robust inversion of seismic data using the huber norm the huber function or huber norm is one of several robust error measures which interpolates between smooth l2 treatment of small residuals and robust l1 treatment of large residuals since the huber function is differentiable it may be minimized reliably with a standard gradient based optimizer we propose to minimize the huber function with a quasi newton method that has the potential of being faster and more robust than conjugate gradient methods when solving nonlinear problems tests with a linear inverse problem for velocity analysis with both synthetic and field data suggest that the huber function gives far more robust model estimates than does a least squares fit with or without damping

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

optimal rates of convergence for deconvolving a density abstract suppose that the sum of two independent random variables x and z is observed where z denotes measurement error and has a known distribution and where the unknown density f of x is to be estimated one application is the estimation of a prior density for a sequence of location parameters a second application arises in the errors in variables problem for nonlinear and generalized linear models when one attempts to model the distribution of the true but unobservable covariates this article shows that if z is normally distributed and f has k bounded derivatives then the fastest attainable convergence rate of any nonparametric estimator of f is only log n k 2 therefore deconvolution with normal errors may not be a practical proposition other error distributions are also treated stefanski carroll 1987a estimators achieve the optimal rates the results given have versions for multiplicative errors where they imply that even optimal rates are exceptionally slow

an optimal 9 point finite difference frequency space 2 d scalar wave extrapolator in this study a new finite difference technique is designed to reduce the number of grid points needed in frequency space domain modeling the new algorithm uses optimal nine point operators for the approximation of the laplacian and the mass acceleration terms the coefficients can be found by using the steepest descent method so that the best normalized phase curves can be obtained this method reduces the number of grid points per wavelength to 4 or less with consequent reductions of computer memory and cpu time that are factors of tens less than those involved in the conventional second order approximation formula when a band type solver is used on a scalar machine

bayesian semiparametric regression in the presence of conditionally heteroscedastic measurement and regression errors summary we consider the problem of robust estimation of the regression relationship between a response and a covariate based on sample in which precise measurements on the covariate are not available but error prone surrogates for the unobserved covariate are available for each sampled unit existing methods often make restrictive and unrealistic assumptions about the density of the covariate and the densities of the regression and the measurement errors for example normality and for the latter two also homoscedasticity and thus independence from the covariate in this article we describe bayesian semiparametric methodology based on mixtures of b splines and mixtures induced by dirichlet processes that relaxes these restrictive assumptions in particular our models for the aforementioned densities adapt to asymmetry heavy tails and multimodality the models for the densities of regression and measurement errors also accommodate conditional heteroscedasticity in simulation experiments our method vastly outperforms existing methods we apply our method to data from nutritional epidemiology

three dimensional frequency domain full waveform inversion with an iterative solver with the acquisition of wide aperture seismic data sets full waveform inversion is an attractive method for deriving velocity models three dimensional implementations require an efficient solver for the wave equation computing 3d time harmonic responses with a frequency domain solver is complicated because a large linear system with negative and positive eigenvalues must be solved time domain schemes are an alternative nevertheless existing frequency domain iterative solvers with an efficient preconditioner are a viable option when full waveform inversion is formulated in the frequency domain an iterative solver with a multigrid preconditioner is competitive because of a high order spatial discretization numerical examples illustrated the efficiency of the iterative solvers three dimensional full waveform inversion was then studied in the context of deep water ocean bottom seismometer acquisition three dimensional synthetic data inversion results showed the behavior of full waveform inversion with respect to the initial model and the minimum frequency available in the data set results on a 3d real ocean bottom seismometer data set demonstrated the relevance of full waveform inversion especially to image the shallow part of the model

an adjoint based jacobi type iterative method for elastic full waveform inversion problem full waveform inversion fwi is a promising technique that is capable of creating high resolution subsurface images of the earth from seismic data however it is computationally expensive especially when 3d elastic wave equation is considered in this paper an adjoint based computational algorithm has been proposed to address the computational challenges the important strategy in this work is to decouple the two lame parameters so that two half sized subproblems are resulted and solved separately mathematically the inverse problem is formulated as a pde constrained optimization problem in which the objective functional is defined as the misfit between observational and synthetic data the parameters to be recovered are the spatially varying lame parameters which are of great interests to geophysicists for the purpose of hydrocarbon exploration and subsurface imaging the gradient of the misfit functional with respect to the lame parameters is calculated by solving the adjoint elastic wave equation whilst the quasi newton method l bfgs is used to minimize the misfit functional numerical experiments demonstrated that the new method is accurate efficient and robust in recovering lame parameters from seismic data

