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

tutorial on seismic interferometry part 2 underlying theory and new advances in the 1990s the method of time reversed acoustics was developed this method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal when ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers they focus at the position of the original source even when the medium is very complex in seismic interferometry the time reversed responses are not physically sent into the earth but they are convolved with other measured responses the effect is essentially the same the time reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers a mathematical derivation based on reciprocity theory formalizes this principle the crosscorrelation of responses at two receivers integrated over different sources gives the green s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver this green s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving recent developments circumventing these assumptions include interferometric representations for attenuating and or moving media as well as unified representations for waves and diffusion phenomena bending waves quantum mechanical scattering potential fields elastodynamic electromagnetic poroelastic and electroseismic waves significant improvements in the quality of the retrieved green s functions have been obtained with interferometry by deconvolution a trace by trace deconvolution process compensates for complex source functions and the attenuation of the medium interferometry by multidimensional deconvolution also compensates for the effects of one sided and or irregular illumination

focusing with plane time reversal mirrors an efficient alternative to closed cavities in this paper a theoretical foundation is proposed and numerical results are provided for focusing by plane time reversal mirrors of finite dimensions in a homogeneous fluid the basic ideas are the same as those used in the closed time reversal cavity ctrc system cassereau et al proc ieee ultrason symp 1613 1618 1990 d cassereau and m fink ieee trans ultrason ferroelec freq control 39 579 592 1992 except that the most unrealistic assumptions made in this theoretical approach are dropped plane mirrors are considered that do not surround the object source and different kinds of radiation conditions are introduced on the surface of these mirrors in order to obtain more realistic situations from an experimental point of view the results are compared with those of the ctrc system and it is shown how the focal pattern is changed in comparison with the pattern of the theoretical and ideal model the differences between several radiation conditions on the surface of the mirror are also analyzed the theory is based on a time domain formulation of diffraction but a frequency analysis provides closed form solutions in some particular cases numerical results show that plane time reversal mirrors of finite dimensions represent an efficient and realistic alternative to the ctrc system

time domain reciprocity theorems for acoustic wave fields in fluids with relaxation time domain reciprocity theorems of the time convolution and the time correlation type for acoustic wave fields in linear time invariant and locally reacting fluids are discussed inhomogeneity inertial anisotropy and arbitrary relaxation effects in inertia and compressibility properties both of the active and the passive type are included the theorems also apply to the equivalent fluid model of a solid in which only compressional waves are considered and shear is neglected the analysis is entirely carried out in space time without intermediate recourse to the frequency or the wave vector domains the application to inverse source and inverse constituency or inverse profiling scattering or imaging problems is briefly indicated

one way versions of the kirchhoff integral the conventional kirchhoff integral based on the two way wave equation states how the acoustic pressure at a point a inside a closed surface s can be calculated when the acoustic wave field is known on s in its general form the integrand consists of two terms one term contains the gradient of a green s function and the acoustic pressure the other term contains a green s function and the gradient of the acoustic pressure the integrand can be simplified by choosing reflecting boundary conditions for the two way green s functions in such a way that either the first term or the second term vanishes on s this conventional approach to deriving rayleigh type integrals has practical value only for media with small contrasts so that the two way green s functions do not contain significant multiple reflections we present a modified approach for simplifying the integrand of the kirchhoff integral by choosing absorbing boundary conditions for the one way green s functions the resulting rayleigh type integr

on seismic interferometry the generalized optical theorem and the scattering matrix of a point scatterer we have analyzed the far field approximation of the green s function representation for seismic interferometry by writing each of the green s functions involved in the correlation process as a superposition of a direct wave and a scattered wave the green s function representation is rewritten as a superposition of four terms when the scattered waves are modeled with the born approximation it appears that a three term approximation of the green s function representation omitting the term containing the crosscorrelation of the scattered waves yields a nearly exact retrieval whereas the full four term expression leads to a significant nonphysical event this is because the born approximation does not conserve energy and therefore is an insufficient model to explain all aspects of seismic interferometry we use the full four term expression of the green s function representation to derive the generalized optical theorem unlike other recent derivations which use stationary phase analysis our derivation uses reciprocity theory from the generalized optical theorem we derive the nonlinear scattering matrix of a point scatterer this nonlinear model accounts for primary and multiple scattering at the point scatterer and conforms with well established scattering theory of classical waves the model is essential to explain fully the results of seismic interferometry even when it is applied to the response of a single point scatterer the nonlinear scattering matrix also has implications for modeling inversion and migration

