direct multichannel predictive deconvolution the levinson principle generally can be used to compute recursively the solution of linear equations it can also be used to update the error terms directly this is used to do single channel deconvolution directly on seismic data without computing or applying a digital filter multichannel predictive deconvolution is used for seismic multiple attenuation in a standard procedure the prediction error filter matrices are computed with a levinson recursive algorithm using a covariance matrix of the input data the filtered output is the prediction errors or the nonpredictable part of the data starting with the classical levinson recursion wehave derived new algorithms for direct recursive calculationof the prediction errors without computing the data covariance matrix or computing the prediction error filters one algorithm generates recursively the one step forward and backward predic tion errors and the l step forward prediction error computing only the filter matrices with the highest index a numeri

a general approach for obtaining joint representations in signal analysis i characteristic function operator method a general approach for obtaining joint representations for arbitrary physical quantities is presented the characteristic function operator method of moyal 1949 and ville 1960 and generalized by cohen 1966 1976 and scully and cohen 1987 for the time frequency case is developed for arbitrary variables

root mean square velocities and recovery of the acoustic impedance the loss of low frequency information in reflection seismograms causes serious difficulties when attempting to generate a full band impedance profile information about the low frequency velocity structure is available from rms stacking velocities we show how rms velocities can be inverted with additional point velocity constraints if they are available to construct either smooth or blocky velocity structures backus gilbert averages of the constructed velocity are then autoregressive solutions for recovering a full band reflectivity from band limited seismograms our final result is therefore a full band acoustic impedance which is consistent with the seismic data section stacking velocities and available point constraints

applications of high resolution time frequency transforms to attenuation estimation abstractattenuation estimates quantify the loss of energy of propagating seismic waves due to anelastic processes it is often carried out in the frequency domain the most well known methods for attenuation estimation such as the spectral ratio and frequency shift methods compare spectral shapes of waveforms along a given raypath they require broad spectra such as those obtained with the fourier transform and the continuous wavelet transform these methods are incompatible with high resolution time frequency transforms which drastically localize time frequency information on the other hand these transforms indicate stronger resistance to noise and can be used in combination with the peak frequency method to estimate attenuation we have applied high resolution transforms namely the synchrosqueezing transform basis pursuit and complete ensemble empirical mode decomposition to a synthetic wedge example and two seismic data set examples a seismic reflection profile and a vertical seismic profile

robust wavelet estimation and blind deconvolution of noisy surface seismics robust blind deconvolution is a challenging problem particularly if the bandwidth of the seismic wavelet is narrow to very narrow that is if the wavelet bandwidth is similar to its principal frequency the main problem is to estimate the phase of the wavelet with sufficient accuracy the mutual information rate is a general purpose criterion to measure whiteness using statistics of all orders we modified this criterion to measure robustly the amplitude and phase spectrum of the wavelet in the presence of noise no minimum phase assumptions were made after wavelet estimation we obtained an optimal deconvolution output using wiener filtering the new procedure performs well even for very band limited data and it produces frequency dependent phase estimates

seismic sparse layer reflectivity inversion using basis pursuit decomposition a basis pursuit inversion of seismic reflection data for reflection coefficients is introduced as an alternative method of incorporating a priori information in the seismic inversion process the inversion is accomplished by building a dictionary of functions representing reflectivity patterns and constituting the seismic trace as a superposition of these patterns basis pursuit decomposition finds a sparse number of reflection responses that sum to form the seismic trace when the dictionary of functions is chosen to be a wedge model of reflection coefficient pairs convolved with the seismic wavelet the resulting reflectivity inversion is a sparse layer inversion rather than a sparse spike inversion synthetic tests suggest that a sparse layer inversion using basis pursuit can better resolve thin beds than a comparable sparse spike inversion application to field data indicates that sparse layer inversion results in the potentially improved detectability and resolution of some thin layers and reveals a

lpc distance measures and statistical tests with particular reference to the likelihood ratio several lpc distance measures and statistical tests have been proposed for use in speech processing the most popular of which is itakura s log likelihood ratio statistic and some simple variants thereof in this paper it is shown that these statistics share some undesirable properties it is argued that there are more tractable and more sensitive measures available including other relevant likelihood ratio statistics it is also shown that when itakura s measure is used to compare two estimated lpc vectors it is not the log likelihood ratio at all and the true likelihood ratio for these conditions is derived

estimating the statistical bandwidth of a time series summary in many time series and signal processing applications such as spectral estimation signal to noise estimation and frequency response estimation it is imperative to have a good estimate of the bandwidth of the time series in many scientific applications deconvolution is carried out over the signal dominated part of the spectrum resulting in a spectrum which is dominantly unimodal and hence a technique like that used for smoothing windows can be used to define the statistical bandwidth of the data this paper demonstrates using bandwidths and data lengths of interest in seismic data investigations that the naive estimator of data bandwidths using an untapered autocovariance is extremely biased a method for removing the bias is found and its success demonstrated on synthetic and real data if the tapered sample autocovariance function is used in the estimator then the best truncation point corresponds to a ratio of smoothing window bandwidth to data bandwidth in the range 02 025 well below the recommended upper bound for spectrum estimation of 0 5

