migration velocity analysis using traveltime wavefield tomography abstractwe introduce an integrated wave equation technique for migration velocity analysis mva that consists of three steps 1 forming the extended data 2 approximating the correct transmitted wavefield and 3 using wavefield tomography to update the velocity model in the first step the crosscorrelation imaging condition is relaxed to produce other nonzero lag common image gathers cig that combined form a common image cube cic slicing the cic at different crosscorrelation lags forms a series of cigs flattened events will occur in the cigs at a lag other than the zero lag when an incorrect velocity model is used in the migration in the second step for each event on the cig we pick the focusing depth and crosscorrelation lag at which it is flattest we then model a green s function by seeding a source at the focusing depth using one way wave equation modeling then shift the modeled wavefield with the focusing crosscorrelation lag this process is repeated for the other primary events

moveout based wave equation migration velocity analysis abstractcurrent wave equation migration velocity analysis schemes suffer from problems such as severe nonlinearity which causes the issue of cycle skipping and imprecise objective functions which can accrue velocity errors by honoring residuals caused by model complexity and incomplete acquisition to provide an improvement we developed an alternative method to perform wave equation migration velocity analysis by maximizing the flatness of the angle domain common image gathers we replaced the ray based tomographic operator with the wave equation based one although keeping the conventional moveout based tomography work flow instead of maximizing the image stack power objective function directly with respect to the slowness we linked the objective function to the slowness indirectly through an intermediate moveout parameter by focusing on the common image gather kinematics this approach greatly reduced the risk of cycle skipping in the absence of low frequency data and it produced high quality g

laplace domain full waveform inversion of seismic data lacking low frequency information the lack of the low frequency information in field data prohibits the time or frequency domain waveform inversions from recovering large scale background velocity models on the other hand laplace domain waveform inversion is less sensitive to the lack of the low frequencies than conventional inversions in theory frequency filtering of the seismic signal in the time domain is equivalent to a constant multiplication of the wavefield in the laplace domain because the constant can be retrieved using the source estimation process the frequency content of the seismic data does not affect the gradient direction of the laplace domain waveform inversion we obtained inversion results of the frequency filtered field data acquired in the gulf of mexico and two synthetic data sets obtained using a first derivative gaussian source wavelet and a single frequency causal sine function they demonstrated that laplace domain inversion yielded consistent results regardless of the frequency content within the seismic data

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

seismic inversion based on proximal objective function optimization algorithm abstractseismic impedance inversion has become a common approach in reservoir prediction at present the critical issue in the application of seismic inversion is its low computational efficiency especially in 3d to improve the computational efficiency we have developed an inversion method derived from the proximal objective function optimization algorithm our inversion method calculates each unknown parameter in the model vector one by one during iteration compared with routine gradient dependent inversion algorithms such as the iteratively reweighted least squares irls algorithm our inversion method has lower computational complexity as well as higher efficiency in addition to obtain a sparse reflectivity series a long tailed cauchy distribution is used as the a priori constraint the weak nonlinear problem owing to the introduction of cauchy sparse constraint is addressed by taking advantage of reweighting strategy results of synthetic and real data tests illustrate that the proposed inv

data domain and image domain wavefield tomography waveform inversion fwi requires a good starting model and or data at very low frequency 1 hz for convergence however this is not a necessary condition but an artifact of the objective function defined using differences of observed and simulated data image domain tomographic methods using the same wavefields and wave equations can converge to a reasonable solution from poor starting models and without long offset and or low frequency data cascading image domain and data domain wavefield tomography eliminates the need for extremely low frequency in the acquired data

the resolving power of seismic amplitude data an anisotropic inversion migration approach a description of the theory and numerical implementation of a 3 d linearized asymptotic anisotropic inversion method based on the generalized radon transform is given we discuss implementation aspects including 1 the use of various coordinate systems 2 regularization by both spectral and bayesian statistical techniques and 3 the effects of limited acquisition apertures on inversion we give applications of the theory in which well resolved parameter combinations are determined for particular experimental geometries and illustrate the interdependence of parameter and spatial resolutions procedures for evaluating uncertainties in the parameter estimates that result from the inversion are derived and demonstrated

