spectra of some composition operators abstract if h is a hilbert space of holomorphic functions on the unit ball bn in cn and is a non constant holomorphic map of the unit ball into itself the composition operator c is the operator on h defined by c f f in this paper we give spectral information for bounded composition operators on some weighted hardy spaces under the condition that is univalent and has a fixed point in the ball when h is the usual hardy space or a standard weighted bergman space on the unit disk this information shows that the spectrum of the composition operator is the disk centered at 0 whose radius is the essential spectral radius of the operator together with some isolated eigenvalues

high order finite difference simulations of marine csem surveys using a correspondence principle for wave and diffusion fields the computer time required to solve a typical 3d marine controlled source electromagnetic surveying csem simulation can be reduced by more than one order of magnitude by transforming low frequency maxwell equations in the quasi static or diffusive limit to a hyperbolic set of partial differential equations that give a representation of electromagnetic fields in a fictitious wave domain the dispersion and stability analysis can be made equivalent to that of other types of wave simulation problems such as seismic acoustic and elastic modeling second order to eighth order spatial derivative operators are implemented for flexibility fourth order and sixth order methods are the most numerically efficient implementations for this particular scheme an implementation with high order operators requires that both electric and magnetic fields are extrapolated simultaneously into the air layer the stability condition given for high order staggered derivative operators here should be equally valid for seismic wave simulation the bandwidth of recovered fields in the diffusive domain is independent of the bandwidth of the fields in the fictitious wave domain the fields in the fictitious wave domain do not represent observable fields propagation paths and interaction reflection amplitudes are not altered by the transform from the fictitious wave domain to the diffusive frequency domain however the transform contains an exponential decay factor that damps down late arrivals in the fictitious wave domain the propagation paths that contribute most to the diffusive domain fields are airwave shallow water plus typically postcritical events such as refracted and guided waves the transform from the diffusive frequency domain to the fictitious wave domain is an ill posed problem the transform is nonunique this gives a large degree of freedom in postulating temporal waveforms for boundary conditions in the fictitious wave domain that reproduce correct diffusive frequency domain fields

fixed point theorems for set valued maps and existence principles for integral inclusions new fixed point theorems of monch type are presented for set valued maps these theorems are then used to establish general existence principles for hammerstein integral inclusions in banach spaces

holomorphic mappings of bounded type abstract for a banach space e we prove that the frechet space h b e is the strong dual of an lb space b b e which leads to a linearization of the holomorphic mappings of bounded type it is also shown that the holomorphic functions defined on dfc spaces are of uniformly bounded type

quasi normable preduals of spaces of holomorphic functions abstract let h u denote the space of all holomorphic functions on an open subset u of a separable frechet space e let denote the compact ported topology on h u introduced by nachbin let g u denote the predual of h u constructed by mazet in our main result we show that e is quasi normable if and only if g u is quasi normable if and only if h u satisfies the strict mackey convergence condition

coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming abstract in this paper the existence and iterative approximation of coupled fixed points for mixed monotone condensing set valued operators are discussed the results presented here extend and improve the corresponding results of d guo and v lakshmikantham coupled fixed points of nonlinear operators 1 2 as an application we utilize the results obtained in section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming

efficient calculation of a partial derivative wavefield using reciprocity for seismic imaging and inversion linearized inversion of surface seismic data for a model of the earth s subsurface requires estimating the sensitivity of the seismic response to perturbations in the earth s subsurface this sensitivity or jacobian matrix is usually quite expensive to estimate for all but the simplest model parameterizations we exploit the numerical structure of the finite element method modern sparse matrix technology and source receiver reciprocity to develop an algorithm that explicitly calculates the jacobian matrix at only the cost of a forward model solution furthermore we show that we can achieve improved subsurface images using only one inversion iteration through proper scaling of the image by a diagonal approximation of the hessian matrix as predicted by the classical gauss newton method our method is applicable to the full suite of wave scattering problems amenable to finite element forward modeling we demonstrate our method through some simple 2 d synthetic examples

