migration inversion revisited 1999 seismic reflection events are typically classified as primary or multiple the standard view considers primary as signal and multiple as a form of coherent noise methods for separating primaries from multiples were reviewed in tle s january 1999 issue

eigenvalue assignment by minimal state feedback gain in lti multivariable systems in this article an improved method for eigenvalue assignment via state feedback in the linear time invariant multivariable systems is proposed this method is based on elementary similarity operations and involves mainly utilisation of vector companion forms and thus is very simple and easy to implement on a digital computer in addition to the controllable systems the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs moreover two types of state feedback gain matrices can be achieved by this method 1 the numerical one which is unique and 2 the parametric one in which its parameters are determined in order to achieve a gain matrix with minimum frobenius norm the numerical examples are presented to demonstrate the advantages of the proposed method

primal dual algorithms for deterministic inventory problems we consider several classical models in deterministic inventory theory the single item lot sizing problem the joint replenishment problem and the multistage assembly problem these inventory models have been studied extensively and play a fundamental role in broader planning issues such as the management of supply chains for each of these problems we wish to balance the cost of maintaining surplus inventory for future demand against the cost of replenishing inventory more frequently for example in the joint replenishment problem demand for several commodities is specified over a discrete finite planning horizon the cost of maintaining inventory is linear in the number of units held but the cost incurred for ordering a commodity is independent of the size of the order furthermore there is an additional fixed cost incurred each time a nonempty subset of commodities is ordered the goal is to find a policy that satisfies all demands on time and minimizes the overall holding and ordering cost we shall give a novel primal dual framework for designing algorithms for these models that significantly improve known results in several ways the performance guarantees for the quality of the solutions improve on or match previously known results the performance guarantees hold under much more general assumptions about the structure of the costs and the algorithms and their analysis are significantly simpler than previous known results finally our primal dual framework departs from the structure of previously studied primal dual approximation algorithms in significant ways and we believe that our approach may find applications in other settings more specifically we provide 2 approximation algorithms for the joint replenishment problem and for the assembly problem and solve the single item lot sizing problem to optimality the results for the joint replenishment and the lot sizing problems also hold for their generalizations with back orders allowed as a byproduct of our work we prove known and new upper bounds on the integrality gap of some linear programming lp relaxations of the abovementioned problems

some new results in the theory of negative imaginary systems with symmetric transfer matrix function abstract this note represents a first attempt to provide a definition and characterisation of negative imaginary systems for not necessarily rational transfer functions via a sign condition expressed in the entire domain of analyticity along the same lines of the classic definition of positive real systems under the standing assumption of symmetric transfer functions we then derive a necessary and sufficient condition that characterises negative imaginary transfer functions in terms of a matrix sign condition restricted to the imaginary axis once again following the same line of argument of the standard positive real case using this definition even transfer functions with a pole at the origin with double multiplicity as well as with a possibly negative relative degree can be negative imaginary

accelerating migration deconvolution using a nonmonotone gradient method new solution methods were considered for migration deconvolution in seismic imaging problems it is well known that direct migration methods using the adjoint operator l yieldalower resolutionorblurredimage andthatthelinearized inversion of seismic data for the reflectivity model usually requires solving a regularized least squares migration problem we observed that the regularized least squares method is computationally expensive which becomes a severeobstacleforpracticalapplications iterativegradient descent methods were studied and an efficient method for migration deconvolution was developed the problem was formulatedbyincorporatingregularizingconstraints andthena nonmonotonegradient descentmethodwasappliedtoaccelerate the convergence to test the potential of the application of the developed method synthetic two dimensional and three dimensionalseismic migration deconvolutionsimulations were performed numerical performance indicates that this method is promising for practical seismic migration imaging

target oriented wave equation least squares migration inversion with phase encoded hessian prestack depth migration produces blurred images resulting from limited acquisition apertures complexities in the velocity model and band limited characteristics of seismic waves this distortion can be partially corrected using the model space least squares migration inversion approach where a target oriented wave equation hessian operator is computed explicitly and then inverse filtering is applied iteratively to deblur or invert for the reflectivity however one difficulty is the cost of computing the explicit hessian operator which requires storing a large number of green s functions making it challenging for large scale applications a new method to compute the hessian operator for the wave equation based least squares migration inversion problem modifies the original explicit hessian formula enabling efficient computation of this operator an advantage is that the method eliminates disk storage of green s functions the modifications however also introduce undesired crosstalk artifacts two different phase encoding schemes plane wave phase encoding and random phase encoding suppress the crosstalk when the randomly phase encoded hessian operator is applied to the sigsbee2a synthetic data set an improved subsalt image with more balanced amplitudes is obtained

