multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

a perspective on 3d surface related multiple elimination surface related multiple elimination srme is an algorithm that predicts all surface multiples by a convolutional process applied to seismic field data only minimal preprocessing is required once predicted the multiples are removed from the data by adaptive subtraction unlike other methods of multiple attenuation srme does not rely on assumptions or knowledge about the subsurface nor does it use event properties to discriminate between multiples and primaries in exchange for this freedom from the subsurface srme requires knowledge of the acquisition wavelet and a dense spatial distribution of sources and receivers although a 2d version of srme sometimes suffices most field data sets require 3d srme for accurate multiple prediction all implementations of 3d srme face a serious challenge the sparse spatial distribution of sources and receivers available in typical seismic field data sets does not conform to the algorithmic requirements there are several approaches to implementing 3d srme that address the data sparseness problem among those approaches are pre srme data interpolation on the fly data interpolation zero azimuth srme and true azimuth srme field data examples confirm that 1 multiples predicted using true azimuth 3d srme are more accurate than those using zero azimuth 3d srme and 2 on the fly interpolation produces excellent results

least squares reverse time migration using controlled order multiple reflections abstractreverse time migration rtm using multiples generates inherent crosstalk artifacts due to the interference among multiples of different orders we have developed a method to remove such crosstalk this approach first separates the recorded seismic data into primary reflections and multiples using the surface related multiples elimination algorithm and then isolates the multiples into different orders we can take any specified say the nth order of multiples data as the incident wave and the next higher order multiples data n 1 th order as the corresponding primary reflection data for imaging we have applied the least squares migration scheme to these two successive orders of multiples our method is denoted as least squares rtm using controlled order multiples lsrtm cm our numerical tests demonstrated that lsrtm cm can significantly improve imaging quality compared with straightforward seismic imaging using multiples without multiples separation

adaptive surface related multiple elimination the major amount of multiple energy in seismic data is related to the large reflectivity of the surface a method is proposed for the elimination of all surface related multiples by means of a process that removes the influence of the surface reflectivity from the data an important property of the proposed multiple elimination process is that no knowledge of the subsurface is required on the other hand the source signature and the surface reflectivity do need to be provided as a consequence the proposed process has been implemented adaptively meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple free data equals the inversion residue results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion

multiple subtraction using statistically estimated inverse wavelets surface related multiple elimination srme typically consists of two steps the first step is prediction and the second step is subtraction in subtraction it is important to effectively attenuate multiple events and preserve primary events when multiples cross with or overlap on primaries least square subtraction usually cannot subtract multiples effectively and may also damage the primaries when multiples overlap with primaries least square subtraction cannot always subtract multiples accurately and often damages the primaries to remedy this problem we propose to statistically estimate the inverse source wavelet correct for errors in the estimate of the inverse wavelet and then use the corrected inverse wavelets for multiple subtraction synthetic tests and real data examples show that the proposed method can effectively attenuate multiples while they also preserve the continuity of reflection events and successfully avoid amplitude distortion the proposed method is characterized by low computational costs and ease of implementation

adaptive multiple subtraction with wavelet based complex unary wiener filters abstractadaptive subtraction is a key element in predictive multiple suppression methods it minimizes misalignments and amplitude differences between modeled and actual multiples and thus reduces multiple contamination in the data set after subtraction due to the high crosscorrelation between their waveforms the main challenge resides in attenuating multiples without distorting primaries as they overlap on a wide frequency range we split this wide band problem into a set of more tractable narrow band filter designs using a 1d complex wavelet frame this decomposition enables a single pass adaptive subtraction via complex single sample unary wiener filters consistently estimated on overlapping windows in a complex wavelet transformed domain each unary filter compensates for amplitude differences within its frequency support and can correct small and large misalignment errors through phase and integer delay corrections this approach greatly simplifies the matching filter estimation and despit

an inverse scattering series method for attenuating multiples in seismic reflection data we present a multidimensional multiple attenuation method that does not require any subsurface information for either surface or internal multiples to derive these algorithms we start with a scattering theory description of seismic data we then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering these include 1 the idea that the inversion process can be viewed as a series of steps each with a specific task 2 the realization that the inverse scattering series provides an opportunity for separating out subseries with specific and useful tasks 3 the recognition that these task specific subseries can have different and more favorable data requirements convergence and stability conditions than does the original complete inverse series and most importantly 4 the development of the first method for physically interpreting the contribution that individual terms and pieces of terms in the inv

time and offset domain internal multiple prediction with nonstationary parameters abstractpractical internal multiple prediction and removal is a high priority area of research in seismic processing technology its significance increases in plays in which data are complex and sophisticated quantitative interpretation methods are apt to be applied when the medium is unknown and or complex and moveout based primary multiple discrimination is not possible inverse scattering based internal multiple attenuation is the method of choice however challenges remain for its application in certain environments for instance when generators are widely distributed and are separated in space by a range of distances optimum prediction parameters such as e which limits the proximity of events combined in the prediction are difficult to determine in some cases we find that no stationary value of e can optimally predict all multiples without introducing damaging artifacts a reformulation and implementation in the time domain permits time nonstationarity to be enforced on e after which a rang

adaptive separation of free surface multiples through independent component analysis we present a three stage algorithm for adaptive separation of free surface multiples the free surface multiple elimination fsme method requires as deterministic prerequisites knowledge of the source wavelet and deghosted data in their absence fsme provides an estimate of free surface multiples that must be subtracted adaptively from the data first we construct several orders from the free surface multiple prediction formula next we use the full recording duration of any given data trace to construct filters that attempt to match the data and the multiple predictions this kind of filter produces adequate phase results but the order by order nature of the free surface algorithm brings results that remain insufficient for straightforward subtraction then we construct trace by trace a mixing model in which the mixtures are the data trace and its orders of multiple predictions we separate the mixtures through a blind source separation technique in particular by employing independent component analysis one of the recovered signals is a data trace without free surface multiples this technique sidesteps the subtraction inherent in most adaptive subtraction methods by separating the desired signal from the free surface multiples the method was applied to synthetic and field data we compared the field data to a published method and found comparable results

adaptive multiple subtraction based on constrained independent component analysis adaptive multiple subtraction is a critical and challenging procedure for the widely used surface related multiple elimination techniques one of the problems encountered in this procedure is that a good result usually is hard to obtain when primaries and multiples have overlap or when the true and predicted multiples have mismatches such as wavelet difference time shift and scalar inconsistency we propose an adaptive multiple subtraction method based on constrained independent component analysis cica it combines the advantages of two current adaptive multiple subtraction methods the independent component analysis method and the multidimensional prediction error filters pef method in cica the prediction error obtained by the pefs which measures the lateral continuity of the primaries is adopted as a constraint term of its objective function