interferometry by deconvolution part 1 theory for acoustic waves and numerical examples interferometry allows for synthesis of data recorded at any two receivers into waves that propagate between these receivers as if one of them behaves as a source this is accomplished typically by crosscorrelations based on perturbation theory and representation theorems we show that interferometry also can be done by deconvolutions for arbitrary media and multidimensional experiments this is important for interferometry applications in which 1 excitation is a complicated source time function and or 2 when wavefield separation methods are used along with interferometry to retrieve specific arrivals unlike using crosscorrelations this method yields only causal scattered waves that propagate between the receivers we offer a physical interpretation of deconvolution interferometry based on scattering theory here we show that deconvolution interferometry in acoustic media imposes an extra boundary condition which we refer to as the free point or clamped point boundary condition depending on the measured field quantity this boundary condition generates so called free point scattering interactions which are described in detail the extra boundary condition and its associated artifacts can be circumvented by separating the reference waves from scattered wavefields prior to interferometry three wavefield separation methods that can be used in interferometry are direct wave interferometry dual field interferometry and shot domain separation each has different objectives and requirements

points of monotonicity in orlicz lorentz function spaces abstract in orlicz lorentz function space m 0 points of upper monotonicity lower monotonicity upper local uniform monotonicity and lower local uniform monotonicity are characterized as the corollary we can easily obtain the criteria for strict monotonicity upper local uniform monotonicity and lower local uniform monotonicity of m 0

estimating and correcting the amplitude radiation pattern of a virtual source in the virtual source vs method we crosscorrelate seismic recordings at two receivers to create a new data set as if one of these receivers were a virtual source and the other a receiver we focus on the amplitudes and kinematics of vs data generated by an array of active sources at the surface and recorded by an array of receivers in a borehole the quality of the vs data depends on the radiation pattern of the virtual source which in turn is controlled by the spatial aperture of the surface source distribution theory suggests that when the receivers are surrounded by multi component sources completely filling a closed surface then the virtual source has an isotropic radiation pattern and vs data possess true amplitudes in practical applications limited sourceaperture and deployment of a single source type create an anisotropic radiation pattern of the virtual source leading to distorted amplitudes this pattern can be estimated by autocorrelating the spatial fourier transform of the downgoing wavefield in the special case of a laterally invariant medium the vs data can be improved by deconvolving the vs data with the estimated amplitude radiation pattern in the frequency wavenumber domain this operation alters the amplitude spectrum but not the phase of the data we can also steer the virtual source by assigning it a new desired amplitude radiation pattern given sufficient illumination exists in the desired directions alternatively time gating the downgoing wavefield before crosscorrelation already common practice in implementing the vs method can improve the radiation characteristics of a virtual source

uniform opial properties in generalized cesaro sequence spaces abstract the main purpose of this paper is considering the generalized cesaro sequence spaces defined by s suantai on some convexity properties of generalized cesaro sequence spaces georgian math j 10 1 2003 193 200 by giving some topological properties and finding condition for ces p equipped with both the amemiya norm and the luxemburg norm to possesses uniform opial property

singular value decomposition analysis of source illumination in seismic interferometry by multidimensional deconvolution we have developed a method to analytically evaluate the relationship between the source receiver configuration and the retrievedwavefieldinseismicinterferometryperformedbymultidimensional deconvolution mdd the mdd method retrieves thewavefieldwiththedesiredsource receiverconfigurationfrom the observed wavefield without source information we used a singular value decomposition svd approach to solve the inverse problem of mdd by introducing svd into mdd we obtained quantities that revealed the characteristics of the mdd inverse problem and interpreted the effect of the initial sourcereceiverconfigurationforasurveydesign wenumericallysimulated the wavefield with a 2d model and investigated the rank of the incident field matrix of the mdd inverse problem with a source array of identical length a sparse and a dense source distribution resulted in an incident field matrix of the same rank and retrievedthesamewavefield therefore theoptimumsourcedistribution can be determined by analyzing the rank of the incident field matrix of the inverse problem in addition the introduction ofscatterersintothemodelimprovedthesourceilluminationand effectively increased the rank enabling mdd to retrieve a better wavefield we found that the ambiguity of thewavefield inferred from the model resolution matrix was a good measure of the amount of illumination of each receiver by the sources we used the field data recorded at the two boreholes from the surface sourcestosupportourresultsofthenumericalmodeling weevaluated the rank of incident field matrix with the dense and sparse source distribution we discovered that these two distributions resulted in an incident field matrix of almost the same rank and retrieved almost the samewavefield as the numerical modeling thisiscrucialinformationfordesigningseismicexperiments using the mdd based approach