entropy guided deconvolution the day to day application of minimum entropy deconvolution has rarely lived up to expectations based on a few of the first selected examples this appears to be the result of a the multimaxima nature of the varimax function or other similar nonlinear norms and b the excessive sensitivity of the estimated filter to the probability distribution of the underlying random series as the distribution approaches gaussian the variance of the filter coefficients becomes unbounded the alternative strategy proposed consists of solving for the inverse operator as a sequence of two term operators each having an independently determined lag the amplitude and sign of the operator coefficient are estimated by least squares the discrimination between minimum or maximum phase is determined by the varimax criterion

lattice boltzmann method for the convection diffusion equation in curvilinear coordinate systems a lattice boltzmann method for simulating convection and diffusion using a curvilinear grid system is presented the proposed method does not require an interpolation or coarse graining procedure and thus maintains the algorithmic simplicity of the original lattice boltzmann scheme the lattice boltzmann scheme is based on uniformly distributed lattice points in a transformed coordinate system and the apparent anisotropy of diffusion that arises due to the coordinate transformation is properly handled using the multiple relaxation time collision operator an asymptotic analysis of the lattice boltzmann equation shows that the proposed method appropriately reproduces the transformed convection diffusion equation several specific problems are numerically analyzed in order to validate the proposed method including an axially symmetric two dimensional problem in which the diffusion flux at an oblate hemispheroid is simulated using a body fitted orthogonal curvilinear grid system

the deconvolution of phase shifted wavelets the assumption that a seismogram can be represented as a convolution of a source wavelet with a set of real impulses breaks down when the wavelet is phase shifted upon reflection from a boundary for plane waves and plane layers this effect occurs only for wide angle supercritical reflections but it may also occur in normal incidence seismograms when either the impinging wavefront or the reflective boundary is curved we show that seismograms containing time displaced phase shifted replications of the source wavelet can be deconvolved to recover both the amplitude and phase of the reflectivity coefficients the method begins by writing the analytic seismogram as the convolution of a complex reflectivity function with an analytic source wavelet linear inverse theory is then used to carry out the deconvolution

could the processed seismic wavelet be simpler than we think j p lindsey 1988 in a clearly written short piece opens an old question which concerns the analytic properties of seismic wavelets this well conceived study concludes that most of the roots of a seismic wavelet as expressed by its z transform representation lie on or are very near the unit circle the present discussion does not seek to characterize the form of all seismic wavelets but only many if not most of those which have been processed with deconvolutions or inversion type operators to have reduced length broadened bandwidth and some desirable phase property for such wavelets despite the diversity by which they are obtained remarkably simple operations having very few parameters can be extremely effective as a case in point constant phase rotations appear to carry such wavelets to zero phase symmetric form to a very good approximation i start with empirical attributes which appear to characterize most processed seismic wavelets such wavelets tend to be of 40 100 ms duration with a

extensive analysis of the lattice boltzmann method on shifted stencils standard lattice boltzmann methods lbms are based on a symmetric discretization of the phase space which amounts to study the evolution of particle distribution functions pdfs in a reference frame at rest this choice induces a number of limitations when the simulated flow speed gets closer to the sound speed such as velocity dependent transport coefficients the latter issue is usually referred to as a galilean invariance defect to restore the galilean invariance of lbms it was proposed to study the evolution of pdfs in a comoving reference frame by relying on asymmetric shifted lattices n frapolli s s chikatamarla and i v karlin phys rev lett 117 010604 2016 from the numerical viewpoint this corresponds to overcoming the rather restrictive courant friedrichs lewy conditions on standard lbms and modeling compressible flows while keeping memory consumption and processing costs to a minimum therefore using the standard first neighbor stencils in the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions edfs and collision models thanks to them it is possible to 1 better understand the effect of this solution on both physics and stability 2 assess its viability as a way to extend the validity range of lbms and 3 quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path the results clearly show that in theory the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity furthermore just like the zero mach flow for the standard stencils it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties in addition a detailed analysis of the obtained results shows that the properties of different collision models and edfs remain unchanged under the shift of stencil in other words by introducing a velocity shift in the stencil the optimal operating point in terms of physics and numerics will also be shifted by the same vector regardless of the edf or collision model considered eventually while limited to the d2q9 stencil with the nine possible first neighbor shifts the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner

time scale energy density functions scale like frequency is a physical characteristic of a signal to measure the scale content of a signal the signal must be appropriately transformed a theory for joint time scale energy density functions is presented and a method for generating such functions for any signal is given examples for synthetic signals and real data are presented the theory and method can be extended to arbitrary joint densities of any variables for example frequency and scale