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

covering problems with hard capacities we consider the classical vertex cover and set cover problems with hard capacity constraints this means that a set vertex can cover only a limited number of its elements adjacent edges and the number of available copies of each set vertex is bounded this is a natural generalization of the classical problems which also captures resource limitations in practical scenarios we obtain the following results for the unweighted vertex cover problem with hard capacities we give a 3 approximation algorithm that is based on randomized rounding with alterations we prove that the weighted version is at least as hard as the set cover problem yielding an interesting separation between the approximability of weighted and unweighted versions of a natural graph problem a logarithmic approximation factor for both the set cover and the weighted vertex cover problem with hard capacities follows from the work of wolsey combinatorica 2 1982 pp 385 393 on submodular set cover we provide here a simple and intuitive proof for this bound

on the imaging of reflectors in the earth in this paper i present a modification of the beylkin inversion operator this modification accounts for the band limited nature of the data and makes the role of discontinuities in the sound speed more precise the inversion presented here partially dispenses with the small parameter constraint of the born approximation this is shown by applying the proposed inversion operator to upward scattered data represented by the kirchhoff approximation using the angularly dependent geometrical optics reflection coefficient a fully nonlinear estimate of the jump in sound speed may be extracted from the output of this algorithm interpreted in the context of these kirchhoff approximate data for the forward problem the inversion of these data involves integration over the source receiver surface the reflecting surface and frequency the spatial integrals are computed by the method of stationary phase the output is asymptotically a scaled singular function of the reflecting surface the singular function of a

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

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

fully polynomial approximation schemes for single item capacitated economic lot sizing problems np hard cases of the single item capacitated lot sizing problem have been the topic of extensive research and continue to receive considerable attention however surprisingly few theoretical results have been published on approximation methods for these problems to the best of our knowledge until now no polynomial approximation method is known that produces solutions with a relative deviation from optimality that is bounded by a constant in this paper we show that such methods do exist by presenting an even stronger result the existence of fully polynomial approximation schemes the approximation scheme is first developed for a quite general model which has concave backlogging and production cost functions and arbitrary monotone holding cost functions subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models

from valid inequalities to heuristics a unified view of primal dual approximation algorithms in covering problems in recent years approximation algorithms based on primal dual methods have been successfully applied to a broad class of discrete optimization problems in this paper we propose a generic primal dual framework to design and analyze approximation algorithms for integer programming problems of the covering type that uses valid inequalities in its design the worst case bound of the proposed algorithm is related to a fundamental relationship called strength between the set of valid inequalities and the set of minimal solutions to the covering problems in this way we can construct an approximation algorithm simply by constructing the required valid inequalities we apply the proposed algorithm to several problems such as covering problems related to totally balanced matrices cyclic scheduling vertex cover general set covering intersections of polymatroids and several network design problems attaining in most cases the best worst case bound known in the literature

robust eigenstructure assignment in geometric control theory in this paper we employ the rosenbrock system matrix pencil for the computation of output nulling subspaces of linear time invariant systems which appear in the solution of a large number of control and estimation problems we also consider the problem of finding friends of these output nulling subspaces i e the feedback matrices that render such subspaces invariant with respect to the closed loop map and output nulling with respect to the output map and which at the same time deliver a robust closed loop eigenstructure we show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

2d frequency domain elastic full waveform inversion using the block diagonal pseudo hessian approximation abstractelastic full waveform inversion efwi of multicomponent seismic data is a powerful tool for estimating the subsurface elastic parameters with high accuracy however the trade offs between multiple parameters increase the nonlinearity of efwi although the conventional diagonal approximate hessian matrix describes the illumination and limited bandwidth effects it ignores the trade off effects and decreases the convergence rate of efwi we have developed a block diagonal pseudo hessian operator for 2d frequency domain efwi to take into account the approximate trade offs among the p wave compressional wave velocity s wave shear wave velocity and density without extra computational costs on forward simulations the hessian matrix tends toward a block diagonal matrix as the frequency grows to infinity thus the proposed block diagonal pseudo hessian matrix is more accurate at higher frequencies the inverse of the block diagonal pseudo hessian matrix is used as a preconditioner for the nonlin