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

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

a note on the existence of multiple fixed points for multivalued maps with applications abstract in this paper we discuss the existence of multiple fixed points for multivalued maps our fixed point results automatically lead to new existence principles for integral inclusions

fixed points of discontinuous multivalued increasing operators in banach spaces with applications by using relatively weakly compactness conditions we obtain existence theorems of fixed points for discontinuous multivalued increasing operators in banach spaces as an application we utilize the results obtained in section 2 to lead to the existence principles for integral inclusions of hammerstein type multivalued maps

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

solvability of nonlinear impulsive volterra integral inclusions and functional differential inclusions abstract this paper presents sufficient conditions for the existence of solutions to nonlinear impulsive volterra integral inclusions and initial value problems for second order impulsive functional differential inclusions in banach spaces our results are obtained via a fixed point theorem due to hong j math anal appl 282 2003 151 162 for discontinuous multivalued increasing operators

factorization of homomorphisms through h d weakly compact homomorphisms between urm algebras with connected maximal ideal space are shown to factor through h d by means of composition operators and to be strongly nuclear the spectrum of such homomorphisms is also described strongly nuclear composition operators between algebras of bounded analytic functions are characterized the path connected components of the space of endomorphisms on h d in the uniform operator topology are determined

the hardy class of geometric models and the essential spectral radius of composition operators let be an analytic map of the disk into itself that fixes the origin then it is well known that induces a bounded composition operatorc on the hardy spaceh2 d also by a classical result of k nigs there is an analytic map such that 0 0 which is one to one when is one to one recently p bourdon and j shapiro found a lower bound for the essential spectral radius ofc in terms of andh sup p 0 hp d and asked for an exact formula in the following we assume that is one to one we determine the hardy class of in terms of the image setg d and then show that bourdon and shapiro s lower bound is also an upper bound hence answering their question in the case of univalent symbols moreover in an earlier paper shapiro smith and stegenga introduced the concept of twisted sectors to estimateh and we showed p poggi corradini trans amer math soc 348 6 1996 2503 2518 how the dynamics of the map and some harmonic measure estimates allow one to completely characterize the caseh in terms of twisted sectors by further analyzing this concept we produce a new characterization ofh in terms of the invariant sector like regions that are contained ing d this different approach also yields another proof of bourdon and shapiro s lower bound mentioned above in our specific case

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

multiscale adjoint waveform difference tomography using wavelets abstractfull waveform seismic inversions based on minimizing the distance between observed and predicted seismograms are in principle able to yield better resolved earth models than those minimizing misfits derived from traveltimes alone adjoint based methods provide an efficient way of calculating the gradient of the misfit function via a sequence of forward modeling steps which using spectral element codes can be carried out in realistically complex media convergence and stability of full waveform difference adjoint schemes are greatly improved when data and synthetics are progressively presented to the algorithms in a constructive multiscale approximation using a bi orthogonal wavelet transform wavelets provide the nonredundant spectral decomposition that paves the way for the inversion to proceed successively from long wavelength fitting to detailed exploration of the phases in the seismogram the choice of wavelet class and type the initial depth of the multiscale decomposition and the min

fixed points for mixed monotone multivalued operators in banach spaces with applications abstract in this paper the existence and iterative approximation of fixed points for a class of systems of mixed monotone multivalued operator are discussed we present some new fixed point theorems of mixed monotone operators and increasing operators which need not be continuous or satisfy a compactness condition we also give some applications to differential inclusions with discontinuous right hand side in banach spaces and to hammerstein integral inclusions on r n

a banach dieudonne theorem for germs of holomorphic functions let h u denote the space of all holomorphic functions on an open subset u of a complex frechet space e let h k denote the space of all holomorphic germs on a compact subset k of e it is shown that h k with a natural topology is the inductive limit of a suitable sequence of compact subsets within the category of all topological spaces as an application of this result it is shown that the compact ported topology introduced by nachbin coincides with the compact open topology on h u whenever u is a balanced open subset of a frechet schwartz space this last result improves earlier results of p boland and s dineen bull soc math france 106 1978 311 336 r meise proc roy irish acad sect a 81 1981 217 223 and others