free surface multiple attenuation using inverse data processing in the coupled plane wave domain free surface multiples contain a large amount of energy in the seismic data because of large reflectivity of the free surface we propose a method for free surface multiple attenuation by a simple muting in the inverse coupled plane wave domain our method is based on inverse data processing and the well known 2d invariant embedding technique if the lateral variation in subsurface structure is smooth the data are well compressed in the 2d coupled plane wave domain reducing computation costs and stabilizing the inversion procedure surface multiples and primaries are well separated in the inverse coupled plane wave domain and multiples can be eliminated by simple muting which does not damage the primary energy to reduce artifacts wraparound and noise introduced by the frequency domain data matrix inversion horizontal and vertical tapers are applied a least squares matrix inversion method is chosen to stabilize the inversion synthetic data examples show that plane wave inverse data processing is stable and successful in attenuating free surface multiples

relative performance of moveout based multiple suppression methods for amplitude variation with offset avo analysis and common midpoint cmp stacking we apply three moveout based methods for multiple suppression to simple synthetic common midpoint cmp gathers and compare their performance in terms of level of multiple rejection and more importantly in terms of 1 suitability of processed output for use in analysis of amplitude variations with offset avo 2 primary to multiple amplitude p m ratio of the data after cmp stacking and 3 preservation of primary wavelet shape and amplitude on the stack the three approaches are filtering in the frequency wavenumber f k domain the hampson method of filtering in the parabolic radon transform domain and a hybrid method that improves upon hampson s approach by using a variation of harlan s statistical pattern recognition approach to separate primaries from multiples in the parabolic radon transform domain the f k approach is unsuitable prior to avo analysis moreover it is little better in suppressing the multiples than the cmp stack itself hampson s method performs considerably better and is su

perturbation approach to depth extrapolation the born series solution of the lippmann schwinger equation does not necessarily converge properly for depth extrapolation problems even more seriously the lippmann schwinger equation is not necessarily self consistent for depth extrapolation unless it is interpreted correctly a solution is proposed by using the generalized lippmann schwinger equation that includes boundary value contributions that normally are ignored a modified version of the lippmann schwinger equation for depth extrapolation is obtained the corrections to the born series expansion for depth extrapolation are demonstrated the new system has the desired convergence and self consistency properties explicit depth extrapolation is discussed in the context of the lippmann schwinger equation a partial explanation for why explicit depth extrapolation works reasonably well in laterally inhomogeneous media may be that the contribution from the perturbation term in the lippmann schwinger equation for that problem is small for a wide var

data driven wavefield focusing and imaging with multidimensional deconvolution numerical examples for reflection data with internal multiples standard imaging techniques rely on the single scattering assumption this requires that the recorded data do not include internal multiples i e waves that have bounced multiple times between reflectors before reaching the receivers at the acquisition surface when multiple reflections are present in the data standard imaging algorithms incorrectly image them as ghost reflectors these artifacts can mislead interpreters in locating potential hydrocarbon reservoirs recently we introduced a new approach for retrieving the green s function recorded at the acquisition surface due to a virtual source located at depth we refer to this approach as data driven wavefield focusing additionally after applying source receiver reciprocity this approach allowed us to decompose the green s function at a virtual receiver at depth in its downgoing and upgoing components these wavefields were then used to create a ghost free image of the medium with either crosscorrelation or multidimensional deconvolution presenting an advantage over standard prestack migration we tested the robustness of our approach when an erroneous background velocity model is used to estimate the first arriving waves which are a required input for the datadriven wavefield focusing process we tested the new method with a numerical example based on a modification of the amoco model

identification of image artifacts from internal multiples first order internal multiples are a source of coherent noise in seismic images because they do not satisfy the single scattering assumption fundamental to most seismic processing there are a number of techniques to estimate internal multiples in data in many cases these algorithms leave some residual multiple energy in the data this energy produces artifacts in the image and the location of these artifacts is unknown because the multiples wereestimatedinthedatabeforetheimagewasformed toavoid this problem we propose a method by which the artifacts caused by internal multiples are estimated directly in the image we use ideas from the generalized bremmer series and the lippmannschwinger scattering series to create a forward scattering series to model multiples and an inverse scattering series to describe

improving multiple removal using least squares dip filters and independent component analysis the suppression of multiple events is a crucial task in seismic data processing and the adaptive subtraction of the predicted multiples is recognized as one of the main challenges for the success of the surface related multiple elimination technique the traditional least squares matching approach can affect the primary events because the estimated multiples tend to adapt to the primaries under the minimum energy condition we investigate two filtering techniques for improving the multiple removal results in the first proposed method we combine the advantages of the least squares and pattern dip based subtraction methods doing so we exploit the separation of primaries and multiples in the dip domain and then we apply the least squares adaptive subtraction in each dip band before recomposing the data to obtain the final subtraction result as a result of the dip decomposition the primary multiple interferences are reduced allowing for a more reliable least squares filtering in the second method w

convolution based interpolation for fast high quality rotation of images this paper focuses on the design of fast algorithms for rotating images and preserving high quality the basis for the approach is a decomposition of a rotation into a sequence of one dimensional translations as the accuracy of these operations is critical we introduce a general theoretical framework that addresses their design and performance we also investigate the issue of optimality and present an improved least square formulation of the problem this approach leads to a separable three pass implementation of a rotation using one dimensional convolutions only we provide explicit filter formulas for several continuous signal models including spline and bandlimited representations finally we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm our results indicate that the present algorithm in its higher order versions outperforms all standard high accuracy methods of which we are aware both in terms of speed and quality its computational complexity increases linearly with the order of accuracy the best quality results are obtained with the sine based algorithm which can be implemented using simple one dimensional ffts

blind source separation of seismic signals based on information maximization abstractprediction methods for seismic multiples are never ideal in practice and an adaptive subtraction process is needed to account for mismatches between the predicted and the actual multiples we are interested in the problem of separating primary and multiple seismic signals based on their statistical properties we link recent advances in the blind source separation problem to the multiple removal problem and present a novel adaptive subtraction method based on an information maximization principle compared with previous methods our proposed method uses higher order statistics of the data and incorporates the filtering nature of the adaptive subtraction problem into our algorithm formulation we use simulations to show that our proposed adaptive subtraction method outperforms the popular least squares adaptive subtraction and the independent component analysis methods quantitatively as measured by the mean squared error and qualitatively as evaluated by the visual quality of the image reconstr

