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

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

tree structured proportional hazards regression modeling a method for fitting piecewise proportional hazards models to censored survival data is described stratification is performed recursively using a combination of statistical tests and residual analysis the bootstrap is employed to keep the probability of a type i error the error of discovering two or more strata when there is only one of the method close to a predetermined value the proposed method can thus also serve as a formal goodness of fit test for the proportional hazards model real and simulated data are used for illustration

data domain and image domain wavefield tomography waveform inversion fwi requires a good starting model and or data at very low frequency 1 hz for convergence however this is not a necessary condition but an artifact of the objective function defined using differences of observed and simulated data image domain tomographic methods using the same wavefields and wave equations can converge to a reasonable solution from poor starting models and without long offset and or low frequency data cascading image domain and data domain wavefield tomography eliminates the need for extremely low frequency in the acquired data

a simultaneous inversion for background velocity and impedance maps full waveform inversion of seismic reflection data is highly nonlinear because of the irregular form of the function measuring the misfit between the observed and the synthetic data since the nonlinearity results mainly from the parameters describing seismic velocities an alternative to the full nonlinear inversion is to have an inversion method which remains nonlinear with respect to velocities but linear with respect to impedance contrasts the traditional approach is to decouple the nonlinear and linear parts by first estimating the background velocity from traveltimes using either traveltime inversion or velocity analysis and then estimating impedance contrasts from waveforms using either waveform inversion or conventional migration a more sophisticated strategy is to obtain both the subsurface background velocities and impedance contrasts simultaneously by using a single least squares norm waveform fit criterion the background velocity that adequately represents the gross features of the mediu

subgroup identification based on differential effect search a recursive partitioning method for establishing response to treatment in patient subpopulations we propose a novel recursive partitioning method for identifying subgroups of subjects with enhanced treatment effects based on a differential effect search algorithm the idea is to build a collection of subgroups by recursively partitioning a database into two subgroups at each parent group such that the treatment effect within one of the two subgroups is maximized compared with the other subgroup the process of data splitting continues until a predefined stopping condition has been satisfied the method is similar to interaction tree approaches that allow incorporation of a treatment by split interaction in the splitting criterion however unlike other tree based methods this method searches only within specific regions of the covariate space and generates multiple subgroups of potential interest we develop this method and provide guidance on key topics of interest that include generating multiple promising subgroups using different splitting criteria choosing optimal values of complexity parameters via cross validation and addressing type i error rate inflation inherent in data mining applications using a resampling based method we evaluate the operating characteristics of the procedure using a simulation study and illustrate the method with a clinical trial example copyright 2011 john wiley sons ltd

from classical reflectivity to velocity inversion to full waveform inversion using phase modified and deconvolved reverse time migration images abstractto obtain a physical understanding of gradient based descent methods in full waveform inversion fwi we find a connection between the fwi gradient and the image provided by reverse time migration rtm the gradient uses the residual data as a virtual source and rtm uses the observed data directly as the boundary condition so the fwi gradient is similar to a time integration of the rtm image using the residual data which physically converts the phase of the reflectivity to the phase of the velocity therefore gradient based fwi can be connected to the classical reflectivity to velocity impedance inversion rvi we have developed a new fwi scheme that provides a self contained and physically intuitive derivation which naturally establishes a connection among the amplitude preserved rtm the zoeppritz equations amplitude variation with angle inversion and rvi and combines them into a single framework to produce a preconditioned inversion formula in this scheme the relative velocity upd

least squares reverse time migration with an angle dependent weighting factor least squares reverse time migration lsrtm produces higher quality images than conventional rtm however directly using the standard gradient formula the inverted images suffer from low wavenumber noise using a simple high pass filter on the gradient can alleviate the effect of the low wavenumber noise but owing to the illumination issue the amplitudes are not balanced and in the deep part they are often weak these two issues can be mitigated by the iterative approach but it needs more iterations we introduced an angle dependent weighting factor to weight the gradient of lsrtm to suppress the low wavenumber noise and also to emphasize the gradient in the deep part an optimal step length for the l2 norm objective function is also presented to scale the gradient to the right order two numerical examples performed with the data synthesized on the sigsbee2a and marmousi models indicate that when using this weighted gradient combined with the preconditioned l bfgs algorithm with the optimal step length only a few iterations can achieve satisfying results

