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

center manifolds and contractions on a scale of banach spaces we give a new proof for the existence of a ck center manifold at a nonhyperbolic equilibrium point of a finite dimensional vector field of class ck the problem is reduced to a fixed point problem on a scale of banach spaces these banach spaces consist of mappings with a certain maximal exponential growth at infinity we give conditions under which there is a unique fixed point depending differentiably on the parameters the main difficulty is that the mappings under consideration become only differentiable after composition with appropriate embeddings on the scale of banach spaces

connected simple systems transition matrices and heteroclinic bifurcations given invariant sets a b and c and connecting orbits a b and b c we state very general conditions under which they bifurcate to produce an a c connecting orbit in particular our theorem is applicable in settings for which one has an admissible semiflow on an isolating neighborhood of the invariant sets and the connecting orbits and for which the conley index of the invariant sets is the same as that of a hyperbolic critical point our proof depends on the connected simple system associated with the conley index for isolated invariant sets

wave propagation in a fitzhugh nagumo type model with modified excitability we examine a generalized fitzhugh nagumo fhn type model with modified excitability derived from the diffusive morris lecar equations for neuronal activity we obtain exact analytic solutions in the form of traveling waves using a piecewise linear approximation for the activator and inhibitor reaction terms we study the existence and stability of waves and find that the inhibitor species exhibits different types of wave forms fronts and pulses while the activator wave maintains the usual kink front shape the nonequilibrium ising bloch bifurcation for the wave speed that occurs in the fhn model where the control parameter is the ratio of inhibitor to activator time scales persists when the strength of the inhibitor nonlinearity is taken as the bifurcation parameter

calculation of the threshold surface for nerve equations in this paper calculations are presented for the threshold surface mathcal m in mckean s caricature for nerve conduction u t u xx u h u a and for the fitzhugh nagumo equation u t u xx u 1 u u a the previous construction of this surface gave no information about data on mathcal m or in particular the value of the amplitude which makes data critical this amplitude is computed by both a standard discretization of the partial differential equation and for mckean s equation by means of an asymptotic calculation for the integral equation satisfied by the free boundary m t defined by u m t t a on this numerical evidence it is conjectured that for a large class of initial data u 0 on mathcal m the value u 0 l 1 depends only ona

existence and uniqueness of traveling wave front of a nonlinear singularly perturbed system of reaction diffusion equations with a heaviside step function abstract the main purpose of this paper is to show the existence and uniqueness of a traveling wave front u w u x v e t w x v e t of the following nonlinear singularly perturbed system of reaction diffusion equations with a heaviside step function u t 2 u x 2 2 h u u w w t 2 w x 2 e u w

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

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

pitfalls of testing non nested hypotheses by the lagrange multiplier method abstract in applied research in econometrics a general model determined from the current knowledge of economic theory often establishes a natural method of embedding a number of otherwise non nested hypotheses under these circumstances significant tests of various hypotheses can be carried out within the classical framework and tests of non nested or separate families of hypotheses do not require development of new statistical methods the application of some suitable variant of likelihood ratio testing procedure will be quite appropriate there are however many ocassions in applied econometrics where the hypotheses under consideration are intended to provide genuine rival explanations of the same given phenomenon and the state of economic theory is not such as to furnish us with a general model that contains both of the rival hypotheses in a natural and theoretically consistent manner a number of investigators have advocated that even when a natural comprehensive model containing both of the hypotheses under consideration cannot be obtained from theoretical considerations it is still appropriate to base significant tests of non nested hypotheses upon a combined model artificially constructed from the rival alternatives moreover in a recent paper on the application of lagrange multiplier lm tests to model specification t s breusch and a r pagan 1980 have claimed that cox s test statistic is connected to an lm or score statistic derived from the application of the lm method to an exponentially combined model earlier employed by a c atkinson 1970 although the use of artificially constructed comprehensive models fortesting separate families of hypotheses is analytically tempting nevertheless it is subject to two major difficulties firstly in many cases of interest in econometrics the structural parameters under the combined hypothesis are not identified secondly the log likelihood function of the artificially constructed model has singularities under both the null and alternative hypotheses the paper firstly examines the derivation of lm statistics in the case of non nested hypotheses and shows that atkinson s general test statistic or breusch and pagan s result can be regarded as an lm test if the parameters of the alternative hypothesis are known the paper also shows that unless all the parameters of the combined models are identified no meaningful test of the separate families of the hypotheses by the artificial embedding procedure is possible and in the identified case an expression for the lm statistic which avoids the problem of the singularity of the information matrix under the null and the alternative hypotheses is obtained the paper concludes that none of the artificially embedding procedures are satisfactory for testing non nested models and should be abandoned it however emphasizes that despite these difficulties associated with the use of artificial embedding procedures cox s original statistic which is not derived as an lm statistic and does not depend on any arbitrary synthetic combination of hypotheses can still be employed as a useful procedure for testing the rival hypotheses often encountered in applied econometrics

