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

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

full waveform inversion using a nonlinearly smoothed wavefield conventional full waveform inversion fwi based on the least squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle skipping phenomena an initial model producing data that are at most a half cycle away from the observed data is needed for convergence to the global minimum low frequencies are helpful in updating low wavenumber components of the velocity model to avoid cycle skipping however low enough frequencies are usually unavailable in field cases the multiplication of wavefields of slightly different frequencies adds artificial low frequency components in the data which can be used for fwi to generate a convergent result and avoid cycle skipping we generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield which is rich in low frequencies the global correlation norm based objective function can

simultaneous multifrequency inversion of full waveform seismic data we present a simultaneous multifrequency inversion approach for seismic data interpretation this algorithm inverts all frequency data components simultaneously a data weighting scheme balances the contributions from different frequency data components so the inversion process does not become dominated by high frequency data components which produce a velocity image with many artifacts a gauss newton minimization approach achieves a high convergence rate and an accurate reconstructed velocity image by introducing a modified adjoint formulation we can calculate the jacobian matrix efficiently allowing the material properties in the perfectly matched layers pmls to be updated automatically during the inversion process this feature ensures the correct behavior of the inversion and implies that the algorithm is appropriate for realistic applications where a priori information of the background medium is unavailable two different regularization schemes an l2 norm and a weighted l2 norm function a

on the performance of mindlin plate elements in modelling plate elastic medium interaction a comparative study this paper discusses the finite element analysis of the flexural interaction between an elastic plate and an elastic half space the applicability of certain mindlin type plate elements based on reduced integration techniques to this class of interaction problem is investigated a series of numerical computations reveal that those elements which possess spurious zero energy modes are deficient in modelling properly the interaction phenomenon it is also found that the heterosis plate element reported in the literature is capable of modelling the plate elastic medium interaction very efficiently

green s function approach to the nonlinear bending of closely spaced parallel plates abstract this article presents a new extension of the green s function method in computational mechanics an iterative procedure is developed for analyzing the contact interaction in a system of closely spaced parallel thin plates possibly situated just above a winkler foundation the plates have uniform thicknesses and are composed of isotropic homogeneous elastic materials frictionless contact is also assumed according to the classification proposed by dundurs and stippes 1970 the advancing contact has been discussed the formulation of the problem brings a combination of two types of nonlinearities of different origins the geometric nonlinearity resulting from relatively large deflections of the plates is accompanied by a nonlinearity which is due to the fact that the boundaries between contact and non contact zones for each pair of plates are initially unknown linear problems appearing within each iteration are attacked by a version of the green s function method the technique utilizes the analytically constructed green s functions and matrices for the biharmonic equation and lame s system of the plane problem in the theory of elasticity contact conditions for each plate in the system are treated by implementing penalty functions numerical results are encouraging and an extension of this study to more complicated formulations is currently under way

determination of background velocities by multiple migration fitting we present an approach called multiple migration fitting mmf designed to automatically determine 2 d background velocities from prestack seismic data in this approach we maximize a scalar similarity index si for a collection of migrated sections obtained by various illuminations of the same earth numerical investigation shows that this index is a rather smooth nonoscillatory function of velocity that tends to be a maximum for good velocity profiles and hence is amenable to maximization by local gradient techniques this maximization will be practically feasible as we prove that the exact gradient of si can be computed at an additional cost of only twice that required for the computation of the collection of migrated sections independently of the number of velocity unknowns application to synthetic data shows that mmf leads to enhanced background velocities and stacked migrated sections

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

long time dynamics for nonlinear porous thermoelasticity with second sound and delay this paper is concerned with the long time behavior of a damped porous thermoelastic problem it has been studied by many authors and most of the known results are concerned with decay issues under different boundary conditions and damping terms there are just a few references on the long time dynamics of such systems the purpose of the present work is to complement and extend some early studies on porous thermoelastic systems by establishing new results on the existence of attractors and some of their properties motivated by this scenario we consider a one dimensional porous thermoelastic system with linear frictional damping nonlinear source terms and a time varying delay term in the internal feedback where the heat flux depends on cattaneo law under some suitable assumptions on the weights of feedback we establish the global well posedness of the system by using the c0 semigroup theory of linear operators then we show the existence of a global attractor for finite energy solutions and we prove its smoothness and finite fractal dimension furthermore the existence of a generalized fractal exponential attractor is also derived this paper is concerned with the long time behavior of a damped porous thermoelastic problem it has been studied by many authors and most of the known results are concerned with decay issues under different boundary conditions and damping terms there are just a few references on the long time dynamics of such systems the purpose of the present work is to complement and extend some early studies on porous thermoelastic systems by establishing new results on the existence of attractors and some of their properties motivated by this scenario we consider a one dimensional porous thermoelastic system with linear frictional damping nonlinear source terms and a time varying delay term in the internal feedback where the heat flux depends on cattaneo law under some suitable assumptions on the weights of feedback we establish the global well posedness of the system by using the c0 semigroup theory of linear operators then we show the existence of a global attractor for finite energy solutions and we pro