simple mechanical control systems with constraints and symmetry we develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure taking the viewpoint of affine connection control systems we derive reduced formulations of the levi civita and the nonholonomic affine connections along with the symmetric product in the presence of symmetries and nonholonomic constraints we note that there are naturally two kinds of connections to be considered here affine and principal connections leading to what we term a connection within a connection these results are then used to describe controllability tests that are specialized to simple underactuated mechanical systems on principal fiber bundles including the notion of fiber configuration controllability we present examples of the use of these tools in studying the planar rigid body with a variable direction vectored thruster and the snakeboard robot

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

an investigation of missing data methods for classification trees applied to binary response data there are many different methods used by classification tree algorithms when missing data occur in the predictors but few studies have been done comparing their appropriateness and performance this paper provides both analytic and monte carlo evidence regarding the effectiveness of six popular missing data methods for classification trees applied to binary response data we show that in the context of classification trees the relationship between the missingness and the dependent variable as well as the existence or non existence of missing values in the testing data are the most helpful criteria to distinguish different missing data methods in particular separate class is clearly the best method to use when the testing set has missing values and the missingness is related to the response variable a real data set related to modeling bankruptcy of a firm is then analyzed the paper concludes with discussion of adaptation of these results to logistic regression and other potential generalizations

an efficient step length formula for correlative least squares reverse time migration abstractin correlative least squares reverse time migration clsrtm the estimation of the optimal step size is usually determined by fitting a parabola and finding its minimum it involves at least two times extra reading of all seismic records which significantly lowers the efficiency of the algorithm to improve the efficiency of the clsrtm algorithm we have deduced an analytical step length asl formula based on the linear property of the demigration operator numerical examples performed with the data synthetized by the marmousi and sigsbee2a models were used to test its validity in complex models with imperfect migration velocity such as the sigabee2a model our formula makes the value of the objective function converges to a much smaller minimum additional numerical tests performed with the data either acquired irregularly or contaminated by different noise levels verify the robustness of the asl formula compared with the commonly used parabolic search method the asl formula is much more e

optimal control for holonomic and nonholonomic mechanical systems with symmetry and lagrangian reduction in this paper we establish necessary conditions for optimal control using the ideas of lagrangian reduction in the sense of reduction under a symmetry group the techniques developed here are designed for lagrangian mechanical control systems with symmetry the benefit of such an approach is that it makes use of the special structure of the system especially its symmetry structure and thus it leads rather directly to the desired conclusions for such systems lagrangian reduction can do in one step what one can alternatively do by applying the pontryagin maximum principle followed by an application of poisson reduction the idea of using lagrangian reduction in the sense of symmetry reduction was also obtained by bloch and crouch proc 33rd cdc ieee 1994 pp 2584 2590 in a somewhat different context and the general idea is closely related to those in montgomery comm math phys 128 1990 pp 565 592 and vershik and gershkovich dynamical systems vii v arnold and s p novikov eds springer verlag 1994 here we develop this idea further and apply it to some known examples such as optimal control on lie groups and principal bundles such as the ball and plate problem and reorientation examples with zero angular momentum such as the satellite with moveable masses however one of our main goals is to extend the method to the case of nonholonomic systems with a nontrivial momentum equation in the context of the work of bloch krishnaprasad marsden and murray arch rational mech anal 1996 to appear the snakeboard is used to illustrate the method

a bayesian approach to estimate uncertainty for full waveform inversion using a priori information from depth migration abstractfull waveform inversion fwi enables us to obtain high resolution subsurface images however estimating model uncertainties associated with this technique is still a challenging problem we have used a bayesian inference framework to estimate model uncertainties associated with fwi the uncertainties were assessed based on an a posteriori covariance operator evaluated at the maximum a posteriori model for the prior distribution we have used a spatially nonstationary covariance operator based on a plane wave construction with local dips measured from migrated images preconditioned frequency domain fwi was used to estimate the maximum a posteriori model efficient manipulation of the posterior covariance was based on a low rank approximation of the data misfit hessian preconditioned by the prior covariance operator the strong decay of the singular values indicated that data were mostly informative about a low dimensional subspace of model parameters to reduce computational cost of the random