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

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

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

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

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

center manifolds for periodic functional differential equations of mixed type abstract we study the behaviour of solutions to nonlinear functional differential equations of mixed type mfdes that remain sufficiently close to a prescribed periodic solution under a discreteness condition on the floquet spectrum we show that all such solutions can be captured on a finite dimensional invariant center manifold that inherits the smoothness of the nonlinearity this generalizes the results that were obtained previously in h j hupkes s m verduyn lunel center manifold theory for functional differential equations of mixed type j dynam differential equations 19 2007 497 560 for bifurcations around equilibrium solutions to mfdes

center projections for smooth difference equations of mixed type we study a class of mixed type difference equations that enjoy a special smoothening property in the sense that solutions automatically satisfy an associated functional differential equation of mixed type using this connection a finite dimensional center manifold is constructed that captures all solutions that remain sufficiently close to an equilibrium the results enable a rigorous analysis of a recently developed model in economic theory that exhibits periodic oscillations in the interest rates of a simple economy of overlapping generations

tracking invariant manifolds with differential forms in singularly perturbed systems abstract a technique is developed for finding homoclinic orbits in singularly perturbed systems the desired orbit lies near a singular solution that has both fast and slow time scales the orbit is to be constructed as the transverse intersection of a center stable and center unstable manifold which requires tracking the invariant manifolds near the singular solution the main technical advance is the exchange lemma which allows one to convert information about transversality of manifolds associated with the singular limit equations to information about behavior of the invariant manifold as it leaves a neighborhood of a slow segment of the singular solution the computations for this lemma are done with the use of differential forms and the lemma is applied to prove the existence of a homoclinic orbit in a class of singularly perturbed equations

a test for distributional assumptions for the stochastic frontier functions abstract some asymptotic tests for testing distributional assumptions namely the half normal and truncated normal distributions for the stochastic frontier functions have been proposed the tests are lagrangean multiplier tests based on the pearson family of truncated distributions the statistics can be easily computed simple interpretations of the statistics and two empirical examples are provided

multiple impulse solutions to mckean s caricature of the nerve equation i existence mckean s caricature of the nerve equation is considered the h in 1 is the heaviside function we prove the existence of multiple impulse solutions consisting of any finite number of pulses these solutions are referred to as n ple impulse solutions where n is an arbitrary positive integer