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

numerical methods for analysis of plates on tensionless elastic foundations abstract a numerical methodology for analysis of plates resting on tensionless elastic foundations described either by the winkler model or as an elastic half space is presented in this paper the contact surface is assumed unbonded and frictionless the finite element method is used to discretize the plate and foundation to overcome the difficulties in solving the plate foundation equilibrium equations together with the inequality constraints due to the frictionless unilateral contact condition a variational formulation equivalent to these equations is presented from which three alternative linear complementary problems lcp are derived and solved by lemke s complementary pivoting algorithm in the first formulation the lcp variables are the plate displacements and the elastic foundation reaction in the second the lcp is derived in terms of the elastic foundation reaction and in the third formulation the variables are the elastic foundation displacements and the gap between the bodies once the lcp is solved the no contact regions where the plate lifts up away from the foundation and the sub grade reaction as well as the plate displacements and stresses can be easily obtained the methodology is illustrated by three examples and the results are compared with existing analytical and numerical results found in the literature

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

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

source receiver compression scheme for full waveform seismic inversion we have developed a source receiver compression approach for reducing the computational time and memory usage of the acoustic and elastic full waveform inversions by detecting and quantifying the extent of redundancy in the data we assembled a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers used in the survey because the numbers of these simultaneous sources and receivers could be significantly less than those of the physical sources and receivers the computational time and memory usage of any gradient type inversion method such as steepest descent nonlinear conjugate gradient contrast source inversion and quasi newton methods could be reduced the scheme is based on decomposing the data into their principal components using a singular value decomposition approach and the data reduction is done through the elimination of the small eigenvalues consequently this would suppress the effect of noise in the data moreover taking advantage

migration of seismic data by phase shift plus interpolation under the horizontally layered velocity assumption migration is defined by a set of independent ordinary differential equations in the wavenumber frequency domain the wave components are extrapolated downward by rotating their phases this paper shows that one can generalize the concepts of the phase shift method to media having lateral velocity variations the wave extrapolation procedure consists of two steps in the first step the wave field is extrapolated by the phase shift method using l laterally uniform velocity fields the intermediate result is l reference wave fields in the second step the actual wave field is computed by interpolation from the reference wave fields the phase shift plus interpolation pspi method is unconditionally stable and lends itself conveniently to migration of three dimensional data the performance of the methods is demonstrated on synthetic examples the pspi migration results are then compared with those obtained from a finite difference method

global and exponential attractors for extensible thermoelastic plate with time varying delay abstract a class of nonlinear problems modeling thermoelastic extensible plates with rotational inertia and time dependent delay in the internal feedback are considered by virtue of galerkin method combined with the priori estimates we prove the existence and uniqueness of global solution the proof with or without rotational inertia does not depend on the parameters 1 and 2 of time dependent delay moreover the existence of compact global and exponential attractors is proved through a stabilizability estimate this estimate which is established under restrictions on 1 and 2 and independently of the rotational inertia parameter provides bounds on the attractors fractal dimension other property such as additional smoothness of global attractors with respect to parameter is also presented furthermore the existence of a generalized fractal exponential attractor is also derived finally we show that the family of global attractors is continuous with respect to the parameter in some sense

smooth attractors of finite dimension for von karman evolutions with nonlinear frictional damping localized in a boundary layer abstract in this paper dynamic von karman equations with localized interior damping supported in a boundary collar are considered hadamard well posedness for von karman plates with various types of nonlinear damping are well known and the long time behavior of nonlinear plates has been a topic of recent interest since the von karman plate system is of hyperbolic type with critical nonlinearity noncompact with respect to the phase space this latter topic is particularly challenging in the case of geometrically constrained nonlinear damping in this paper we first show the existence of a compact global attractor for finite energy solutions and we then prove that the attractor is both smooth and finite dimensional thus the hyperbolic like flow is stabilized asymptotically to a smooth and finite dimensional set