the space of kahler metrics this paper the second of a series deals with the function space mathcal h of all smooth kahler metrics in any given n dimensional closed complex manifold v these metrics being restricted to a given fixed real cohomology class called a polarization of v this function space is equipped with a pre hilbert metric structure introduced by t mabuchi 10 who also showed that formally this metric has nonpositive curvature in the first paper of this series 4 the second author showed that the same space is a path length space he also proved that mathcal h is geodesically convex in the sense that for any two points of mathcal h there is a unique geodesic path joining them which is always length minimizing and of class c1 1 this partially verifies two conjectures of donaldson 8 on the subject in the present paper we show first of all that the space is as expected a path length space of nonpositive curvature in the sense of a d aleksandrov a second result is related to the theory of extremal kahler metrics namely that the gradient flow in mathcal h of the k energy of v has the property that it strictly decreases the length of all paths in mathcal h except those induced by one parameter families of holomorphic automorphisms of m

retrieving the green s function in an open system by cross correlation a comparison of approaches l we compare two approaches for deriving the fact that the green s function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions one approach is based on physical arguments exploiting the principle of time reversal invariance of the acoustic wave equation the other approach is based on rayleigh s reciprocity theorem using a unified notation we show that the result of the time reversal approach can be obtained as an approximation of the result of the reciprocity approach

retrieving the exact green s function by wavefield crosscorrelation recent development on the green s function retrieval by wavefield crosscorrelation has substantially advanced the physical research in a multidisciplinary and unprecedented fashion however the underlying assumption of the theory that the sources are in the far field limits the technology to extracting only the high frequency part of the green s function in an open system this critical approximation can be eliminated using the exact boundary integral equation method a scheme involving the crosscorrelation kernel is proposed to recover the exact green s function including all frequency content symmetric difference kernels are analytically constructed for sources on a plane or on a circle and can be reduced to the known dirac delta kernel under the far field approximation

green s function representations for seismic interferometry the term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations the first version of this principle was derived by claerbout 1968 who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response for an arbitrary 3d inhomogeneous lossless medium it follows from rayleigh s reciprocity theorem and the principle of time reversal invariance that the acoustic green s function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points the integral is along sources on an arbitrarily shaped surface enclosing these points no assumptions are made with respect to the diffusivity of the wavefield the rayleigh betti reciprocity theorem leads to a similar representation of the elastodynamic green s function when a part of the enclosing surface is the earth s free surface the integral needs only to be evaluated over the remaining part of the closed surface in practice not all sources are equally important the main contributions to the reconstructed green s function come from sources at stationary points when the sources emit transient signals a shaping filter can be applied to correct for the differences in source wavelets when the sources are uncorrelated noise sources the representation simplifies to a direct crosscorrelation of wavefield observations at two points similar as in methods that retrieve green s functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface

reverse time wave field extrapolation imaging and inversion the scattered wave field propagated backward in time into an arbitrary background medium is related via a volume integral to perturbations in velocity about the background which are expressed as a scattering potential in general there is no closed form expression for the kernel of this integral representation although it can be expressed asymptotically as a superposition of plane waves backpropagated from the receiver array when the receiver array completely surrounds the scatterer the kernel reduces to the imaginary part of the green s function for the background medium this integral representation is used to relate the images obtained by imaging algorithms to the actual scattering potential two such relations are given 1 for the migrated image obtained by deconvolving the extrapolated field with the incident field and 2 for the reconstructed image obtained by applying a one way wave operator to the extrapolated field and then deconvolving by the incident field the migrated image highlig

rotundity properties in banach spaces via sublinear operators abstract conditions for extreme points strongly extreme points lur points su points points in direction of which the space is uniformly rotund and points with the kadec klee property with respect to the convergence almost everywhere for the space d e s generated by a kothe space e and a sublinear operator s defined on a linear space x and with values in l 0 are given as corollaries conditions for rotundity midpoint local uniform rotundity local uniform rotundity uniform rotundity in every direction and the kadec klee property for the convergence locally in measure of these spaces are deduced interpretations of the results in cases of kothe bochner spaces cesaro orlicz spaces and k interpolation spaces are presented