iterative multiparameter waveform inversion of precritical reflection data using prestack time kirchhoff approximation abstractwe have studied elastic wave scattering and iterative inversion in the context of the kirchhoff approximation the approach is more consistent with the weak contrast reflectivity functions of zoeppritz equations as compared to the born approximation to reduce the computational cost associated with inversion we demonstrated the use of amplitude variation with offset avo analysis prestack time migrations pstms and the corresponding forward modeling in an iterative scheme forward modeling and migration inversion operators are based on the double square root dsr equations of pstm and linearized reflectivity functions all operators involved in the inversion including the background model for dsr and avo are defined in p to p traveltime and are updated at each iteration our method is practical for real data applications because all operators of the inversion are known to be applicable for standard methods we have evaluated the inversion on synthetic and real data using the waveform chara

from classical reflectivity to velocity inversion to full waveform inversion using phase modified and deconvolved reverse time migration images abstractto obtain a physical understanding of gradient based descent methods in full waveform inversion fwi we find a connection between the fwi gradient and the image provided by reverse time migration rtm the gradient uses the residual data as a virtual source and rtm uses the observed data directly as the boundary condition so the fwi gradient is similar to a time integration of the rtm image using the residual data which physically converts the phase of the reflectivity to the phase of the velocity therefore gradient based fwi can be connected to the classical reflectivity to velocity impedance inversion rvi we have developed a new fwi scheme that provides a self contained and physically intuitive derivation which naturally establishes a connection among the amplitude preserved rtm the zoeppritz equations amplitude variation with angle inversion and rvi and combines them into a single framework to produce a preconditioned inversion formula in this scheme the relative velocity upd

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

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

wave equation processing using finite difference propagators part 1 wavefield dissection and imaging of marine multicomponent seismic data abstractmethods for wavefield injection are used in for instance reverse time extrapolation of shot gathers in reverse time migration for correct injection of recorded data without any ambiguity of the propagation direction the wavefield injection methodology requires pressure and particle velocity data such as multicomponent towed marine or seabed seismic recordings we discovered that by carefully considering the models medium parameters and boundary conditions for injection wavefield injection of multicomponent data can also be used to solve several long standing challenges in marine seismic data processing by means of conventional time space domain finite difference propagators we outlined and demonstrated several of these important applications including up down separation of wavefields deghosting direct wave removal source signature estimation multiple removal and imaging using primaries and multiples only acoustic models are considered but the concepts are straightforward to general

on the solution of an inverse scattering problem in seismic while drilling technology abstract this paper concerns the solution of an inverse scattering problem arising in seismic exploration the problem to be analyzed is the prediction of the acoustic wave speeds ahead of a drill bit device located at the center of a well bore and regarded as a seismic source from measurements of the displacements at recording positions located near the surface of the exploration well the forward model is stated in terms of displacements assuming cylindrical symmetry with the symmetry axis located at the center of the borehole absorbing boundary conditions are employed at the artificial boundaries the inverse problem is formulated as the minimization of a quadratic cost functional which is solved using a nonlinear iterative procedure known as quasilinearization that uses the frechet derivatives of the displacements with respect to the wave speed parameters to update the parameter values during the iteration approximations to the solution of the differential equations associated with the forward problem and the frechet derivatives which are needed to discretize the optimization procedure were obtained using an explicit finite element procedure results on the existence uniqueness and regularity of the differential problem and the frechet derivatives are derived as well as on their continuity with respect to the parameter convergence results for the iterative estimation procedure are also given numerical examples illustrating the application of the algorithm to estimate the wave speeds in model problems within the context of the seismic while drilling technique are presented

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

a discrepancy based penalty method for extended waveform inversion abstractextended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model thus permitting it to fit the data well throughout the inversion process these extra degrees of freedom must be curtailed at the solution for example by penalizing them as part of an optimization formulation for separable partly linear models a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical linear degrees of freedom the linear variables are eliminated in an inner optimization step leaving a function of the outer nonlinear variables to be optimized this variable projection method is convenient for computation but it requires that the penalty weight be increased as the estimated model tends to the physical solution we describe an algorithm based on discrepancy that is maintaining the data residual at the inner optimum within a prescribed range to control the pena