removal of internal multiples with the common focus point cfp approach part 1 explanation of the theory removal of surface and internal multiples can be formulated by removing the influence of downward scattering boundaries and downward scattering layers the involved algorithms can be applied in a model driven or a data driven way a unified description is proposed that relates both types of algorithms based on wave theory the algorithm for the removal of surface multiples shows that muted shot records play the role of multichannel prediction filters the algorithm for the removal of internal multiples shows that muted cfp gathers play the role of multichannel prediction filters the internal multiple removal algorithm is illustrated with numerical examples the conclusion is that the layer related version of the algorithm has significant practical advantages

on removing interpolation and resampling artifacts in rigid image registration we show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts these artifacts negatively affect the accuracy of registration by producing local optima altering the gradient shifting the global optimum and making rigid registration asymmetric in this paper after an extensive literature review we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically we show the sum of squared differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration we then discuss aliasing that occurs in rotation which is due to the fact that an image represented in the cartesian grid is sampled with different rates in different directions and propose the use of oscillatory isotropic interpolation kernels which allow better recovery of true global optima by overcoming this type of aliasing through our experiments on brain fingerprint and white noise images we illustrate the superior performance of the integral registration cost function in both the cartesian and spherical coordinates and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration

estimation of multiple scattering by iterative inversion part i theoretical considerations a review has been given of the surface related multiple problem by making use of the so called feedback model from the resulting equations it has been concluded that the proposed solution does not require any properties of the subsurface however source detector and reflectivity properties of the surface need be specified those properties have been quantified in a surface operator and this operator is estimated as part of the multiple removal problem the surface related multiple removal algorithm has been formulated in terms of a neumann series and in terms of an iterative equation the neumann formulation requires a nonlinear optimization process for the surface operator while the iterative formulation needs a number of linear optimizations the iterative formulation also has the advantage that it can be integrated easily with another multiple removal method an algorithm for the removal of internal multiples has been proposed as well this algorithm is an extension of the surface related method removal of internal multiples requires knowledge of the macro velocity model between the surface and the upper boundary of the multiple generating layer in part ii also published in this issue the success of the proposed algorithms has been demonstrated on numerical experiments and field data examples

improving adaptive subtraction in seismic multiple attenuation in seismic multiple attenuation once the multiple models have been built the effectiveness of the processing depends onthesubtractionstep usuallytheprimaryenergyispartially attenuated during the adaptive subtraction if an l 2 norm matching filter is used to solve a least squares problem the expandedmultichannelmatchingemcmfiltergenerallyis effective but conservative parameters adopted to preserve theprimarycouldleadtosomeremainingmultiples wehave managed to improve the multiple attenuation result through aniterativeapplicationoftheemcmfiltertoaccumulatethe effect of subtraction a butterworth type masking filter based on the multiple model can be used to preserve most of the primary energy prior to subtraction and then subtraction canbeperformedontheremainingparttobettersuppressthe multiples without affecting the primaries meanwhile subtraction can be performed according to the orders of the multiples as a single subtraction window usually covers different order multiples with different amplitudes theoretical analyses and synthetic and real seismic data set demonstrations provedthatacombinationofthesethreestrategiesiseffective in improving the adaptive subtraction during seismic multipleattenuation

a model independent finite difference method for removal of free surface generated multiples abstractwe have developed a new data driven method to solve the free surface related multiple problem using forward space time domain modeling we build a finite difference fd modeling engine in which the interaction of any desired wavefield with an unknown subsurface but without the reflecting sea surface on top can be modeled this can either be used to predict the desired primary reflections of the subsurface or to simultaneously model all orders of free surface related multiples in this method we use conventional forward modeling techniques in combination with a novel type of boundary condition the wave propagation in the known part of the medium i e the homogeneous water layer is modeled on an fd grid whereas the wave propagation in the unknown part of the medium i e the subsurface is predicted using the recorded multicomponent data the methodology dynamically links these two distinct domains we demonstrate the exact method and an adapted version that works under realistic conditi

free surface multiple attenuation for blended data abstractblended data sets are now being acquired because of improved efficiency and reduction in cost compared with conventional seismic data acquisition we have developed two methods for blended data free surface multiple attenuation the first method is based on an extension of surface related multiple elimination srme theory in which free surface multiples of the blended data can be predicted by a multidimensional convolution of the seismic data with the inverse of the blending operator a least squares inversion method is used which indicates that crosstalk noise existed in the prediction result due to the approximate inversion an adaptive subtraction procedure similar to that used in conventional srme is then applied to obtain the blended primary this can damage the energy of primaries the second method is based on inverse data processing idp theory adapted to blended data we derived a formula similar to that used in conventional idp and we attenuated free surface multiples by simple mut

estimating intensity variance due to noise in registered images applications to diffusion tensor mri image registration techniques which require image interpolation are widely used in neuroimaging research we show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space we describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images the spatial transformations computed by the registration procedure and the interpolation or approximation kernel chosen the method is general and could handle various sources of signal variability such as thermal noise and physiological noise provided that their effects can be assessed in the original images our approach is applied to diffusion tensor dt mri data assuming only thermal noise as the source of variability in the data we show that incorrect noise variance estimates in registered diffusion weighted images can affect dt parameters as well as indices of goodness of fit such as chi square maps in addition to dt mri we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data such as in relaxometry and functional mri studies

inverse scattering theory inverse scattering series method for one dimensional non compact support potential the reversion of the born neumann series of the lippmann schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem one limitation of the current inversion methods based on the reversion of the born neumann series is that the velocity potential should have compact support however this assumption cannot be satisfied in certain cases especially in seismic inversion based on the idea of distorted wave scattering we explore an inverse scattering method for velocity potentials without compact support the strategy is to decompose the actual medium as a known single interface reference medium which has the same asymptotic form as the actual medium and a perturbative scattering potential with compact support after introducing the method to calculate the green s function for the known reference potential the inverse scattering series and volterra inverse scattering series are derived for the perturbative potential analytical and numerical examples demonstrate the feasibility and effectiveness of this method besides to ensure stability of the numerical computation the lanczos averaging method is employed as a filter to reduce the gibbs oscillations for the truncated discrete inverse fourier transform of each order our method provides a rigorous mathematical framework for inverse acoustic scattering with a non compact support velocity potential