equivalence of the virtual source method and wave field deconvolution in seismic interferometry seismic interferometry and the virtual source method are related approaches for extracting the green s function that accounts for wave propagation between receivers by making suitable combinations of the waves recorded at these two receivers these waves can either be excited by active controlled sources or by natural incoherent sources we compare this technique with the deconvolution of the wave field recorded at different receivers we show that the deconvolved wave field is a solution of the same wave equation as that for the physical system but that the deconvolved wave forms may satisfy different boundary conditions than those of the original system we apply this deconvolution approach to the wave motion recorded at various levels in a building after an earthquake and show how to extract the building response for different boundary conditions extracting the response of the system with different boundary conditions can be used to enhance or suppress the normal mode response in seismic exploration this principle can be used for the suppression of surface related multiples

exact wave field simulation for finite volume scattering problems an exact boundary condition is presented for scattering problems involving spatially limited perturbations of arbitrary magnitude to a background model in generally inhomogeneous acoustic media the boundary condition decouples the wave propagation on a perturbed domain while maintaining all interactions with the background model thus eliminating the need to regenerate the wave field response on the full model the method which is explicit relies on a kirchhoff type integral extrapolation to update the boundary condition at every time step of the simulation the green s functions required for extrapolation through the background model are computed efficiently using wave field interferometry

another look at cesaro sequence spaces abstract we consider the cesaro sequence space ces p as a closed subspace of the infinite l p sum of finite dimensional spaces we easily obtain many known results for example ces p has property of rolewicz uniform opial property and weak uniform normal structure we also consider some generalized cesaro sequence spaces finally we compute the von neumann jordan and james constants of the two dimensional cesaro sequence space ces p 2 when 1 p 2

a representation for green s function retrieval by multidimensional deconvolution green s function retrieval by crosscorrelation may suffer from irregularities in the source distribution asymmetric illumination intrinsic losses etc multidimensional deconvolution mdd may overcome these limitations a unified representation for green s function retrieval by mdd is proposed from this representation it follows that the traditional crosscorrelation method gives a green s function of which the source is smeared in space and time this smearing is quantified by a space time point spread function psf which can be retrieved from measurements at an array of receivers mdd removes this psf and thus deblurs and deghosts the source of the green s function obtained by correlation

kahler einstein metrics and the kahler ricci flow on log fano varieties we prove the existence and uniqueness of kahler einstein metrics on q fano varieties with log terminal singularities and more generally on log fano pairs whose mabuchi functional is proper we study analogues of the works of perelman on the convergence of the normalized kahler ricci flow and of keller rubinstein on its discrete version ricci iteration in the special case of non singular fano manifolds our results on ricci iteration yield smooth convergence without any additional condition improving on previous results our result for the kahler ricci flow provides weak convergence independently of perelman s celebrated estimates

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

monotonicity characteristic of kothe bochner spaces abstract estimates of the characteristic of monotonicity in kothe bochner function spaces e x with some consequences are given characterizations of strict and uniform monotonicity of the sequence lattice e x n n 1 are obtained

retrieving reflections by source receiver wavefield interferometry source receiver wavefield interferometry has been proposed recently as an extension of classical correlation based interferometry under idealized assumptions it allows the green s function between a source and a receiver to be reconstructed from boundary data that are collected using two closed contours of sources and receivers respectively an intuitive geometric description of this method based on ray theory can be used to design a method for reconstructing virtual gather events that typically are lost when conventional interferometry is employed in classical interferometry events in the green s function between two receiver locations are reconstructed by automatically finding a ray that emanates from a stationary source passes through the virtual source reflects off the structure and finally is recorded by the second receiver the common path to both receivers is then canceled by a suitable crosscorrelation if illumination of the structure is not ideal such a ray may not exist and the reflection is not reconstructed source receiver wave interferometry can be given a similar geometric description the reflection off the structure can be constructed using not one but multiple rays produced simultaneously by two stationary sources this new redatuming technique proves successful in geometries in which classical interferometry fails extensive numerical simulations support these theoretical conclusions

a thermodynamical formalism for monge ampere equations moser trudinger inequalities and kahler einstein metrics we develop a variational calculus for a certain free energy functional on the space of all probability measures on a kahler manifold x this functional can be seen as a generalization of mabuchi s k energy functional and its twisted versions to more singular situations applications to monge ampere equations of mean field type twisted kahler einstein metrics and moser trudinger type inequalities on miller manifolds are given tian s alpha invariant is generalized to singular measures allowing in particular a proof of the existence of kahler einstein metrics with positive ricci curvature that are singular along a given anti canonical divisor which combined with very recent developments concerning miller metrics with conical singularities confirms a recent conjecture of donaldson as another application we show that if the calabi flow in the anti canonical class exists for all times then it converges to a kahler einstein metric when a unique one exists which is in line with a well known conjecture c 2013 elsevier inc all rights reserved