an efficient step length formula for correlative least squares reverse time migration abstractin correlative least squares reverse time migration clsrtm the estimation of the optimal step size is usually determined by fitting a parabola and finding its minimum it involves at least two times extra reading of all seismic records which significantly lowers the efficiency of the algorithm to improve the efficiency of the clsrtm algorithm we have deduced an analytical step length asl formula based on the linear property of the demigration operator numerical examples performed with the data synthetized by the marmousi and sigsbee2a models were used to test its validity in complex models with imperfect migration velocity such as the sigabee2a model our formula makes the value of the objective function converges to a much smaller minimum additional numerical tests performed with the data either acquired irregularly or contaminated by different noise levels verify the robustness of the asl formula compared with the commonly used parabolic search method the asl formula is much more e

a bayesian approach to estimate uncertainty for full waveform inversion using a priori information from depth migration abstractfull waveform inversion fwi enables us to obtain high resolution subsurface images however estimating model uncertainties associated with this technique is still a challenging problem we have used a bayesian inference framework to estimate model uncertainties associated with fwi the uncertainties were assessed based on an a posteriori covariance operator evaluated at the maximum a posteriori model for the prior distribution we have used a spatially nonstationary covariance operator based on a plane wave construction with local dips measured from migrated images preconditioned frequency domain fwi was used to estimate the maximum a posteriori model efficient manipulation of the posterior covariance was based on a low rank approximation of the data misfit hessian preconditioned by the prior covariance operator the strong decay of the singular values indicated that data were mostly informative about a low dimensional subspace of model parameters to reduce computational cost of the random

source independent time domain waveform inversion using convolved wavefields application to the encoded multisource waveform inversion full waveform inversion requires a good estimation of the source wavelet to improve our chances of a successful inversion this is especially true for an encoded multisource time domain implementation which conventionally requires separate source modeling as well as the fourier transform of wavefields as an alternative we have developed the source independent time domain waveform inversion using convolved wavefields specifically the misfit function consists of the convolution of the observed wavefields with a reference trace from the modeled wavefield plus the convolution of the modeled wavefields with a reference trace from the observed wavefield in this case the source wavelet of the observed and the modeled wavefields are equally convolved with both terms in the misfit function and thus the effects of the source wavelets are eliminated furthermore because the modeled wavefields play a role of low pass filtering the observed wavefields in the misfit function the frequency selection stra

full waveform inversion based on kaniadakis statistics full waveform inversion fwi is a wave equation based methodology to estimate the subsurface physical parameters that honor the geologic structures classically fwi is formulated as a local optimization problem in which the misfit function to be minimized is based on the least squares distance between the observed data and the modeled data residuals or errors from a probabilistic maximum likelihood viewpoint the minimization of the least squares distance assumes a gaussian distribution for the residuals which obeys gauss s error law however in real situations the error is seldom gaussian and therefore it is necessary to explore alternative misfit functions based on non gaussian error laws in this way starting from the ensuremath kappa generalized exponential function we propose a misfit function based on the ensuremath kappa generalized gaussian probability distribution associated with the kaniadakis statistics or ensuremath kappa statistics which we call ensuremath kappa fwi in this study we perform numerical simulations on a realistic acoustic velocity model considering two noisy data scenarios in the first one we considered gaussian noisy data while in the second one we considered realistic noisy data with outliers the results show that the ensuremath kappa fwi outperforms the least squares fwi providing better parameter estimation of the subsurface especially in situations where the seismic data are very noisy and with outliers independently of the ensuremath kappa parameter although the ensuremath kappa parameter does not affect the quality of the results it is important for the fast convergence of fwi

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

variational data assimilation for the initial value dynamo problem the secular variation of the geomagnetic field as observed at the earth s surface results from the complex magnetohydrodynamics taking place in the fluid core of the earth one way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation in much the same way as is employed in meteorology and oceanography the aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations taking the earth s core to be an electrically conducting fluid sphere in which convection takes place we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method these adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution the initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere for the magnetic field conservation of the divergence free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition we thus find that solving the forward and adjoint dynamo system requires different numerical algorithms in this paper an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere one is a kinematic problem with prescribed velocity field and the second is associated with the hall effect dynamo exhibiting considerable nonlinearity the algorithm exhibits reliable numerical accuracy and stability using both the analytical and the numerical techniques of this paper the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem these numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