incorporating geologic information into reflection tomography in areas of complex geology prestack depth migration is often necessary if we are to produce an accurate image of the subsurface prestack depth migration requires an accurate interval velocity model with few exceptions the subsurface velocities are not known beforehand and should be estimated when the velocity structure is complex with significant lateral variations reflection tomography methods are often an effective tool for improving the velocity estimate unfortunately reflection tomography often converges slowly to a model that is geologically unreasonable or it does not converge at all the large null space of reflection tomography problems often forces us to add a sparse parameterization of the model and or regularization criteria to the estimation standard tomography schemes tend to create isotropic features in velocity models that are inconsistent with geology these isotropic features result in large part from using symmetric regularization operators or from choosing a poor model parameterization if we replace the symmetric operators with nonstationary operators that tend to spread information along structural dips the tomography will produce velocity models that are geologically more reasonable in addition by forming the operators in helical 1d space and performing polynomial division we apply the inverse of these space varying anisotropic operators the inverse operators can be used as a preconditioner to a standard tomography problem thereby significantly improving the speed of convergence compared with the typical regularized inversion problem results from 2d synthetic and 2d field data are shown in each case the velocity obtained improves the focusing of the migrated image

local optimization of dynamic programs with guaranteed satisfaction of path constraints an algorithm is proposed for locating a feasible point satisfying the kkt conditions to a specified tolerance of feasible inequality path constrained dynamic programs pcdp within a finite number of iterations the algorithm is based on iteratively approximating the pcdp by restricting the right hand side of the path constraints and enforcing the path constraints at finitely many time points the main contribution of this article is an adaptation of the semi infinite program sip algorithm proposed in mitsos 2011 to pcdp it is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first order kkt conditions of the pcdp to a specified tolerance the main assumptions are i availability of a nonlinear program nlp local solver that generates a kkt point of the constructed approximation to pcdp at each iteration if this problem is indeed feasible ii existence of a slater point of the pcdp that also satisfies the first order kkt conditions of the pcdp to a specified tolerance iii all kkt multipliers are nonnegative and uniformly bounded with respect to all iterations the performance of the algorithm is analyzed through two numerical case studies

formation control of multiple elliptical agents with limited sensing ranges this paper presents a design of cooperative controllers that force a group of n mobile agents with an elliptical shape and with limited sensing ranges to perform a desired formation the controllers guarantee no collisions between any agents in the group the desired formation can be stabilized at feasible reference trajectories with bounded time derivatives the formation control design is based on an algebraic separation condition between ellipses lyapunov s method and smooth or p times differentiable step functions these functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings under the agents limited sensing ranges

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

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

fast 2 d ray born migration inversion in complex media in this paper we evaluate the capacity of a fast 2 d ray born migration inversion algorithm to recover the true amplitude of the model parameters in 2 d complex media the method is based on a quasi newtonian linearized inversion of the scattered wavefield asymptotic green s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method the model is described by velocity perturbations associated with diffractor points both the first traveltime and the strongest arrivals can be inverted the algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2 d marmousi example comparison between logs extracted from the exact marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations

classification trees with unbiased multiway splits two univariate split methods and one linear combination split method are proposed for the construction of classification trees with multiway splits examples are given where the trees are more compact and hence easier to interpret than binary trees a major strength of the univariate split methods is that they have negligible bias in variable selection both when the variables differ in the number of splits they offer and when they differ in the number of missing values this is an advantage because inferences from the tree structures can be adversely affected by selection bias the new methods are shown to be highly competitive in terms of computational speed and classification accuracy of future observations

simple mechanical control systems with constraints we apply some recently developed control theoretic techniques to the analysis of a class of mechanical systems with constraints certain simple aspects of the theory of affine connections play an important part in our presentation the necessary background is presented in order to illustrate how the methods may be applied the bulk of this paper is devoted to a detailed analysis of some examples of nonholonomic mechanical control systems we look at the heisenberg system the upright rolling disk the roller racer and the snakeboard

