenuation and dispersion in seismic modeling their inclusion even for marine surveys is clearly important for lossy ocean bottoms our procedure for more accurate modeling of physical dispersion and attenuation may increase future motivation to include viscoelasticity in seismic inversion

nonliner inversion of seismic reflection data in a laterally invariant medium interpretation of seismic waveforms can be expressed as an optimization problem based on a non linear least squares criterion to find the model which best explains the data an initial model is corrected iteratively using a gradient method conjugate gradient at each iteration computation of the direction of the model perturbation requires the forward propagation of the actual sources and the reverse time propagation of the residuals misfit between the data and the synthetics the two wave fields thus obtained are then correlated an extra forward propagation is required to compute the amplitude of the perturbation along the conjugate gradient direction the number of propagations to be simulated numerically in each iteration equals three times the number of shots since a 2 d finite difference code is employed to solve forward and backward propagation problems the method is general and can handle arbitrary 2 d source receiver configurations and lateral heterogeneities using conventional velocity

modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional laplacians we evaluated a time domain wave equation for modeling acoustic wave propagation in attenuating media the wave equation was derived from kjartansson s constant q constitutive stress strain relation in combination with the mass and momentum conservation equations our wave equation expressed by a second order temporal derivative and two fractional laplacian operators described very nearly constant q attenuation and dispersion effects the advantage of using our formulation of two fractional laplacians over the traditional fractional time derivative approach was the avoidance of time history memory variables and thus it offered more economic computations in numerical simulations we formulated the first order constitutive equations with the perfectly matched layer absorbing boundaries the temporal derivative was calculated with a staggered grid finite difference approach the fractional laplacians are calculated in the spatial frequency domain using a fourier pseudospectral implementation we validated our numerical results through comparisons with theoretical constant q attenuation and dispersion solutions field measurements from the pierre shale and results from 2d viscoacoustic analytical modeling for the homogeneous pierre shale we also evaluated different formulations to show separated amplitude loss and dispersion effects on wavefields furthermore we generalized our rigorous formulation for homogeneous media to an approximate equation for viscoacoustic waves in heterogeneous media we then investigated the accuracy of numerical modeling in attenuating media with different q values and its stability in largecontrast heterogeneous media finally we tested the applicability of our time domain formulation in a heterogeneous medium with high attenuation

elastic least squares reverse time migration abstractwe use elastic least squares reverse time migration lsrtm to invert for the reflectivity images of p and s wave impedances elastic lsrtm solves the linearized elastic wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration numerical tests on synthetic data and field data reveal the advantages of elastic lsrtm over elastic reverse time migration rtm and acoustic lsrtm for our examples the elastic lsrtm images have better resolution and amplitude balancing fewer artifacts and less crosstalk compared with the elastic rtm images the images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic lsrtm images similar to conventional least squares migration elastic lsrtm also requires an accurate estimation of the p and s wave migration velocity models however the problem remains that when there are moderate errors in the velocity model and strong multiples lsrtm

2d frequency domain elastic full waveform inversion using time domain modeling and a multistep length gradient approach abstractto decouple the parameters in elastic full waveform inversion fwi we evaluated a new multistep length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction to perform wavefield extrapolations for the inversion we used parallelized high precision finite element fe modeling in the time domain the inversion was implemented in the frequency domain the data were obtained at every subsurface grid point using the discrete fourier transform at each time domain extrapolation step we also used frequency selection to reduce cycle skipping time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data and source wavelet estimation at the receivers over the full frequency spectrum by using a fast fourier transform in the inversion the velocity and density reconstructions behaved differently as a low wavenumber tomography for v