nonparametric regression in the presence of measurement error summary in many regression applications the independent variable is measured with error when this happens conventional parametric and nonparametric regression techniques are no longer valid we consider two diverent approaches to nonparametric regression the first uses the simex simulation extrapolation method and makes no assumption about the distribution of the unobserved error prone predictor for this approach we derive an asymptotic theory for kernel regression which has some surprising implications penalised regression splines are also considered for fixed number of known knots the second approach assumes that the error prone predictor has a distribution of a mixture of normals with an unknown number of components and uses regression splines simulations illustrate the results

full waveform inversion based on kaniadakis statistics full waveform inversion fwi is a wave equation based methodology to estimate the subsurface physical parameters that honor the geologic structures classically fwi is formulated as a local optimization problem in which the misfit function to be minimized is based on the least squares distance between the observed data and the modeled data residuals or errors from a probabilistic maximum likelihood viewpoint the minimization of the least squares distance assumes a gaussian distribution for the residuals which obeys gauss s error law however in real situations the error is seldom gaussian and therefore it is necessary to explore alternative misfit functions based on non gaussian error laws in this way starting from the ensuremath kappa generalized exponential function we propose a misfit function based on the ensuremath kappa generalized gaussian probability distribution associated with the kaniadakis statistics or ensuremath kappa statistics which we call ensuremath kappa fwi in this study we perform numerical simulations on a realistic acoustic velocity model considering two noisy data scenarios in the first one we considered gaussian noisy data while in the second one we considered realistic noisy data with outliers the results show that the ensuremath kappa fwi outperforms the least squares fwi providing better parameter estimation of the subsurface especially in situations where the seismic data are very noisy and with outliers independently of the ensuremath kappa parameter although the ensuremath kappa parameter does not affect the quality of the results it is important for the fast convergence of fwi

deconvolution of a distribution function abstract we consider the estimation of a distribution function when observations from this distribution are contaminated by measurement error the unknown distribution is modeled as a mixture of a finite number of known distributions model parameters can be estimated and confidence intervals constructed using well known likelihood theory we show that it is also possible to apply this approach to estimation of a unimodal distribution an application is presented using data from a dietary survey simulation results are given to indicate the performance of the estimators and the confidence interval procedures

deconvolution of microfluorometric histograms with b splines abstract we consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors we propose a method of estimation using spline functions discuss the numerical implementation of the method and prove its consistency the problem is motivated by the analysis of dna content obtained by microfluorometry and an example of such an analysis is included

traveltime and amplitude calculations using the damped wave solution because of its computational efficiency prestack kirchhoff depth migration remains the method of choice for all but the most complicated geological depth structures further improvement in computational speed and amplitude estimation will allow us to use such technology more routinely and generate better images to this end we developed a new accurate and economical algorithm to calculate first arrival traveltimes and amplitudes for an arbitrarily complex earth model our method is based on numerical solutions of the wave equation obtained by using well established finite difference or finite element modeling algorithms in the laplace domain where a damping term is naturally incorporated in the wave equation we show that solving the strongly damped wave equation is equivalent to solving the eikonal and transport equations simultaneously at a fixed reference frequency which properly accounts for caustics and other problems encountered in ray theory using our algorithm we can easily calculate first arrival traveltimes for given models we present numerical examples for 2 d acoustic models having irregular topography and complex geological structure using a finite element modeling code

application of the boundary integral equation method to reissner s plate model numerical solution of reissner s model for the bending of elastic plates by an advanced boundary integral equation method is outlined construction of fundamental solutions and computational strategy is fully described implementation of the resulting one dimensional model is illustrated by two test problems including comparison to analytical solutions

adaptive wavelet estimator for nonparametric density deconvolution 1999 institute of mathematical statistics the electronic version of this article is the complete one and can be found online at http projecteuclid org euclid aos 1017939249

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

sensitivity analysis for boundary element error estimation and mesh refinement the subject of this paper is the sensitivity analysis of approximate boundary element solutions with respect to the positions of the collocation points the direct differentiation approach is considered here and the analysis is performed analytically since only the collocation points are perturbed the shape of the body and the corresponding discretization remain unaltered this aspect makes the present work quite different in spirit with respect to earlier analyses on shape sensitivities sensitivities of approximate bem solutions with respect to the positions of collocation points are shown to be related to the residual of hypersingular integral equations numerical results confirm that the present approach can be seen as the analytical counterpart of an adaptive scheme for mesh refinement presented by the same author in some recent papers some other advantages of the present approach over the former one are also outlined