a unified approach to the stft tfds and instantaneous frequency cohen s class of time frequency representations tfrs is reformulated into a discrete time discrete frequency computer implementable form it is shown how in this form many of the properties of the continuous time continuous frequency formulation are either lost or altered intuitions applicable in the continuous time case do not necessarily carry over to the discrete time case examined the properties of the discrete variable formulation examined are the presence and form of cross terms instantaneous frequency estimation and relationships between cohen s class of tfrs a parameterized class of distributions which is a blending between the short time fourier transform stft and the wigner ville distribution the two main conclusions are that all tfrs of cohen s class implementable in the given form which includes all commonly used tfrs possess cross terms and that instantaneous frequency estimation using periodic moments of these tfrs is purposeless since simpler methods obtain the same result

linear modeling and the coherence function in this paper a tutorial introduction to the magnitude squared ms coherence function and its relation to linear modeling is interleaved with new methods for characterizing bidirectional and unidirectional linear association between two time series a new method for characterizing bidirectional linear association is based on the new concept of an ms coherence sequence which is the inverse z transform of the ms coherence function the ms coherence function is approximated as a single real valued ratio of polynominals in z the ratio is determined by a matrix equation whose entries are convolutions of correlation functions solutions for the corresponding ms coherence parameters employ an eigenvalue eigenvector decomposition the algorithm is compared to a traditional periodogram based method using computer simulations the computer simulations also demonstrate the effects of parameter overdetermination and overordering the sensitivity of the matrix equations for the computer simulations is computed via the numerical linear algebra concept of condition number

nonstationary spectral analysis based on time frequency operator symbols and underspread approximations we present a unified framework for time varying or time frequency tf spectra of nonstationary random processes in terms of tf operator symbols we provide axiomatic definitions and tf operator symbol formulations for two broad classes of tf spectra one of which is new these classes contain all major existing tf spectra such as the wigner ville evolutionary instantaneous power and physical spectrum our subsequent analysis focuses on the practically important case of nonstationary processes with negligible high lag tf correlations so called underspread processes we demonstrate that for underspread processes all tf spectra yield effectively identical results and satisfy several desirable properties at least approximately we also show that gabor frames provide approximate karhunen loeve kl functions of underspread processes and tf spectra provide a corresponding approximate kl spectrum finally we formulate simple approximate input output relations for the tf spectra of underspread processes that are passed through underspread linear time varying systems all approximations are substantiated mathematically by upper bounds on the associated approximation errors our results establish a tf calculus for the second order analysis and time varying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes

simulation of micro and nano scale flows via the lattice boltzmann method abstract we use the lattice boltzmann method lbm for analysis of high and moderate knudsen number phenomena simulation results are presented for microscale couette and poiseuille flows the slip velocity nonlinear pressure drop and mass flow rate are compared with previous numerical results and or experimental data the knudsen minimum is successfully predicted for the first time within the lbm framework these results validate the usage of the lbm based commercial arbitrary geometry code powerflow for simulating nanoscale problems

recovery of the acoustic impedance from reflection seismograms this paper examines the problem of recovering the acoustic impedance from a band limited normal incidence reflection seismogram the convolutional model for the seismogram is adopted at the outset and it is therefore required that initial processing has removed multiples and recovered true amplitudes as well as possible in the first portion of the paper we investigate the effect of substituting the deconvolved seismic trace that is the band limited version of the reflectivity function into the standard recursion formula for the acoustic impedance the formalism of linear inverse theory is used to show that the logarithm of the normalized acoustic impedance estimated from the deconvolved seismogram is approximately an average of the true logarithm of the impedance moreover the averaging function is identical to that used in deconvolving the initial seismogram the advantage of these averages is that they are unique their disadvantage is that low frequency information which is crucial to making a g

principal domains of the trispectrum signal bandwidth and implications for deconvolution fourth order statistics can be useful in many signal processing applications offering advantages over or supplementing second order statistical techniques one reason is that fourth order statistics can discriminate between non gaussian signals and gaussian noise another is that fourth order statistics contain phase information whereas second order statistics do not in the continuing development of the mathematical properties of fourth order statistics several researchers have derived existence conditions and definitions for the unaliased and aliased principal domains of the discrete trispectrum which is significantly more complex than the power or energy spectrum the consistencies and inconsistencies of these results are presented and resolved in this paper the most flexible definitions give four individual principal domains for the discrete trispectrum two unaliased and two aliased the most useful combinations are those that combine the two unaliased domains together and the two aliased domains together which can be done easily from the four individual domains the relationship between the individual trispectral domains and signal bandwidth is important when using the fourth order statistic for applications because they have particular properties that can be detrimental to some deconvolution algorithms the reasons for this as well as the validity of proposed solutions to this problem are explained by the trispectral structure and its origins