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

automatic wave equation migration velocity inversion using multiobjective evolutionary algorithms to solve nonlinear seismic velocity inversion problems we have developed an automatic velocity estimation technique based on the stochastic method called multiobjective evolutionary algorithms moea semblance and differential semblance are used as objective functions to cope with the high computational cost we customized moea added domain knowledge velocity increases with depth slowly varies along layers and so forth which improves the conditioning of the problem and accelerates convergence this approach is robust because it can cope with large velocity errors computational cost of this algorithm is at least two orders of magnitude faster than other stochastic methods and comparable to that of direct gradient methods

simultaneous estimation of velocity and density in acoustic multiparameter full waveform inversion using an improved scattering integral approach abstractdensity is known to be difficult to reconstruct in multiparameter full waveform inversion fwi this difficulty results from the similarity of the diffraction patterns of velocity and density at small scattering angles in addition the sensitivities of seismic data with respect to velocity and density have different orders of magnitude which make the inversion ill conditioned the inverse hessian has been shown to mitigate the coupling effects and rescale the magnitudes of different parameters such that reliable updates for all parameters are available we have investigated the possibility of simultaneous estimations of velocity and density in acoustic media using the truncated gauss newton method the model updates are calculated using a matrix free conjugate gradient solution of the gauss newton normal equation the gradients of the misfit function with respect to the model parameters and the hessian vector products are computed using an improved scattering integral approach to give some ins

estimating a starting model for full waveform inversion using a global optimization method abstractfull waveform inversion fwi has become a popular method to estimate elastic earth properties from seismograms it is formulated as a data fitting least squares minimization problem that iteratively updates an initial velocity model with the scaled gradient of the misfit until a satisfactory match between the real and synthetic data is obtained however such a local optimization approach can converge to a local minimum if the starting model used is not close enough to an optimal model we have developed a two step process in which we first estimate a starting model using a global optimization method unlike local optimization methods a global optimization method starts with a random starting model and is not generally susceptible to be trapped in a local minimum the starting model for fwi that we aim to estimate is sparsely parameterized and contains a set of interfaces and velocities that are used to represent the entire velocity model we have obtained the depth of the interfaces and the vel

simultaneous inversion of full data bandwidth by tomographic full waveform inversion abstractthe convergence of full waveform inversion can be improved by extending the velocity model along either the subsurface offset axis or the time lag axis the extension of the velocity model along the time lag axis enables us to linearly model large time shifts caused by velocity perturbations this linear modeling was based on a new linearization of the scalar wave equation in which perturbation of the extended slowness squared was convolved in time with the second time derivative of the background wavefield the linearization was accurate for reflected events and transmitted events we determined that it can effectively model conventional reflection data as well as modern long offset data containing diving waves it also enabled the simultaneous inversion of reflections and diving waves even when the starting velocity model was far from being accurate we solved the optimization problem related to the inversion with a nested algorithm the inner iterations were based on the proposed linearization

sturmian words structure combinatorics and their arithmetics abstract we prove some new results concerning the structure the combinatorics and the arithmetics of the set per of all the words w having two periods p and q p q which are coprimes and such that w p q 2 a basic theorem relating per with the set of finite standard sturmian words was proved in de luca and mignosi 1994 the main result of this paper is the following simple inductive definition of per the empty word belongs to per if w is an already constructed word of per then also aw and bw belong to per where denotes the operator of palindrome left closure i e it associates to each word u the smallest palindrome word u having u as a suffix we show that by this result one can construct in a simple way all finite and infinite standard sturmian words we prove also that up to the automorphism which interchanges the letter a with the letter b any element of per can be codified by the irreducible fraction p q this allows us to construct for any n 0 a natural bijection that we call farey correspondence of the set of the farey series of order n 1 and the set of special elements of length n of the set st of all finite sturmian words finally we introduce the concepts of farey tree and farey monoid this latter is obtained by defining a suitable product operation on the developments in continued fractions of the set of all irreducible fractions p q

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

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

on the full waveform inversion of lame parameters in semi infinite solids in plane strain abstract we are concerned with imaging the spatially varying lame parameters of semi infinite arbitrarily heterogeneous solids when probed by elastic waves in the time domain we use a full waveform inversion approach to tackle the inverse medium problem and seek the lame distributions that minimize the misfit between measured and computed responses subject to the governing pdes as is commonly the case the resulting inverted profiles of the second lame parameter are of better quality than those of the first to improve the resolution of both lame parameters we discuss the use of three robustifying schemes namely source frequency continuation regularization factor continuation and a search direction biasing scheme we demonstrate with numerical experiments the effect the schemes have on the inversion process and conclude with an application of the robustified full waveform method to a challenging adaptation of the marmousi2 model