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

measurement errors in line transect surveys where detectability varies with distance and size summary when using bivariate line transect methods to estimate the biomass density of a tightly clustered biological population it is generally assumed that both the perpendicular distance from the trackline to the cluster and the cluster size or biomass are measured without error this is unlikely to be the case in practice in this article assuming additive mean zero errors in distance and multiplicative errors in size we develop an estimator of density that corrects for these errors we use the method of moments for the case of gamma cluster size randomly placed transect lines and the generalized exponential detection function we derive results that show that it may not be necessary to correct for errors in distance or size when the distance and size estimates are not biased when the size estimates are biased the biomass density estimate has approximately the same bias as the size estimates the work is illustrated in the context of annual aerial surveys for juvenile southern bluefin tuna in the great australian bight

analysis of optimal transport and related misfit functions in full waveform inversion abstractfull waveform inversion has evolved into a powerful computational tool in seismic imaging new misfit functions for matching simulated and measured data have recently been introduced to avoid the traditional lack of convergence due to cycle skipping we have introduced the wasserstein distance from optimal transport for computing the misfit and several groups are currently further developing this technique we evaluate three essential observations of this new metric with implication for future development one is the discovery that trace by trace comparison with the quadratic wasserstein metric works remarkably well together with the adjoint state method another is the close connection between optimal transport based misfits and integrated techniques with normalization as for example the normalized integration method finally we study the convexity with respect to selected model parameters for different normalizations and remark on the effect of normalization on the convergence of the adjoint

multiple testing of composite null hypotheses in heteroscedastic models in large scale studies the true effect sizes often range continuously from zero to small to large and are observed with heteroscedastic errors in practical situations where the failure to reject small deviations from the null is inconsequential specifying an indifference region or forming composite null hypotheses can greatly reduce the number of unimportant discoveries in multiple testing the heteroscedasticity issue poses new challenges for multiple testing with composite nulls in particular the conventional framework in multiple testing which involves rescaling or standardization is likely to distort the scientific question we propose the concept of a composite null distribution for heteroscedastic models and develop an optimal testing procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate the proposed approach is different from conventional methods in that the effect size statistical significance and multiplicity issues are addressed in

regression with covariates and outcome calculated from a common set of variables measured with error estimation using the simex method in medical research a situation commonly arises where new variables are calculated from a common set of directly measured variables when the directly measured variables each contain an error component the relationship between the observed calculated variables can often be distorted a source of this distortion is the presence of common measurement error in the observed calculated variables often known as coupled error it is still possible to estimate the relationship between the calculated variables when measurement error is present this paper presents two general methodologies that account for the presence of correlated measurement error when working with calculated variables the equivalence of the methods will be established for one case while the general advantage of the simulation extrapolation technique will be shown for more complicated situations the performance of the estimators will be examined with examples arising from the medical literature

taylor expansions for singular kernels in the boundary element method the problem treated is the integration of singular functions which arise in three dimensional isoparametric formulations of boundary integral equations a taylor expansion in the local parametric co ordinates is developed for the singular integrand so allowing singular terms to be integrated in closed form even for curved surface elements the remainder integral obtained by subtracting out the worst singularities is integrated by repeated gaussian quadrature two groups of tests are presented first the accuracy of the integrations has been checked for plane parallelograms for which exact solutions have been developed and for curved elements on a sphere secondly results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems zonal surface harmonics on a sphere and the capacitance of an ellipsoid the agreement obtained with few degrees of freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration

toward an automatic full wave inversion synthetic study cases full waveform inversion fwi in seismic scenarios continues to be a complex procedure for subsurface imaging that might require extensive human interaction in terms of model setup constraints and data preconditioning the underlying reason is the strong nonlinearity of the problem that forces the addition of a priori knowledge or bias in order to obtain geologically sound results in particular when the use of a long offset receiver is not possible or may not favor the reconstruction of the fine structure of the model one needs to rely on reflection data as a consequence the inversion process is more prone to becoming stuck in local minima nevertheless misfit functionals can be devised that can either cope with missing long wavenumber features of initial models e g cross correlation based misfit or invert reflection dominated data whenever the models are sufficiently good e g normalized offset limited least squares misfit by combining both high frequency data content with poor initial models can be successfully inverted if one can figure out simple parameterizations for such functionals the amount of uncertainty and manual work related to tuning fwi would be substantially reduced thus fwi might become a semiautomatized imaging tool

application of optimal transport and the quadratic wasserstein metric to full waveform inversion conventional full waveform inversion fwi using the least squares norm as a misfit function is known to suffer from cycle skipping issues which increases the risk of computing a local rather than the global minimum of the misfit the quadratic wasserstein metric has been proved to have many ideal properties with regards to convexity and insensitivity to noise when the observed and predicted seismic data are considered to be two density functions the quadratic wasserstein metric corresponds to the optimal cost of rearranging one density into the other where the transportation cost is quadratic in distance unlike the least squares norm the quadratic wasserstein metric measures not only amplitude differences but also global phase shifts which helps to avoid cycle skipping issues we propose a new way of using the quadratic wasserstein metric trace by trace in fwi and compare it to the global quadratic wasserstein metric via the solution of the monge ampere equation we incorporate the quadratic wasser