norms and essential norms of linear combinations of endomorphisms we compute norms and essential norms of linear combinations of endomorphisms on uniform algebras

finite difference time dispersion transforms for wave propagation the finite difference fd wave equation is widely implemented in seismic imaging for oil exploration but the numerical dispersion due to discretization of time and space derivatives can introduce severe numerical errors we have investigated time dispersion which might distort the phase and introduce severe artifacts to the data and images especially for long time propagation we first studied precisely how the time dispersion was produced and then we developed an efficient approach the time dispersion transforms to cope with time dispersion errors in wave propagation the proposed forward time dispersion transform can predict or simulate the time dispersion errors and it can be applied to remove time dispersion errors in reverse time migration the inverse time dispersion transform can be used to eliminate time dispersion errors from synthetic data after modeling the proposed method is general and works for low and high order time fd schemes by using this method large time steps were allowed in wave propagation thus we can remove the time dispersion errors at a negligible numerical cost and the efficiency is not affected to test the effectiveness and robustness of the proposed time dispersion transforms we used isotropic and anisotropic examples as well as modeling and imaging examples

linearization of bounded holomorphic mappings on banach spaces the main result in this paper is the following linearization theorem for each open set u in a complex banach space e there is a complex banach space goo u and a bounded holomorphic mapping gu u g u with the following universal property for each complex banach space f and each bounded holomorphic mapping f u f there is a unique continuous linear operator tf goo u f such that tf gu f the correspondence f tf is an isometric isomorphism between the space ho u f of all bounded holomorphic mappings from u into f and the space l g u f of all continuous linear operators from g u into f these properties characterize g u uniquely up to an isometric isomorphism the rest of the paper is devoted to the study of some aspects of the interplay between the spaces h o u f and l g u f this paper consists of five sections in 1 we establish our notation and terminology in 2 we prove the aforementioned linearization theorem in 3 we translate certain properties of a mapping f e h u f into properties of the corresponding operator tf e l g u f we show for instance that f has a relatively compact range if and only if tf is a compact operator in 4 we give a seminorm characterization of the unique locally convex topology t y on h u f such that the correspondence f tf is a topological isomorphism between the spaces h u f ty and l g u f t where tc denotes the compact open topology finally in 5 we use the preceding results to establish necessary and sufficient conditions for the spaces g u and h u to have the approximation property these are holomorphic analogues of classical results of a grothendieck 8 and complement results of r aron and m schottenloher 2 we show in particular that if u is a balanced bounded open set in a complex banach space e then g u has the approximation property if and only if e has the approximation property we also show that if u is an arbitrary open set in a complex banach space e then h u has the approximation property if and only if for each complex banach space f each mapping in h u f with a relatively compact range can be uniformly approximated on u by mappings in h u f with finite dimensional range since it is still unknown whether received by the editors april 10 1989 1980 mathematics subject classification 1985 revision primary 46g20 46e15 secondary 46e10 d 1991 american mathematical society 0002 9947 91 1 00 25 per page

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

a polynomial hutton theorem with applications abstract extending a classical linear result due to hutton to a nonlinear setting we prove that a continuous homogeneous polynomial between banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be approximated by finite rank linear operators among other consequences we apply this result to generalize a classical result due to aron and schottenloher about the approximation property on spaces of polynomials and a recent result due to caliskan and rueda about the quasi approximation property on projective symmetric tensor products

time evolution of the wave equation using rapid expansion method forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields for the case of spatially varying velocity we have worked on two approaches to evaluate the time evolution of seismic wavefields an exact solution for the constant velocity acoustic wave equation can be used to simulate the pressure response at any time for a spatially varying velocity a one step method can be developed where no intermediate time responses are required using this approach we have solved for the pressure response at intermediate times and have developed a recursive solution the solution has a very high degree of accuracy and can be reduced to various finite difference time derivative methods depending on the approximations used although the two approaches are closely related each has advantages depending on the problem being solved