nonminimum phase wavelet estimation using higher order statistics seismic data are often represented by the well known convolutional model batchmode documentclass fleqn 10pt legalpaper article usepackage amssymb usepackage amsfonts usepackage amsmath pagestyle empty begin document s t w t otimes r t n t end document 1 where w t denotes the seismic wavelet r t the reflectivity series and n t additive noise the goal of seismic deconvolution is to design a filter f t capable of removing or compressing the wavelet to understand the effect of removing the wavelet from the seismogram convolve both sides of equation 1 with the filter batchmode documentclass fleqn 10pt legalpaper article usepackage amssymb usepackage amsfonts usepackage amsmath pagestyle empty begin document f t otimes s t f t otimes w t otimes r t f t otimes n t end document 2 the last equation says that deconvolution can be successfully carried out if and only if two conditions are satisfied batchmode documentclass fleqn 10pt legalpaper article usepackage amssymb usepackage amsfonts usepackage amsmath pagestyle empty begin document f t otimes w t approx delta t end document 3 batchmode documentclass fleqn 10pt legalpaper article usepackage amssymb usepackage amsfonts usepackage amsmath pagestyle empty begin document f t otimes n t e t approx 0 end document 4 when these two conditions are simultaneously satisfied one can write batchmode documentclass fleqn 10pt legalpaper article usepackage amssymb usepackage amsfonts usepackage amsmath pagestyle empty begin document f t otimes s t approx r t end document 5 equations 3 and 4 define a filter design problem however in order to design f t one must first know the wavelet w t unfortunately in most exploration scenarios w t is not known and therefore needs to be estimated this article focuses on estimating a wavelet with unknown amplitude and phase spectrum explicitly the problem has one noisy observation the seismogram and two unknowns the reflectivity and the seismic wavelet we will examine how under certain conditions the stochastic nature of the reflectivity sequence can be exploited to estimate the wavelet stochastic wavelet estimation is often divided into two distinct problems problem 1 estimation under proper assumptions we can compute a functional of the wavelet directly from s t the observed data the functional must be capable of reducing the unknown random r t to a tractable quantity it is also desirable to have a functional that annihilates the additive random noise n t in mathematical terms we seek an operator f such that batchmode documentclass fleqn 10pt legalpaper article usepackage amssymb usepackage amsfonts usepackage amsmath pagestyle empty begin document f s t k r bullet g w t end document 6 where k r is a constant and g another functional to determine problem 2 spectral factorization this can be summarized as given an estimate of g w t how do we estimate w t the latter leads to a new problem

sparse reflectivity inversion for nonstationary seismic data abstractconventional reflectivity inversion methods are based on a stationary convolution model and theoretically require stationary seismic traces as input i e those free of attenuation and dispersion effects reflectivity inversion for nonstationary data which is typical for field surveys requires us to first compensate for the earth s q filtering effects by inverse q filtering however the attenuation compensation for inverse q filtering is inherently unstable and offers no perfect solution thus we presented a sparse reflectivity inversion method for nonstationary seismic data we referred to this method as nonstationary sparse reflectivity inversion nsri it makes the novel contribution of avoiding intrinsic instability associated with inverse q filtering by integrating the earth s q filtering operator into the stationary convolution model nsri also avoids time variant wavelets that are typically required in time variant deconvolution although nsri is initially designed for nonstationary

transition kernels for bilinear time frequency distributions the author proposes a sequence of time frequency signal representations which offer a continuous transition from time smoothed pseudo wigner ville distributions pwvd to a specified class of positive representations this allows the selection of a representation which offers the desired tradeoff between the inherent localization properties of the pwvd and the lack of interference terms present in the class of positive representations a cause of some criticism of the method the sequence converges uniformly to the specified positive distribution

single channel nonstationary stochastic signal separation using linear time varying filters separability of signal mixtures given only one mixture observation is defined as the identification of the accuracy to which the signals can be separated the paper shows that when signals are separated using the generalized wiener filter the degree of separability can be deduced from the signal structure to identify this structure the processes are represented on an general spectral domain and a sufficient solution to the wiener filter is obtained the filter is composed of a term independent of the signal values corresponding to regions in the spectral domain where the desired signal components are not distorted by interfering noise components and a term dependent on the signal correlations corresponding to the region where components overlap an example of determining perfect separability of modulated random signals is given with application in radar and speech processing

positive time frequency distribution functions we demonstrate the existence of positive joint distributions of time and frequency for arbitrary signals a method is given to readily generate an infinite number of them for any signal general properties of these distribution functions are derived and specific examples for some common signals are presented

reconstruction of a sparse spike train from a portion of its spectrum and application to high resolution deconvolution an algorithm is proposed for the reconstruction of a sparse spike train from an incomplete set of its fourier components it is shown that as little as 20 25 percent of the fourier spectrum is sufficient in practice for a high quality reconstruction the method employs linear programming to minimize the l1 norm of the output because minimization of this norm favors solutions with isolated spikes given a wavelet this technique can be used to perform deconvolution of noisy seismograms when the desired output is a sparse spike series relative reliability of the data is assessed in the frequency domain and only the reliable spectral data are included in the calculation of the spike series equations for the unknown spike amplitudes are solved to an accuracy compatible with the uncertainties in the reliable data in examples with 10 percent random noise the output is superior to that obtained using conventional least squares techniques