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

multiscale seismic waveform inversion iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models e g the marmousi model the primary difficulty being the presence of numerous local minima in the objective function the presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum the multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale at long scales there are fewer local minima and those that remain are further apart from each other thus at long scales iterative methods can get closer to the neighborhood of the global minimum we apply the multigrid method to a subsampled low frequency version of the marmousi data set although issues of source estimation source bandwidth and noise are not treated results show that iterative inversion methods perform much better when employed with a decomposition by scale furthermore the method greatly reduces the computational burden of the inversion that will be of importance for 3 d extensions to the method

evaluation of the stress tensor in 3 d elastoplasticity by direct solving of hypersingular integrals a new method of direct numerical evaluation of hypersingular boundary integrals has been applied to the differentiated form of the somigliana identity hypersingular identity in 3d elastostatics through this method it is possible to evaluate the stress tensor on the boundary of a complex 3d structure in a very accurate manner by employing the direct boundary element method bem the geometry of the elements and their arrangements over the boundary of the structure are not subjected to any restrictions numerical examples illustrate the accuracy of the proposed method

simex variance component tests in generalized linear mixed measurement error models in the analysis of clustered data with covariates measured with error a problem of common interest is to test for correlation within clusters and heterogeneity across clusters we examined this problem in the framework of generalized linear mixed measurement error models we propose using the simex method to construct a score test for the null hypothesis that all variance components are zero a key feature of this simex score test is that no assumptions need to be made regarding the distributions of the random eects and the unobserved covariates we illustrate this test by analyzing framingham heart disease data and evaluate its performance by simulation we also propose individual simex score tests for testing the variance components separately both tests can be easily implemented using existing statistical software

quasi newton full waveform inversion with a projected hessian matrix abstractwe present a method in realistic size full waveform inversion fwi to explicitly construct a projected hessian matrix and its inverse matrix which we subsequently used to solve fwi with a quasi newton method newton s method is practically unfeasible in solving realistic size fwi problems because of the prohibitive cost computing time and memory consumption of calculating the hessian matrix and the inverse hessian therefore the gauss newton method and various quasi newton methods are proposed to approximate a hessian matrix particularly current quasi newton fwi qnfwi commonly uses the limited memory bfgs l bfgs method which however only implicitly approximates an inverse hessian we repose fwi as a sparse optimization problem in a sparse model space which contains substantially fewer model parameters that are constrained by structures of the model with respect to fewer parameters in the sparse model we can avoid the limited memory approximation and are able to explicitly comp

a helmholtz iterative solver for 3d seismic imaging problems a preconditioned iterative solver for the 3d frequency domain wave equation applied to seismic problems is evaluated the preconditioner corresponds to an approximate inverse of a heavily damped wave equation deduced from the undamped wave equation the approximate inverse is computed with one multigrid cycle numerical results show that the method is robust and that the number of iterations increases roughly linearly with frequency when the grid spacing is adapted to keep a constant number of discretization points per wavelength to evaluate the relevance of this iterative solver the number of floating point operations required for two imaging problems are roughly evaluated this rough estimate indicates that the time domain migration approach is more than one order of magnitude faster the full wave form tomography based on a least squares formulation and a scale separation approach has the same complexity in both domains

hypersingular residuals a new approach for error estimation in the boundary element method summary this paper presents a new approach for a posteriori pointwise error estimation in the boundary element method the estimator relies upon evaluation of the residual of hypersingular integral equations and is therefore intrinsic to the boundary integral equation approach a methodology is developed for approximating the error on the boundary as well as in the interior of the domain extensive computational experiments have been performed for the two dimensional laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve moreover a reasonable estimate of the magnitude of the actual error is also predicted

fast line searches for the robust solution of linear systems in the hybrid l1 l2 and huber norms linear systems of equations arise in traveltime tomography deconvolution and many other geophysical applications nonlinear problems are often solved by successive linearization leading to a sequence of linear systems overdetermined linear systems are solved by minimizing some measure of the size of the misfit or residual the most commonly used measure is the l2 norm squared leading to least squares problems the advantage of least squares problems for linear systems is that they can be solved by methods for example qr factorization that retain the linear behavior of the problem the disadvantage of least squares solutions is that the solution is sensitive to outliers more robust norms approximating the l1 norm can be used to reduce the sensitivity to outliers unfortunately these more robustnorms lead to nonlinear minimization problems even for linear systems and many efficient algorithms for nonlinear minimiza tion problems require line searches one iterative method for solving linear