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

nonsmooth dynamics in spiking neuron models large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue one approach in computational neuroscience has been to consider the detailed electrophysiological properties of neurons and build vast computational compartmental models an alternative has been to develop minimal models of spiking neurons with a reduction in the dimensionality of both parameter and variable space that facilitates more effective simulation studies in this latter case the single neuron model of choice is often a variant of the classic integrate and fire model which is described by a nonsmooth dynamical system in this paper we review some of the more popular spiking models of this class and describe the types of spiking pattern that they can generate ranging from tonic to burst firing we show that a number of techniques originally developed for the study of impact oscillators are directly relevant to their analysis particularly those for treating grazing bifurcations importantly we highlight one particular single neuron model capable of generating realistic spike trains that is both computationally cheap and analytically tractable this is a planar nonlinear integrate and fire model with a piecewise linear vector field and a state dependent reset upon spiking we call this the pwl if model and analyse it at both the single neuron and network level the techniques and terminology of nonsmooth dynamical systems are used to flesh out the bifurcation structure of the single neuron model as well as to develop the notion of liapunov exponents we also show how to construct the phase response curve for this system emphasising that techniques in mathematical neuroscience may also translate back to the field of nonsmooth dynamical systems the stability of periodic spiking orbits is assessed using a linear stability analysis of spiking times at the network level we consider linear coupling between voltage variables as would occur in neurobiological networks with gap junction coupling and show how to analyse the properties existence and stability of both the asynchronous and synchronous states in the former case we use a phase density technique that is valid for any large system of globally coupled limit cycle oscillators whilst in the latter we develop a novel technique that can handle the nonsmooth reset of the model upon spiking finally we discuss other aspects of neuroscience modelling that may benefit from further translation of ideas from the growing body of knowledge on nonsmooth dynamics

traveling waves of calcium in a pancreatic acinar cells model construction and bifurcation analysis abstract we construct and study a model for intracellular calcium wave propagation with particular attention to pancreatic acinar cells the model is based on a model of the inositol trisphosphate ip3 receptor which assumes that calcium modulates the binding affinity of ip3 to the receptor two versions of the model one simpler than the other are studied numerically in both versions solitary waves in the excitable regime arise via homoclinic bifurcations in the traveling wave equations as the background concentration of ip3 is increased the wave speed increases and for some values of the ip3 concentration the initial pulse gives rise to secondary pulses that travel in both directions this can give rise to irregular spatio temporal behavior or to trains of pulses in the simpler model these secondary waves are related to the presence of a t point a heteroclinic cycle and an associated spiral of homoclinic orbits which terminate the branch of homoclinic orbits

analytical and numerical investigation of mixed type functional differential equations this paper is concerned with the approximate solution of a linear non autonomous functional differential equation with both advanced and delayed arguments we search for a solution x t defined for t 1 k k n that satisfies this equation almost everywhere on 0 k 1 and assumes specified values on the intervals 1 0 and k 1 k we provide a discussion of existence and uniqueness theory for the problems under consideration and describe numerical algorithms for their solution giving an analysis of their convergence

smooth centre manifolds for impulsive delay differential equations abstract the existence and smoothness of centre manifolds and a reduction principle are proven for impulsive delay differential equations several intermediate results of theoretical interest are developed including a variation of constants formula for linear equations in the phase space of right continuous regulated functions linear variational equation and smoothness of the nonautonomous process and a floquet theorem for periodic systems three examples are provided to illustrate the results

symmetric and antisymmetric pulses in parallel coupled nerve fibres travelling wave solutions for equations that model two parallel coupled nerve fibres are found the travelling wave here represents the action potential it is shown that the introduction of weak coupling between the fibres induces either symmetry or antisymmetry of the action potentials a symmetric pulse is a solution where both fibres fire simultaneously and the action potentials propagate locked in phase at the same wave speed along the length of each fibre an antisymmetric pulse is a solution where one fibre fires resulting in an action potential propagating along it while the other remains at rest geometric singular perturbation theory and the exchange lemma are used to prove the existence of solutions in addition a technique which involves the use of differential forms for detecting transversalities of small order is introduced