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

time domain multiscale full waveform inversion using the rapid expansion method and efficient step length estimation full waveform inversion fwi is rapidly becoming a standard tool for high resolution velocity estimation however the application of this method is usually limited to low frequencies due to the high computational cost of the wavefield propagation and the inversion scheme to mitigate this problem we have developed a rapid expansion method rem for numerical wavefield extrapolation inside the fwi workflow this method approximated the partial time derivative of the wave equation using chebyshev polynomials instead of the conventional finite difference fd approximation this allowed the rem to accurately propagate wavefields with bigger time steps thus improving the computational efficiency of fwi we have compared high frequency fwi results using rem and the traditional fd approximation of the time derivative to illustrate the ability of rem to remain stable and free of numerical dispersion noise even with large grid and time samplings in addition we studied a step length estimation scheme with the objective of avoiding an extra forward wavefield propagation during the line search at each fwi iteration in this scheme we estimated the step length value based on prior iterations and validated this value using the wolfe conditions if the value was accepted then the forward modeling was availed in the next iteration and no extra propagation was necessary we tried seven different step length estimation methods from which we highlighted the adaptive barzilai borwein method when combined with the steepest descent inversion scheme and the unitary step length for the l bfgs algorithm through synthetic numerical results we showed how this scheme could achieve convergence while keeping the number of extra forward modelings way below the number of fwi iterations

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

facilitating score and causal inference trees for large observational studies assessing treatment effects in observational studies is a multifaceted problem that not only involves heterogeneous mechanisms of how the treatment or cause is exposed to subjects known as propensity but also differential causal effects across sub populations we introduce a concept termed the facilitating score to account for both the confounding and interacting impacts of covariates on the treatment effect several approaches for estimating the facilitating score are discussed in particular we put forward a machine learning method called causal inference tree cit to provide a piecewise constant approximation of the facilitating score with interpretable rules cit splits data in such a way that both the propensity and the treatment effect become more homogeneous within each resultant partition causal inference at different levels can be made on the basis of cit together with an aggregated grouping procedure cit stratifies data into strata where causal effects can be conveniently assessed within each besides a feasible way of predicting individual causal effects ice is made available by aggregating ensemble cit models both the stratified results and the estimated ice provide an assessment of heterogeneity of causal effects and can be integrated for estimating the average causal effect ace mean square consistency of cit is also established we evaluate the performance of proposed methods with simulations and illustrate their use with the nsw data in dehejia and wahba 1999 where the objective is to assess the impact of a labor training program the national supportedwork nsw demonstration on post intervention earnings

monte carlo full waveform inversion of crosshole gpr data using multiple point geostatistical a priori information we present a general monte carlo full waveform inversion strategy that integrates a priori information described by geostatistical algorithms with bayesian inverse problem theory the extended metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems such as full waveform inversion sequential gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two point e g gaussian or multiple point statistics we outline the theoretical framework for a full waveform inversion strategy that integrates the extended metropolis algorithm with sequential gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included at the same time we show how temporally and or spatially correlated data uncertainties can be taken into account during the inversion the suggested inversion strategy is tested on synthetic tomographic crosshole ground penetrating radar full waveform data using multiple point based a priori information this is to our knowledge the first example of obtaining a posteriori realizations of a full waveform inverse problem benefits of the proposed methodology compared with deterministic inversion approaches include 1 the a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information which provides a means of obtaining resolution analysis 2 based on a posteriori realizations complicated statistical questions can be answered such as the probability of connectivity across a layer 3 complex a priori information can be included through geostatistical algorithms these benefits however require more computing resources than traditional methods do moreover an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates the latter may be a key challenge when considering field experiments which will not be addressed here