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

dual boundary element formulation for fracture mechanics analysis of shear deformable shells this paper presents a new boundary element formulation for fracture mechanics analysis of shear deformable shells hyper singular boundary integral equations for shear deformable shells are derived dual boundary element formulations are constructed by using traction integral equations on one side of the crack surface and displacement integral equations on the other side of the crack surface and all other boundaries five stress intensity factors two for membrane behaviour and three for shear and bending are computed several crack configurations are analysed to demonstrate the efficiency and accuracy of the proposed formulation

empirical bias bandwidths for local polynomial nonparametric regression and density estimation abstract a data based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials the estimator called the empirical bias bandwidth selector ebbs is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function ebbs minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term the variance term used is exact not asymptotic though it involves the conditional variance of the response given the predictors that must be estimated the bias term is estimated empirically not from an asymptotic expression thus ebbs is similar to the double smoothing approach of hardle hall and marron and a local bandwidth selector of schucany but is developed here for a far wider class of estimation problems than what those authors considered ebbs is tested on simulated data and its performance seems quite satisfactory local polynomial smoothing of a histogram is a high

a hierarchical elastic full waveform inversion scheme based on wavefield separation and the multistep length approach abstractelastic full waveform inversion fwi updates model parameters by minimizing the residuals of the p and s wavefields resulting in more local minima and serious nonlinearity in addition the coupling of different parameters degrades the inversion results to address these problems we have developed a hierarchical elastic fwi scheme based on wavefield separation and a multistep length gradient approach first we have derived the gradients expressed by different wave modes analyzed the crosstalk between various parameters and evaluated the sensitivity of separated p wave separated s wave and p and s wave misfit functions then a practical four stage inversion workflow was developed in the first stage conventional fwi is used to achieve rough estimates of the p and s wave velocities in the second stage we only invert the p wave velocity applying the separated p wavefields when strong s wave energy is involved or we merely update the s wave velocity by matching the separated s wavefiel

which data residual norm for robust elastic frequency domain full waveform inversion elastic full waveform inversion is an ill posed data fitting procedure that is sensitive to noise inaccuracies of the starting model definitionofmultiparameterclasses andinaccuratemodeling of wavefield amplitudes we have investigated the performance of different minimization functionals as the least squares norm 2 the least absolute values norm 1 and combinations of both the huber and so called hybrid criteria with reference to twonoisyoffshorevalhallmodelandonshoreoverthrustmodel synthetic data sets the four minimization functionals were implemented in 2d elastic frequency domain full waveform inversion fwi where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies for the offshore and onshore case studies the 1 norm provided the most reliable models for p and s wave velocities vp and vs even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data the 2 norm can provide reliable results in the presence of uniform white noise for vp and vs if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency the 1 norm and the huber and hybrid criteria unlike the 2 norm allowforsuccessfulimagingofthevsmodelfromnoisydataina soft seabed environment where the p to s waves have a small footprint in the data however the huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial and error investigations for reliable estimation the 1 norm provides a robust alternativetothe2 normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency domainfwi

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

hybrid l 1 l 2 minimization with applications to tomography least squares or l2 solutions of seismic inversion and tomography problems tend to be very sensitive to data points with large errors the lp minimization for 1 p 2 gives more robust solutions but usually with higher computational cost iteratively reweighted least squares irls gives efficient approximate solutions to these lp problems we apply irls to a hybrid l2 l2 minimization problem that behaves like an l2 fit for small residuals and like an l1 fit for large residuals the smooth transition from l2 to l1 behavior is controlled by a parameter that we choose using an estimate of the standard deviation of the data error for linear problems of full rank the hybrid objective function has a unique minimum and irls can be proven to converge to it we obtain a robust efficient method for nonlinear problems a version of the gauss newton algorithm can be applied synthetic crosswell tomography examples and a field data vsp tomography example demonstrate the improvement of the hybrid method over le

hypersingular boundary element formulation for reissner plates in this work the hypersingular boundary element formulation for plate bending analysis based on reissner theory is presented first order taylor expansion are used to deal with the strong singularity o 1 r whereas rigid body considerations together with the taylor expansion are used to compute the hypersingular kernels o l r2 the plate boundary is discretised into quadratic isoparametric discontinuous boundary elements to satisfy the continuity requirements for the boundary unknowns several examples are tested including thin and thick plates the results show a good agreement with both the analytical solutions and the corresponding results for the standard displacement boundary element formulation 1998 elsevier science ltd all rights reserved

