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

oscillation for second order nonlinear neutral delay difference equations in this paper we obtain sufficient conditions for the oscillation of all solutions of the second order nonlinear delay difference email protected a n d x n p nx g n a f n x s n 0 where dx n x n 1 x n is the forward difference operator p n is a sequence of nonnegative real numbers and a 1 is a quotient of positive odd integers our results extend and improve the known results in the literature an example that dwell up the advantage of our results is included

periodic solutions for nonlinear second order difference equations abstract this paper is devoted to introduce a new approach to investigate the existence of periodic solutions for nonlinear difference equations transforming a second order nonlinear difference equation on a finite discrete segment with periodic boundary conditions into a continuous system we obtain the existence conditions of periodic solutions of the equation the proof relies on coincidence degree theory and matrix theory without using green s function

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

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

sample size for testing differences in proportions for the paired sample design miettinen 1968 biometrics 24 339 352 presented an approximation for power and sample size for testing the differences between proportions in the matched pair case duffy 1984 biometrics 40 1005 1015 gave the exact power for this case and showed that miettinen s approximation tends to slightly overestimate the power or underestimate the sample size necessary for the design power a simple alternative approximation that is more conservative is presented here in many cases the sample size for the independent sample case provides a conservative approximation for the matched pair design

oscillation of certain second order nonlinear difference equations abstract in this paper we consider the second order nonlinear difference equation formula where y n y n 1 y n is the forward difference operator f c r r f is nondecreasing and uf u 0 as u 0 q n is a real sequence some new sufficient conditions for the oscillation of all solutions of 1 are obtained

multiple attenuation in the image space multiples can be suppressed in the angle domain image space after migration for a given velocity model primaries and multiples have different angle domain moveout and therefore can be separated using techniques similar to the ones employed in the data space prior to migration we use radon transforms in the image space to discriminate between primaries and multiples and employ accurate functions describing angledomain moveouts since every individual angle domain common image gather incorporates complex 3d propagation effects our method has the advantage of working with 3d data and complicated geology therefore our method offers an alternative to the more expensive surface related multiple elimination srme approach operating in the data space radon transforms are cheap but not necessarily ideal for separating primaries and multiples particularly at small angles where the moveout discrepancy between the two kinds of events are not large better techniques involving signal noise separation using prediction error filters can be employed as well although such approaches fall outside the scope of this paper we demonstrate using synthetic and real data examples the power of our method in discriminating between primaries and multiples after migration by wavefield extrapolation followed by transformation to the angle domain

oscillation of second order damped dynamic equations on time scales abstract the study of dynamic equations on time scales has been created in order to unify the study of differential and difference equations the general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so called time scale which may be an arbitrary closed subset of the reals this way results not only related to the set of real numbers or set of integers but those pertaining to more general time scales are obtained in this paper by employing the riccati transformation technique we will establish some oscillation criteria for second order linear and nonlinear dynamic equations with damping terms on a time scale t our results in the special case when t r and t n extend and improve some well known oscillation results for second order linear and nonlinear differential and difference equations and are essentially new on the time scales t h n h 0 t q n for q 1 t n 2 etc some examples are considered to illustrate our main results

oscillation criteria for difference equations with damping terms by means of generalized riccati transformation techniques we establish some new oscillation criteria for second order nonlinear difference equations with damping

bounded oscillation criteria for certain third order nonlinear difference equations with several delays and advances this paper deals with the third order nonlinear difference equations with several delays and advances d a email protected 2x n f n x n x n d 1 n x n d k n 0 n n 0 and d a email protected 2x n b ng x n x n d 1 n x n d k n 0 n n 0 sufficient conditions of the existence of uncountably many bounded positive negative and nonoscillatory solutions respectively and necessary and sufficient conditions of the bounded oscillation of and with certain asymptotic behavior are given in addition a sufficient condition of the oscillatory behavior of all bounded solutions of with a special of asymptotic property is also presented nine nontrivial examples which dwell upon the importance of the results obtained in this paper are also included

interpolation of near offsets using multiples and prediction error filters reflection seismic data typically are undersampled missing near offsets can be interpolated in reflection seismic data with pseudoprimaries generated by crosscorrelating multiples and primaries in incomplete recorded data these pseudoprimary data can be generated at the missing near offsets but contain many artifacts so it is undesirable simply to replace the missing data with the pseudoprimaries a nonstationary prediction error filter pef can instead be estimated from the pseudoprimaries and used to interpolate missing data to produce an interpolated output that is superior to direct substitution of the pseudoprimaries into the missing offsets this approach is applied successfully to 2d synthetic and field data limitations in conventional acquisition geometry limit this approach in 3d which can be illustrated using a synthetic data set

oscillation criteria for second order functional difference equations with summation small coefficient we consider the second order functional difference equation a n n p n x g n 0 where n p n are sequences of integers with a n 0 0 g n n limn g n p n 0 and p n 0 we obtain some necessary conditions for equation 1 exists nonoscillatory solutions and some sufficient conditions for equation 1 is oscillatory

asymptotic and oscillatory behavior of solutions of certain second order nonlinear difference equations mingshu peng department of applied mathematics beijing institute of technology beijing 100081 p r china qianli xu department of mathematics yiyang teachers college yiyang 413049 p r china lihong huang department of applied mathematics hunan university changsha 410082 p r china weigao ge

linear oscillation of second order nonlinear difference equations with damped term abstract in this paper we shall establish relations between the oscillation of second order nonlinear difference equations with damped term and the oscillation of their linear limiting equations