optimal control of underactuated nonholonomic mechanical systems in this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic underactuated mechanical systems in particular we aim to minimize the norm squared of the control input to move the system from an initial to a terminal state we consider systems evolving on general manifolds the class of nonholonomic systems we study in this paper includes in particular wheeled type vehicles which are important for many robotic locomotion systems the two special aspects of this optimal control problem are the nonholonomic constraints and underactuation nonholonomic constraints restrict the evolution of the system to a distribution on the manifold the nonholonomic connection is used to express the constrained equations of motion many robotic systems are underactuated since control inputs are usually applied through the robot s internal configuration space only while we do not consider symmetries with respect to group actions in this paper the fact that the system is underactuated is taken into account in our problem formulation this allows one to compute reaction forces due to any inputs applied in directions orthogonal to the constraint distribution we illustrate our ideas by considering a simple example on a three dimensional manifold including obstacle avoidance using the method of navigation functions

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

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

constrained full waveform inversion by model reparameterization the waveform inversion problem is inherently ill posed traditionally regularization schemes are used to address this issue for waveform inversion where the model is expected to have many details reflecting the physical properties of the earth regularization and data fitting can work in opposite directions the former smoothing and the latter adding details to the model we propose constraining estimated velocity fields by reparameterizing the model this technique also called model space preconditioning is based on directional laplacian filters it preserves most of the details of the velocity model while smoothing the solution along known geological dips preconditioning also yields faster convergence at early iterations the laplacian filters have the property to smooth or kill local planar events according to a local dip field by construction these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models we illustrate with 2d syn

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

efficient pseudo gauss newton full waveform inversion in the τ p domain abstractfull waveform inversion fwi seeks to estimate subsurface elastic properties by iterative minimization of the difference between synthetic and observed data its industrial application suffers from several well defined obstacles including high computational cost slow convergence rate and the phenomenon of cycle skipping we have developed an efficient p domain waveform inversion aimed at reducing the computational burden of fwi with a phase encoding technique the gradient is constructed in the p domain using linear phase encoding and a slant update strategy further reduces the computational burden poorly scaled and blurred gradient updates can be enhanced using exact or approximate versions of the inverse hessian which leads to a faster convergence rate we developed a new chirp phase encoding strategy for diagonal hessian construction preconditioning the gradient using the diagonal phase encoded approximate hessian forms what we refer to as a pseudo gauss newton pgn step to test t

multiple elimination using a pattern recognition technique standard prestack multiple elimination techniques such as predictive deconvolution or radon transforms fail in the presence of complex structures

subgroup identification using covariate adjusted interaction trees we consider the problem of identifying subgroups of participants in a clinical trial that have enhanced treatment effect recursive partitioning methods that recursively partition the covariate space based on some measure of between groups treatment effect difference are popular for such subgroup identification the most commonly used recursive partitioning method the classification and regression tree algorithm first creates a large tree by recursively partitioning the covariate space using some splitting criteria and then selects the final tree from all the subtrees of the large tree in the context of subgroup identification calculation of the splitting criteria and the evaluation measure used for final tree selection rely on comparing differences in means between the treatment and control arm when covariates are prognostic for the outcome covariate adjusted estimators have the ability to improve efficiency compared to using differences in averages between the treatment and control group this manuscript develops two covariate adjusted estimators that can be used to both make splitting decisions and for final tree selection the performance of the resulting covariate adjusted recursive partitioning algorithm is evaluated using simulations and by analyzing a clinical trial that evaluates if motivational interviews improve treatment engagement for substance abusers

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

identification of subgroups with differential treatment effects for longitudinal and multiresponse variables we describe and evaluate a regression tree algorithm for finding subgroups with differential treatments effects in randomized trials with multivariate outcomes the data may contain missing values in the outcomes and covariates and the treatment variable is not limited to two levels simulation results show that the regression tree models have unbiased variable selection and the estimates of subgroup treatment effects are approximately unbiased a bootstrap calibration technique is proposed for constructing confidence intervals for the treatment effects the method is illustrated with data from a longitudinal study comparing two diabetes drugs and a mammography screening trial comparing two treatments and a control copyright 2016 john wiley sons ltd