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

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

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

continuation of bifurcations in periodic delay differential equations using characteristic matrices in this paper we describe a method for continuing periodic solution bifurcations in periodic delay differential equations first the notion of characteristic matrices of periodic orbits is introduced and equivalence with the monodromy operator is demonstrated an alternative formulation of the characteristic matrix is given which can be computed efficiently defining systems of bifurcations are constructed in a standard way including the characteristic matrix and its derivatives for following bifurcation curves in two parameters the pseudo arclength method is used combined with newton iteration two test examples an interrupted machining model and a traffic model with driver reaction time conclude the paper the algorithm has been implemented in the software tool pdde cont

construction and asymptotic stability of structurally stable internal layer solutions we introduce a geometric asymptotic method to treat structurally stable internal layer solutions we consider asymptotic expansions of the internal layer solutions and the critical eigenvalues that determine their stability proofs of the existence of exact solutions and eigenvalue eigenfunctions are outlined multi layered solutions are constructed by a new shooting method through a sequence of pseudo poincare mappings that do not require the transversality of the flow to cross sections the critical eigenvalues are determined by a coupling matrix that generates the slep matrix the transversality of the shooting method is related to the nonzeroness of the critical eigenvalues an equivalent approach is given to mono layer solutions they can be determined by the intersection of a fast jump surface and a slow switching curve which reduces fenichel s transversality condition to the slow manifold the critical eigenvalue is determined by the angle of the intersection we present three examples the first treats the critical eigenvalues of the system studied by angenent mallet paret peletier the second shows that a key lemma in the slep method may not hold the third is a perturbed activator inhibitor system that can have any number of mono layer solutions some of the solutions can only be found with the new shooting method

traveling wave solutions to a coupled system of spatially discrete nagumo equations we consider a coupled system of discrete nagumo equations and derive traveling wave solutions to this system using mckean s caricature of the cubic a certain form of this system is used to model ephaptic coupling between pairs of nerve axons we study the difference g c a 1 a 2 between the detuning parameters a i that is required to make both waves move at the same speed c of particular interest is the effect of a coupling parameter alpha and an alignment parameter a on the function g numerical investigation indicates that for fixed a there exists a time delay value beta that results in g 0 and for large enough wave speeds multiple such beta values exist also numerical results indicate that the perturbation of alpha away from zero will yield additional solutions with positive wave speed when a 1 over 2 we employ both analytical and numerical results to demonstrate our claims

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

theoretical and experimental study of two discrete coupled nagumo chains we analyze front wave kink and antikink propagation and pattern formation in a system composed of two coupled discrete nagumo chains using analytical and numerical methods in the case of homogeneous interaction among the chains we show the possibility of the effective control on wave propagation in addition physical experiments on electrical chains confirm all theoretical behaviors

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

multifrequency viscoacoustic modeling and inversion modeling and inversion for seismic wavefields that include the attenuation and phase dispersion effects of q can be implemented in the space frequency domain the viscoacoustic wave equation is solved by the moment method absorbing boundary conditions are implemented by reducing q and adjusting the complex velocity to reduce q dependent reflectivity in a zone around the edges of the model grid nonlinear inversion is performed using iterative linearized inversions the residual wavefield at a single frequency is back projected using an anticausal green s function along the viscoacoustic wavepath in an estimate of the model to get updated velocity and q distributions the model obtained from data at one frequency becomes input to inversion at the next higher frequency velocity and q are inverted simultaneously as they are interdependent both modeling and inversion algorithms are successfully tested with synthetic examples data at two or three frequencies are sufficient to produce reliable images from noise free synthetic data

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

accuracy of finite difference and finite element modeling of the scalar and elastic wave equations numerical solutions of the scalar and elastic wave equations have greatly aided geophysicists in both forward modeling and migration of seismic wave fields in complicated geologic media and they promise to be invaluable in solving the full inverse problem this paper quantitatively compares finite difference and finite element solutions of the scalar and elastic hyperbolic wave equations for the most popular implicit and explicit time domain and frequency domain techniques in addition to versatility and ease of implementation it is imperative that one choose the most cost effective solution technique for a fixed degree of accuracy to be of value a solution technique must be able to minimize 1 numerical attenuation or amplification 2 polarization errors 3 numerical anisotropy 4 errors in phase and group velocities 5 extraneous numerical parasitic modes 6 numerical diffraction and scattering and 7 errors and transmission coefficients this paper shows that in homogeneous media the