bi expansion approximation of the bessel functions applied to analytical integration based bem for reissner plates the paper deals with the boundary element analysis of plates modeled by the reissner theory the integral equations are obtained in standard fashion by boundary collocation the fundamental solution is expressed in terms of modified bessel functions using different series expansions for small and large arguments the transition from one to the other form is regulated by an error based criterion for selecting the number of terms which have to be used in the series expansion attention is paid to the computational aspects influencing the accuracy of the numerical model the boundary variables are described by using a quadratic b spline interpolation and the evaluation of the boundary integrals is developed almost entirely in analytical form some numerical experiments test and compare the performances of the numerical model in particular the solution within the boundary layer is studied

a design adaptive local polynomial estimator for the errors in variables problem local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature their simplest version the local constant estimator can be easily extended to the errors in variables context by exploiting its similarity with the deconvolution kernel density estimator the generalization of the higher order versions of the estimator however is not straightforward and has remained an open problem for the last 15 years we propose an innovative local polynomial estimator of any order in the errors in variables context derive its design adaptive asymptotic properties and study its finite sample performance on simulated examples we provide not only a solution to a long standing open problem but also provide methodological contributions to error in variable regression including local polynomial estimation of derivative functions

accurate viscoelastic modeling by frequency domain finite differences using rotated operators the viscoelastic wave equation is an integro differential equation that requires special methods when using time domain numerical finite difference methods in the frequency domain the integral terms are easily represented by complex valued elastic media properties there are further significant advantages to using the frequency domain if the forward or the inverse problem requires modeling or inverting a large number of prestack source gathers numerical modeling is expensive for seismic data because of the large number of wavelenghths typically separating sources from receivers which results in a need for a large number of grid points a major obstacle to using frequency domain methods is the consequent storage requirements to reduce these we maximize the accuracy and simultaneously minimize the spatial extent of the numerical operators we achieve this by extending earlier published methods introduced for the viscoacoustic case to the viscoelastic case this requires the formulation of two new nume

elastic full waveform inversion using the second generation wavelet and an adaptive operator length scheme abstractelastic full waveform inversion fwi can generally yield subsurface model parameters of high spatial resolution however the computational and storage burden is tremendous to mitigate this problem we developed the following three strategies first we derived a time space domain adaptive staggered grid finite difference method the size of the calculation was reduced by using smaller operator lengths for high s wave velocities second we evaluated a multiscale elastic fwi scheme based on the second generation wavelet by which scale decompositions of data and model space were implemented with the scale increasing spatial sampling intervals and time steps became larger therefore the minimum computational cost could be achieved by combining the variable operator length scheme with the multiscale scheme third to economize the memory consumption we extended the efficient boundary storage and checkpointing schemes into elastic fwi only wavefields of several parts in the boundary area betwe

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

local polynomial regression and simulation extrapolation summary the paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error we address the measurement error with cook and stefanski s simulation extrapolation simex algorithm our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses simex s particular estimation method and considers higher degree local polynomial estimators we illustrate the accuracy of our asymptotic expressions with a monte carlo study compare our method with other estimators with a second set of monte carlo simulations and apply our method to a data set from nutritional epidemiology simex was originally developed for parametric models although simex is in principle applicable to nonparametric models a serious problem arises with simex in nonparametric situations the problem is that smoothing parameter selectors that are developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing we believe that this is the first paper to address this difficulty

isotonic inverse estimators for nonparametric deconvolution a new nonparametric estimation procedure is introduced for the distribution function in a class of deconvolution problems where the convolution density has one discontinuity the estimator is shown to be consistent and its cube root asymptotic distribution theory is established known results on the minimax risk for the estimation problem indicate the estimator to be efficient

waveform inversion using a back propagation algorithm and a huber function norm waveforminversionfacesdifficultieswhenappliedtoreal seismic data including the existence of many kinds of noise the 1 norm is more robust to noise with outliers than the least squares method nevertheless the least squares method is preferred as an objective function in many algorithms because the gradient of the 1 norm has a singularity when the residual becomes zero we propose a complex valued huber function for frequency domain waveform inversion that combines the 2 norm for small residuals with the 1 norm for large residuals we also derive a discretized formula for the gradient of the huber function through numericaltestsonsimplesyntheticmodelsandmarmousidata we find the huber function is more robust to outliers and coherent noise we apply our waveform inversion algorithm to field data taken from the continental shelf under the east sea in korea in this setting we obtain a velocity model whose syntheticshotprofilesaresimilartotherealseismicdata