3d prediction of surface related and interbed multiples multiple attenuation during data processing does not guarantee a multiple free final section multiple identification plays an important role in seismic interpretation a target oriented method for predicting 3d multiples on stacked or migrated cubes in the time domain is presented the method does not require detailed knowledge of the subsurface geological model or access to prestack data and is valid for both surface related and interbed multiples the computational procedure is based on kinematic properties of the data and uses fermat s principle to define the multiples since no prestack data are required the method can calculate 3d multiples even when only multi 2d survey data are available the accuracy and possible use of the method are demonstrated on synthetic and real data examples

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

multidimensional inverse scattering series internal multiple prediction in the coupled plane wave domain the inverse scattering series internal multiple prediction and attenuation algorithm predicts multiples using certain combinations of input seismic reflection data events which are computed in the wavenumber pseudo depth or plane wave vertical travel time i e p domains significant differences can arise in the algorithms output and computational expense depending on which domain is used many of these are traceable to the response of the algorithm to the users choice of the search limiting parameter the question of which domain is optimal can be addressed with benchmark synthetics the compactness of the input to the plane wave domain algorithm leads to the expectation that it will have a reduced computational expense also the lack of increase in the dominant period i e width of input events as the horizontal slowness increases leads to the expectation that it will respond well to a constant both of these expectations are borne out with a 1 5d benchmark example a 2d plane wave pred

multiple prediction through inversion theoretical advancements and real data application wave equation based multiple attenuation seismic methods may be divided into the two distinct phases of multiple modeling and multiple subtraction these two are interrelated and must be optimized in order to produce an optimal final result the multiple prediction through inversion mpi scheme updates the multiple model iteratively as we usually do in a linearized inverse problem the scheme models the multiple wavefield without an explicit knowledge of surface and subsurface structures or of the source signature both are generally unknown in seismic surveys however compared to a conventional surface related multiple attenuation method the accuracy of the multiple model is improved both kinematically and dynamically it is because the mpi scheme implicitly takes account of the spatial variation of the surface reflectivity the source signature the detector patterns and receiver ghosts and other effects included in the so called surface operator when the mpi scheme is used in the first phase it also significantly reduces the nonlinearity of the problem in the second phase that involves attenuating multiples without removing or altering primaries the effectiveness of the mpi scheme is demonstrated by examples involving real marine seismic data

imaging of multiple reflections current multiple removal algorithms in seismic processing use either differential moveout or predictability if the differential moveout between primaries and multiples is small prediction is the only option available in the last decade multidimensional prediction error filtering by weighted convolution such as surface related multiple elimination srme have proved to be very successful in practice so far multiples have been considered as noise and have been discarded after the removal process in this paper we argue that multiple reflections contain a wealth of information that can be used in seismic processing to improve the resolution of reservoir images beyond current capability in the near future one may expect that the so called weighted crosscorrelation wcc concept may offer an attractive alternative in approaching the multiple problem wcc creates an option to avoid the adaptive subtraction process as applied in prediction error algorithms moreover it allows the transformation of multiples into primaries the latter means that seismic imaging with primaries and multiples nonlinear process can be implemented by a sequence of linear processes including the transformation of multiples into primaries and the imaging of primaries

estimation of primaries by sparse inversion with scattering based multiple predictions for data with large gaps abstractwe have solved the estimation of primaries by sparse inversion problem for a seismic record with large near offset gaps and other contiguous holes in the acquisition grid without relying on explicit reconstruction of the missing data eliminating the unknown data as an explicit inversion variable is desirable because it sidesteps possible issues arising from overfitting the primary model to the estimated data instead we have simulated their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the area of the unobserved trace locations each term in this scattering series involves convolution of the total predicted wavefield once more with the current estimated green s function for a medium without the free surface at these unobserved locations it is important to note that our method cannot by itself mitigate regular undersampling issues that result in significant aliases whe

a continuous method for reducing interpolation artifacts in mutual information based rigid image registration we propose an approach for computing mutual information in rigid multimodality image registration images to be registered are modeled as functions defined on a continuous image domain analytic forms of the probability density functions for the images and the joint probability density function are first defined in 1d we describe how the entropies of the images the joint entropy and mutual information can be computed accurately by a numerical method we then extend the method to 2d and 3d the mutual information function generated is smooth and does not seem to have the typical interpolation artifacts that are commonly observed in other standard models the relationship between the proposed method and the partial volume pv model is described in addition we give a theoretical analysis to explain the nonsmoothness of the mutual information function computed by the pv model numerical experiments in 2d and 3d are presented to illustrate the smoothness of the mutual information function which leads to robust and accurate numerical convergence results for solving the image registration problem

higher order nonlinear diffraction tomography inversion of the rytov series nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large possibly infinite number of terms in the rytov series the algorithms attain the form of a volterra series of nonlinear operators with the usual filtered backpropagation algorithm of diffraction tomography as the leading linear term a computer simulation study is included to illustrate the performance of the algorithms for the case of scattering objects with cylindrical symmetry

relating source receiver interferometry to an inverse scattering series to derive a new method to estimate internal multiples we have evaluated an explicit relationship between the representations of internal multiples by source receiver interferometry and an inverse scattering series this provides a new insight into the interaction of different terms in each of these internal multiple prediction equations and explains why amplitudes of estimated multiples are typically incorrect a downside of the existing representations is that their computational cost is extremely high which can be a precluding factor especially in 3d applications using our insight from source receiver interferometry we have developed an alternative computationally more efficient way to predict internal multiples the new formula is based on crosscorrelation and convolution two operations that are computationally cheap and routinely used in interferometric methods we have compared the results of the standard and the alternative formulas qualitatively in terms of the constructed wavefields and quantitatively in terms of the computational cost using examples from a synthetic data set

estimation of primaries and near offset reconstruction by sparse inversion marine data applications ost wave equation based multiple removal algorithms are based on prediction and subtraction of multiples especially for shallow water the prediction strongly relies on a correct interpolation of the missing near offsets the subtraction of predicted multiples from the data can easily lead to the distortion of primaries if primaries and multiples overlap recently a new approach for surface related multiple removal was proposed the estimation of primaries by sparse inversion epsi which is based on a full waveform inversion approach epsi is based on the same primary multiple model as surface related multiple elimination srme and does not require a subsurface model in contrast to srme epsi estimates the primaries as unknowns in a multidimensional inversion process rather than a subtraction process the multidimensional primary impulse responses are parameterized by band limited spikes which are estimated such that they along with their corresponding multiples match the input data an interesting aspect of the epsi method is that it produces a residual which is the part of the input data not explained by primaries and multiples this residual can be analyzed and may provide useful information on the primary estimation process furthermore it has been demonstrated that epsi is also capable of reconstructing the missing near offsets from the multiples the proposed method is applied to a field data set with moderate water depth where it is demonstrated that the results are comparable with srme this data set is used to illustrate the residual for a shallow water field data set it is shown that epsi gives a better result than the standard srme result caused by epsi s capability to reconstruct the missing near offsets