cross spectral analysis of nonstationary processes consideration is given to the generalization of stationary cross spectral analysis methods to a class of nonstationary processes specifically the class of semistationary finite energy processes possessing sample functions that are of finite energy almost surely a new quantity called the time frequency coherence tfc is defined and it is demonstrated that its properties are analogous to those possessed by the stationary coherence function the problem of estimating the tfc by using elements of l cohen s 1966 class of joint time frequency representations is investigated it is shown that the only admissible estimators are those based on the class of time frequency smoothed periodograms thus the familiar procedure of segmentation and smoothed short time fourier analysis cannot be improved upon within the framework considered by the use of the higher resolution nonparametric time frequency methods procedures for selection of the appropriate estimators and a possible application are suggested

bandwidth enhancement inverse q filtering or time varying wiener deconvolution abstractdispersion and attenuation corrections can improve the resolution of seismic data this significantly facilitates interpretation in principle inverse q filtering and the time varying wiener deconvolution can achieve this inverse q filtering is a deterministic process that requires knowledge of the quality factor q whereas the time varying wiener deconvolution is a statistical approach based on the estimation of the nonstationary propagating wavelet dispersion corrections based on phase only inverse q filtering is an inherently stable method that is robust in the presence of noise attenuation corrections via amplitude only inverse q filtering on the other hand is likely to lead to noise amplification as well as bandwidth enhancement dispersion corrections via the time varying wiener deconvolution are challenging because these require estimation of a nonstationary frequency dependent nonminimum phase wavelet fortunately attenuation corrections via the wiener deconvolution need only esti

dynamic estimation of reflectivity by minimum delay seismic trace decomposition abstractspiking deconvolution corrects for the effect of the seismic wavelet assumed to be minimum delay by applying an inverse filter to the seismic trace to get an estimate of reflectivity to compensate for propagation and absorption effects one may use time varying deconvolution in which a different inverse filter is computed and applied for each output sample position we modified this procedure by estimating a minimum delay wavelet for each time sample position of the seismic trace this gives a decomposition of the seismic trace as a sum of minimum delay wavelets each multiplied by a reflectivity coefficient the data vector is equal to a lower triangular wavelet matrix with element 1 on the diagonal multiplied by the seismic reflectivity vector recursive solution of this equation provides an estimate of reflectivity the reflectivity estimation is a single trace process that is sensitive to nonwhite noise and it does not take into account lateral continuity of reflections therefore we h

multiple relaxation time lattice boltzmann model for the convection and anisotropic diffusion equation a lattice boltzmann model with a multiple relaxation time mrt collision operator for the convection diffusion equation is presented the model uses seven discrete velocities in three dimensions d3q7 model the off diagonal components of the relaxation time matrix which originate from the rotation of the principal axes enable us to take into account full anisotropy of diffusion an asymptotic analysis of the model equation with boundary rules for the dirichlet and neumann type specified flux conditions is carried out to show that the model is first and second order accurate in time and space respectively the results of the analysis are verified by several numerical examples it is also shown numerically that the error of the mrt model is less sensitive to the variation of the relaxation time coefficients than that of the classical bgk model in addition an alternative treatment for the neumann type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary

deconvolution bandwidth and the trispectrum abstract in the largest application area of time series analysis geophysical exploration the underlying innovations sequence is of primary interest and must be estimated this sequence is estimated by deconvolving the non gaussian noninvertible time series this involves estimation of a phase shift correction from the time series which can be carried out by maximizing the kurtosis of the series unfortunately the method is hampered by the fact that the time series is typically deficient in power in certain bands of frequencies band limited the consequences of this can be analyzed by studying the trispectrum the third of the polyspectra of the series this reveals two important results first we are able to easily appreciate why for certain types of band limitation kurtosis cannot be used to determine a phase correction second by looking at the inner and outer subvolumes of the support volume for the discrete parameter trispectrum we see that for the standard linear model the trispectrum is no

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

sparse multichannel blind deconvolution abstractwe developed a sparse multichannel blind deconvolution smbd method the method is a modification of the multichannel blind deconvolution technique often called euclid deconvolution in which the multichannel impulse response of the earth is estimated by solving an homogeneous system of equations classical euclid deconvolution is unstable in the presence of noise and requires the correct estimation of the length of the seismic wavelet the proposed method on the other hand can tolerate moderate levels of noise and does not require a priori knowledge of the length of the wavelet smbd solves the homogeneous system of equations arising in euclid deconvolution by imposing sparsity on the unknown multichannel impulse response trivial solutions to the aforementioned homogeneous system of equations are avoided by seeking sparse solutions on the unit sphere we tested smbd with synthetic and real data examples synthetic examples were used to judge the viability of the method in terms of noise we f