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

asymptotic pseudounitary stacking operators stacking operators are widely used in seismic imaging and seismic data processing examples include kirchhoff datuming migration offset continuation dip moveout and velocity transform two primary approaches exist for inverting such operators the first approach is iterative least squares optimization which involves the construction of the adjoint operator the second approach is asymptotic inversion where an approximate inverse operator is constructed in the high frequency asymptotics adjoint and asymptotic inverse operators share the same kinematic properties but their amplitudes weighting functions are defined differently this paper describes a theory for reconciling the two approaches i introduce a pair of asymptotic pseudounitary operators which possess both the property of being adjoint and the property of being asymptotically inverse the weighting function of the asymptotic pseudounitary stacking operators is shown to be completely defined by the derivatives of the operator kinematics i exemplify the general theory by considering several particular examples of stacking operators simple numerical experiments demonstrate a noticeable gain in efficiency when the asymptotic pseudounitary operators are applied for preconditioning iterative least squares optimization

two grid genetic algorithm full waveform inversion full waveform inversion fwi tries to estimate velocity models of the subsurface with improved accuracy and resolution compared to conventional methods to be successful it needs input data that is rich in low frequencies and possibly characterized by long source to receiver offsets the correct solution of the inverse problem by means of local methods is facilitated if the starting model lies in the valley of the cost function global minimum we explore the possibility of relaxing this requirement by using genetic algorithms a stochastic optimization method as the driver of the fwi ga fwi however stochastic methods are affected by the curse of dimensionality meaning that they require huge and sometimes even unaffordable computer resources for inverse problems with many unknowns and costly forward modeling therefore we need to adopt proper stratagems in the inversion and limit our goal to the estimation of a velocity macromodel that is of a model with only the long wavelength velocity struc

immersive boundary conditions theory implementation and examples abstractmany applications in computational geophysics involve the modeling of seismic wave propagation on a set of closely related subsurface models in such scenarios it is of interest to recompute the seismic wavefields locally only in the regions of change instead of in the full subsurface model we have developed a method for local acoustic wavefield recomputation that makes it possible to fully immerse a local modeling domain within a larger domain of arbitrary extent and complexity such that the wave propagation in the full domain is completely accounted for the method enables wavefield modeling on much smaller local domains while relying on the up front generation of a large number of green s functions and a wavefield extrapolation step at each time step of the simulation a kirchhoff helmholtz extrapolation integral is used to predict the interaction of the wavefield leaving the local domain with the exterior domain the outward propagating wavefield and the wavefield reentering the local d

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

interrelation between laplace constants and the gradient distortion effect in laplace domain waveform inversion abstractlaplace domain waveform inversion wi is generally used to generate smooth initial velocity models for frequency or time domain full waveform inversion however in the inversion results of laplace domain wi anomalies such as salt domes are sometimes shifted we evaluate the gradient distortion effect that causes undesirable changes in parameter updates and found that this is caused by the relationship between the partial derivatives of laplace wavefields with respect to two different parameters by analyzing the gradient of the laplace domain misfit function we found that the gradient distortion effect increases as the laplace constants used in the laplace domain wi decrease the velocity model inverted in the laplace domain is generally blurred from shallower parameters to deeper parameters because the partial derivatives of the laplace wavefields with respect to shallower parameters tend to be larger than those of deeper parameters we found two solutions for suppressing the gradient dist

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

source wavelet and its angular spectrum from plane wave seismograms in a typical seismic experiment land or marine the generated source wavelet is either unknown or known only approximately in order to solve many geophysical problems an accurate wavelet estimation is crucial this paper demonstrates a fast numerical algorithm which allows not only estimating the source wavelet but also its angular spectrum radiation pattern from plane wave decomposed seismograms surprisingly literature on this subject is virtually missing although a nonuniform angular spectrum of the generated wavelet can substantially affect the recorded data the technique presented here is based on the downward continuation dc and reverse time extrapolation rte of the recorded data both pressure and its vertical derivative the proposed method is iterative the rate of convergence does not depend on phase characteristics of the generated wavelet we demonstrate that both the wavelet signature and its angular spectrum can be estimated accurately from plane wave seismograms we also illu