well ties for seismic with severe stratigraphic filtering abstractstratigraphic filtering sf or short period multiples is prominent in cyclically stratified sedimentation with large impedance contrasts that result in normal incident reflection magnitudes greater than 0 5 because sf attenuates and delays the propagating wavelet similar to the effects of q attenuation the integrity of well ties is often jeopardized a method is proposed to obtain better well ties in areas with severe sf starting with a well log acoustic impedance curve two way transmitted wavefields and their equivalent inverse filters are generated at each time sample because a time varying convolution of the transmitted wavefields with the primary only reflectivity yields the multiple reflectivity a time varying deconvolution of the multiple synthetic with the inverse filters yields the primary only reflectivity in essence when the multiple synthetic matches the near angle stack at a well location the near angle stack is deconvolved in a time varying fashion to match the primary on

multimodel adaptive subtraction with regularized parameter selection via generalized information criterion abstractadaptive subtraction remains a critical part of today s seismic data processing many existing adaptive subtraction methods can be formulated as a parameter estimation problem and all of them although fundamentally different have a common restriction that the dimension of the unknown parameters must be determined in advance we have developed an adaptive subtraction framework called multimodel adaptive subtraction mmas that aims to relax this restriction as well as regularize the estimation of the parameters through a generalized information criterion combined with a nonconcave penalized likelihood function mmas is a fully general framework that can be applied to many existing adaptive subtraction methods as an example we determined how mmas can be applied to the popular least squares adaptive subtraction lsas method and we call the resulting algorithm the multimodel lsas mmasls furthermore we studied its computational complexity and developed an efficient implementation for mmasls

internal multiple prediction and removal using marchenko autofocusing and seismic interferometry standard seismic processing steps such as velocity analysis and reverse time migration imaging usually assume that all reflections are primaries multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts many suppression methods are relatively ineffective for internal multiples we show how to predict and remove internal multiples using marchenko autofocusing and seismic interferometry we first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected up and downgoing green s functions from virtual sources in the subsurface we then generate the relevant up and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing then we convolve purely scattered components of up and downgoing green s functions to reconstruct only the internal multiple field which is adaptively subtracted from the measured data crucially this is all possible without detailed modeled information about the earth s subsurface the method only requires surface reflection data and estimates of direct nonreflected arrivals between subsurface virtual sources and the acquisition surface the method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used

interpolation artifacts in multimodality image registration based on maximization of mutual information mutual information mi is an increasingly popular match metric for multimodality image registration however its value is affected by interpolation which may limit registration accuracy the purpose of this study was to characterize the artifacts from eight interpolators and to investigate efficient strategies to overcome these artifacts the interpolators were 1 nearest neighbor 2 linear 3 cubic catmull rom 4 hamming windowed sinc 5 partial volume 6 nn with jittered sampling jit 7 nn with histogram blurring blur and 8 nn with jit and blur the impact of interpolation on mi was evaluated in two dimensions over different translational and rotational misregistration interpolation caused spurious fluctuations in mi whenever the voxel grids had coinciding periodicities and were nearly aligned the artifacts did not lessen by using intensity interpolators with wider support e g cubic catmull rom hamming windowed sinc pv could lead to either arch artifacts or inverted arch artifacts depending on the relative voxel sizes several strategies reduced artifacts and improved registration robustness jit blur avoiding an extreme number of intensity bins and resampling the images in a rotated orientation with different relative voxel sizes e g spl pi 3 these findings also apply to related methods including normalized mi joint entropy and hill s third moment

generalized linear inversion and the first born theory for acoustic media a procedure is derived which incorporates a generalized linear inverse viewpoint within a multidimensional born inversion method the method we present is a more general born theory which can accommodate insufficient and inaccurate data this general method reduces to the ordinary born procedure when the data requirements of the latter technique are satisfied

racah polynomials and a three term recurrence relation for the racah coefficients a three term recurrence relation is derived for the racah coefficients or 6 j symbols based on a set of orthogonal polynomials called racah polynomials that generalise these coefficients this relation is shown to be a consequence of the well known biedenharn elliot identity

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

multiple attenuation in the parabolic τ p domain using wavefront characteristics of multiple generating primaries the problem of multiple attenuation has been solved only partially one of the most common methods of attenuating multiples is an approach based on the radon transform it is commonly accepted that the parabolic radon transform method is only able to attenuate multiples with significant moveouts we propose a new 2 d method for attenuation of both surface related and interbed multiples in the parabolic p domain the method is based on the prediction of a multiple model from the wavefront characteristics of the primary events multiple prediction comprises the following steps 1 for a given multiple code the angles of emergence and the radii of wavefront curvatures are estimated for primary reflections for each receiver in the common shotpoint gather 2 the intermediate points which compose a specified multiple event are determined for each shot receiver pair 3 traveltimes of the multiples are calculated wavefields within time windows around the predicted traveltime curves may be considered as mult

kirchhoff scattering series insight into the multiple attenuation method there are two basic integral equations used to represent wavefields in theoretical seismology the lippmann schwinger integral equation and the representation theorem the born scattering series currently used for attenuating free surface multiples has been derived from the lippmann schwinger integral equation similarly we have used the representation theorem here to derive a kirchhoff scattering series for attenuating free surface multiples in towed streamer data the kirchhoff series for attenuating free surface multiples is in theory equivalent to the born series most important like the born series it does not require any knowledge of the subsurface however it still provides useful insight into the multiple attenuation methods because the form of some quantities involved in the kirchhoff series is different from the form in the born series for example in towed streamer seismic data the kirchhoff series requires measurements of the vertical derivative of the pressure field in addition to the