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

solution of the static state feedback decoupling problem for linear systems with two outputs we give for linear systems with two outputs a necessary and sufficient condition for the solvability of the restricted decoupling problem rdp in terms of some structural invariants a geometric characterization is also given which provides the least dynamical extension needed when rdp is not solvable

single item lot sizing with non decreasing capacities we consider the single item lot sizing problem with capacities that are non decreasing over time when the cost function is i non speculative or wagner whitin for instance constant unit production costs and non negative unit holding costs and ii the production set up costs are non increasing over time it is known that the minimum cost lot sizing problem is polynomially solvable using dynamic programming when the capacities are non decreasing we derive a compact mixed integer programming reformulation whose linear programming relaxation solves the lot sizing problem to optimality when the objective function satisfies i and ii the formulation is based on mixing set relaxations and reduces to the known convex hull of solutions when the capacities are constant over time we illustrate the use and potential effectiveness of this improved lp formulation on a few test instances including instances with and without wagner whitin costs and with both non decreasing and arbitrary capacities over time

a unified method for optimal arbitrary pole placement abstract we consider the classic problem of pole placement by state feedback we offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole placing feedback matrix that can deliver any set of desired closed loop eigenvalues with any desired multiplicities this parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain lastly we compare the performance of our method against several others from the recent literature

modified imaging principle an alternative to preserved amplitude least squares wave equation migration impedance contrast images can result from a least squares migration or from a modified imaging principle theoretically the two approaches should give similar results but in practice they lead to different estimates of the impedance contrasts because of limited acquisition geometry difficulty in computing exact weights for least squares migration and small contrast approximation to analyze those differences we compare the two approaches based on 2d synthetics forward modeling is either a finite difference solver of the full acoustic wave equation or a one way wave equation solver that correctly models the amplitudes the modified imaging principle provides better amplitude estimates of the impedance contrasts and does not suffer from the artifacts at tributable to diving waves which can be seen in two way least squares migrated sections however because of the shot based formulation artifacts appear in the modified imaging principle results in shadow zones where energy is defocused those artif

regularization and datuming of seismic data by weighted damped least squares the possibility of improving regularization datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem weighted damped least squares is then used to produce the regularized datumed wavefield regularization datuming is extremely costly because of computing the hessian so an efficient approximation is introduced approximation is achieved by computing a limited number of diagonals in the operators involved real and synthetic data examples demonstrate the utility of this approach for synthetic data regularization datuming is demonstrated for large extrapolation distances using a highly irregular recording array without approximation regularization datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation pspi approximate regularization datuming returns a regularized wavefield for approximately two orders of magnitude less in cost but it is dip limi

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

decoupling by restricted static state feedback the general case in this paper we tackle the general block decoupling problem for linear constant dynamical systems c a b with m inputs and p outputs with restricted static state feedback in other words with control laws of type u gfx gv we give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in 2 for the simple case k p leq m where k denotes the number of blocks to be decoupled

robust deadbeat regulation the synthesis of state feedback gains that provide robustness against perturbation in deadbeat regulation is considered the problem is formulated as an unconstrained optimization problem through a posteriori perturbation analysis of the closed loop eigenvalues the justification of the use of a new objective function to measure the robustness of deadbeat systems is established the objective function does not require the computation of eigenvectors and has simple analytical gradient and hessian a numerical example is employed to illustrate the effectiveness of the proposed method

pole assignment via the schur form abstract we propose an algorithm for the state feedback pole assignment problem the algorithm is the first of its kind making direct use of the schur form and minimizing the departure from normality of the closed loop poles for a given first schur vector x 1 the robust pole assignment problem can then be solved via choosing x 1 optimally several numerical examples were presented to illustrate the feasibility of the algorithm