waveform inversion using a logarithmic wavefield although waveform inversion has been studied extensively since its beginning 20 years ago applications to seismic field data have been limited and most of those applications have been for global seismology or engineering seismology scale problems not for exploration scale data as an alternative to classical waveform inversion we propose the use of a new objective function constructed by taking the logarithm of wavefields allowing consideration of three types of objective function namely amplitude only phase only or both in our waveform inversion we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function we compute the steepest descent directions by using a matrix formalism derived from a frequency domain finite element finite difference modeling technique our numerical algorithms are similar to those of reverse time migration and waveform inversion based on the adjoint state of the wave equation in order to demonstrate the practical applicability of our algorithm we use a synthetic data set from the marmousi model and seismic data collected from the korean continental shelf for noisefree synthetic data the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion when random noise is added the inverted velocity model is also close to the true marmousi model but when frequencies below 5 hz are removed from the data the velocity structure is not as good as those for the noise free and noisy data for field data we compare the time domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short period features of the subsurface although we use wrapped phases in our examples we still obtain reasonable results we expect that if we were to use correctly unwrapped phases in the inversion algorithm we would obtain better results

a homotopy method for well log constraint waveform inversion the primary difficulty posed by the method of waveform inversion for the acoustic wave equation is the presence of local minima of the objective function waveform inversion fails to converge to the global minimum unless the wavefield contains very low frequencies or the starting model is very close to the true model constraints can improve the convergence of the method however if the starting model is far from the correct model normal iterative methods will still get trapped in local minima we designed a homotopy method to improve the robustness of waveform inversion it makes natural use of constraints such as well logs in addition to further condition the inverse problem we incorporate standard tikhonov regularization we demonstrate through a synthetic example that our method is more likely to find a global minimum than normal iterative methods

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

a strategy for nonlinear elastic inversion of seismic reflection data the problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory in its roughest formulation the inverse problem consists of obtaining the earth model for which the predicted data best fit the observed data if an adequate forward model is used this best model will give the best images of the earth s interior three parameters are needed for describing a perfectly elastic isotropic earth the density x and the lame parameters x and x or the density x and the p wave and s wave velocities x and x the choice of parameters is not neutral in the sense that although theoretically equivalent if they are not adequately chosen the numerical algorithms in the inversion can be inefficient in the long spatial wavelengths of the model adequate parameters are the p wave and s wave velocities while in the short spatial wavelengths p wave impedance s wave impedance and density are adequate the problem of inversion o

migration based traveltime waveform inversion of 2 d simple structures a synthetic example migration based traveltime mbtt formulation provides algorithms for automatically determining background velocities from full waveform surface seismic reflection data using local optimization methods in particular it addresses the difficulty of the nonconvexity of the least squares data misfit function the method consists of parameterizing the reflectivity in the time domain through a migration step and providing a multiscale representation for the smooth background velocity we present an implementation of the mbtt approach for a 2 d finite difference fd full wave acoustic model numerical analysis on a 2 d synthetic example shows the ability of the method to find much more reliable estimates of both long and short wavelengths of the velocity than the classical least squares approach even when starting from very poor initial guesses this enlargement of the domain of attraction for the global minima of the least squares misfit has a price each evaluation of the new objective function requires besides the usual fd full wave forward modeling an additional full wave prestack migration hence the fd implementation of the mbtt approach presented in this paper is expected to provide a useful tool for the inversion of data sets of moderate size

nonholonomic control systems on riemannian manifolds this paper gives a general formulation of the theory of nonholonomic control systems on a riemannian manifold modeled by second order differential equations and using the unique riemannian connection defined by the metric the main concern is to introduce a reduction scheme replacing some of the second order equations by first order equations the authors show how constants of motion together with the nonholonomic constraints may be combined to yield such a reduction the theory is applied to a particular class of nonholonomic control systems that may be thought of as modeling a generalized rolling ball this class reduces to the classical example of a ball rolling without slipping on a horizontal plane

