common hypercyclic vectors for multiples of backward shift we prove that l 2 contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift oper ator by constants of absolute value greater than 1

shaping regularization in geophysical estimation problems regularization is a required component of geophysical estimation problems that operate with insufficient data the goal of regularization is to impose additional constraints on the estimated model i introduce shaping regularization a general method for imposing constraints by explicit mapping of the estimated model to the space of admissible models shaping regularization is integrated in a conjugate gradient algorithm for iterative least squares estimation it provides the advantage of better control on the estimated model in comparison with traditional regularization methods and in some cases leads to a faster iterative convergence simple data interpolation and seismic velocity estimation examples illustrate the concept

generalized nonelliptic moveout approximation in τ p domain we have derived a generalized nonelliptic moveout approximation in the p domain that is a companion to the generalized nonhyperbolic moveout approximation in the t x domain approximation requires five parameters three parameters that can be determined from the zero slowness ray and two parameters that can be determined from one additional ray we convert the generalized approximation from the p domain to the t x domain and vice versa the generalized nonelliptic moveout approximation in the p domain admits other moveout approximations as special cases several analytical and numerical tests showed a superior accuracy of the generalized nonelliptic moveout approximation

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

some questions about subspace hypercyclic operators abstract a bounded linear operator t on a banach space x is called subspace hypercyclic for a subspace m if orb t x m is dense in m for a vector x m we show examples that answer some questions posed by h rezaei 2013 7 in particular we provide an example of an operator t such that orb t x m is somewhere dense in m but it is not everywhere dense in m

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

velocity independent marchenko focusing in time and depth imaging domains for media with mild lateral heterogeneity abstractthe marchenko method retrieves green s functions between the acquisition surface and any arbitrary point in the medium the process generally involves solving an inversion starting with an initial focusing function e g a direct wave green s function from the desired subsurface position typically obtained using an approximate velocity model we have formulated the marchenko method in the time imaging domain in that domain we recognize that the traveltime of the direct wave green s function is related to the cheop s traveltime pyramid commonly used in time domain processing which in turn can be readily obtained from the local slopes of the common midpoint gathers this observation allows us to substitute the velocity model based initial focusing operator with that from a data driven slope estimation process moreover we found that working in the time imaging domain allows for the specification of the desired subsurface position in terms of vertical time which is connected to the cartesian depth position via the time to depth conversion our results suggest that the prior velocity model is only required when specifying the position in depth but this requirement can be circumvented by making use of the time imaging domain within its usual assumptions e g mild lateral heterogeneity provided that those assumptions are satisfied the estimated green s functions from the proposed method have comparable quality to those obtained with the knowledge of a prior velocity model

genericity of wild holomorphic functions and common hypercyclic vectors abstract let t be the translation operator by in the space of entire functions h c defined by t f z f z we prove that there is a residual set g of entire functions such that for every f g and every c 0 the sequence t n f is dense in h c that is g is a residual set of common hypercyclic vectors functions for the family t c 0 also we prove similar results for many families of operators as multiples of differential operator multiples of backward shift weighted backward shifts

velocity independent time domain seismic imaging using local event slopes by estimating local event slopes in prestack seismic reflection data it is possible to accomplish all common time domain imaging tasks from normal moveout to prestack time migration without the need to estimate seismic velocities or any other attributes local slopes contain complete information about the reflection geometry once they are estimated seismic velocities and all other moveout parameters turn into data attributes and are directly mappable from the prestack data domain into the time migrated image domain i develop an analytical theory which defines the transformation from data and local slopes to the image space for different time domain imaging operators computational experiments with synthetic and field data examples confirm theoretical expectations and demonstrate practical effectiveness of the proposed method

normal moveout revisited inhomogeneous media and curved interfaces the equation of normal moveout t2 t02 x2 va2 is valid for a reflection from the base of a single homogeneous and isotropic bed but is only an approximation in the real world of multilayered inhomogeneous media and curved interfaces using the theory of geometrical optics we can find another second order equation which represents hyperbolas that are also symmetrical about the time axis however the centers of these hyperbolas do not coincide with the center of coordinates but are shifted along the time axis the equation describing this second type of hyperbola is t tp t0 2 tp2 x2 v12 where tp is the time of focusing depth and v1 the velocity of the input medium this equation is not only more accurate than the usual normal moveout but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the tp analysis this procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity secti