extremity in kothe bochner function spaces abstract letebe a kothe function space over a complete measurable space andxa banach space recall an elementhineis said to beorder continuousif for any decreasing sequence gn inse ngn 0 andgn h implies limn gn 0 we show that every denting point of the unit ball ofeis order continuous using this result we prove thatfis a denting point of the unit ball ofe x if and only if is a denting point of the unit ball of for almost all supp is a denting point of the unit ball of suppose thateis order continuous we also prove that for any unit vectorfine x if f xis a strongly exposed point of the unit ball ofeand for almost allt supp f f t f t xis a strongly exposed point of the unit ball ofx thenfis a strongly exposed point of the unit ball ofe x

nonreciprocal green s function retrieval by cross correlation the cross correlation of two recordings of a diffuse acoustic wave field at different receivers yields the green s function between these receivers in nearly all cases considered so far the wave equation obeys time reversal invariance and the green s function obeys source receiver reciprocity here the theory is extended for nonreciprocal green s function retrieval in a moving medium it appears that the cross correlation result is asymmetric in time the causal part represents the green s function from one receiver to the other whereas the acausal part represents the time reversed version of the green s function along the reverse path

nonlinear extended images via image domain interferometry wave equation finite frequency imaging and inversion still face many challenges in addressing the inversion of highly complexvelocitymodelsaswellasindealingwithnonlinearimaging e g migration of multiples amplitude preserving migration extended images eis are particularly important for designing image domain objective functions aimed at addressing standing issues in seismic imaging such as two way migration velocity inversion or imaging inversion using multiples general oneand two way representations for scattered wavefields can describe and analyze eis obtained in wave equation imaging we have developed a formulation that explicitly connects the wavefield correlations done in seismic imaging with the theory and practiceofseismicinterferometry inlightofthisconnection we define eis as locally scattered fields reconstructed by model dependent image domain interferometry because they incorporate the same one and two way scattering representations used for seismic interferometry the reciprocity based eis can in principle account for all possible nonlinear effects in the imaging process i e migrationofmultiplesandamplitudecorrections in this case the practice of two way imaging departs considerably from the one way approach we have studied the differences betweentheseapproachesinthecontextofnonlinearimaging analyzingthedifferencesinthewavefieldextrapolationstepsaswell as in imposing the extended imaging conditions when invoking single scatteringeffectsandignoringamplitudeeffectsingenerating eis the one and two way approaches become essentially the same as those used in today s migration practice with the straightforwardadditionofspaceandtimelagsinthecorrelationbased imaging condition our formal description of the eis and theinsightthattheyarescatteredfieldsintheimagedomainmay beusefulinfurtherdevelopmentofimagingandinversionmethodsinthecontextoflinear migration basedvelocityinversionor inmoresophisticatedimage domainnonlinearinversescattering approaches

classical wave experiments on chaotic scattering we review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems scattering theory has to be applied for a quantitative interpretation of the measurements most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation in all studied examples a quantitative agreement between experiment and theory is achieved to this end it is necessary however to take absorption and imperfect coupling into account concepts that were ignored in most previous theoretical investigations classical phase space signatures of scattering are being examined in a small number of experiments

on kahler einstein metrics on certain kahler manifolds with c1 m 0 on demontre qu il existe une metrique de kahler einstein sur une hypersurface de fermat a m dimensions de degre superieur a m 1

on the spectrum of weighted laplacian operator and its application to uniqueness of kahler einstein metrics the purpose of this paper is to provide a new proof of bando mabuchi s uniqueness theorem of kahler einstein metrics on fano manifolds based on the convexity of ding functional on chen s weak mathcal c 1 bar 1 geodesic without using any further regularities unlike the smooth case the lack of regularities on the geodesic forbids us to use futaki s spectral formula of the weighed laplacian operator directly however we can use smooth epsilon geodesics to approximate the weak one then prove that a sequence of eigenfunctions will converge into the first eigenspace of the weighted laplacian operator