integrated receiver deghosting and closed loop surface multiple elimination abstractaccurate surface related multiple removal is an important step in conventional seismic processing and more recently primaries and surface multiples are separated such that each of them is available for imaging algorithms current developments in the field of surface multiple removal aim at estimating primaries in a large scale inversion process using such a so called closed loop process in each iteration primaries and surface multiples will be updated until they fit the measured data the advantage of redefining surface multiple removal as a closed loop process is that certain preprocessing steps can be included which can lead to an improved multiple removal in principle the surface related multiple elimination process requires deghosted data as input thus the source and receiver ghost must be removed we have focused on the receiver ghost effect and assume that the source is towed close to the sea surface such that the source ghost effect is well represented by a dipole source the rece

estimating primaries by sparse inversion and application to near offset data reconstruction accurate removal of surface related multiples remains a challenge in many cases to overcome typical inaccuracies in current multiple removal techniques we have developed a new primary estimation method estimation of primaries by sparse inversion epsi epsi is based on the same primary multiple model as surface related multiple elimination srme and also requires no subsurface model unlike srme epsi estimates the primaries as unknowns in a multidimensional inversion process rather than in a subtraction process furthermore it does not depend on interpolated missing near offset data because it can reconstruct missing data simultaneously sparseness plays a key role in the new primary estimation procedure the method was tested on 2d synthetic data

accounting for free surface multiples in marchenko imaging imagine placing a receiver at any location in the earth and recording the response at that location to sources on the surface in such a world we could place receivers around our reservoir to better image the reservoir and understand its properties realistically this is not a feasible approach for understanding the subsurface we have developed an alternative and realizable approach to obtain the response of a buried virtual receiver for sources at the surface our method is capable of retrieving the green s function for a virtual point in the subsurface to the acquisition surface in our case a physical receiver is not required at the subsurface point instead we require the reflection measurements for sources and receivers at the surface of the earth and a macromodel of the velocity no small scale details of the model are necessary we can interpret the retrieved green s function as the response to sources at the surface for a virtual receiver in the subsurface we obtain this green s function by solving the marchenko equation an integral equation pertinent to inverse scattering problems our derivation of the marchenko equation for the green s function retrieval takes into account the free surface reflections present in the reflection response previous work considered a response without free surface multiples we decompose the marchenko equation into up and downgoing fields and solve for these fields iteratively the retrieved green s function not only includes primaries and internal multiples as do previous methods but it also includes freesurface multiples we use these up and downgoing fields to obtain a 2d image of our area of interest in this case below a synclinal structure

an illustration of adaptive marchenko imaging in marchenko imaging wavefields are retrieved at specified focal points in the subsurface through an iterative scheme derived from the multidimensional marchenko equation the method requires seismic reflection data at the earth s surface after free surface multiple elimination and an estimate of the direct wavefield from the surface to each focal point which can be computed for instance in a macrovelocity model in the first iteration the direct wavefield is crosscorrelated with the reflection data this operation is identical to inverse wavefield extrapolation as is applied commonly in various imaging schemes for instance in reverse time migration rtm at each succeeding iteration the result of the previous iteration is truncated in time and crosscorrelated with the reflection data again to obtain a seismic image a multidimensional deconvolution based imaging condition can be applied to the retrieved wavefields by this approach both primary reflections and internal multiples contribute to the construction of the image alternatively a crosscorrelation based imaging condition can be used in which only the primary reflections are imaged and the contributions of internal multiples are subtracted the latter strategy offers more flexibility because the subtraction of redatumed internal multiples can be implemented adaptively through this approach the artifacts from internal multiples can be removed effectively from a conventional rtm image

a pyramid approach to subpixel registration based on intensity we present an automatic subpixel registration algorithm that minimizes the mean square intensity difference between a reference and a test data set which can be either images two dimensional or volumes three dimensional it uses an explicit spline representation of the images in conjunction with spline processing and is based on a coarse to fine iterative strategy pyramid approach the minimization is performed according to a new variation ml of the marquardt levenberg algorithm for nonlinear least square optimization the geometric deformation model is a global three dimensional 3 d affine transformation that can be optionally restricted to rigid body motion rotation and translation combined with isometric scaling it also includes an optional adjustment of image contrast differences we obtain excellent results for the registration of intramodality positron emission tomography pet and functional magnetic resonance imaging fmri data we conclude that the multiresolution refinement strategy is more robust than a comparable single stage method being less likely to be trapped into a false local optimum in addition our improved version of the marquardt levenberg algorithm is faster

bayesian wavefield separation by transform domain sparsity promotion successful removal of coherent noise sources greatly determines seismic imaging quality major advances have been made in this direction e g surface related multiple elimination srme and interferometric ground roll removal still moderate phase timing amplitude errors and clutter in predicted signal components can be detrimental adopting a bayesian approach along with assuming approximate curvelet domain independence of the to be separated signal components we construct an iterative algorithm that takes predictions produced by for example srme as input and separates these components in a robust manner in addition the proposed algorithm controls the energy mismatch between separated and predicted components such a control lacking in earlier curvelet domain formulations improves results for primary multiple separation on synthetic and real data

nonlinear impedance inversion for attenuating media applications of seismic impedance inversion normally assume the data are free of multiples and transmission effects requiring knowledge of the seismic pulse that is assumed to be stationary an alternative formulation for impedance inversion is based on an exact frequency domain zero offset reflectivity function for a 1d medium analytical formulas for the frechet derivatives are derived for efficient implementation of an iterative nonlinear inversion the exact zero offset reflectivity accounts for internal multiples and transmission effects in the data absorption and dispersion are also conveniently handled if a reasonable estimate for the quality q factor of the medium is available a series of convenient features are included in the inversion algorithm an automatic estimation of the amplitude spectrum of the seismic pulse an impedance transform that makes the inversion independent from the initial smooth model and a practical approach to estimate the regularization weight numerical tests usin

removal of water layer multiples from multicomponent sea bottom data a method for suppressing water layer multiples in multicomponent sea floor measurements is presented the multiple suppression technique utilizes the concept of wavefield separation into upgoing and downgoing modes just below the sea floor for eliminating the sea floor ghost the sea surface ghost and the accompanying water layer reverberations the theory applies to each of the recorded components pressure vertical velocity and horizontal velocities the fundamental physical principle for the multiple suppression technique rests on identifying these multiples as downgoing waves just below the sea floor while the primaries of interest arriving from the subsurface are upgoing waves white presented this realization for the pressure component three decades ago hence the theory for the velocity field is an extension of the theory in this paper the theory is derived for an experiment with a marine source in the water layer above a locally flat elastic sea floor with known elastic parameters the method is otherwise multidimensional and operates on a shot to shot basis hence it is computationally fast aside from this we show that this demultiple method removes the strongest multiples in sea floor data without knowledge of the source wavelet synthetic and real data examples are provided to illustrate the application of the algorithms to the pressure in line velocity and vertical velocity components the numerical tests show that strong multiples have been attenuated on the pressure and the velocity recordings producing promising results