multivariate methods for quantitative and qualitative data abstract in this paper several multivariate analysis methods are analyzed by means of the errors in variables model two specifications viz the principal relations and the principal factors model for the set of unobserved latent variables are introduced and shown to be complementary for particular choices of the error covariance matrix the general model reduces to several well known multivariate techniques including ordinary least squares principal components orthogonal regression and canonical correlations the same apparatus is used to arrive at a set of multivariate techniques in case the data is qualitative instead of quantitative the relationship with optimal scaling techniques for qualitative data is shown an empirical example is given of a regression involving a dependent latent variable having two ordered categorical indicator variables

loglinear models and categorical data analysis with psychometric and econometric applications revision abstract the past decade has seen the publication of a large number of books and papers on the analysis of multi way contingency tables using loglinear and logic models the present article presents a summary of the statistical theory that underlies much of this work and provides some linkage to models and methods of special interest to psychometricians and econometricians the discussion includes a review of recent and current research on the computation of maximum likelihood estimates for loglinear and logit models especially for large multi way contingency tables

fast least squares migration with a deblurring filter least squares migration lsm is a linearized waveform inversion for estimating a subsurface reflectivity model that relative to conventional migration improves spatial resolution of migration images the cost however is high because lsm typically requires 10 or more iterations which is at least 20 times more than the cpu cost of conventional migration to alleviate this expense we offer a deblurring filter that can be used in a regularization scheme or a preconditioning scheme to give acceptable lsm images with less than one third the cost of the standard lsm method our results in applying deblurred lsm to synthetic data and field data support this claim in particular a marmousi2 model test shows that the data residual for preconditioned deblurred lsm decreases rapidly in the first iteration which is equivalent to 10 or more iterations of lsm empirical results suggest that regularized deblurred lsm after three iterations is equivalent to about 10 iterations of lsm applying deblurred lsm to 2d marine data gives a higher resolution image compared to those from migration or lsm with three iterations these results suggest that lsm combined with a deblurring filter allows lsm to be a fast practical tool for improved imaging of complicated structures

q compensated least squares reverse time migration using low rank one step wave extrapolation abstractattenuation of seismic waves needs to be taken into account to improve the accuracy of seismic imaging in viscoacoustic media reverse time migration rtm can be performed with q compensation which is also known as q rtm least squares rtm lsrtm has also been shown to be able to compensate for attenuation through linearized inversion however seismic attenuation may significantly slow down the convergence rate of the least squares iterative inversion process without proper preconditioning we have found that incorporating attenuation compensation into lsrtm can improve the speed of convergence in attenuating media obtaining high quality images within the first few iterations based on the low rank one step seismic modeling operator in viscoacoustic media we have derived its adjoint operator using nonstationary filtering theory the proposed forward and adjoint operators can be efficiently applied to propagate viscoacoustic waves and to implement attenuation compensation recognizing that

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

on universal codeword sets the set of all binary strings terminated by a specific pattern is countably infinite and regular and satisfies the prefix property some properties of such codeword sets in the context of source coding are studied it is shown that some of them are universal and some of them are not but none is asymptotically optimal

the em approach to the multiple indicators and multiple causes model via the estimation of the latent variable abstract this article considers both likelihood and bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable the model is complicated by its reduced form which displays a mixture of econometric and psychometric themes we avoid this complexity via the estimation of the unobservable latent variable through direct use of the original structural form this approach not only provides maximum likelihood estimates that are equivalent to those derived from the reduced form but it also permits a feasible bayesian approach which would be technically complex to execute otherwise

a new parameter set for anisotropic multiparameter full waveform inversion and application to a north sea data set abstractparameterization lies at the center of anisotropic full waveform inversion fwi with multiparameter updates this is because fwi aims to update the long and short wavelengths of the perturbations thus it is important that the parameterization accommodates this recently there has been an intensive effort to determine the optimal parameterization centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations and aiming to determine which is best suited for multiparameter inversion we have developed a new parameterization in the scope of fwi based on the concept of kinematically equivalent media as originally proposed in other areas of seismic data analysis our analysis is also based on radiation patterns as well as the relation between the perturbation of this set of parameters and perturbation in traveltime the radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with on