time lapse image domain tomography using adjoint state methods adjoint state methods asms have proven successful for calculating the gradients of the functionals commonly found in geophysical inverse problems the 3d asm imagedomain tomography idt formulation of the seismic velocity estimation problem highlights imperfections in migrated image volumes and using appropriate penalty functions e g differential semblance forms an objective function that can be minimized using standard optimization approaches for time lapse 4d seismic scenarios we show that the 3d asm idtapproach can be extended to multiple e g baseline and monitor data sets and offers high quality estimates of subsurface velocity change we discuss two different penalty operators that lead to absolute and relative 4d inversion strategies the absolute approach uses the difference of two independent 3d inversions to estimate a 4d model perturbation i e slowness squared the relative approach inverts for the model perturbation that optimally matches the monitor image to the baseline image even if migrated energy is imperfectly focused both approaches yield good 4d slowness estimates however we assert that the relative approach is more robust given the ubiquitous presence of nonrepeatable 4d acquisition noise and imperfect baseline model estimates

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

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

time space domain implicit finite difference methods for modeling acoustic wave equations it was proved that the implicit spatial finite difference fd method can obtain a higher accuracy than the explicit fd by using even a smaller operator length however when only second order fd in time is used the combined fd is prone to temporal dispersion and easily becomes unstable when a relatively large time step is used the time space domain fd can suppress the temporal dispersion however because the spatial derivatives are solved explicitly the method suffers from spatial dispersion and a large spatial operator length has to be adopted we propose two effective time space domain implicit fd methods for modeling 2d and 3d acoustic wave equations the high order fd is first incorporated into the discretization for the second order temporal derivative and is combined with the implicit spatial fd the plane wave analysis method is used to derive the time space domain dispersion relations and two novel methods are proposed to determine the spatial and temporal fd coefficients in the joint time

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

composite boundary valued solution of the 2 5 d green s function for arbitrary acoustic media theoretically the green s function can be used to calculate the wavefield response of a specified source and the frechet derivative with respect to the model parameters for crosshole seismic full waveform inversion in this paper we apply the finite element method to numerically compute the 2 5 d green s function for an arbitrary acoustic medium by solving a composite boundary valued problem in the wavenumber frequency domain the composite boundary condition consists of a 2 5 d absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling a numerical experiment performed for a uniform earth having a known exact solution shows the accuracy of the computation in the frequency and time domain an inhomogeneous medium test involving an embedded low velocity layer demonstrates that the permissible range of ky at each frequency can be determined rationally from the critical wavenumber value of the medium around the sou

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

efficient laplace domain modeling and inversion using an axis transformation technique abstractwe tested an axis transformation technique for modeling wave propagation in the laplace domain using a finite difference method this technique enables us to use small grids near the surface and large grids at depth accordingly we can reduce the number of grids and attain computational efficiency in modeling and inversion in the laplace domain we used a dispersion analysis and comparisons between modeled wavefields obtained on the regular and transformed axes we demonstrated in a synthetic laplace domain inversion technique shows that this method is efficient and yields a result comparable to that of a laplace domain inversion using a regular grid in a synthetic inversion example the memory usage reduced to less than 33 and the computation time reduced to 39 of those required for the regular grid case using a logarithmic transformation function

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

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

transdimensional seismic inversion using the reversible jump hamiltonian monte carlo algorithm abstractprestack or angle stack gathers are inverted to estimate pseudologs at every surface location for building reservoir models recently several methods have been proposed to increase the resolution of the inverted models all of these methods however require that the total number of model parameters be fixed a priori we have investigated an alternate approach in which we allow the data themselves to choose model parameterization in other words in addition to the layer properties the number of layers is also treated as a variable in our formulation such transdimensional inverse problems are generally solved by using the reversible jump markov chain monte carlo rjmcmc approach which is a tool for model exploration and uncertainty quantification this method however has very low acceptance we have developed a two step method by combining rjmcmc with a fixed dimensional mcmc called hamiltonian monte carlo which makes use of gradient information to take large steps acceptance probability