least squares wave equation migration for avp ava inversion we present an acoustic migration inversion algorithm that uses extended double square root wave equation migration and modeling operators to minimize a constrained least squares data misfit function least squares migration we employ an imaging principle that allows for the extraction of ray parameter domain common image gathers cigs from the propagated seismic wavefield the cigs exhibit amplitude variations as a function of half offset ray parameter avp closely related to the amplitude variation with reflection angle ava our least squares wave equation migration inversion is constrained by a smoothing regularization along the ray parameter this approach is based on the idea that rapid amplitude changes or discontinuities along the ray parameter axis result from noise incomplete wavefield sampling and numerical operator artifacts these discontinuities should therefore be penalized in the inversion the performance of the proposed algorithm is examined with two synthetic examples in the first

a general approximation technique for constrained forest problems we present a general approximation technique for a large class of graph problems our technique mostly applies to problems of covering at minimum cost the vertices of a graph with trees cycles or paths satisfying certain requirements in particular many basic combinatorial optimization problems fit in this framework including the shortest path minimum cost spanning tree minimum weight perfect matching traveling salesman and steiner tree problems our technique produces approximation algorithms that run in o n 2 log n time and come within a factor of 2 of optimal for most of these problems for instance we obtain a 2 approximation algorithm for the minimum weight perfect matching problem under the triangle inequality our running time of o n 2 log n time compares favorably with the best strongly polynomial exact algorithms running in o n 3 time for dense graphs a similar result is obtained for the 2 matching problem and its variants we also derive the first approximation algorithms for many np complete problems including the non fixed point to point connection problem the exact path partitioning problem and complex location design problems moreover for the prize collecting traveling salesman or steiner tree problems we obtain 2 approximation algorithms therefore improving the previously best known performance guarantees of 2 5 and 3 respectively math programming 59 1993 pp 413 420

pole assignment via sylvester s equation it is shown that the pole assignment problem can be reduced to solving the linear matrix equations ax xa bg fx g successively for x and then f for almost any choice of g the result is a new pole assignment procedure and proof of the pole assignment theorem that should play an important role in both theoretical and practical applications

valid linear inequalities for fixed charge problems many problems in the operations research management science literature can be formulated with both zero one and continuous variables however the exact optimization of such mixed zero one models remains a computational challenge in this paper we propose to study mixed problems from a mathematical point of view that is similar in spirit to recent research on purely combinatorial problems that has investigated systems of defining linear inequalities or facets of the underlying polytope at least two numerical studies have validated this line of research computationally and the advances in the problem solving capabilities are considerable we expect that similar gains are possible for the mixed zero one problem more precisely we consider the mixed integer programs whose feasible region x is composed of i a simple additive constraint in the continuous variables xj for j 1 2 n and ii constraints 0 xj mjyj defined by binary variables yj for j 1 2 n this type of feasible region arises in a variety of mixed integer problems and particularly in network problems with fixed charges on the arcs we derive two classes of facet defining linear inequalities of the convex hull of x and show that the second of these classes gives a complete description of the convex hull when mj m for all j we also develop methods to detect violated inequalities from these classes so that these facets can be used as cutting planes to strengthen the formulations of certain mixed integer problems

theory of nonstationary linear filtering in the fourier domain with application to time variant filtering a general linear theory describes the extension of the convolutional method to nonstationary processes this theory can apply any linear nonstationary filter with arbitrary time and frequency variation in the time fourier or mixed domains the filter application equations and the expressions to move the filter between domains are all ordinary fourier transforms or generalized convolutional integrals nonstationary transforms such as the wavelet transform are not required there are many possible applications of this theory including the one way propagation of waves through complex media time migration normal moveout removal time variant filtering and forward and inverse q filtering two complementary nonstationary filters are developed by generalizing the stationary convolution integral the first called nonstationary convolution corresponds to the linear superposition of scaled impulse responses of a nonstationary filter the second called nonstationary combination does not correspond to such a superposition but is shown to be a linear process capable of achieving arbitrarily abrupt temporal variations in the output frequency spectrum both extensions have stationary convolution as a limiting form and in the discrete case can be formulated as matrix operations fourier transformation shows that both filter types are nonstationary filter integrals in the fourier domain as well this result is a generalization of the convolution theorem for stationary signals because as the filter becomes stationary in one domain the integral in the other domain collapses to a scalar multiplication for discrete signals stationary filters are a matrix multiplication of the input signal spectrum by a diagonal spectral matrix while nonstationary filters require off diagonal terms for quasi stationary filters a computational advantage is obtained by computing only the significant terms near the diagonal unlike stationary theory a mixed domain of time and frequency is also possible in this context the nonstationary filter is applied simultaneously with the transform from time to frequency or the reverse nonstationary convolution becomes a generalized forward fourier integral and nonstationary combination is a generalized inverse fourier integral