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

symplectic scheme and the poynting vector in reverse time migration abstractwe developed a new numerical solution for the wave equation that combines symplectic integrators and the rapid expansion method rem this solution can be used for seismic modeling and reverse time migration rtm in seismic modeling and rtm spatial derivatives are usually calculated by finite differences fds or by the fourier method and the time evolution is normally obtained by a second order fd approach if the spatial derivatives are computed by higher order fd schemes then the time step needs to be small enough to avoid numerical dispersion therefore increasing the computational time however by using rem with the fourier method for the spatial derivatives we can apply the proposed method to propagate the wavefield for larger time steps moreover if the appropriate number of expansion terms is chosen this method is unconditionally stable and propagates seismic waves free of numerical dispersion the use of a symplectic numerical scheme provides the solution of the wave equation an

essential angular derivatives and maximum growth of koenigs eigenfunctions abstract we introduce the notion of essential angular derivative for functions mapping the open unit disk u holomorphically into itself after exploring some of its basic properties we show how the essential angular derivative of determines the maximum growth rate of the koenigs eigenfunction for when has an attractive fixed point in u our work answers some questions about growth of koenigs functions recently posed by pietro poggi corradini

laplace fourier domain elastic full waveform inversion using time domain modeling to obtain subsurface information from onshore seismic exploration data using full waveform inversion fwi based on the acoustic wave equation elastic waves such as ground roll and mode converted waves should be suppressed through heavy preprocessing however such preprocessing deforms not only the elastic waves but also the acoustic waves moreover it is not easy to separate body waves from surface waves in seismic traces for these reasons we need to generate both types of waves in the modeling step to obtain seismic waves that are similar to real seismic waves therefore elastic fwi using the elastic wave equation is necessary to achieve a more accurate fwi in addition elastic fwi can provide better geologic information than acoustic fwi because it inverts the p wavevelocity s wave velocity and density laplace fourier domain elastic fwi is an effective method because it inverts these multiple parameters and can be applied to real seismic data that lack low frequency components however the conventional laplace fourier domain fwi requires a matrix solver with a huge memory cost to perform the modeling in the laplace fourierdomain and memory usage becomes more intensive in the elastic case in the present study we combined time domain wave propagation modeling and laplace fourier domain elastic fwi to invert multiple parameters with less memory cost by using time domain modeling which does not require a matrix solver we obtainedthe forwardand adjoint wavefields withless memory cost the residuals between the recorded and modeled data the virtual sources the hessian matrices and the gradient directions were calculated in the laplace fourier domain to validate the proposed algorithm we performed numerical tests with model 94 synthetic data and benjamin creek real seismic data

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

fixed points of multivalued operators in ordered metric spaces with applications abstract the purpose of this paper is to present some new hybrid fixed point theorems involving multivalued operators which satisfy weakly generalized contractive conditions in an ordered complete metric space an example of the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is given to illustrate the usability of our results

on the approximation property for banach spaces predual to h spaces abstract a major open problem asks about the grothendieck approximation property for the space h h d of bounded holomorphic functions in the unit disk d c motivated by this problem we establish approximation properties for banach spaces predual to the spaces h for being finite direct products of starlike domains and unbranched coverings of strongly pseudoconvex domains in stein manifolds

waveform inversion by one way wavefield extrapolation one way riemannian wavefield extrapolation rwe on computational meshes conforming to the direction of turning wave propagation is an alternative forward modeling procedure for waveform inversion forward modeling tests demonstrate that the rwe approach may be a sufficiently accurate approximation for calculating the wavefield phases important for early arrival waveform inversion initial results indicate that rwe waveforms are well matched at wide offsets to finite difference data and can be used in a waveform inversion scheme to invert synthetic data for moderate 1d velocity perturbations