window length selection for optimum slowness resolution of the local slant stack transform one of the most critical decisions in the design of a local slant stack transform lsst is the selection of its aperture or more precisely the selection of the appropriate number of traces and their weighting coefficients for each slant stack the challenge is to achieve a good compromise between the slowness and the spatial resolution conventionally the window size is chosen in a more intuitive manner by visual inspection and some limited tests we analyzed the lsst to establish rigorous criteria for the window selection to achieve the optimum slowness and spatial resolution in the transformed domain for a given data set for this purpose we estimated the slowness resolution in the lsst domain as a function of the spatial window bandwidth and of the spectral characteristics of the waves for a wave with a given bandpass spectrum the slowness resolution the stopband attenuation and the wavefront tracking capability are determined by the spatial window for narrowband signals the spatial window m

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

hypercyclic orbits intersect subspaces in wild ways abstract let t x x be a hypercyclic operator of an infinite dimensional separable banach space x by modifying a construction of grivaux we will show that the t orbit of a hypercyclic vector can intersect certain closed vector subspaces of x in many strange ways moreover the set of visiting times of the orbit to the subspace can also be quite exotic especially when the operator satisfies a stronger form of hypercyclicity as a by product we will improve and or supply new proofs to some of the recent results about subspace hypercyclicity

automatic data extrapolation to zero offset along local slope abstractvelocity independent seismic data processing requires information about the local slope in the data from estimates of local time and space derivatives of the data a total least squares algorithm gives an estimate of the local slope at each data point total least squares minimizes the orthogonal distance from the data points the local time and space derivatives to the fitted straight line defining the local slope this gives a more consistent estimate of the local slope than standard least squares because it takes into account uncertainty in the temporal and spatial derivatives the total least squares slope estimate is the same as the one obtained from using the structure tensor with a rectangular window function the estimate of the local slope field is used to extrapolate all traces in a seismic gather to the smallest recorded offset without using velocity information extrapolation to zero offset is done using a hyperbolic traveltime function in which slope information replaces the knowled

fast and robust common reflection surface parameter estimation abstractthe common reflection surface crs method offers a stack with higher signal to noise ratio at the cost of a time consuming semblance search to obtain the stacking parameters we have developed a fast method for extracting the crs parameters using local slope and curvature we estimate the slope and curvature with the gradient structure tensor and quadratic structure tensor on stacked data this is done under the assumption that a stacking velocity is already available our method was compared with an existing slope based method in which the slope is extracted from prestack data an experiment on synthetic data shows that our method has increased robustness against noise compared with the existing method when applied to two real data sets our method achieves accuracy comparable with the pragmatic and full semblance searches our method has the advantage of being approximately two and four orders of magnitude faster than the semblance searches

automatic time domain velocity estimation based on an accelerated clustering method abstracttime domain velocity and moveout parameters can be directly obtained from local event slopes which are estimated on the prestack seismic gathers in practice there are always some errors in the estimated local slopes especially in low signal to noise ratio s n situations thus subsurface velocity information may be hidden in the image domain spanned by velocity and other moveout parameters we have developed an accelerated clustering algorithm to find cluster centers without prior information about the number of clusters first plane wave destruction is implemented to estimate the local event slopes for every sample in the seismic gathers we obtain the estimations of velocity and its location in the image domain according to the local event slopes these mapped data points in the new domain exhibit the structure of groups we represent these points by a mixture distribution model then the cluster centers of the mixture distribution model are located which correspond to maximum likelih