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

kinetic boundary conditions in the lattice boltzmann method derivation of the lattice boltzmann method from the continuous kinetic theory x he and l s luo phys rev e 55 r6333 1997 x shan and x he phys rev lett 80 65 1998 is extended in order to obtain boundary conditions for the method for the model of a diffusively reflecting moving solid wall the boundary condition for the discrete set of velocities is derived and the error of the discretization is estimated numerical results are presented which demonstrate convergence to the hydrodynamic limit in particular the knudsen layer in the kramers problem is reproduced correctly for small knudsen numbers

stochastic sparse spike deconvolution sparse spike deconvolution can be viewed as an inverse problem where the locations and amplitudes of a number of spikes reflectivity are estimated from noisy data seismic traces the main objective is to find the least number of spikes that when convolved with the available band limited seismicwaveletestimate fitthedatawithinagiventolerance errormisfit thedetectionofthespikes timelagsisahighly nonlinearoptimizationproblemthatcanbesolvedusingvery fastsimulatedannealingsa amplitudesareeasilyestimated using linear least squares at each sa iteration at this stage quadratic regularization is used to stabilize the solution to reduce its nonuniqueness and to provide meaningful reflectivitysequences thusavoidingtheneedtoconstrainthe spikes time lags and or amplitudes to force valid solutions impedanceconstraintsalsocanbeincludedatthisstage providing the low frequencies required to recover the acoustic impedance oneadvantageoftheproposedmethodoverother sparse spike deconvolution techniques is that the uncertaintyoftheobtainedsolutionscanbeestimatedstochastically further errorsinthephaseofthewaveletestimatearetolerated foranoptimumconstant phaseshiftisobtainedtocalibratetheeffectivewaveletthatispresentinthedata results using synthetic data including simulated data for the marmousi2 modelandfield 3d data show that physically meaningful high resolution sparse spike sections can be derived fromband limitednoisydata evenwhentheavailablewaveletestimateisinaccurate

bilinear time frequency representations new insights and properties an analysis of the interference terms of cohen class bilinear time frequency representations tfr of multicomponent signals is presented constraints for achieving new interference properties are derived imposing these interference time and interference frequency concentration constraints on a tfr guarantees that the tfr will be zero everywhere the signal s t is zero and the tfr will contain only those frequencies that occur in the signal thus these new constraints guarantee strong finite support in a tfr when these interference concentration properties are combined with interference attenuation tradeoffs between finite support the marginals and the interference properties are shown to be unavoidable the useful class of product kernels are considered and generalized further to allow tfr with potentially superior interference properties the interference frequency concentration and attenuation properties allow tfr with spectrogram like interference suppression but without the spectrogram s inherent time frequency resolution tradeoff other useful combinations of properties are discussed and analyzed and properties and tradeoffs are illustrated by examples

time varying spectral estimation using the instantaneous power spectrum ips the spectral content of time varying signals is examined using a modified version of the instantaneous power spectrum ips the short duration periodogram and the pseudo wigner ville distribution pwd have been used extensively to display the time varying spectral information a disadvantage of the periodogram is its inherently poor resolution due to the requirement of matching the resolution width to the spectral dynamics of the signal potential problems associated with pwd are spectral cross terms and an inability to resolve spectral components at the endpoints of the analysis segment a modified version of ips is shown to be less sensitive to these types of problems in addition ips can work with real valued signals sampled at the traditional nyquist rate

feature sets for nonstationary signals derived from moments of the singular value decomposition of cohen posch positive time frequency distributions this article presents a new method for determining the principal features of a nonstationary time series process based on the singular value decomposition svd of the cohen posch 1985 positive time frequency distribution this new method uses density functions derived from the svd singular vectors to generate moments that are associated with the principal features of the nonstationary process since the svd singular vectors are orthonormal the vectors whose elements are composed of the squared elements of the svd vectors are discrete density functions moments generated from these density functions are the principal features of the nonstationary time series process the main reason for determining features of a time series process is to characterize it by a few simple descriptors

efficient kinetic method for fluid simulation beyond the navier stokes equation we present a further theoretical extension to the kinetic theory based formulation of the lattice boltzmann method of shan j fluid mech 550 413 2006 in addition to the higher order projection of the equilibrium distribution function and a sufficiently accurate gauss hermite quadrature in the original formulation a regularization procedure is introduced in this paper this procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the galerkin sense using this formulation we construct a specific lattice boltzmann model that accurately incorporates up to third order hydrodynamic moments numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice boltzmann models so that fluid flows at finite knudsen number kn can be more quantitatively simulated results from force driven poiseuille flow simulations predict the knudsen s minimum and the asymptotic behavior of flow flux at large kn

time varying wavelet estimation and deconvolution by kurtosis maximization phase mismatches sometimes occur between final processedsectionsandzero phasesyntheticsbasedonwelllogs despite best efforts for controlled phase acquisition and processing the latter are often based on deterministic corrections derived from field measurements and physical laws a statisticalanalysisofthedatacanrevealwhetheratime varying nonzero phase is present this assumes that the data should be white with respect to all statistical orders after proper deterministic corrections have been applied kurtosis maximizationbyconstantphaserotationisastatisticalmethod that can reveal the phase of a seismic wavelet it is robust enough to detect time varying phase changes phase only corrections can then be applied by means of a time varying phase rotation alternatively amplitude and phase deconvolution can be achieved using time varying wiener filtering time varyingwaveletextractionanddeconvolutioncanalso be used as a data driven alternative to amplitude only inverse qdeconvolution