modeling of a constant q methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique linear anelastic phenomena in wave propagation problems can be well modeled through a viscoelastic mechanical model consisting of standard linear solids in this paper we present a method for modeling of constant q as a function of frequency based on an explicit closed formula for calculation of the parameter fields several standard linear solids connected in parallel can be tuned through a single parameter to yield an excellent constant q approximation the proposed method enables substantial savings in computations and memory requirements experiments show that the new method also yields higher accuracy in the modeling of q than e g the pade approximant method

comments and additions to robust transmission of unbounded strings using fibonacci representations an ambiguous point in the paper by apostolico and fraenkel see ibid vol it 33 no 2 p 238 45 march 1987 is clarified new codes that have better asymptotic performances and better synchronization capability are introduced

on testing functional constraints in structural equation models summary in the context of a robust generalized least squares approach a new statistic for testing the validity of constraints in structural equation models is proposed it is shown that the new test requires significantly less computational effort than the traditional one extension to models in several populations is also considered illustrative applications based on real data are given

elastic least squares reverse time migration abstractleast squares migration can produce images with improved resolution and reduced migration artifacts compared with conventional imaging we have developed a method for elastic least squares reverse time migration lsrtm based on a new perturbation imaging condition that yields scalar images of squared p and s velocity perturbations these perturbation images do not suffer from polarity reversals that are common for more conventional elastic imaging methods we use 2d synthetic and field data examples to demonstrate the proposed lsrtm algorithm using the perturbation imaging condition our results show that elastic lsrtm improves the energy focusing and illumination of the elastic images and it attenuates artifacts resulting for instance from sparseness in the wavefield sampling and crosstalk of the p and s modes compared with rtm images the lsrtm images provide more accurate relative amplitude information that is useful for reservoir characterization

on the construction of maximal prefix synchronized codes we present a systematic procedure for mapping data sequences into codewords of a prefix synchronized code ps code as well as for performing the inverse mapping a ps code proposed by gilbert 1960 belongs to a subclass of comma free codes and is useful to recover word synchronization when errors have occurred in the stream of codewords a ps code is defined as a set of codewords with the property that each codeword has a known sequence as a prefix followed by a coded data sequence in which this prefix is not allowed to occur the largest ps code among all ps codes of the same code length is called a maximal prefix synchronized code mps code we develop an encoding and decoding algorithm for gilbert s mps code with a prefix of the form 11 10 and extend the algorithm to the class ps codes of which the prefix is self uncorrelated the computational complexity of the entire mapping process is proportional to the length of the codewords

covariance structure analysis in several populations this paper is concerned with the study of covariance structural models in several populations estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach asymptotic properties of the constrained estimator are studied and asymptotic chi square tests are presented to evaluate appropriate model comparisons the method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates the methodology is demonstrated by a set of real data

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

latent trait models abstract latent trait models deal with a set of binary responces from an individual in a given population the aim of the statistical analysis is to estimate the value of an assumed latent parameter characteristic of the individual and to describe the variation of the latent parameters among individuals in the paper various approaches to such statistical analyses are discussed and the methods of analysis are illustrated with a set of consumer complaint behaviour data

inverse q filtering by fourier transform although some attention has been paid to the idea that seismic migration is equivalent to a type of deconvolution of the spatial wavelet less thought has been given to the opposite perspective that deconvolution of the earth q filter might itself be equivalent to a form of migration the key point raised in this paper is that a dispersive 1 d backward propagation can form the basis of a number of different algorithms for inverse q filtering each of which is akin to a particular migration algorithm an especially efficient algorithm can be derived by means of a coordinate transformation equivalent to that in the stolt frequency wavenumber migration this fast algorithm valid for q constant with depth can be extended to accommodate depth variable q by cascading a series of constant q compensations as in cascaded migration by combining a cascaded phase compensation with a windowed approach to amplitude compensation we obtain an algorithm that is sufficiently efficient to be used routinely for pre