a general approach to the eigenstructure assignment for reachability and stabilizability subspaces abstract this paper is concerned with the problem of determining basis matrices for the supremal output nulling reachability and stabilizability subspaces and the simultaneous computation of the associated friends that place the assignable closed loop eigenvalues at desired locations our aim is to show that the moore laub algorithm in moore and laub 1978 for the computation of these subspaces was stated under unnecessary restrictive assumptions we prove the same result under virtually no system theoretic hypotheses this provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust and as general as the standard ones based on the computation of sequences of subspaces

eigenstructure assignment in linear multivariable systems a parametric solution this paper generalizes a recently reported method 1 of closed loop eigenstructure assignment via state feedback in a linear multivariable system with n states and r control inputs by introducing a lemma on the differentiation of determinants the class of assignable eigenvectors and generalized eigenvectors associated with the assigned eigenvalues is explicitly described by a complete set of n r dimensional free parameter vectors this parametric characterization conveniently organizes the nonuniqueness of the solution of the eigenvalue assignment problem and thereby provides an efficient means of further modifying the system dynamic response a numerical example is worked out to demonstrate the feasibility of the method

primal dual schema for capacitated covering problems primal dual algorithms have played an integral role in recent developments in approximation algorithms and yet there has been little work on these algorithms in the context of lp relaxations that have been strengthened by the addition of more sophisticated valid inequalities we introduce primal dual schema based on the lp relaxations devised by carr et al for the minimum knapsack problem as well as for the single demand capacitated facility location problem our primal dual algorithms achieve the same performance guarantees as the lp rounding algorithms of carr et al which rely on applying the ellipsoid algorithm to an exponentially sized lp furthermore we introduce new flow cover inequalities to strengthen the lp relaxation of the more general capacitated single item lot sizing problem using just these inequalities as the lp relaxation we obtain a primal dual algorithm that achieves a performance guarantee of 2 computational experiments demonstrate the effectiveness of this algorithm on generated problem instances

infinite structure and exact model matching problem a geometric approach we first generalize to a b c d quadruples the geometric characterization of the infinite zero structure we then give a new geometric proof for a solvability condition of the exact model matching problem expressed in terms of this concept and previously established in the polynomial context by morse verghese and pernebo this emphasizes the approach independent character of the infinite zero structure

least squares migration data domain versus image domain using point spread functions abstract conventional amplitude inversion assumes that the migrated image preserves relative amplitude information however illumination effects caused by complex geologic settings undersampled acquisition geometry and limited recording aperture pose a challenge to even the most advanced imaging algorithms in addition standard depth migration images can suffer from lack of resolution caused by wavelet stretch attenuation and suboptimal deghosting least squares migration lsm can mitigate many of these problems and produce better resolved migration images suitable for avo inversion however whether formulated in the data domain or the image domain lsm is an inversion algorithm and is sensitive to inaccuracies in the source wavelet velocity model data preprocessing and the propagator used practical considerations to mitigate these problems under nonideal conditions and cost reduction strategies differ between the data and image domain formulations the relative merits of each approach are ev

iterative asymptotic inversion in the acoustic approximation we propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation for this purpose we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods the different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image in the linearized inversion we use the background velocity model obtained by velocity analysis we determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model because the inverse operator is not exact and because the source and station distribution is limited the first iteration of our asymptotic inversion technique is not exact we improve the images by an iterative procedure since the background velocity does not change between iterations there is no need to retrace rays