nonlinear waveform inversion of plane wave seismograms in stratified elastic media we present a method for determining the elastic parameters of a horizontally stratified medium from its plane wave reflectivity the nonlinear inverse problem is iteratively solved by using a generalized least squares formalism the proposed method uses the relatively fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields the solution method is implemented in the frequency wave slowness domain and can be readily adapted to various source receiver configurations the behavior of the algorithm conforms to the predictions of generalized least squares inverse the ory the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model in practice the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations the suggested inversion strategy consists of first inverting for the density and p wave velocity or p wave impedance by considering plane waves in the low slowness region near normal angles of incidence then in optimizing for the s wave velocity by progressively including contributions from the high slowness region steep angles of incidence numerical experiments performed with noise free synthetic data prove that the proposed inversion method satisfactorally reconstructs the elastic properties of a stratified medium from a limited set of plane wave components at a reasonable computing cost

subgroups from regression trees with adjustment for prognostic effects and postselection inference identification of subgroups with differential treatment effects in randomized trials is attracting much attention many methods use regression tree algorithms this article addresses 2 important questions arising from the subgroups how to ensure that treatment effects in subgroups are not confounded with effects of prognostic variables and how to determine the statistical significance of treatment effects in the subgroups we address the first question by selectively including linear prognostic effects in the subgroups in a regression tree model the second question is more difficult because it falls within the subject of postselection inference we use a bootstrap technique to calibrate normal theory t intervals so that their expected coverage probability averaged over all the subgroups in a fitted model approximates the desired confidence level it can also provide simultaneous confidence intervals for all subgroups the first solution is implemented in the guide algorithm and is applicable to data with missing covariate values 2 or more treatment arms and outcomes subject to right censoring bootstrap calibration is applicable to any subgroup identification method it is not restricted to regression tree models two real examples are used for illustration a diabetes trial where the outcomes are completely observed but some covariate values are missing and a breast cancer trial where the outcome is right censored

velocity analysis using similarity weighted semblance weighted semblance can be used for improving the performance of traditional semblance for specific data sets we have developed a novel approach for prestack velocity analysis using weighted semblance the novelty came from a different weighting criteria in which the local similarity between each trace and a reference trace is used on the one hand low similarity corresponded to a noise point or a point indicating incorrect moveout which should be given a small weight on the other hand high similarity corresponded to a point indicating correct moveout that should be given a high weight our approach could also be effectively used for analyzing avo anomalies with increased resolution compared with ab semblance synthetic and field common midpoint gathers demonstrated higher resolution using the approach we developed applications of the proposed method on a prestack data set further confirmed that the stacked data using the similarity weighted semblance could obtain better energy focused events which indicated a more precise velocity picking

estimation of elastic constants for hti media using gauss newton and full newton multiparameter full waveform inversion abstractin seismic full waveform inversion fwi subsurface parameters are estimated by iteratively minimizing the difference between the modeled and the observed data we have considered the problem of estimating the elastic constants of a fractured medium using multiparameter fwi and modeling naturally fractured reservoirs as equivalent anisotropic media multiparameter fwi although promising remains exposed to a range of challenges one being the parameter crosstalk problem resulting from the overlap of frechet derivative wavefields parameter crosstalk is strongly influenced by the form of the scattering pattern for each parameter we have derived 3d radiation patterns associated with scattering from a range of elastic constants in general anisotropic media then we developed scattering patterns specific to a horizontal transverse isotropic hti medium to draw conclusions about parameter crosstalk in fwi bare gradients exhibit crosstalk as well as artifacts caused by doubly scattered energy in

nonholonomic mechanical systems with symmetry this work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of lagrangian mechanics and with a view to control theoretical applications the basic methodology is that of geometric mechanics applied to the formulation of lagrange d alembert generalizing the use of connections and momentum maps associated with a given symmetry group to this case we begin by formulating the mechanics of nonholonomic systems using an ehresmann connection to model the constraints and show how the curvature of this connection enters into lagrange s equations unlike the situation with standard configuration space constraints the presence of symmetries in the nonholonomic case may or may not lead to conservation laws however the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables this momentum equation which plays an important role in control problems involves parallel transport operators and is computed explicitly in coordinates an alternative description using a body reference frame relates part of the momentum equation to the components of the euler poincar e equations along those symmetry directions consistent with the constraints one of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not an example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard a modified version of the skateboard which uses momentum coupling for locomotion generation we construct a synthesis of the mechanical connection and the ehresmann connection defining the constraints obtaining an important new object we call the nonholonomic connection when the nonholonomic connection is a principal connection for the given symmetry group we show how to perform lagrangian reduction in the presence of nonholonomic constraints generalizing previous results which only held in special cases several detailed examples are given to illustrate the theory september 1994 revised march 1995 revised june 1995