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

3d finite difference frequency domain modeling of visco acoustic wave propagation using a massively parallel direct solver a feasibility study we present a finite difference frequency domain method for 3d visco acoustic wave propagation modeling in the frequency domain the underlying numerical problem is the resolution of a large sparse system of linear equations whose right hand side term is the source this system is solved with a massively parallel direct solver we first present an optimal 3d finite difference stencil for frequency domain modeling the method is based on a parsimonious staggered grid method differential operators are discretized with second order accurate staggered grid stencils on different rotated coordinate systems to mitigate numerical anisotropy an antilumped mass strategy is implemented to minimize numerical dispersion the stencil incorporates 27 grid points and spans two grid intervals dispersion analysis shows that four grid points per wavelength provide accurate simulations in the 3d domain to assess the feasibility of the method for frequency domain full waveform inversion we computed simulations in the 3d seg eage overthrust model for frequencies 5 7 and 10 hz results confirm the huge memory requirement of the factorization several hundred figabytes but also the cpu efficiency of the resolution phase few seconds per shot heuristic scalability analysis suggests that the memory complexity of the factorization is o 35n 4 for a n 3 grid our method may provide a suitable tool to perform frequency domain full waveform inversion using a large distributed memory platform further investigation is still necessary to assess more quantitatively the respective merits and drawbacks of time and frequency domain modeling of wave propagation to perform 3d full waveform inversion

accelerated convergence for nonparametric regression with coarsened predictors we consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened that is less precise or contaminated predictors specifically while one has available a sample w 1 y 1 w n y n of independent and identically distributed data representing observations with precisely measured predictors where e y i w i g w i instead ofthe smooth regression function g the target of interest is another smooth regression function m that pertains to predictors x i that are noisy versions of the w i our target is then the regression function m x e y x x where x is a contaminated version of w that is x w it is assumed that either the density of the errors is known or replicated data are available resembling but not necessarily the same as the variables x in either case and under suitable conditions we obtain n rates of convergence of the proposed estimator and its derivatives and establish a functional limit theorem weak convergence to a gaussian limit process implies pointwise and uniform confidence intervals and n consistent estimators of extrema and zeros of m it is shown that these results are preserved under more general models in which x is determined by an explanatory variable finite sample performance is investigated in simulations and illustrated by a real data example

robust inversion dimensionality reduction and randomized sampling we consider a class of inverse problems in which the forward model is the solution operator to linear odes or pdes this class admits several dimensionality reduction techniques based on data averaging or sampling which are especially useful for large scale problems we survey these approaches and their connection to stochastic optimization the data averaging approach is only viable however for a least squares misfit which is sensitive to outliers in the data and artifacts unexplained by the forward model this motivates us to propose a robust formulation based on the student s t distribution of the error we demonstrate how the corresponding penalty function together with the sampling approach can obtain good results for a large scale seismic inverse problem with 50 corrupted data

on the optimal rates of convergence for nonparametric deconvolution problems deconvolution problems arise in a variety of situations in statistics an interesting problem is to estimate the density f of a random variable x based on n i i d observations from y x varepsilon where varepsilon is a measurement error with a known distribution in this paper the effect of errors in variables of nonparametric deconvolution is examined insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions the smoother the harder in fact there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth it is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

nonparametric methods for solving the berkson errors in variables problem summary it is common in errors in variables problems in regression to assume that the errors are incurred after the experiment in that the observed value of the explanatory variable is an independent perturbation of its true value however if the errors are incurred before the experiment then the true value of the explanatory variable equals a perturbation of its observed value this is the context of the berkson model which is increasingly attracting attention in parametric and semiparametric settings we introduce and discuss nonparametric techniques for analysing data that are generated by the berkson model our approach permits both random and regularly spaced values of the target doses in the absence of data on dosage error it is necessary to propose a distribution for the latter but we show numerically that our method is robust against that assumption the case of dosage error data is also discussed a practical method for smoothing parameter choice is suggested our techniques for errors in variables regression are shown to achieve theoretically optimal convergence rates

elastic least squares reverse time migration with hybrid l1 l2 misfit function abstract we have developed the theory and synthetic tests of elastic least squares reverse time migration elsrtm in this method a least squares reverse time migration algorithm is used to image multicomponent seismic data based on the first order elastic velocity stress wave equation in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint state method for back propagating the data residuals also we have developed another elsrtm scheme based on the wavefield separation technique in which the p wave image is obtained using p wave forward and adjoint wavefields and the s wave image is obtained using p wave forward and s wave adjoint wavefields in this way the crosstalk artifacts can be minimized to a significant extent in general seismic data inevitably contain noise we apply the hybrid l1 l2 misfit function to the elsrtm algorithm to improve the robustness of our elsrtm to noise numerical tests on synthetic dat