multiple impulse solutions to mckean s caricature of the nerve equation ii stability we study mckean s caricature of a nerve conduction equation where h is the heaviside function it is proved that an n ple impulse solution resembling the superposition of n unstable solitary impulses has at most 2n 1 and at least n unstable modes exactly n unstable modes corresponding to the amplitudes and the rest of them corresponding to the spacings the n amplitude modes always exist we prove also that for an n ple impulse solution resembling the superposition of n stable solitary impulses there are at most n 1 unstable modes and all of them are of spacing type

weak almost periodic motions minimality and stability in impulsive semidynamical systems abstract in this paper we study topological properties of semidynamical systems whose continuous dynamics are interrupted by abrupt changes of state first we establish results which relate various concepts as stability of lyapunov weakly almost periodic motions recurrence and minimality in the sequel we study the stability of zhukovskij for impulsive systems and we obtain some results about uniform attractors

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

simple tests of alternative specifications in stochastic frontier models abstract previous work on stochastic production frontiers has generated a family of models of varying degrees of complexity since this family is nested in the sense that the more general models contain the less general we can test the restrictions that distinguish the model in this paper we provide tests of these restrictions based on the results of estimating the simpler restricted models some of our tests are lm tests however in other cases the lm test fails so we provide alternative simple tests

homoclinic orbits in a parametrized saddle focus system abstract we consider a parametrized dynamical system with a saddle focus equilibrium point and which for one value of the parameter has a homoclinic orbit conditions on the eigenvalues for the equilibrium point together with transversality conditions imply the existence of an infinite discrete set of parameter values for which the system has a homoclinic orbit such systems arise in the study of nerve axon equations where a homoclinic orbit corresponds to a finite train of nerve impulses traveling at a velocity identified by the associated parameter value

existence and stability of traveling pulse solutions of the fitzhugh nagumo equation abstract the fitzhugh nagumo model is a reaction diffusion equation describing the propagation of electrical signals in nerve axons and other biological tissues one of the model parameters is the ratio of two time scales which takes values between 0 001 and 0 1 in typical simulations of nerve axons based on the existence of a singular limit at 0 it has been shown that the fitzhugh nagumo equation admits a stable traveling pulse solution for sufficiently small 0 here we prove the existence of such a solution for 0 01 both for circular axons and axons of infinite length this is in many ways a completely different mathematical problem in particular it is non perturbative and requires new types of estimates some of these estimates are verified with the aid of a computer the methods developed in this paper should apply to many other problems involving homoclinic orbits including the fitzhugh nagumo equation for a wide range of other parameter values

evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations abstract the main purposes of this paper are to accomplish the existence stability instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations u t u x x h u u w w t e u w and to establish the existence stability instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation u t u x x h u u under different conditions on the model constants to establish the bifurcation for the system we will study the existence and instability of a standing pulse solution if 0 2 1 the existence and stability of two standing wave fronts if 2 1 and 2 e 1 the existence and instability of two standing wave fronts if 2 1 and 0 2 e 1 the existence and instability of an upside down standing pulse solution if 0 1 2 1 to establish the bifurcation for the scalar equation we will study the existence and stability of a traveling wave front as well as the existence and instability of a standing pulse solution if 0 2 the existence and stability of two standing wave fronts if 2 the existence and stability of a traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 2 by the way we will also study the existence and stability of a traveling wave back of the nonlinear scalar reaction diffusion equation u t u x x h u u w 0 where w 0 2 0 is a positive constant if 0 2 to achieve the main goals we will make complete use of the special structures of the model equations and we will construct evans functions and apply them to study the eigenvalues and eigenfunctions of several eigenvalue problems associated with several linear differential operators it turns out that a complex number 0 is an eigenvalue of the linear differential operator if and only if 0 is a zero of the evans function the stability instability and bifurcations of the nonlinear waves follow from the zeros of the evans functions a very important motivation to study the existence stability instability and bifurcations of the nonlinear waves is to study the existence and stability instability of infinitely many fast slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations the existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience

local and global behavior near homoclinic orbits we study the local behavior of systems near homoclinic orbits to stationary points of saddle focus type we explicitly describe how a periodic orbit approaches homoclinicity and with the help of numerical examples discuss how these results relate to global patterns of bifurcations