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

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

improvements to elastic full waveform inversion using cross gradient constraints seismic full waveform inversion fwi is potentially a powerful method for obtaining high resolution subsurface images but the results are often distorted by non linear effects and parameter trade offs such distortions can be particularly severe in the case of multi parameter fwi such as elastic fwi where inversion is performed simultaneously for p and s wave velocities and density the problem can be alleviated by adding additional constraints in form of plausible a priori information a usually well justified constraint includes the structural similarity of different model parameters that is an anomalous body likely exhibits variations in all elastic properties although their magnitudes may be different to consider such type of a priori information we have developed a structurally constrained elastic fwi which is based on minimization of cross products of gradients of different model parameters our synthetic 2d experiments show that the structurally constrained fwi can significantly improve mo

a critical appraisal of asymptotic 3d to 2d data transformation in full waveform seismic crosshole tomography abstractseismic full waveform inversion fwi is often based on forward modeling in the computationally attractive 2d domain this implies the assumption of a line source extended in the out of plane medium invariant direction with far field amplitudes decaying inversely with the square root of distance realistic point sources however generate amplitudes that decay approximately with the inverse of distance conventionally practitioners correct for this amplitude difference and the associated phase shift by transforming the recorded 3d field data to the approximate 2d equivalent by using simplistic asymptotic filter algorithms such filters assume straight raypaths a constant velocity medium and far field recordings we have assessed the validity of 3d to 2d data transformation in the context of crosshole seismic full waveform tomography by propagating 3d and 2d wavefields through 2d media and comparing 2d reference synthetics with their filtered 3d equivalent the filter performs well in simple si

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

love wave waveform inversion in time domain for shallow shear wave velocity abstracthigh frequency surface wave techniques are widely used to estimate s wave velocity of near surface materials surface wave methods based on inversions of dispersion curves are only suitable to laterally homogeneous or smoothly laterally varying heterogeneous earth models due to the layered model assumption during calculation of dispersion curves waveform inversion directly fits the waveform of observed data and it can be applied to any kinds of earth models we have used the love wave waveform inversion in the time domain to estimate near surface s wave velocity we used the finite difference method as the forward modeling method the source effect was removed by the deconvolution technique which made our method independent of the source wavelet we defined the difference between the deconvolved observed and calculated waveform as the misfit function we divided the model into different sizes of blocks depending on the resolution of the love waves and we updated the s wave velocity of each blo

elastic full waveform inversion using the second generation wavelet and an adaptive operator length scheme abstractelastic full waveform inversion fwi can generally yield subsurface model parameters of high spatial resolution however the computational and storage burden is tremendous to mitigate this problem we developed the following three strategies first we derived a time space domain adaptive staggered grid finite difference method the size of the calculation was reduced by using smaller operator lengths for high s wave velocities second we evaluated a multiscale elastic fwi scheme based on the second generation wavelet by which scale decompositions of data and model space were implemented with the scale increasing spatial sampling intervals and time steps became larger therefore the minimum computational cost could be achieved by combining the variable operator length scheme with the multiscale scheme third to economize the memory consumption we extended the efficient boundary storage and checkpointing schemes into elastic fwi only wavefields of several parts in the boundary area betwe

an improved immersed boundary finite difference method for seismic wave propagation modeling with arbitrary surface topography abstractto accurately simulate seismic wave propagation for the purpose of developing modern land data processing tools especially full waveform inversion fwi we have developed an efficient high order finite difference forward modeling algorithm with the capability of handling arbitrarily shaped free surface topography unlike most existing forward modeling algorithms using curvilinear grids to fit irregular surface topography this finite difference algorithm based on an improved immersed boundary method uses a regular cartesian grid system without suffering from staircasing error which is inevitable in a conventional finite difference method in this improved immersed boundary finite difference ibfd algorithm arbitrarily curved surface topography is accounted for by imposing the free surface boundary conditions at exact boundary locations instead of using body conforming grids or refined grids near the boundaries thus greatly reducing the complexity of its preprocessing procedures and the com

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

preserving the discontinuities in least squares reverse time migration of simultaneous source data abstractthe simultaneous source shooting technique can accelerate field acquisition and improve spatial sampling but it will cause strong interferences in the recorded data and artifacts in the final image the previously proposed structural smoothing operator can effectively attenuate artifacts for relatively simple reflection structures during least squares inversion but it will cause damage to complicated reflection events such as discontinuities to preserve discontinuities in a seismic image we apply the singular spectrum analysis ssa operator to attenuate artifacts during least squares inversion considering that global ssa cannot deal with overcomplicated data very well we use local ssa to remove noise and to better preserve the steeply dipping components the local ssa operator corresponds to a local low rank constraint applied in the inversion process the migration operator used in the study is the reverse time migration rtm operator tests using the marmousi model showed the superior per