estimating a green s function from field field correlations in a random medium traditional imaging methods use coherent signals as data here we discuss recent developments in imaging that aim at exploiting as data incoherent noisy signals that are not associated with well defined arrival times indeed signal constituents that in a classical setting may be regarded as noise may contain important information about the medium to be imaged we show how it is possible to use the statistics of such noisy signals specifically the second order statistics for imaging we consider two particular situations first the estimation of an empirical green s function from noisy signals which can subsequently be used in imaging second the localization of a cluster of random sources from noisy signals passive imaging the analysis presented here is based on assuming a remote sensing scaling and the paraxial approximation and it uses in part the results set forth in papanicolaou ryzhik and solna siam j appl math 64 2004 pp 1133 1155 that relate to time reversal statistical

green s function estimation using secondary sources in a shallow water environment this work provides a new way to measure the green s function between two points in an acoustic channel without emitting a pulse by any of the two points the green s function between a and b is obtained from a set of secondary sources in the guide by averaging either the correlation or the convolution of the signals received in a and b a theoretical approach based on mode propagation in a monochromatic regime is presented results are then extended to the time domain estimation of the green s function is performed numerically in a range independent and a range dependent environment application to discreet acoustic communications is discussed

removal of surface related wave phenomena the marine case removal of the effects of the free surface from seismic reflection data is an essential preprocessing step before prestack migration the problem can be formulated by means of rayleigh s reciprocity theorem which leads to an integral equation of the second kind for the desired pressure field that does not include these free surface effects this integral equation can be solved numerically both in the spatial domain and in the double radon domain solving the integral equation in the double radon domain has the advantage of reducing the computation time significantly since the kernel of the integral equation becomes dominant diagonally two methods are proposed to solve the integral equation direct matrix inversion and a recursive subtraction of the free surface multiples using a neumann series both methods have been developed and tested on a synthetic data set which was computed with the help of an independent forward modeling scheme

wave equation based seismic illumination analysis we present a wave equation based method for seismic illumination analysis a one way wave equation based generalized screen propagator is used to extrapolate the wavefields from sources and receivers to the subsurface target a local plane wave analysis is used at the target to calculate localized directionalenergyfluxesforbothsourceandreceiver wavefields we construct an illumination matrix using these energy fluxes to quantify the target illumination conditions the target geometry information is used to manipulate the illumination matrix and generate different types of illumination measures the wave equation based approach can properly handle forward multiple scattering phenomena including focusing defocusing diffraction and interference effects itcanbedirectlyappliedtocomplexvelocitymodels velocity model smoothing and fresnel zone smoothing are not required different illumination measurements derived from this method can be applied to target oriented or volumetric illumination analyses this new method is flexible and practical for illumination analysis in complex 2d and 3d velocity models with nontrivial acquisition and target

a simple and exact acoustic wavefield modeling code for data processing imaging and interferometry applications improvements in industrial seismic seismological acoustic or interferometric theory and applications often result in quite subtle changes in sound quality seismic images or information which are nevertheless crucial for improved interpretation or experience when evaluating new theories and algorithms using synthetic data an important aspect of related researchisthereforethat numerical errors due towavefield modeling are reduced to a minimum we present a new matlab code based on the foldy method that models theoretically exact direct and scattered parts of a wavefield its main advantage lies in the fact that while all multiple scattering interactions aretakenintoaccount unlikefinite difference or finite element methods numerical dispersion errors are avoided the method is therefore ideal for testing new theory in industrial seismics seismology acoustics and in wavefield interferometry in particular because the latter is particularly sensitive to the dynamics of scattering interactions we present the theory behind the foldy acoustic modeling method and provide examples of its implementation we also benchmark the code against a good finite difference code because our foldy code was written and optimized to test new theory in seismic interferometry examples of its application to seismicinterferometryarealsopresented showing its validity and importance when exact modeling results are needed

k β and k nearly uniformly convex banach spaces vol 162 no 2 1991 k and k nearly uniformly convex banach spaces denka kutzarova different uniform geometrical properties have been defined between the uniform convexity and the reflexivity of banach spaces in the present paper we introduce other properties of this type namely k and k nearly uniform convexity the definitions as well as some of the results presented here are announced in 7 sullivan 24 has defined k uniformly rotund banach spaces which by a suggestion of davis are all superreflexive fan and glicksberg 1 have introduced fully k convex banach spaces let x1 xk 1 be vectors in a banach space x the k dimensional volume enclosed by x1 xk 1 is given by v x1 x2 xk 1

radon nikodym property for the projective tensor product of kothe function spaces abstract let e be an order continuous kothe function space or an order continuous banach lattice and x be a dual banach space then e x the projective tensor product of e and x has the radon nikodym property if and only if both e and x do