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

konigs eigenfunction for composition operators on bloch and h type spaces abstract we discuss when the konigs eigenfunction associated with a non automorphic selfmap of the complex unit disc that fixes the origin belongs to banach spaces of holomorphic functions of bloch and h type in the latter case our characterization answers a question of p bourdon some spectral properties of composition operators on h for unbounded konigs eigenfunction are obtained

spectra and essential spectral radii of composition operators on weighted banach spaces of analytic functions we determine the spectra of composition operators acting on weighted banach spaces hv of analytic functions on the unit disc defined for a radial weight v when the symbol of the operator has a fixed point in the open unit disc we also investigate in this case the growth rate of the koenigs eigenfunction and its relation with the essential spectral radius of the composition operator

cascaded wavefield tomography and inversion using extended common image point gathers a case study abstractimage domain wavefield tomography wt exploits focusing characteristics of extended images for updating the velocity field to make good use of this information one must understand how such images behave if the migration velocity is accurate this is not trivial because focusing depends on not only the model error but also on the acquisition setup the data bandwidth and illumination variation caused by the overburden we address this problem by constructing penalty functions based on the point spread functions of the imaging operator that characterize focusing in extended images moreover instead of sampling the extended images at preset distances along the surface we sample the image by constructing common image point gathers which are more economical from a computational point of view and also measure the spatial and temporal focusing of the wavefield coupled with image residuals exploiting illumination based penalty functions we construct robust wavefield tomographic updates from spar

forward modeling by a fourier method a fourier or pseudospectral forward modeling algorithm for solving the two dimensional acoustic wave equation is presented the method utilizes a spatial numerical grid to calculate spatial derivatives by the fast fourier transform time derivatives which appear in the wave equation are calculated by second order differcncing the scheme requires fewer grid points than finite diffcrcnce methods to achieve the same accuracy it is therefore believed that the fourier method will prove more efficient than finitedifference methods especially when dealing with threedimensional models the fourier forward modeling method was tested against two problems a single layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling the numerical results agreed with both the analytic and physical model results furthermore the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account

seismic envelope inversion and modulation signal model abstractwe recognized that the envelope fluctuation and decay of seismic records carries ultra low frequency ulf i e the frequency below the lowest frequency in the source spectrum signals that can be used to estimate the long wavelength velocity structure we then developed envelope inversion for the recovery of low wavenumber components of media smooth background so that the initial model dependence of waveform inversion can be reduced we derived the misfit function and the corresponding gradient operator for envelope inversion to understand the long wavelength recovery by the envelope inversion we developed a nonlinear seismic signal model the modulation signal model as the basis for retrieving the ulf data and studied the nonlinear scale separation by the envelope operator to separate the envelope data from the wavefield data envelope extraction a demodulation operator envelope operator was applied to the waveform data numerical tests using synthetic data for the marmousi model pro

correlation based reflection full waveform inversion because modeling for full waveform inversion fwi cannot produce reflections unless the velocity model has the scattering potential high wavenumbers using a migration demigration process to generate modeling data which is a key step in what is now known as reflection fwi rfwi is a credible alternative to tackle the reflection nonlinearity associated with fwi however because rfwi depends on a conventional data residual or zero lag correlation objective function high nonlinearity can still exist when the true amplitude migration is not used as well as at far offsets due to cycle skipping to avoid the cycle skipping and the need for a true amplitude migration we have developed a correlation based reflection full waveform inversion method to update the low wavenumber components of the velocity model the success of this method relies on a sensitivity kernel decomposition and a correlation based objective function the sensitivity kernel decomposition makes it possible to separate out the contributions of different subkernels and to smear the reflected wave residuals along the rabbit ear wavepath to obtain middle and deep background model estimates the correlation based objective function measures differences in kinematic information and behaves in a more linear way than the traditional waveform residual misfit moreover our approach is less sensitive to the frequency content and amplitude information of the seismic data enabling reliable background velocity estimates to be obtained without the need for low frequencies and full physics modeling because the kinematic features of reflected waves are described correctly the inversion result of the proposed method can be used as a migration model or an initial model for conventional fwi to achieve a correct high wavenumber model update