subgroup analysis via recursive partitioning subgroup analysis is an integral part of comparative analysis where assessing the treatment effect on a response is of central interest its goal is to determine the heterogeneity of the treatment effect across subpopulations in this paper we adapt the idea of recursive partitioning and introduce an interaction tree it procedure to conduct subgroup analysis the it procedure automatically facilitates a number of objectively defined subgroups in some of which the treatment effect is found prominent while in others the treatment has a negligible or even negative effect the standard cart breiman et al 1984 methodology is inherited to construct the tree structure also in order to extract factors that contribute to the heterogeneity of the treatment effect variable importance measure is made available via random forests of the interaction trees both simulated experiments and analysis of census wage data are presented for illustration

a regression tree approach to identifying subgroups with differential treatment effects in the fight against hard to treat diseases such as cancer it is often difficult to discover new treatments that benefit all subjects for regulatory agency approval it is more practical to identify subgroups of subjects for whom the treatment has an enhanced effect regression trees are natural for this task because they partition the data space we briefly review existing regression tree algorithms then we introduce three new ones that are practically free of selection bias and are applicable to data from randomized trials with two or more treatments censored response variables and missing values in the predictor variables the algorithms extend the guide approach by using three key ideas i treatment as a linear predictor ii chi squared tests to detect residual patterns and lack of fit and iii proportional hazards modeling via poisson regression importance scores with thresholds for identifying influential variables are obtained as by products a bootstrap technique is used to construct confidence intervals for the treatment effects in each node the methods are compared using real and simulated data

a general statistical framework for subgroup identification and comparative treatment scoring summary many statistical methods have recently been developed for identifying subgroups of patients who may benefit from different available treatments compared with the traditional outcome modeling approaches these methods focus on modeling interactions between the treatments and covariates while by pass or minimize modeling the main effects of covariates because the subgroup identification only depends on the sign of the interaction however these methods are scattered and often narrow in scope in this article we propose a general framework by weighting and a learning for subgroup identification in both randomized clinical trials and observational studies our framework involves minimum modeling for the relationship between the outcome and covariates pertinent to the subgroup identification under the proposed framework we may also estimate the magnitude of the interaction which leads to the construction of scoring system measuring the individualized treatment effect the proposed methods are quite flexible and include many recently proposed estimators as special cases as a result some estimators originally proposed for randomized clinical trials can be extended to observational studies and procedures based on the weighting method can be converted to an a learning method and vice versa our approaches also allow straightforward incorporation of regularization methods for high dimensional data as well as possible efficiency augmentation and generalization to multiple treatments we examine the empirical performance of several procedures belonging to the proposed framework through extensive numerical studies

adaptive fuzzy hierarchical sliding mode control for the trajectory tracking of uncertain underactuated nonlinear dynamic systems the trajectory tracking of uncertain underactuated nonlinear dynamic systems is tackled by an adaptive fuzzy hierarchical sliding mode control afhsmc first one of the subsystems is assigned as the first layer sliding surface next a second layer sliding surface from the first layer sliding surface and the sliding surface of another subsystem is constructed in this paper the nth layer is supposed to be the top layer or hierarchical layer for including the sliding surfaces of all subsystems because two nonlinear system functions and the time varying external disturbance of each subsystem are supposed to be unknown different online fuzzy models are employed to approximate these nonlinear system functions and the upper bounded functions of external disturbances moreover the upper bound of uncertainties caused by these fuzzy modeling errors is estimated online based on these learning fuzzy models and the estimated upper bound of these modeling errors an afhsmc is developed the stability analysis and tracking performance of the closed loop system are verified by lyapunov stability theory finally two simulation examples including different amplitudes of external disturbance and comparison with hierarchical sliding mode control confirm the effectiveness and robustness of the proposed control