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

hypercyclic operators are subspace hypercyclic abstract in this short note we prove that for a dense set a x x is a banach space there is a non trivial closed subspace m x such that a m is dense in m we use this result to answer a question posed in madore and martinez avendano 2011 9 in particular we show that every hypercyclic operator is subspace hypercyclic

invariant gaussian measures for operators on banach spaces and linear dynamics we give conditions for an operator t on a complex separable banach space x with sufficiently many eigenvectors associated to eigenvalues of modulus 1 to admit a non degenerate invariant gaussian measure with respect to which it is weak mixing the existence of such a measure depends on the geometry of the banach space and on the possibility of parametrizing the mathbb t eigenvector fields of t in a regular way we also investigate the connection with frequent hypercyclicity

direct mapping of seismic data to the domain of intercept time and ray parameter a plane wave decomposition marine seismic data recorded as a function of source receiver offset and traveltime are mapped directly to the domain of intercept or vertical delay time and horizontal ray parameter this is a plane wave decomposition based on beam forming of wide aperture seismic array data to determine automatically the loci of coherent seismic reflection and refraction events in this computation semblance in addition to the required slowness or horizontal ray parameter stack is found for linear x t trajectories across subarrays subsequently semblance is used to derive a windowing filter that is applied to the slowness stack to determine the points of stationary phase and eliminate aliasing the resulting filtered slowness stacks for multiple subarrays can then be linearly transformed and combined according to ray parameter range and time the resulting function of intercept time and horizontal ray parameter offers significant computational and interpretational advantages for the case of horizontal homogeneou

an adaptive receiver with an antenna array for channels with correlated non gaussian interference and noise using the sage algorithm an adaptive receiver that uses multiple antennas to provide diversity against fading is developed for operation in an impulsive noise environment the noise components at each sensor are assumed to be correlated a mixture of multivariate gaussian distributions is used to model the noise using a training sequence model parameters are estimated by iterative procedures derived from the expectation maximization em algorithm these estimated parameters are then used in a likelihood ratio test to recover the transmitted signals simulations show that the proposed adaptive receiver is robust and near optimum performance can be achieved when sufficient training data is available

sums of hypercyclic operators abstract every bounded operator on a complex infinite dimensional separable hilbert space can be written as the sum of two hypercyclic operators and also as the sum of two chaotic operators

maximum likelihood array processing in non gaussian noise with gaussian mixtures many approaches have been studied for the array processing problem when the additive noise is modeled with a gaussian distribution but these schemes typically perform poorly when the noise is non gaussian and or impulsive this paper is concerned with maximum likelihood array processing in non gaussian noise we present the cramer rao bound on the variance of angle of arrival estimates for arbitrary additive independent identically distributed iid symmetric non gaussian noise then we focus on non gaussian noise modeling with a finite gaussian mixture distribution which is capable of representing a broad class of non gaussian distributions that include heavy tailed impulsive cases arising in wireless communications and other applications based on the gaussian mixture model we develop an expectation maximization em algorithm for estimating the source locations the signal waveforms and the noise distribution parameters the important problems of detecting the number of sources and obtaining initial parameter estimates for the iterative em algorithm are discussed in detail the initialization procedure by itself is an effective algorithm for array processing in impulsive noise novel features of the em algorithm and the associated maximum likelihood formulation include a nonlinear beamformer that separates multiple source signals in non gaussian noise and a robust covariance matrix estimate that suppresses impulsive noise while also performing a model based interpolation to restore the low rank signal subspace the em approach yields improvement over initial robust estimates and is valid for a wide snr range the results are also robust to pdf model mismatch and work well with infinite variance cases such as the symmetric stable distributions simulations confirm the optimality of the em estimation procedure in a variety of cases including a multiuser communications scenario we also compare with existing array processing algorithms for non gaussian noise

data adaptive algorithms for signal detection in sub gaussian impulsive interference we address the problem of coherent detection of a signal embedded in heavy tailed noise modeled as a sub gaussian alpha stable process we assume that the signal is a complex valued vector of length l known only within a multiplicative constant while the dependence structure of the noise i e the underlying matrix of the sub gaussian process is not known we implement a generalized likelihood ratio detector that employs robust estimates of the unknown noise underlying matrix and the unknown signal strength the performance of the proposed adaptive detector is compared with that of an adaptive matched filter that uses gaussian estimates of the noise underlying matrix and the signal strength and is found to be clearly superior the proposed new algorithms are theoretically analyzed and illustrated in a monte carlo simulation