inversion gradients for acoustic vti wavefield tomography abstractwavefield tomography can handle complex subsurface geology better than ray based techniques and ultimately provide a higher resolution here we implement forward and adjoint wavefield extrapolation for vti transversely isotropic with a vertical symmetry axis media using a generalized pseudospectral operator based on a separable approximation for the p wave dispersion relation this operator is employed to derive the gradients of the differential semblance optimization dso and modified image power objective functions we also obtain the gradient expressions for a data domain objective function that can more easily incorporate borehole information necessary for stable vti velocity analysis these gradients are similar to the ones obtained with a space time finite difference fd scheme for a system of coupled wave equations but the pseudospectral method is not hampered by the imprint of the shear wave artifact numerical examples also show the potential advantages of the modified image power

comparison of multifrequency selection strategies for simultaneous source full waveform inversion abstractthe computational cost of full waveform inversion fwi is a major obstacle to estimating the velocity model for large scale problems one way to reduce the overall cost of waveform inversion is by adopting a simultaneous source strategy in other words multiple sources are simultaneously fired to simulate supershot gathers and thereby reduce the number of seismic modeling simulations that are performed during the inversion however the use of simultaneous sources introduces crosstalk artifacts that arise from the interference among the sources that constitute a supershot we analyzed the influence of different simultaneous multifrequency selection strategies on crosstalk artifacts our analysis focused on a frequency domain fwi algorithm that is implemented with simultaneous sources that are randomly encoded with random time shifts in the multiscale conventional fwi strategies a finite set of discrete frequencies was selected and the inversion was carried out sequentially from low to high fr

linearization of functions given a space u of functions f u which are continuous we construct another space u and a map e u u linearizing all functions f u i e there are lf u such that lf e f such linearizations are stronger than mere preduals for u for example for u l1 linearizations correspond to preduals of l1 which are isomorphic to c0 we also address the vector valued case a number of such linearizing constructions are to be found in the literarture mostly for certain spaces of holomorphic functions the procedure presented here generalizes all these special cases

on p compact mappings and the p approximation property abstract the notion of p compact sets arises naturally from grothendieck s characterization of compact sets as those contained in the convex hull of a norm null sequence the definition due to sinha and karn 2002 leads to the concepts of p approximation property and p compact operators which form an ideal with its ideal norm p this paper examines the interaction between the p approximation property and certain space of holomorphic functions the p compact analytic functions in order to understand these functions we define a p compact radius of convergence which allows us to give a characterization of the functions in the class we show that p compact holomorphic functions behave more like nuclear than compact maps we use the product of schwartz to characterize the p approximation property of a banach space in terms of p compact homogeneous polynomials and in terms of p compact holomorphic functions with range on the space finally we show that p compact holomorphic functions fit into the framework of holomorphy types which allows us to inspect the p approximation property our approach also allows us to solve several questions posed by aron maestre and rueda 2010

wave field reciprocity and optimization in remote sensing a unified approach to local optimization techniques and wave field reciprocity as applied to constructing solutions to remote sensing imaging and inversion problems in acoustic elastic and electromagnetic wave theory is presented the starting point is a system of linear first order partial differential equations in space time of the class to which the indicated wave phenomena gives rise for this system three types of remote sensing problems the inverse source the inverse scattering and the inverse transducted wave field problems are formulated and the construction of their solutions via local optimization techniques is discussed emphasis is placed on iterative algorithms that are based on a guaranteed decrease in the mismatch between modelled and observed data at each update of the medium subsequently the wave field reciprocity theorems of the time convolution and the time correlation types are derived and their occurrence in the optimization procedures is discussed also attention is paid to approximate methods in particular to the rayleigh gans born approximation approximations of this sort provide the means to invoke the method of preconditioning in the process of inverting the operator equations exotic media for example chiral media in electromagnetics are included in the analysis