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

existence and stability of multiple impulse solutions of a nerve equation a piecewise linear partial differential equation which models the propagation of a nerve impulse along an axon is studied for the equation parameters used there are two solutions which represent solitary impulses traveling with fixed form one with a slower velocity c s1 than the velocity c f1 of the other we show that near these velocities there exist multiple impulse solutions and exhibit four such solutions each of which has two pulses the local stability of these solutions is analyzed the two solutions whose velocities are near c s1 demonstrate instabilities which indicate growth or decay of the separate pulses for one of the multiple impulse solutions with velocity near c s1 and for one of those with velocity near c f1 the second pulse deomonstrates an instability which indicates a change in the spacing between the two pulses the other solution with velocity near c f1 is stable

the mckean s caricature of the fitzhugh nagumo model i the space clamped system within the context of lienard equations we present the fitzhugh nagumo model with an idealized nonlinearity we give an analytical expression i for the transient regime corresponding to the emission of a finite number of action potentials or spikes and ii for the asymptotic regime corresponding to the existence of a limit cycle we carry out a global analysis to study periodic solutions the existence of which is linked to the solutions of a system of transcendental equations the periodic solutions are obtained with the help of the harmonic balance method or as limit behavior of the transient regime we show how the appearance of periodic solutions corresponds either to a fold limit cycle bifurcation or to a hopf bifurcation at infinity the resultsobtained are in agreement with local analysis methods i e the melnikov method and the averaging method the generalization of the model leads us to formulate two conjectures concerning the number of limit cycles for the piecewise linear lienard equ

bifurcations of systems with structurally unstable homoclinic orbits and moduli of ω equivalence abstract bifurcations of both two dimensional diffeomorphisms with a homoclinic tangency and three dimensional flows with a homoclinic loop of an equilibrium state of saddle focus type are studied in one and two parameter families due to the well known impossibility of a complete study of such bifurcations the problem is restricted to the study of the bifurcations of the so called low round periodic orbits in this connection the idea of taking moduli continuous invariants of the topological conjugacy on the nonwandering set as the main control parameters together with the standard splitting parameter is proposed on this way new bifurcational effects are found which do not occur at a one parameter analysis in particular the density of cusp bifurcations is revealed

characteristic matrices and spectral properties of evolutionary systems in this paper we introduce the notion of a characteristic matrix for a large class of unbounded operators and study the precise connection between characteristic matrices and spectral properties of evolutionary systems in particular we study so called multiplicity theorems several examples will illustrate our results

anisotropy propagation failure and wave speedup in traveling waves of discretizations of a nagumo pde this article is concerned with effect of spatial and temporal discretizations on traveling wave solutions to parabolic pdes nagumo type possessing piecewise linear bistable nonlinearities solution behavior is compared in terms of waveforms and in terms of the so called a c relationship where a is a parameter controlling the bistable nonlinearity by varying the potential energy difference of the two phases and c is the wave speed of the traveling wave uniform spatial discretizations and a stable linear multistep methods in time are considered results obtained show that although the traveling wave solutions to parabolic pdes are stationary for only one value of the parameter a a0 spatial discretization of these pdes produce traveling waves which are stationary for a nontrivial interval of a values which include a0 i e failure of the solution to propagate in the presence of a driving force this is true no matter how wide the interface is with respect to the discretization for temporal discretizations at large wave speeds the set of parameter a values for which there are traveling wave solutions is constrained an analysis of a complete discretization points out the potential for nonuniqueness in the a c relationship

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

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

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

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