simulated annealing wavelet estimation via fourth order cumulant matching the fourth order cumulant matching method has been developed recently for estimating a mixed phase wavelet from a convolutional process matching between the trace cumulant and the wavelet moment is done in a minimum mean squared error sense under the assumption of a non gaussian stationary and statistically independent reflectivity series this leads to a highly nonlinear optimization problem usually solved by techniques that require a certain degree of linearization and that invariably converge to the minimum closest to the initial model alternatively we propose a hybrid strategy that makes use of a simulated annealing algorithm to provide reliability of the numerical solutions by reducing the risk of being trapped in local minima beyond the numerical aspect the reliability of the derived wavelets depends strongly on the amount of data available however by using a multidimensional taper to smooth the trace cumulant we show that the method can be used even in a trace by trace implementation which is very important from the point of view of stationarity and consistency we demonstrate the viability of the method under several reflectivity models finally we illustrate the hybrid strategy using marine and field real data examples the consistency of the results is very encouraging because the improved cumulant matching strategy we describe can be effectively used with a limited amount of data

linear stability and isotropy properties of athermal regularized lattice boltzmann methods the present work proposes a general methodology to study stability and isotropy properties of lattice boltzmann lb schemes as a first investigation such a methodology is applied to better understand these properties in the context of regularized approaches to this extent linear stability analyses of two dimensional models are proposed the standard bhatnagar gross krook collision model the original precollision regularization and the recursive regularized model where off equilibrium distributions are partially computed thanks to a recursive formula a systematic identification of the physical content carried by each lb mode is done by analyzing the eigenvectors of the linear systems stability results are then numerically confirmed by performing simulations of shear and acoustic waves this work allows drawing fair conclusions on the stability properties of each model in particular among the aforementioned models recursive regularization turns out to be the most stable one for the d2q9 lattice especially in the zero viscosity limit two major properties shared by every regularized model are highlighted 1 a mode filtering property and 2 an incorrect and broadly anisotropic dissipation rate of the modes carrying physical waves in under resolved conditions the first property is the main source of increased stability especially for the recursive regularization it is a direct consequence of the reconstruction of off equilibrium populations before each collision process decreasing the rank of the system of discrete equations the second property seems to be related to numerical errors directly induced by the equilibration of high order moments in such a case this property is likely to occur with any collision model that follows such a stabilization methodology

wavelet estimation revisited this article deals with the ubiquitous problem of wavelet estimation in essence the problem consists of estimating at best two unknowns from one equation in the seismic case as it is well known the model of the recorded seismic trace xt is generally formulated as a convolution xt wt rt where wt is the seismic source signature or wavelet and rt is the reflectivity series which is comprised of all primary and multiple reflections since in general we can assume that rt is white or nearly so the amplitude signature of wt may be estimated with some degree of confidence it is of course the phase of wt that presents the difficulty it turns out perhaps somewhat counterintuitively that except for rather special circumstances the phase of a signal uniquely determines the signal to within a scale factor the amplitude spectrum plays no part whatsoever we explore this further below no wonder then that the phase is the all important factor

autoregressive recovery of the acoustic impedance this paper presents a method of recovering the acoustic impedance from reflection seismograms using autoregressive ar modeling an approach originally applied to deconvolution by lines and clayton 1977 the algorithm which we describe is novel both in the manner in which the missing low and high frequency information is predicted and in the fact that the prediction may be constrained if acoustic impedance information is available the prediction of the low frequencies treats the missing data as a gap which extends from the low frequency cut off in the negative frequency band to the corresponding frequency in the positive frequency band the conjugate symmetry which governs the behavior of the spectrum in the band is taken into account in the prediction the missing high frequencies are predicted using a modified minimum entropy norm in the frequency domain both synthetic and field examples are presented and illustrate the robustness of the new ar algorithm under a variety of conditions the field e

a time varying wavelet extraction using local similarity abstractseismic wavelet extraction is an integral part of high resolution seismic analysis however most extraction methods ignore the time varying characteristic of wavelets introduced by attenuation scattering and other physical processes during propagation we have developed a time varying wavelet extraction method based on local similarity this method estimates the amplitude spectra by spectral modeling in the time frequency domain we estimated the phase of each spectrum in two steps first the phase range was estimated by the bispectrum of the high order cumulants and then the phase spectrum at every point was extracted with additional local similarity optimization the extracted nonstationary wavelet improved the resolution of the wavelet estimation in the adjacent layers we have determined the practicability and reliability of the proposed method using a numerical simulation and we have compared the results of this method with those of the adaptive segmentation method

automatic phase correction of common midpoint stacked data the residual wavelet on a processed seismic section is often not zero phase despite all efforts to make it so in this paper we adopt the convolutional model for the processed seismogram assume that the residual phase shift can be approximated by a frequency independent constant and use the varimax norm to generate an algorithm to estimate the residual phase directly application of our algorithm to reflectivities from well logs suggests that it should work in the majority of cases so long as the reflectivity is non gaussian an application of our algorithm to stacked data enhances the interpretability of the seismic section and leads to an improved match between the recovered relative acoustic impedance and a measured velocity log