using the rapid expansion method for accurate time stepping in modeling and reverse time migration reverse time migration is based on seismic forward modeling algorithms where spatial derivatives usually are calculated by finite differences or by the fourier method time integration in general is done by finite difference time stepping of low orders if the spatial derivatives are calculated by high order methods and time stepping is based on low order methods there is an imbalance that might require that the time step size needs to be very small to avoid numerical dispersion as a result computing times increase using the rapid expansion method rem avoids numerical dispersion if the number of expansion terms is chosen properly comparisons with analytical solutions show that the rem is preferable especially at larger propagation times for reverse time migration the rem needs to be applied in a time stepping manner this is necessary because the original implementation based on very large time spans requires that the source term is separable in space and time this is not appropriate for reverse time migration where the sources have different time histories in reverse time migration it might be desirable to use the poynting vector information to estimate opening angles to improve the quality of the image in the solution of the wave equation this requires that one calculates not only the pressure wavefield but also its time derivative the rapid expansion method can be extended easily to provide this time derivative with negligible extra cost

seismic waveform inversion in the frequency domain part 1 theory and verification in a physical scale model seismic waveforms contain much information that is ignored under standard processing schemes seismic waveform inversion seeks to use the full information content of the recorded wavefield in this paper i present apply and evaluate a frequency space domain approach to waveform inversion the method is a local descent algorithm that proceeds from a starting model to refine the model in order to reduce the waveform misfit between observed and model data the model data are computed using a full wave equation viscoacoustic frequency domain finite difference method ray asymptotics are avoided and higher order effects such as diffractions and multiple scattering are accounted for automatically the theory of frequency domain waveform wavefield inversion can be expressed compactly using a matrix formalism that uses finite difference finite element frequency domain modeling equations expressions for fast local descent inversion using back propagation techniques then follow naturally implementation of

mean growth of koenigs eigenfunctions in 1884 g koenigs solved schroeder s functional equation f o a af in the following context is a given holomorphic function mapping the open unit disk u into itself and fixing a point a e u f is holomorphic on u and a is a complex scalar koenigs showed that if 0 equation for p has a unique holomorphic solution cr satisfying a co p a a and o 0 1 moreover he showed that the only other solutions are the obvious ones given by constant multiples of powers of a we call a the koenigs eigenfunction of motivated by fundamental issues in operator theory and function theory we seek to understand the growth of integral means of koenigs eigenfunctions for 0 of to belong to the hardy space hp and show that the condition is necessary when is analytic on the closed disk for many mappings the condition may be expressed as a relationship between p a and derivatives of at points on ou that are fixed by some iterate of our work depends upon a formula we establish for the essential spectral radius of any composition operator on the hardy space hp department of mathematics washington and lee university lexington virginia 24450 e mail address pbourdonfwlu edu department of mathematics michigan state university east lansing michigan 48824 e mail address shapirofmath msu edu this content downloaded from 157 55 39 211 on sat 25 jun 2016 06 33 26 utc all use subject to http about jstor org terms

linearized wave equation migration velocity analysis by image warping seismic imaging produces images of contrasts in physical parameters in the subsurface e g velocity or impedance to build such images a background model describing the wave kinematics in the earth is necessary in practice the structural image and background velocity model are unknown and have to be estimated from the acquired data migration velocity analysis deals with estimation of the background model in the framework of seismic migration and relies on two main elements data redundancy and invariance of the structures with respect to different seismic experiments because all the experiments probe the same model the reflectors must be invariant in suitable domains e g shots or reflection angle the semblance principle is the tool used to measure the invariance of a set of multiple images we measure the similarity of the structural features between pairs of single shot migrated images obtained from adjacent experiments by using the estimated warping vector field between two migrated images we construct an image perturbation which describes the difference in reflectivity observed by two shots we derive an expression for the image perturbation that drives a migration velocity analysis procedure based on a linearization of the wave equation with respect to the model parameters synthetic 2d examples show promising results in retrieving errors in the velocity model this methodology can be directly applied to 3d

spectra of composition operators on algebras of analytic functions on banach spaces let e be a banach space with unit ball b e we study the spectrum and the essential spectrum of a composition operator on h b e determined by an analytic symbol with a fixed point in b e we relate the spectrum of the composition operator to that of the derivative of the symbol at the fixed point we extend a theorem of zheng to the context of analytic symbols on the open unit ball of a hilbert space