globally convergent algorithms for robust pole assignment by state feedback it is observed that an algorithm proposed in 1985 by kautsky nichols and van dooren knv amounts to maximizing at each iteration the determinant of the candidate closed loop eigenvector matrix x with respect to one of its columns with unit length constraint subject to the constraint that it remains an achievable closed loop eigenvector matrix this interpretation is used to prove convergence of the knv algorithm it is then shown that a more efficient algorithm is obtained if det x is concurrently maximized with respect to two columns of x and such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs variations exploiting the availability of multiple processors are suggested convergence properties of the proposed algorithms are established their superiority is demonstrated numerically

imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized radon transform this paper treats the linearized inverse scattering problem for the case of variable background velocity and for an arbitrary configuration of sources and receivers the linearized inverse scattering problem is formulated in terms of an integral equation in a form which covers wave propagation in fluids with constant and variable densities and in elastic solids this integral equation is connected with the causal generalized radon transform grt and an asymptotic expansion of the solution of the integral equation is obtained using an inversion procedure for the grt the first term of this asymptotic expansion is interpreted as a migration algorithm as a result this paper contains a rigorous derivation of migration as a technique for imaging discontinuities of parameters describing a medium also a partial reconstruction operator is explicitly derived for a limited aperture when specialized to a constant background velocity and specific source receiver geometries our results are directly related to some known migration algorithms

a nine fold canonical decomposition for linear systems the zero structure for non minimal proper systems in state space form is investigated the approach is geometric and a complete characterization in geometric terms is given of the invariant decoupling system and transmission zeros as defined by rosenbrock the first main result is a formula for the transmission zeros second a canonical lattice diagram is presented of a decomposition of the state space which can be viewed as the product of the kalman canonical decomposition and the morse canonical decomposition this decomposition gives a straightforward characterization of all zeros just mentioned in terms of spectral properties of subspaces under a certain class of feedback and injection mappings via this diagram a number of equivalent formulae for the transmission zeros are derived the freedom in pole assignment leads to new characterizations for the invariant and system zeros in terms of greatest common divisors of characteristic polynomials finally the relation is demonstrated be

elastic least squares reverse time migration via linearized elastic full waveform inversion with pseudo hessian preconditioning abstracttime domain elastic least squares reverse time migration lsrtm is formulated as a linearized elastic full waveform inversion problem the elastic born approximation and elastic reverse time migration rtm operators are derived from the time domain continuous adjoint state method our approach defines p and s wave impedance perturbations as unknown elastic images our algorithm is obtained using continuous functional analysis in which the problem is discretized at the final stage optimize before discretize approach the discretized numerical versions of the elastic born operator and its adjoint elastic rtm operator pass the dot product test the conjugate gradient least squares method is used to solve the least squares migration quadratic optimization problem in other words the hessian operator for elastic lsrtm is implicitly inverted via a matrix free algorithm that only requires the action of forward and adjoint operators on vectors the diagonal of the pseudo hessian operator is used t

prestack migration by split step dsr the double square root dsr prestack migration equation though defined for depth variable velocity can be used to image media with strong velocity variations using a phase shift plus interpolation pspi or split step correction the split step method is based on applying a phase shift correction to the extrapolated wavefield a correction that attempts to compensate for the lateral velocity variations i show how to extend dsr prestack migration to lateral velocity media and exemplify the method by applying the new algorithm to the marmousi data set the split step dsr migration is very fast and offers excellent imaging results

approaches to robust pole assignment abstract robust pole assignment is a non linear optimization problem in many variables we describe numerical methods for determining robust or well conditioned so lutions to the problem of pole assignment by state feedback the solutions are chosen to minimize various objective functions based on the condition number of the eigenvector matrix careful choice of parametrization and objective function avoids singularities and artificial variable constraints explicit formulae for the gradient and hessian permit rigorous stopping criteria and rapid local convergence several computational examples are included

refined schur method for robust pole assignment with repeated poles schur type methods in 6 and 11 solve the robust pole assignment problem by employing the departure from normality of the closed loop system matrix as the measure of robustness they work well generally when all poles to be assigned are simple however when some poles are close or even repeated the eigenvalues of the computed closed loop system matrix might be inaccurate in this paper we present a refined schur method which is able to deal with the case when some or all of the poles to be assigned are repeated more importantly the refined schur method can still be applied when place 14 and robpole 28 fail to output a solution when the multiplicity of some repeated poles is greater than the input freedom

adaptive multiple subtraction using regularized nonstationary regression stationary regression is the backbone of seismic data processing algorithms including match filtering which is commonly applied for adaptive multiple subtraction however the assumption of stationarity is not always adequate for describing seismic signals i have developed a general method of nonstationary regression and that applies to nonstationary match filtering the key idea is the use of shaping regularization to constrain the variability of nonstationary regression coefficients simple computational experiments demonstrate advantages of shaping regularization over classic tikhonov s regularization including a more intuitive selection of parameters and a faster iterative convergence using benchmark synthetic data examples i have successfully applied this method to the problem of adaptive subtraction of multiple reflections