adaptive eigenspace for multi parameter inverse scattering problems abstract a nonlinear optimization method is proposed for inverse scattering problems in the frequency domain when the unknown medium is characterized by one or several spatially varying parameters the time harmonic inverse medium problem is formulated as a pde constrained optimization problem and solved by an inexact truncated newton type method combined with frequency stepping instead of a grid based discrete representation each parameter is projected to a separate finite dimensional subspace which is iteratively adapted during the optimization each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori the small and slowly increasing finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard tikhonov type regularization numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi parameter problems including the well known marmousi model from geosciences

robust inversion dimensionality reduction and randomized sampling we consider a class of inverse problems in which the forward model is the solution operator to linear odes or pdes this class admits several dimensionality reduction techniques based on data averaging or sampling which are especially useful for large scale problems we survey these approaches and their connection to stochastic optimization the data averaging approach is only viable however for a least squares misfit which is sensitive to outliers in the data and artifacts unexplained by the forward model this motivates us to propose a robust formulation based on the student s t distribution of the error we demonstrate how the corresponding penalty function together with the sampling approach can obtain good results for a large scale seismic inverse problem with 50 corrupted data

multiscale adjoint waveform tomography for surface and body waves abstractwe have developed a wavelet multiscale adjoint scheme for the elastic full waveform inversion of seismic data including body waves bws and surface waves sws we start the inversion on the sw portion of the seismograms to avoid cycle skipping and reduce the dependence on the initial model of these dispersive waves we commence by minimizing an envelope based misfit function subsequently we proceed to the minimization of a waveform difference wd metric applied to the sws only after that we fit bws and sws indiscriminately using a wd misfit metric in each of these three steps we guide the iterative inversion through a sequence of nested subspace projections in a wavelet basis sw analysis preserves a wealth of near surface features that would be lost in conventional bw tomography we used a toy model to illustrate the dispersive and cycle skipping behavior of the sws and to introduce the two ways by which we combat the nonlinearity of waveform inversions involving sws the first is the

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

adjoint based acoustic inversion for the physical characterization of a shallow water environment recently the concept of adjoint modeling has been introduced in shallow water acoustics for solving inverse problems analytical adjoints have been derived for normal modes and for both the standard parabolic equation and claerbout s wide angle approximation wape this paper proposes the application of a semiautomatic adjoint approach that has been successfully applied in the past for multidimensional variational data assimilation in meteorological and climate modeling starting from a modular graph representation of the underlying forward model a programming tool facilitates the generation and coding of both the tangent linear and the adjoint models the potential of this numerical adjoint approach for the physical characterization of a shallow water environment is illustrated with two applications for geoacoustic inversion and ocean acoustic tomography using claerbout s wape in combination with nonlocal boundary conditions furthermore the adjoint optimization is extended to multiple frequencies and

source receiver reverse time imaging of dual source vector acoustic seismic data abstractnovel technologies in seismic data acquisition allow for recording full vector acoustic va data pointwise recordings of pressure and its multicomponent gradient excited by pressure only as well as dipole gradient sources building on recent connections between imaging and seismic interferometry we present a wave equation based nonlinear reverse time imaging approach that takes full advantage of dual source multicomponent data the method s formulation relies on source receiver scattering reciprocity thus making proper use of va fields in the wavefield extrapolation and imaging condition steps in a self consistent manner the va imaging method is capable of simultaneously focusing energy from all in and outgoing waves the receiver side up and downgoing receiver ghosts fields are handled by the va receiver extrapolation whereas source side in and outgoing source ghosts arrivals are accounted for when combining dual source data at the imaging condition additionally va imaging handl

building good starting models for full waveform inversion using adaptive matching filtering misfit abstractwe have proposed a misfit function based on adaptive matching filtering amf to tackle challenges associated with cycle skipping and local minima in full waveform inversion fwi this amf is designed to measure time varying phase differences between observations and predictions compared with classical least squares waveform differences our misfit function behaves as a smooth quadratic function with a broad basin of attraction these characters are important because local gradient based optimization approaches used in most fwi schemes cannot guarantee convergence toward true models if misfit functions include local minima or if the starting model is far away from the global minimum the 1d and 2d synthetic experiments illustrate the advantages of the proposed misfit function compared with the classical least squares waveform misfit furthermore we have derived adjoint sources associated with the proposed misfit function and applied them in several 2d time domain acoustic fwi experiments nume

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