interpolating sequences in the polydisc on donne une condition suffisante pour que des suites de points soient des suites d interpolation pour l ensemble h d n des fonctions analytiques bornees definies sur le polydisque d n de c n on discute quelques conditions d interpolation des domaines generaux

full waveform inversion with extrapolated low frequency data abstractthe availability of low frequency data is an important factor in the success of full waveform inversion fwi in the acoustic regime the low frequencies help determine the kinematically relevant low wavenumber components of the velocity model which are in turn needed to avoid convergence of fwi to spurious local minima however acquiring data less than 2 or 3 hz from the field is a challenging and expensive task we have explored the possibility of synthesizing the low frequencies computationally from high frequency data and used the resulting prediction of the missing data to seed the frequency sweep of fwi as a signal processing problem bandwidth extension is a very nonlinear and delicate operation in all but the simplest of scenarios it can only be expected to lead to plausible recovery of the low frequencies rather than their accurate reconstruction even so it still requires a high level interpretation of band limited seismic records into individual events each of which can be extr

weak sequential completeness of spaces of homogeneous polynomials abstract let p w e n f be the space of all continuous n homogeneous polynomials from a banach space e into another f that are weakly continuous on bounded sets we give sufficient conditions for the weak sequential completeness of p w e n f these sufficient conditions are also necessary if both e and f have the bounded compact approximation property we also show that the weak sequential completeness and the reflexivity of p w e n f are equivalent whenever both e and f are reflexive

an efficient multiscale method for time domain waveform tomography this efficient multiscale method for time domain waveform tomography incorporates filters that are more efficient than hamming window filters a strategy for choosing optimal frequency bands is proposed to achieve computational efficiency in the time domain a staggered grid explicit finite difference method with fourth order accuracy in space and second order accuracy in time is used for forward modeling and the adjoint calculation the adjoint method is utilized in inverting for an efficient computation of the gradient directions in the multiscale approach multifrequency data and multiple grid sizes are used to overcome somewhat the severe local minima problem of waveform tomography the method is applied successfully to 1d and 2d heterogeneous models it can accurately recover low and high wavenumber components of the velocity models the inversion result for the 2d model demonstrates that the multiscale method is computationally efficient and converges faster than a conventional single scale method

composition operators on uniform algebras essential norms and hyperbolically bounded sets let a be a uniform algebra and let o be a self map of the spectrum m a of a that induces a composition operator c o on a the object of this paper is to relate the notion of hyperbolic boundedness introduced by the authors in 2004 to the essential spectrum of c o it is shown that the essential spectral radius of c o is strictly less than 1 if and only if the image of m a under some iterate o n of o is hyperbolically bounded the set of composition operators is partitioned into hyperbolic vicinities that are clopen with respect to the essential operator norm this partition is related to the analogous partition with respect to the uniform operator norm

comparison results for initial value problems of second order impulsive integro differential inclusions abstract in this paper we present new maximum and minimum principles for the initial value problem for a class of second order nonlinear impulsive integro differential inclusions with discontinuous multivalued functions on the right hand side in a real banach space this allows us to lead on to the development of the comparison principle and monotone iterative technique for a nonlinear second order impulsive integro differential inclusion

an iterative inversion of back scattered acoustic waves the application of the born approximation to the scattered wave field followed by a wkbj and far field approximation on the propagation green s function for a slowly varying background medium leads to a simple integral relation between the density and bulk modulus anomalies superimposed on the background medium and the scattered wave field an iterative inversion scheme based on successive back projections of the wave field is used to reconstruct the two acoustic parameters the scheme when applied to data generated using the direct integral relation shows that the variations of the parameters can be reconstructed the procedure is readily applicable to actual data since every iterative step is essentially a prestack kirchhoff migration followed by the application of the direct born approximation and far field operator

ergodic properties of composition operators on banach spaces of analytic functions abstract the composition operators defined on little bloch spaces bergman spaces hardy spaces or little weighted bergman spaces of infinite type when well defined are shown to be mean ergodic if and only if they are power bounded if and only if the symbol has an interior fixed point for these operators uniform mean ergodicity is equivalent to quasicompactness in the sense of yosida and kakutani