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

multidimensional recursive filters via a helix wind a wire onto a cylinder to create a helix i show that a filter on the 1 d space of the wire mimics a 2 d filter on the cylindrical surface thus 2 d convolution can be done with a 1 d convolution program i show some examples of 2 d recursive filtering also called 2 d deconvolution or 2 d polynomial division in 2 d as in 1 d the computational advantage of recursive filters is the speed with which they propagate information over long distances we can estimate 2 d prediction error filters pefs that are assured of being stable for 2 d recursion such 2 d and 3 d recursions are general purpose preconditioners that vastly speed the solution of a wide class of geophysical estimation problems the helix transformation also enables use of the partial differential equation of wave extrapolation as though it were an ordinary differential equation

the resolution of the equation xa xbx hx and the pole assignment problem a general approach abstract in this paper we generalize an existing technique which is relevant to a pole placement problem and state feedback control design with constraints on control inputs the existing technique concerns only a restrictive class of systems for which many assumptions should be satisfied the generalization aims then at avoiding those assumptions the advantages of generalizing this technique are to determine linear feedback controllers that asymptotically stabilize a wide class of systems which are subject to input constraints without violating these constraints to derive a simple formula for the state feedback and to assign the whole spectrum when stable poles are not suitably located for performances moreover there will be no need to assume a lack of overlap between open and closed loop spectra illustrative examples are presented to point out these advantages

arbitrary pole placement with the extended kautsky nichols van dooren parametric form abstractwe consider the classic problem of pole placement by state feedback the well known eigenstructure assignment algorithm of kautsky nichols and van dooren is extended to obtain a parametric formula for the pole placing feedback matrix that can deliver any desired closed loop eigenvalues with any desired multiplicities

target oriented wave equation inversion a target oriented strategy can be applied to estimate a wave equation least squares inverse lsi image by explicitly computing the wave equation hessian the lsi image is obtained as the solution of a nonstationary least squares inverse filtering problem the rows of the hessian are the nonstationary filters containing information about the acquisition geometry the velocity model and the band limited characteristics of the seismic data by exploiting the sparsity and the structure of the hessian matrix a large number of iterations necessary to achieve convergence can be computed cheaply the results on a structurally complex model show the improvements of the lsi image versus the migrated image

when trees collide an approximation algorithm for thegeneralized steiner problem on networks we give the first approximation algorithm for the generalized network steiner problem a problem in network design an instance consists of a network with link costs and for each pair i j of nodes an edge connectivity requirement r ij the goal is to find a minimum cost network using the available links and satisfying the requirements our algorithm outputs a solution whose cost is within 2 lceil log 2 r 1 rceil of optimal where r is the highest requirement value in the course of proving the performance guarantee we prove a combinatorial min max approximate equality relating minimum cost networks to maximum packings of certain kinds of cuts as a consequence of the proof of this theorem we obtain an approximation algorithm for optimally packing these cuts we show that this algorithm has application to estimating the reliability of a probabilistic network

robust exact pole placement via an lmi based algorithm this technical note deals with the robust exact pole placement problem pole placement algorithms that guarantee a small variation of the assigned poles against possible perturbations the solution to this problem is related to the solvability of a sylvester like equation thus the main issue is to compute a well conditioned solution to this equation also the best candidate solution must possess the minimal condition number to reduce sensitivity to perturbation this problem is cast as a global optimization under linear matrix inequality constraints for which a numerical convergent algorithm is provided and compared with the most attractive methods in the literature