direct nonlinear inversion of multiparameter 1d elastic media using the inverse scattering series in the direct nonlinear inversion method and in algorithms for 1d elastic media p wave velocity s wave velocity and density are depth dependent direct nonlinear means that the method uses explicit formulas that 1 input data and directly output changes in material properties without the need for indirect procedures such as model matching searching optimization or other assumed aligned objectives or proxies and that 2 the algorithms recognize and directly invert the intrinsic nonlinear relationship between changes in material properties and the recorded reflection wavefields to achieve full elastic inversion all components of data such as pp sp and ss data are needed the method assumes that only data and reference medium propertiesare input and terms in the inverse series for moving mislocated reflectors resulting from the linear inverse term are separated from amplitude correction terms although in principle this direct inversion approach requires all components of elastic data synth

extension of phase correlation to subpixel registration in this paper we have derived analytic expressions for the phase correlation of downsampled images we have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak but rather in several coherent peaks mostly adjacent to each other these coherent peaks correspond to the polyphase transform of a filtered unit impulse centered at the point of registration the analytic results provide a closed form solution to subpixel translation estimation and are used for detailed error analysis excellent results have been obtained for subpixel translation estimation of images of different nature and across different spectral bands

clarifying the underlying and fundamental meaning of the approximate linear inversion of seismic data linearinversionisdefinedasthelinearapproximationofa direct inverse solution this definition leads to data requirements and specific direct inverse algorithms which differ with all current linear and nonlinear approaches and is immediately relevant for target identification and inversion in an elastic earth common practice typically starts with a directforwardormodelingexpressionandseekstosolveaforward equation in an inverse sense attempting to solve a direct forward problem in an inverse sense is not the same as solvinganinverseproblemdirectly distinctionsincludedifferences in algorithms in the need for a priori information and in data requirements the simplest and most accessible examples are the direct inversion tasks derived from the inverse scattering series iss for the removal of free surface and internal multiples the iss multiple removal algorithms require no subsurface information and they are independent ofearthmodeltype adirectforwardmethodsolvedinaninverse sense for modeling and subtracting multiples would require accurate knowledge of every detail of the subsurface the multiple has experienced in addition it requires a different modeling and subtraction algorithm for each different earth model type the iss methods for direct removal of multiples are not a forward problem solved in an inverse sense similarly the direct elastic inversion provided by the issisnotamodelingformulaforppdatasolvedinaninverse sense direct elastic inversion calls for pp ps ss data for direct linear and nonlinear estimates of changes in mechanical properties in practice a judicious combination of directandindirectmethodsarecalleduponforeffectivefield dataapplication

signal and noise separation in prestack seismic data using velocity dependent seislet transform abstractthe seislet transform is a waveletlike transform that analyzes seismic data by following varying slopes of seismic events across different scales and provides a multiscale orthogonal basis for seismic data it generalizes the discrete wavelet transform dwt in the sense that the dwt in the lateral direction is simply the seislet transform with a zero slope our earlier work used plane wave destruction pwd to estimate smoothly varying slopes however the pwd operator can be sensitive to strong noise interference which makes the seislet transform based on pwd pwd seislet transform occasionally fail in providing a sparse multiscale representation for seismic field data we adopted a new velocity dependent vd formulation of the seislet transform in which the normal moveout equation served as a bridge between local slope patterns and conventional moveout parameters in the common midpoint domain the vd slope has better resistance to strong random noise which indicated the potential of vd sei

removal of internal multiples with the common focus point cfp approach part 2 application strategies and data examples in the past the surface multiple removal method based on the feedback model has been successfully applied to many different field data sets the extension of surface to internal multiples can be made by replacing shot records with common focus point cfp gathers a cfp gather representing focused data with one source in the subsurface and all receivers at the surface or vice versa for a receiver gather the internal multiple removal algorithm can be formulated in terms of boundary related and layer related versions in the boundary related version the internal multiples are removed for one downward scattering reflector at a time in the layer related version the internal multiples are removed for a sequence of downward scattering reflectors at a time an exact velocity model is not required but proper muting is critical muting becomes straightforward in the cfp domain the strategy for applying the two versions of the multiple removal algorithm is demonstrated on physical model and field data one can conclude that the layer related version is the most appropriate in most situations because it requires less user action and does not need exact knowledge of the multiple generating boundary

antileakage least squares spectral analysis for seismic data regularization and random noise attenuation spatial transformation of irregularly sampled data series to regularly sampled data series is a challenging problem in many areas such as seismology the classical fourier analysis is limited to regularly sampled data series on the other hand the least squares spectral analysis lssa can analyze irregularly sampled data series although the lssa method takes into account the correlation among the sinusoidal basis functions of irregularly spaced series it still suffers from the problem of spectral leakage energy leaks from one spectral peak into another we propose an iterative method called antileakage lssa to attenuate the spectral leakage and consequently regularize irregular data series in this method we first search for a spectral peak with the highest energy and then we remove suppress it from the original data series in the next step we search for a new peak with the highest energy in the residual data series and remove the new and the old components simultaneously from the original data

seismic processing in the inverse data space until now seismic processing has been carried out by applying inverse filters in the forward data space because the acquired data of a seismic survey is always discrete seismic measurements in the forward data space can be arranged conveniently in a data matrix p each column in the data matrix represents one shot record if we represent seismic data in the temporal frequency domain then each matrix element consists of a complex valued number considering the dominant role of multiple scattering in seismic data it is proposed to replace data matrix p by its inverse p 1 before starting seismic processing making use of the feedback model for seismic data multiple scattered energy is mapped onto the zero time axis of the inverse data space the practical consequence of this remarkable property may be significant multiple elimination in the inverse data space simplifies to removing data at zero time only moving to the inverse data space may cause a fundamental change in the way we preprocess and image seismic data