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

green s function for migration continuous recording geometry analytical formulas are derived to give the point scatterer responses for the zero offset and nonzero offset migration operators these formulas are derived under the far field approximation for a continuous distribution of sources and receivers and are denoted as migration green s functions by specifying a homogeneous velocity model with irregular layers these green s functions can be used to quickly compute the synthetic migrated sections without having to compute the modeled data thus these formulas provide a fundamental understanding of migration artifacts and their relationship to the image point location and source receiver configuration this understanding lays the foundation for the next step elimination of these artifacts by migration deconvolution

virtual reflector representation theorem acoustic medium the virtual reflector method simulates new seismic signals by processing traces recorded by a plurality of sources and receivers the approach is based on the crossconvolution of the recorded signals and makes it possible to obtain the green s function of virtual reflected signals as if in the position of the receivers or sources there were a reflector even if said reflector is not present this letter presents the virtual reflector theory based on the kirchhoff integral representation theorem for wave propagation in an acoustic medium with and without boundary and a generalization to variable reflection coefficients for scattered wavefields

von neumann jordan constant of absolute normalized norms on c2 abstract we determine and estimate the von neumann jordan constant of absolute normalized norms on c 2 by means of their corresponding continuous convex functions on 0 1 this provides many new interesting examples including those of non lp type as well as some previous ones it is also shown that all such norms are uniformly non square except l1 and l norms

acoustic daylight imaging via spectral factorization helioseismology and reservoir monitoring the acoustic time history of the sun s surface is a stochastic t x y cube of information helioseismologists cross correlate these noise traces to produce impulse response seismograms providing the proof of concept for a long standing geophysical conjecture we pack the x y mesh of time series into a single super long one dimensional time series we apply kolmogoroff spectral factorization to the super trace unpack and findthe multidimensional acoustic impulse response of the sun state of the art seismic exploration recording equipment offers tens of thousands of channels and permanent recording installations are becoming economically realistic helioseismology therefore provides a conceptual prototype for using natural noises for continuous reservoir monitoring

modeling of wave propagation in inhomogeneous media we present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time reversal invariance and reciprocity in generally inhomogeneous media the approach relies on a representation theorem of the wave equation to express the green function between points in the interior as an integral over the response in those points due to sources on a surface surrounding the medium following a predictable initial computational effort green s functions between arbitrary points in the medium can be computed as needed using a simple cross correlation algorithm

one channel time reversal in chaotic cavities theoretical limits one channel time reversal experiments in closed chaotic cavities produce excellent but not perfect time reversed focusing this paper investigates such experiments by a simple eigenmode analysis of the system it shows that the process is even for long reversed signals subject to an information loss during recording and re emission which prevents perfect time reversal this fact can be expressed by a simple equation called the cavity equation which states that the signal of a one channel time reversal is equal to the signal of a perfect time reversal after convolution with the backscattering impulse response of the reversal point i e from this point to this point the latter convolution describes the introduction of the loss of information furthermore arguments are presented suggesting that one third of the total energy of the time reversed wave field is actually contained in the refocusing wavefront the predictions are verified by numerical finite difference time domain simulations

monotonicity properties in banach spaces via sublinear operators and corrigendum to rotundity properties in banach spaces via sublinear operators nonlinear analysis 64 2006 1171 1188 abstract various kinds of monotone points namely lower and upper strictly monotone lower and upper locally uniformly monotone points are studied in the space d e s generated by a kothe space e and a sublinear operator s defined on a banach lattice x and with values in e some results on global monotonicity properties are easily deduced from those results interpretations of the result in three different classes of the space d e s are given at the end a small corrigendum to our paper rotundity properties in banach spaces via sublinear operators published in nonlinear analysis 64 2006 1171 1188 is given

on the james constant and b convexity of cesaro and cesaro orlicz sequence spaces abstract the classical james constant and the nth james constants which are measure of b convexity for the cesaro sequence spaces ces p and the cesaro orlicz sequence spaces ces m are calculated these investigations show that ces p ces m are not uniformly non square and even they are not b convex therefore the classical cesaro sequence spaces ces p are natural examples of reflexive spaces which are not b convex moreover the james constant for the two dimensional cesaro space ces 2 2 is calculated

cancellation of spurious arrivals in green s function extraction and the generalized optical theorem the extraction of the green s function by cross correlation of waves recorded at two receivers nowadays finds much application we show that for an arbitrary small scatterer the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position this constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise after integration over a complete source aperture this puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem this work constitutes an alternative derivation of this theorem when the source aperture is incomplete the spurious arrival is not canceled and could be misinterpreted to be part of the green s function we give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves the spurious waves can thus potentially be used to better constrain the medium