smoothing imaging condition for shot profile migration amplitudes in shot profile migration can be improved if the imaging condition incorporates a division deconvolution in the time domain of the upgoing wavefield by the downgoing wavefield this division can be enhanced by introducing an optimal wienerfilterwhichassumesthatthenoisepresentinthedatahas a white spectrum this assumption requires a damping parameter related to the signal to noise ratio often chosen by trial and error in practice the damping parameter replaces the small valuesofthespectrumofthedowngoingwavefieldandavoidsdivision by zero the migration results can be quite sensitive to the damping parameter and in most applications the upgoing and downgoing wavefields are simply multiplied alternatively the division can be made stable by filling the small values of the spectrumwithanaverageoftheneighboringpoints thisaveraging is obtained by running a smoothing operator on the spectrum ofthedowngoingwavefield thisoperationcalledthesmoothing imaging condition our results show that where the spectrum of the downgoing wavefield is high the imaging condition with dampingandsmoothingyieldssimilarresults thuscorrectingfor illumination effects where the spectrum is low the smoothing imaging condition tends to be more robust to the noise level present in the data thus giving better images than the imaging condition with damping in addition our experiments indicate that the parameterization of the smoothing imaging condition i e choice of window size for the smoothing operator is easy and repeatable from one data set to another making it a valuable additiontoourimagingtoolbox

continuous time singular linear quadratic control necessary and sufficient conditions for the existence of regular solutions abstract the purpose of this paper is to provide a full understanding of the role that the constrained generalized continuous algebraic riccati equation plays in singular linear quadratic lq optimal control indeed in spite of the vast literature on lq problems only recently a sufficient condition for the existence of a non impulsive optimal control has for the first time connected this equation with the singular lq optimal control problem in this paper we establish four equivalent conditions providing a complete picture that connects the singular lq problem with the constrained generalized continuous algebraic riccati equation and with the geometric properties of the underlying system

q least squares reverse time migration with viscoacoustic deblurring filters abstractviscoacoustic least squares reverse time migration also denoted as q lsrtm linearly inverts for the subsurface reflectivity model from lossy data compared with conventional migration methods it can compensate for the amplitude loss in the migrated images due to strong subsurface attenuation and can produce reflectors that are accurately positioned in depth however the adjoint q propagators used for backward propagating the residual data are also attenuative thus the inverted images from q lsrtm with a small number of iterations are often observed to have lower resolution when compared with the benchmark acoustic lsrtm images from acoustic data to increase the resolution and accelerate the convergence of q lsrtm we used viscoacoustic deblurring filters as a preconditioner for q lsrtm these filters can be estimated by matching a simulated migration image to its reference reflectivity model numerical tests on synthetic and field data demonstrate that q lsrtm combined with viscoacoustic de

block row recursive least squares migration abstractrecursive estimates of large systems of equations in the context of least squares fitting is a common practice in different fields of study for example recursive adaptive filtering is extensively used in signal processing and control applications the necessity of solving least squares problems recursively stems from the need for fast real time signal processing strategies the computational cost of least squares solvers can also limit the applicability of this technique in geophysical problems we have considered a recursive least squares solution for least squares wave equation migration with sliding windows involving several fixed rank downdating and updating computations this technique can be applied for dynamic and stationary processes if we use enough data in each windowed setup the spectrum of the preconditioned system is clustered around one and the method will converge superlinearly with probability one numerical experiments were performed to test the effectiveness of the technique

least squares gaussian beam migration abstractleast squares migration lsm can be effective to mitigate the limitation of finite seismic acquisition balance the subsurface illumination and improve the spatial resolution of the image but it requires iterations of migration and demigration to obtain the desired subsurface reflectivity model the computational efficiency and accuracy of migration and demigration operators are crucial for applying the algorithm we have developed a test of the feasibility of using the gaussian beam as the wavefield extrapolating operator for the lsm denoted as least squares gaussian beam migration our method combines the advantages of the lsm and the efficiency of the gaussian beam propagator our numerical evaluations including two synthetic data sets and one marine field data set illustrate that the proposed approach could be used to obtain amplitude balanced images and to broaden the bandwidth of the migrated images in particular for the low wavenumber components

capacitated facility location valid inequalities and facets we examine the polyhedral structure of the convex hull of feasible solutions of the capacitated facility location problem in particular we derive necessary and sufficient conditions for a family of effective capacity inequalities to be facet defining and further results on a more general family called submodular inequalities