a method for calculating synthetic seismograms which include the effects of absorption and dispersion a method is outlined for the calculation of synthetic seismograms which include the effects of absorption and dispersion the absorption model used is the usual model of exponential decay of amplitude with distance given by a a0e z where is a linear function of frequency this attenuation is accounted for mathematically by allowing the elastic modulus to be a complex function of frequency this results in a complex velocity and wavenumber and the reflection and transmission coefficients also become complex functions of frequency the method is based upon the communication theory approach and is applicable to plane waves in a flat layered model the source can be placed at an arbitrary depth the equations are outlined in detail for a particular absorption dispersion pair taken from futterman 1962 an example with a surface synthetic seismogram and synthetic traces at several depths is presented

multivariable wilson polynomials a multivariable biorthogonal generalization of the wilson polynomials is presented these are four distinct families which in a special case occur in two complex conjugate pairs that satisfy four biorthogonality relations among them an interesting limit case is the multivariable continuous dual hahn polynomials

low frequency reflection data augmentation by an inpainting method 1d acoustic media abstractthe augmentation of low frequencies is an important problem for inverting seismic reflection data through an acoustic scattering approach we have characterized how the data down to zero frequency grows in importance with increasing depth and the size of the velocity contrast we have developed a hermite distributed approximation functional hdaf inpainting method that provides a least squares fitting of the acoustic reflection data down to zero frequency the hdaf data fitting is applied to the first born approximation for compact velocity contrasts the top and bottom depth velocities are equal several fitting constraints are derived using a taylor expansion of the reflection data near zero frequency they provide a coupling with the first born approximation of the velocity contrast the method can be extended to the general geophysical case in which the final velocity i e is different from the starting velocity by use of the distorted wave born approximation numerical results for 1d t

direct nonlinear q compensation of seismic primaries reflecting from a stratified two parameter absorptive medium q compensation of seismic primaries that have reflected from a stratified absorptive dispersive medium may be posed as a direct nonlinear inverse scattering problem if the reference medium is chosen to be nonattenuating and homogeneous an inverse scattering q compensation procedure may be derived that is highly nonlinear in the data but which operates in the absence of prior knowledge of the properties of the subsurface including its q structure it is arrived at by 1 performing an order by order inversion of a subset of the born series 2 isolating and extracting a component of the resulting nonlinear inversion equations argued to enact q compensation and 3 mapping the result back to data space once derived the procedure can be understood in terms of nonlinear interaction of the input primary reflection data the attenuation of deeper primaries is corrected by an operator built automatically using the angle and frequency variations of all shallower primaries a simple synthetic exam

adaptive overburden elimination with the multidimensional marchenko equation abstractiterative substitution of the multidimensional marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process in so called marchenko imaging a macro velocity model of the subsurface is required to meet this objective the model is used to back propagate the data during the first iteration and to truncate integrals in time during all successive iterations in case of an erroneous model the image will be blurred akin to conventional imaging and artifacts may arise from inaccurate integral truncations however the scheme is still successful in removing artifacts from internal multiple reflections inspired by these observations we rewrote the marchenko equation such that it can be applied early in a processing flow without the need of a macro velocity model instead we have required an estimate of the two way traveltime surface of a selected horizon in the subsurface we have introduced an approximation such that adaptive subtracti

closed loop surface related multiple elimination and its application to simultaneous data reconstruction surface related multiple elimination srme is one of the most commonly used methods for suppressing surface multiples however to obtain an accurate surface multiple estimation dense source and receiver sampling is required the traditional approach to this problem is performing data interpolation prior to multiple estimation although appropriate in many cases this methodology fails when big data gaps are present or when relevant information is not recovered e g near offset data in shallow water environments we have developed a solution in which multiple estimation was performed simultaneously with data reconstruction such that data reconstruction helped obtain better multiple estimates and in which the physical primary multiple relationship helped constrain the data interpolation to accomplish this we proposed to extend the recently introduced closed loop srme cl srme algorithm to account for primary estimation in the case of coarsely sampled data we achieved this by introducing a focal domain parameterization of the primaries in a sparsity promoting cl srme method results proved that the method was capable of reliably estimating primaries data in case of shallow water and with large undersampling factors

interpolation artifacts in sub pixel image registration we consider the problem of registering aligning two images to sub pixel accuracy by optimization of objective functions constructed from the images intensity values we show that some widely used interpolation methods can introduce multiple local optima in the energy of the interpolated image which if not counter balanced by other terms can cause local optima in registration objective functions including the sum of squared differences cross correlation and mutual information we discuss different solutions to address the problem based on high degree b spline interpolation low pass filtering the images and stochastic integration numerical examples using synthetic and real signals and images are shown

fredholm integral equation for shape reconstruction of an underwater object using backscattered ramp response signatures inverse scattering problems for identifying underwater objects are of importance for all kinds of applications in seas that occupy more than two thirds of the surface of the earth the physical optics approximation has been applied to the acoustic scattering integral representation yielding an inverse scattering equation which relates the profile function of a submerged object to the fourier transform of the complex backscattered acoustic field this technique is the so called ramp response technique and usually requires the full scattering information for all frequencies to obtain accurate profile function of an object in order to retrieve the shape information of an object from the band limited backscattered frequency data a fredholm integral equation is formulated in this paper for calculating the ramp response of the submerged object this fredholm integral equation is for the unknown ramp response of an object in terms of the known incomplete scattering information the kernel of this integral equ

multidimensional signature deconvolution and free surface multiple elimination of marine multicomponent ocean bottom seismic data this paper presents a wave equation method for multidimensional signature deconvolution designature and elimination of free surface related multiples demultiple in four component 4c ocean bottom seismic data the designature demultiple method has the following characteristics it preserves primary amplitudes while attenuating free surface related multiples it requires no knowledge of the sea floor parameters and the subsurface it requires information only of the local density and acoustic wave propagation velocity just above the sea floor it accommodates source arrays and no information except location of the physical source array its volume and its radiation characteristics wavelet is required designature is an implicit part of the demultiple process hence the method is capable of transforming recorded reflection data excited by any source array below the sea surface into free surface demultipled data that would be recorded from a point source with any desired signature in addition the incident wavefield is not subtracted from the data prior to free surface demultiple hence separation of incident and scattered fields is not an issue as it is for most other free surface demultiple schemes the designature demultiple algorithm can be divided into two major computational steps first a multidimensional deconvolution operator inversely proportional to the time derivative of the downgoing part of the normal component of the particle velocity just above the sea floor is computed second an integral equation is solved to find any component of the designatured free surface demultipled multicomponent field when the geology is horizontally layered the designature and free surface demultiple scheme greatly simplifies and lends itself toward implementation in the p domain or frequency wavenumber domain as deterministic deconvolution of common shot gathers or common receiver gathers when source array variations are negligible