alternative test criteria in covariance structure analysis a unified approach in the context of covariance structure analysis a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided the discussion develops within a general framework that distinguishes whether or not the fitting function is asymptotically optimal and allows the null and alternative hypothesis to be only approximations of the true model also the equivalent of the information matrix and the asymptotic covariance matrix of the vector of summary statistics are allowed to be singular when the fitting function is not asymptotically optimal test statistics which have asymptotically a chi square distribution are developed as a natural generalization of more classical ones issues relevant for power analysis and the asymptotic theory of a testing related statistic are also investigated

regular universal codeword sets corresp proof is given that no regular or synchronizable universal codeword sets can achieve optimality some asymptotic properties of a remarkable class of regular codeword sets related to the fibonacci representation of integers are also obtained

latent variable models for ordered categorical data abstract the multivariate analysis of ordered categorical data is an important growth point in statistics especially as applied to the social sciences this paper is concerned with the situation in which the associations between a set of categorical variables are assumed to arise from their dependence on a small number of latent variables the problem of modelling this relationship is first posed in very general terms and then specialized to particular cases for which statistical methods are available or in course of development such models can be viewed as tools for data reduction or for scaling and both aspects are reviewed the possible relevance of the method in economics and their relationship to other methods for categorical variables is briefly discussed

simultaneous analysis of multivariate polytomous variates in several groups the frequencies ofm independentp way contingency tables are analyzed by a model that assumes that the ordinal categorical data in each ofm groups are generated from a latent continuous multivariate normal distribution the parameters of these multivariate distributions and of the relations between the ordinal and latent variables are estimated by maximum likelihood goodness of fit statistics based on the likelihood ratio criterion and the pearsonian chisquare are provided to test the hypothesis that the proposed model is correct that is it fits the observed sample data hypotheses on the invariance of means variances and polychoric correlations of the latent variables across populations are tested by wald statistics the method is illustrated on an example involving data on three five point ordinal scales obtained from male and female samples

latent variable structural equation modeling with categorical data abstract structural equation modeling with latent variables is overviewed for situations involving a mixture of dichotomous ordered polytomous and continuous indicators of latent variables special emphasis is placed on categorical variables models in psychometrics econometrics and biometrics are interrelated via a general model due to muthen limited information least squares estimators and full information estimation are discussed an example is estimated with a model for a four wave longitudinal data set where dichotomous responses are related to each other and a set of independent variables via latent variables with a variance component structure

viscoelastic finite difference modeling real earth media disperse and attenuate propagating mechanical waves this anelastic behavior can be described well by a viscoelastic model we have developed a finite difference simulator to model wave propagation in viscoelastic media the finite difference method was chosen in favor of other methods for several reasons finite difference codes are more portable than for example pseudospectral codes moreover finite difference schemes provide a convenient environment in which to define complicated boundaries a staggered scheme of second order accuracy in time and fourth order accuracy in space appears to be optimally efficient because of intrinsic dispersion no fixed grid points per wavelength rule can be given instead we present tables which enable a choice of grid parameters for a given level of accuracy since the scheme models energy absorption natural and efficient absorbing boundaries may be implemented merely by changing the parameters near the grid boundary the viscoelastic scheme is

flexibly preconditioned extended least squares migration in shot record domain abstractwe have developed a method for accelerating the convergence of iterative least squares migration the algorithm uses a pseudodifferential scaling dip and spatially varying filter preconditioner together with a variant of conjugate gradient cg iteration with iterate dependent flexible preconditioning the migration is formulated without the image stack thus producing a shot dependent image volume that retains offset information useful for velocity updating and amplitude variation with offset analysis numerical experiments indicate that flexible preconditioning with pseudodifferential scaling not only attains considerably smaller data misfit and gradient error for a given computational effort but also produces higher resolution image volumes with more balanced amplitude and fewer artifacts than is achieved with a nonpreconditioned cg method