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

efficient electric resistivity inversion using adjoint state of mixed finite element method for poisson s equation we propose an electric resistivity inversion method that is similar to the reverse time migration technique applied to seismic data for calculating model responses and inversion we use the mixed finite element method with the standard p 1 p 0 pair for triangular decompositions which makes it possible to compute both the electric potential and the electric field vector economically in order to apply the adjoint state of the poisson equation in the resistivity inverse problem we introduce an apparent electric field defined as the dot product between the computed electric field vector and a weighting factor and then defining a virtual source to compute the partial derivative of the electric field vector we exploit the adjoint state the symmetry of green s function of matrix equations derived from solving the poisson equation by the mixed finite element method for the calculation of the steepest descent direction of our objective function by computing the steepest descent direction by a dot product of backpropagated residual and virtual source we can avoid the cumbersome and expensive process of computing the jacobian matrix directly we calibrate our algorithm on a synthetic of a buried conductive block and obtain an image that is compatible with the limits of the resistivity method

understanding cmp stacking hyperbola in terms of partial derivative wavefield common midpoint cmp stacking and velocity analysis are fundamental seismic imaging concepts based on a layered velocity model we relate these concepts to partial derivative seismograms which give seismic amplitude variations as a function of layer coordinates the cmp stacking hyperbola can be described kinematically by partial derivative seismograms resulting in an interesting seismic imaging relationship

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

3d scalar wave absorbing boundary conditions with optimal coefficients in the frequency space domain abstractto improve the computational efficiency for the solution of the 3d helmholtz equation in the frequency space domain high order compact forms of finite differences are preferred we applied a pointwise pade approximation to develop a 3d 27 point fourth order compact finite difference fd stencil in the grid interior with a space differentiated source term for the scalar wave equation this has similar high accuracy 4 5 grid points per the shortest wavelength to another 27 point fourth order fd stencil using a parsimonious mixed grid and staggered grid combination but is much simpler for absorbing boundary conditions abcs a damping zone is expensive and a perfectly matched layer can not be straightforwardly introduced into the compact fd form for the second order wave equation thus we developed 3d one way wave equation owwe abcs with adjustable coefficients they have different angle approximations and fd forms for the six faces twelve edges and eight corners in 3d models to fit wi

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

inversion versus migration a new perspective to an old discussion seismic imaging techniques can be subdivided into inversion and migration the object functions for inversion and migration are respectively the medium contrast parameters and reflectivity in this paper the relationship between inversion and migration is approached by analyzing the underlying representations the forward models it appears that the two way representation which underlies inversion as well as the one way representation which underlies migration can both be expressed in terms of a volume integral over the appropriate object function in their linearized form these representations account for primaries only in this case the one way representation in terms of reflectivity is the most accurate of the two which implies that proper migration is more accurate than linearized inversion internal multiples can be taken into account by the nonlinear representations as an alternative however the generalized primary representation is introduced in its explicit form this one way

reduced integration and the shear flexible beam element the timoshenko beam element is studied in an investigation of shear locking in the development of c 0 continuous elements using shear flexible or penalty function type formulations a penalty type argument is used to degenerate thick elements to thin elements and the various approximations of the shear related energy terms act as different types of constraints depending on the formulation two types of constraints may emerge which are classified as true or spurious formulations that ensure only true constraints in the extreme penalty limit cases display superior performance in the thick element situation the argument is extended to a shallow curved timoshenko beam and another mechanism inplane locking arises if all energy terms corresponding to the membrane energy are exactly integrated

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

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

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

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

an optimal true amplitude least squares prestack depth migration operator in order to define an optimal true amplitude prestack depth migration for multishot and multitrace data we develop a general methodology based on the least squares data misfit function associated with a forward model the amplitude of the migrated events are restored at best for any given geometry and any given preliminary filtering and amplitude correction of the data the migrated section is then the gradient of the cost function multiplied by a weight matrix a study of the hessian associated with this data misfit shows how efficiently to find a good weight matrix via the computation of only few elements of this hessian thanks to this matrix the resulting migration operator is optimal in the sense that it ensures the best possible restoration of the amplitudes among the large class of least squares migrations applied to a forward model based on born ray tracing and diffracting points approximation this optimal migration outperforms or at least equals the classic kirchhoff formula since the latter belongs to the class of least squares migrations and is only optimal for one shot and an infinite aperture numerical results illustrate this construction and confirm the above expectations

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

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

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

velocity model building by 3d frequency domain full waveform inversion of wide aperture seismic data we assessed 3d frequency domain fd acoustic fullwaveforminversionfwidataasatooltodevelophigh resolution velocity models from low frequency global offset data the inverse problem was posed as a classic leastsquares optimization problem solved with a steepest descent method inversion was applied to a few discrete frequencies allowing management of a limited subset of the 3d data volume the forward problem was solved with a finite difference frequency domain method based on a massively paralleldirectsolver allowingefficientmultiple shotsimulations the inversion code was fully parallelized for distributedmemory platforms taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver after validation on simple synthetic tests fwi was applied to two targets channel and thrust system of the 3d seg eageoverthrustmodel correspondingto3ddomains of 78 752 25 km and 13 513 54 65 km respectively the maximum inverted frequencies are 15 and 7 hz for the two applications amaximum of 30 dual core biprocessor nodes with 8 gb of shared memory per node were used for the second target the main structures were imaged successfully at a resolution scale consistent with the inverted frequencies our study confirms the feasibility of 3d frequency domain fwi of global offset data on large distributed memory platforms to develop high resolution velocity models these high velocity models may provide accurate macromodelsforwave equationprestackdepthmigration