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

frequently hypercyclic operators we investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators t on separable complex f spaces t is frequently hypercyclic if there exists a vector x such that for every nonempty open subset u of x the set of integers n such that t n x belongs to u has positive lower density we give several criteria for frequent hypercyclicity and this leads us in particular to study linear transformations from the point of view of ergodic theory several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting

migration velocity analysis using residual diffraction moveout in the poststack depth domain abstractdiffraction events contain more direct information on the medium velocity than reflection events we have developed a method for migration velocity improvement and diffraction localization based on a moveout analysis of over or undermigrated diffraction events in the depth domain the method uses an initial velocity model as input it provides an update to the velocity model and diffraction locations in the depth domain as a result the algorithm is based on the focusing of remigration trajectories from incorrectly migrated diffraction curves these trajectories are constructed by applying a ray tracing like approach to the image wave equation for velocity continuation the starting points of the trajectories are obtained from fitting an ellipse or hyperbola to the picked uncollapsed diffraction events in the depth migrated domain focusing of the remigration trajectories points out the approximate location of the associated diffractor as well as local velocity attributes apart from the migrati

velocity continuation and the anatomy of residual prestack time migration velocity continuation is an imaginary continuous process of seismic image transformation in the postmigration domain it generalizes the concepts of residual and cascaded migrations understanding the laws of velocity continuation is crucially important for a successful application of time migration velocity analysis these laws predict the changes in the geometry and intensity of reflection events on migrated images with the change of the migration velocity in this paper i derive kinematic and dynamic laws for the case of prestack residual migration from simple geometric principles the main theoretical result is a decomposition of prestack velocity continuation into three different components corresponding to residual normal moveout residual dip moveout and residual zero offset migration i analyze the contribution and properties of each of the three components separately this theory forms the basis for constructing efficient finite difference and spectral algorithms for time migration velocity ana

signal and noise separation in prestack seismic data using velocity dependent seislet transform abstractthe seislet transform is a waveletlike transform that analyzes seismic data by following varying slopes of seismic events across different scales and provides a multiscale orthogonal basis for seismic data it generalizes the discrete wavelet transform dwt in the sense that the dwt in the lateral direction is simply the seislet transform with a zero slope our earlier work used plane wave destruction pwd to estimate smoothly varying slopes however the pwd operator can be sensitive to strong noise interference which makes the seislet transform based on pwd pwd seislet transform occasionally fail in providing a sparse multiscale representation for seismic field data we adopted a new velocity dependent vd formulation of the seislet transform in which the normal moveout equation served as a bridge between local slope patterns and conventional moveout parameters in the common midpoint domain the vd slope has better resistance to strong random noise which indicated the potential of vd sei

a theory of normal moveout three geophysical principles are shown to be sufficient to determine the most general practical normal moveout nmo equation the principles are reciprocity in a common midpoint cmp gather finite slowness and exact constant velocity limit the resulting equation is the shifted hyperbola nmo equation that has three parameters comparisons at both near and far offsets between the shifted hyperbola nmo equation and the results for layered media assign geophysical meaning to the parameters two of the parameters zero offset time and nmo velocity are constants and control the very near offset behavior the third parameter is dimensionless and controls the far offset behavior of the nmo curve but it may be a function of offset so as to exactly fit any traveltime curve the parameters may be found by a linear least squares fit to data the theory applies to all offsets for nonturning wave reflections in an isotropic earth for both p waves and converted p sv waves

accelerated plane wave destruction abstractwhen plane wave destruction pwd is implemented by implicit finite differences the local slope is estimated by an iterative algorithm we propose an analytical estimator of the local slope that is based on convergence analysis of the iterative algorithm using the analytical estimator we design a noniterative method to estimate slopes by a three point pwd filter compared with the iterative estimation the proposed method needs only one regularization step which reduces computation time significantly with directional decoupling of the plane wave filter the proposed algorithm is also applicable to 3d slope estimation we present synthetic and field experiments to demonstrate that the proposed algorithm can yield a correct estimation result with shorter computational time

notes on subspace hypercyclic operators a bounded linear operator t on a banach space x is called subspace hypercyclic for a subspace m if orb t x m is dense in m for a vector x m in this case we show that p t has a relatively dense range for every real or complex polynomial p which in turn answers a question posed in madore and martinez avendano 2011 8 as a consequence the algebraic structure of the set of subspace hypercyclic vectors can be described