determination of effective brain connectivity from functional connectivity using propagator based interferometry and neural field theory with application to the corticothalamic system it is shown how to compute both direct and total effective connection matrices decms and tecms which embody the strengths of neural connections between regions from correlation based functional cms using propagator based interferometry a method that stems from geophysics and acoustics coupled with the recent identification of decms and tecms with bare and dressed propagators respectively the approach incorporates excitatory and inhibitory connections multiple structures and populations and measurement effects the propagator is found for a generalized scalar wave equation derived from neural field theory and expressed in terms of neural activity correlations and covariances and wave damping rates it is then related to correlation matrices that are commonly used to express functional and effective connectivities in the brain the results are illustrated in analytically tractable test cases

the reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem by analyzing correlation type reciprocity theorems for wavefields in perturbed media it is shown that the correlation type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem this reciprocity theorem in contrast to the generalized optical theorem allows for inhomogeneous background properties and does not make use of a far field condition this theorem specializes to the generalized optical theorem when considering a finite size scatterer embedded in a homogeneous background medium and when utilizing the far field condition moreover it is shown that the reciprocity theorem for the scattered field is responsible for the cancellation of non physical spurious arrivals in seismic interferometry and as such provides the mathematical description of such arrivals even though here only acoustic waves are treated the presented treatment is not limited to such wavefields and can be generalized to general wavefields therefore this work provides the framework for deriving equivalents of the generalized optical theorem for general wavefields

source receiver wave field interferometry correlation or convolution of recordings of diffuse fields at a pair of locations have been shown to result in estimates of the green s function between the two locations variously referred to as wave field or seismic interferometry in different fields of research green s functions can thus be constructed between either pairs of receivers or pairs of energy sources proofs of these results rely on representation theorems we show how to derive three acoustic and elastic representation theorems that unify existing correlational and convolutional approaches we thus derive three forms of interferometry that provide green s functions on source to receiver paths using only energy that has propagated from surrounding sources or to surrounding receivers the three forms correspond to three possible canonical geometries we thus allow interferometric theory and methods to be applied to commonly used source receiver configurations

q least squares reverse time migration with viscoacoustic deblurring filters abstractviscoacoustic least squares reverse time migration also denoted as q lsrtm linearly inverts for the subsurface reflectivity model from lossy data compared with conventional migration methods it can compensate for the amplitude loss in the migrated images due to strong subsurface attenuation and can produce reflectors that are accurately positioned in depth however the adjoint q propagators used for backward propagating the residual data are also attenuative thus the inverted images from q lsrtm with a small number of iterations are often observed to have lower resolution when compared with the benchmark acoustic lsrtm images from acoustic data to increase the resolution and accelerate the convergence of q lsrtm we used viscoacoustic deblurring filters as a preconditioner for q lsrtm these filters can be estimated by matching a simulated migration image to its reference reflectivity model numerical tests on synthetic and field data demonstrate that q lsrtm combined with viscoacoustic de

a higher order energy conserving parabolic equqation for range dependent ocean depth sound speed and density outgoing solutions of the wave equation including parabolic equation pe and normal mode solutions are usually formulated so that pressure is continuous with range for range dependent problems the accuracy of normal mode solutions has been improved by conserving energy rather than maintaining continuity of pressure porter et al the problem of energy conservation in one way equations j acoust soc am 89 1058 1067 1991 this approach is applied to derive a higher order energy conserving pe that provides improved accuracy for problems involving large ocean bottom slopes and large range and depth variations in sound speed and density a special numerical approach and complex pade coefficients are applied to suppress gibbs oscillations the back propagated half space field an improved pe starter is applied to handle wide propagation angles reference solutions generated with a complex ray model and with the rotated pe are used for comparison

generalized reaction principles and reciprocity theorems for the wave equations and the relationship between the time advanced and time retarded fields generalized reaction principles and generalized reciprocity theorems for the scalar and vector wave equations are derived it is shown that the reaction principles of rumsey phys rev 9 4 1483 1491 1954 and the reciprocity theorems of welsh ire trans antennas propag 8 1 68 73 1960 are special cases of these generalized reaction principles and generalized reciprocity theorems the generalized reciprocity theorems are cast in terms of the time retarded fields only as well as in terms of the time retarded and time advanced fields it is shown that the advanced fields are an improper solution of the wave equations subject to the proper sommerfeld radiation boundary conditions at infinity a relationship between the time advanced and time retarded fields is derived