on the time decay of solutions in porous elasticity with quasi static microvoids in this paper we investigate the temporal asymptotic behavior of the solutions of the one dimensional porous elasticity problem with porous dissipation when the motion of microvoids is assumed to be quasi static this question has been recently studied in the general dynamical case thus the natural question is to know if the assumption of quasi static motion for the microvoids implies significant differences in the behavior of the solutions from the results obtained in the general dynamical case it is worth noting that this assumption involves a qualitative change in the system of equations to be analyzed because it arises from the combination of a parabolic equation with an hyperbolic one rather different from the well known system of the thermo elastic problem first we study the coupling of elasticity with porosity and we show that if only porous dissipation is present the decay of solutions is slow but if viscoelasticity is added then the solutions decay exponentially after that we introduce thermal effects in the system and we show that while temperature brings exponential stability to the solutions microtemperature does not

magnetotelluric inversion via reverse time migration algorithm of seismic data we propose a new algorithm for two dimensional magnetotelluric mt inversion our algorithm is an mt inversion based on the steepest descent method borrowed from the backpropagation technique of seismic inversion or reverse time migration introduced in the middle 1980s by lailly and tarantola the steepest descent direction can be calculated efficiently by using the symmetry of numerical green s function derived from a mixed finite element method proposed by nedelec for maxwell s equation without calculating the jacobian matrix explicitly we construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversion algorithm by shin and min these objective functions can be naturally separated into amplitude inversion phase inversion and simultaneous inversion we demonstrate our algorithm by showing three inversion results for synthetic data

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

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

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

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

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

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

waveform inversion using a back propagation algorithm and a huber function norm waveforminversionfacesdifficultieswhenappliedtoreal seismic data including the existence of many kinds of noise the 1 norm is more robust to noise with outliers than the least squares method nevertheless the least squares method is preferred as an objective function in many algorithms because the gradient of the 1 norm has a singularity when the residual becomes zero we propose a complex valued huber function for frequency domain waveform inversion that combines the 2 norm for small residuals with the 1 norm for large residuals we also derive a discretized formula for the gradient of the huber function through numericaltestsonsimplesyntheticmodelsandmarmousidata we find the huber function is more robust to outliers and coherent noise we apply our waveform inversion algorithm to field data taken from the continental shelf under the east sea in korea in this setting we obtain a velocity model whose syntheticshotprofilesaresimilartotherealseismicdata

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

a consistent control of spurious singular modes in the 9 node lagrange element for the laplace and mindlin plate equations abstract when 2 2 quadrature is used with the 9 node lagrange element which is essential in c 0 plate elements to avoid locking spurious singular modes appear on the element level which can lead to singularity or near singularity of the global equations here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired hence the procedure passes the patch test applications to the diffusion and mindlin plate equations are presented results show that h 3 convergence in the l 2 norm is almost retained

modeling of seismic data in the downward continuation approach seismic data are commonly modeled by a high frequency single scattering approximation this amounts to a linearization in the medium coefficient about a smooth background the discontinuities are contained in the medium perturbation the high frequency part of the wavefield in the background medium is described by a geometrical optics representation it can also be described by a one way wave equation based on this we derive a downward continuation operator for seismic data this operator solves a pseudodifferential evolution equation in depth the so called double square root equation we consider the modeling operator based on this equation if the rays in the background that are associated with the reflections due to the perturbation are nowhere horizontal the singular part of the data is described by the solution to an inhomogeneous double square root equation

global existence asymptotic stability and uniform attractors for non autonomous thermoelastic systems with constant time delay in this paper we first consider a non autonomous thermoelastic system with a boundary delay and obtain the asymptotic behavior then using the contractive function method and multiplier techniques we establish the asymptotic behavior and the existence of a uniform attractor of the system with a boundary time delay the main advantage of this method is that we only need to verify compactness condition with the type of energy estimates same as those for establishing the absorbing set moreover we investigate an alternative result of solutions to semilinear thermoelastic systems by virtue of the semigroup method

a unified approach to acoustical reflection imaging ii the inverse problem using the forward matrix model as derived in part i a j berkhout j acoust soc am 93 xxx 1993 it is shown that the first and main part of numerical acoustic imaging consists of a wave field extrapolation process by double matrix inversion physically the wave field extrapolation process means that the downward propagation effects and the upward propagation effects are eliminated from the measurements next the reflection information is extracted from the wave field extrapolation result optionally the reflection information is translated to discipline oriented material parameters by some data fitting process double focusing i e focusing in emission and focusing in detection is closely related to the above numerical imaging process finally it is shown that imaging of zero offset or puls echo data can be formulated by single matrix inversion involving phase shifts only

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