elastic wave scattering and dynamic stress concentrations in cylindrical shells with a circular cutout in this paper based on the theory of elastic wave motion for open cylindrical shell wave scattering and dynamic stress concentrations in open cylindrical shells with a hole are studied by making use of small parameter perturbation methods and boundary integral equation techniques the boundary integral equations and iterative imminent series of scattered waves around the cavity of the cylindrical shell are derived by employing this method the approximately analytical solutions of scattered waves on the edge of cutout are gained the computational formula for getting the dynamic stress concentration factors on the contour of cavity is developed as an example the numerical results of these dynamic stress concentration factors are graphically presented and discussed the analytical methods put forward in the present work have practical significances for solving the problem of elastic wave scattering and dynamic stress concentrations in cylindrical shells with a circular cutout

density estimation for the case of supersmooth measurement error abstract the problem is to estimate the probability density of a random variable contaminated by an independent measurement error i explore one of the worst case scenario when the characteristic function of this measurement error decreases exponentially and thus optimal estimators converge only with logarithmic rate the particular example of such measurement error is any random variable contaminated by normal cauchy or another stable random variable for this setting and circular data i suggest an asymptotically efficient data driven estimator that is adaptive to both smoothness of estimated density and distribution of measurement error moreover this estimator is universal in sense that its derivatives and integral are sharp estimators of the corresponding derivatives and the cumulative distribution function and these estimators are sharp both globally and pointwise for the case of small sample sizes i suggest a modified estimator that mimics an optimal linear pseudoestimator i explore this est

symmetric galerkin bem for shear deformable plates a symmetric galerkin boundary element formulation is developed for shear deformable plates a mixed strategy is used for the integration process i e partial regularization using simple solutions followed by a singularity subtraction technique for the shear equation full regularization is achieved using new kernel relationships found through a constant shear mode of deformation some of the strong singular integrals are avoided altogether by using a modified traction obtained through a very simple variable change appropriate boundary conditions are defined details of the implementation are given and several example problems solved to verify the accuracy of the proposed formulation copyright 2003 john wiley sons ltd

nonparametric function estimation for clustered data when the predictor is measured without with error abstract we consider local polynomial kernel regression with a single covariate for clustered data using estimating equations we assume that at most m observations are available on each cluster in the case of random regressors with no measurement error in the predictor we show that it is generally the best strategy to ignore entirely the correlation structure within each cluster and instead pretend that all observations are independent in the further special case of longitudinal data on individuals with fixed common observation times we show that equivalent to the pooled data approach is the strategy of fitting separate nonparametric regressions at each observation time and constructing an optimal weighted average we also consider what happens when the predictor is measured with error using the simex approach to correct for measurement error we construct an asymptotic theory for both the pooled and the weighted average estimators surprisingly for the same amount of smoothing the weighted a

simulation extrapolation deconvolution of finite population cumulative distribution function estimators summary we study estimation of a finite population cumulative distribution function when sample units are measured with error we propose a simple bias adjusted estimator that eliminates much of the bias induced by measurement error a variance estimator for the proposed cumulative distribution function estimator is also obtained

corrected score estimation via complex variable simulation extrapolation a monte carlo method of computing unbiased estimating equations for the analysis of data measured with error is described asymptotic distribution results are obtained for estimators derived from the monte carlo estimating equations the method is illustrated with examples applications and simulation studies the monte carlo estimating equations are corrected scores in the sense of nakamura and the proposed methods are closely related to the simulation method described by cook and stefanski

quasilikelihood estimation in measurement error models with correlated replicates summary we consider quasilikelihood models when some of the predictors are measured with error in many cases the true but fallible predictor is impossible to measure and the best one can do is to obtain replicates of the fallible predictor we consider the case that the replicates are not independent if one assumes that replicates are independent and they are not one typically underestimates the extent of the measurement error leading to an inconsistent errors in variables correction we devise techniques for estimating the measurement error covariance matrix in addition we discuss how one might perform a quasilikelihood analysis by computing the mean and variance functions of the observed data both using approximations and also exactly through a monte carlo method the methods are illustrated on a data set involving systolic blood pressure and urinary sodium chloride where the measurement errors appear to be approximately normally distributed but highly correlated and the distribution of the true predictor is reasonably modeled as a mixture of normals