mixed phase deconvolution we describe a new algorithm for mixed phase deconvolution it is valid only for pulses whose z transform has no zeros on the unit circle that is the amplitude spectrum cannot be zero for any frequency using the z transform of a discrete time signal and assuming that the signal has zeros inside the unit circle the inverse of its minimum delay component may be estimated by solving the extended yule walker eyw system of equations with the lag of the autocorrelation function acf on diagonal of the coefficient matrix this property of the solution of eyw equations is exploited to derive mixed phase inverse filters and their corresponding mixed phase pulses for different values of a suite of inverse filters is generated using the same acf to choose the best decomposition and its corresponding mixed phase inverse filter we have used the value of which gives the maximum value of the lp norm of the filtered signal the optimal value of does not seem to be very sensitive to the choice of norm

inverse q filtering by fourier transform although some attention has been paid to the idea that seismic migration is equivalent to a type of deconvolution of the spatial wavelet less thought has been given to the opposite perspective that deconvolution of the earth q filter might itself be equivalent to a form of migration the key point raised in this paper is that a dispersive 1 d backward propagation can form the basis of a number of different algorithms for inverse q filtering each of which is akin to a particular migration algorithm an especially efficient algorithm can be derived by means of a coordinate transformation equivalent to that in the stolt frequency wavenumber migration this fast algorithm valid for q constant with depth can be extended to accommodate depth variable q by cascading a series of constant q compensations as in cascaded migration by combining a cascaded phase compensation with a windowed approach to amplitude compensation we obtain an algorithm that is sufficiently efficient to be used routinely for pre

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

modified cohen lee time frequency distributions and instantaneous bandwidth of multicomponent signals cohen 1989 1995 has introduced and extensively studied and developed the concept of the instantaneous bandwidth of a signal specifically instantaneous bandwidth is interpreted as the spread in frequency about the instantaneous frequency which is itself interpreted as the average frequency at each time this view stems from a joint time frequency distribution tfd analysis of the signal where instantaneous frequency and instantaneous bandwidth are taken to be the first two conditional spectral moments respectively of the distribution however the traditional definition of instantaneous frequency namely as the derivative of the phase of the signal is not consistent with this interpretation and new definitions have therefore been proposed previously we show that similar problems arise with the cohen lee 1988 1989 instantaneous bandwidth of a signal and propose a new formulation for the instantaneous bandwidth that is consistent with its interpretation as the conditional standard deviation in frequency of a tfd we give the kernel constraints for a distribution to yield this new result which is a modification of the kernel proposed by cohen and lee these new kernel constraints yield a modified cohen lee tfd whose first two conditional moments are interpretable as the average frequency and bandwidth at each time respectively

kinetic lattice boltzmann method for microscale gas flows issues on boundary condition relaxation time and regularization it is well known that the navier stokes equations cannot adequately describe gas flows in the transition and free molecular regimes in these regimes the boltzmann equation be of kinetic theory is invoked to govern the flows however this equation cannot be solved easily either by analytical techniques or by numerical methods hence in order to efficiently maneuver around this equation for modeling microscale gas flows a kinetic lattice boltzmann method lbm has been introduced in recent years this method is regarded as a numerical approach for solving the be in discrete velocity space with gauss hermite quadrature in this paper a systematic description of the kinetic lbm including the lattice boltzmann equation the diffuse scattering boundary condition for gas surface interactions and definition of the relaxation time is provided to capture the nonlinear effects due to the high order moments and wall boundaries an effective relaxation time and a modified regularization procedure of the nonequilibrium part of the distribution function are further presented based on previous work guo et al j appl phys 99 074903 2006 shan et al j fluid mech 550 413 2006 the capability of the kinetic lbm of simulating microscale gas flows is illustrated based on the numerical investigations of micro couette and force driven poiseuille flows

evaluation of a lattice boltzmann method in a complex nanoflow in order to establish a cost effective strategy to simulate complex flows in continuum to slip and transitional regimes the present study assesses the performance of a lattice boltzmann method lbm formerly discussed by the present authors group niu et al phys rev e 76 036711 2007 this lbm is based on a diffuse scattering wall boundary condition a regularization procedure and an effective relaxation time associated with the knudsen number the present assessment is on its regularization procedure and third order truncated system based on the two dimensional twenty one discrete velocity d2q21 model for the cartesian lattices the test flow cases are force driven poiseuille flows the couette flows and a flow around a square cylinder situated in a nanochannel for producing the reference data of the square cylinder flow the molecular dynamics simulation using lennard jones potential is also performed although the flow profiles and the slip velocities of the poiseuille flows and the couette flows are more accurately predicted by the third order truncated system the general velocity profiles around the square cylinder are also well predicted by the second order truncated system based on the two dimensional nine discrete velocity d2q9 model it is also confirmed that without the regularization process the entire flow field prediction suffers unphysical momentum oscillations around the square cylinder