test equality in binary data for a 4 4 crossover trial under a latin square design when there are four or more treatments under comparison the use of a crossover design with a complete set of treatment receipt sequences in binary data is of limited use because of too many treatment receipt sequences thus we may consider use of a 4 4 latin square to reduce the number of treatment receipt sequences when comparing three experimental treatments with a control treatment under a distribution free random effects logistic regression model we develop simple procedures for testing non equality between any of the three experimental treatments and the control treatment in a crossover trial with dichotomous responses we further derive interval estimators in closed forms for the relative effect between treatments to evaluate the performance of these test procedures and interval estimators we employ monte carlo simulation we use the data taken from a crossover trial using a 4 4 latin square design for studying four treatments to illustrate the use of test procedures and interval estimators developed here copyright 2016 john wiley sons ltd

formulae and tables for the determination of sample sizes and power in clinical trials for testing differences in proportions for the two sample design a review this paper is a compendium of exact and asymptotic formulae and tables for estimating the sample size in a clinical trial with two treatment groups and a dichotomous outcome the paper provides separate formulae for equal and unequal treatment group sizes formulae for the calculation of power given the sample size and complete references for all formulae and tables cited

oscillation of certain two dimensional nonlinear difference systems abstract several new oscillation criteria for two dimensional nonlinear difference systems are established examples which dwell upon the importance of our results are also included

oscillation criteria for two dimensional difference systems of first order linear difference equations sufficient conditions are established for the oscillation of the linear two dimensional difference system dx n p ny n dy n 1 q nx n n n n 0 n 0 n 0 1 where p n q n are nonnegative real sequences our results extend the results in the literature

constrained full waveform inversion by model reparameterization the waveform inversion problem is inherently ill posed traditionally regularization schemes are used to address this issue for waveform inversion where the model is expected to have many details reflecting the physical properties of the earth regularization and data fitting can work in opposite directions the former smoothing and the latter adding details to the model we propose constraining estimated velocity fields by reparameterizing the model this technique also called model space preconditioning is based on directional laplacian filters it preserves most of the details of the velocity model while smoothing the solution along known geological dips preconditioning also yields faster convergence at early iterations the laplacian filters have the property to smooth or kill local planar events according to a local dip field by construction these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models we illustrate with 2d syn

adaptive multiple subtraction using independent component analysis surface related multiple attenuation srma can effectively remove multiples from seismic data when other e g radon transform methods have difficulty srma generally includes two steps multiple prediction or multiple modeling and adaptive multiple subtraction ams in some cases adaptive subtraction is the main challenge for the success of srma adaptive subtraction is often posed as a least squares minimization problem that minimizes the energy difference between the original input traces and the modeled multiple traces the minimum output energy approach can be implemented by either single or multichannel matching filters these methods assume orthogonality between the primaries and multiples meaning that the two classes of events are uncorrelated

theory of nonstationary linear filtering in the fourier domain with application to time variant filtering a general linear theory describes the extension of the convolutional method to nonstationary processes this theory can apply any linear nonstationary filter with arbitrary time and frequency variation in the time fourier or mixed domains the filter application equations and the expressions to move the filter between domains are all ordinary fourier transforms or generalized convolutional integrals nonstationary transforms such as the wavelet transform are not required there are many possible applications of this theory including the one way propagation of waves through complex media time migration normal moveout removal time variant filtering and forward and inverse q filtering two complementary nonstationary filters are developed by generalizing the stationary convolution integral the first called nonstationary convolution corresponds to the linear superposition of scaled impulse responses of a nonstationary filter the second called nonstationary combination does not correspond to such a superposition but is shown to be a linear process capable of achieving arbitrarily abrupt temporal variations in the output frequency spectrum both extensions have stationary convolution as a limiting form and in the discrete case can be formulated as matrix operations fourier transformation shows that both filter types are nonstationary filter integrals in the fourier domain as well this result is a generalization of the convolution theorem for stationary signals because as the filter becomes stationary in one domain the integral in the other domain collapses to a scalar multiplication for discrete signals stationary filters are a matrix multiplication of the input signal spectrum by a diagonal spectral matrix while nonstationary filters require off diagonal terms for quasi stationary filters a computational advantage is obtained by computing only the significant terms near the diagonal unlike stationary theory a mixed domain of time and frequency is also possible in this context the nonstationary filter is applied simultaneously with the transform from time to frequency or the reverse nonstationary convolution becomes a generalized forward fourier integral and nonstationary combination is a generalized inverse fourier integral

multiple elimination using a pattern recognition technique standard prestack multiple elimination techniques such as predictive deconvolution or radon transforms fail in the presence of complex structures

seismic trace interpolation in the f x domain interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing a major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated in this respect a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events nor estimation of these directions the method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly regardless of the original spatial interval without any attempt to determine their true dips the predictability of linear events in the f x domain allows the missing traces to be expressed as the output of a linear system the input of which consists of the recorded traces the interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations assessment of the method with a real data set shows that the interpolation yields an improved migrated section

comparison theorems for second order nonlinear difference equations abstract new oscillation results are obtained for the second order nonlinear difference equation r n f x n 1 g n x n 0 and its functional form r n f x n 1 g n x n 0 the role played by the argument n on the oscillation of the functional equation is explored in particular we characterize a class of sequences n which have a harmless effect on the oscillation of this type of equations some of our results generalize improve or unify known fundamental oscillation results for several particular cases of the above equations

interferometric interpolation of missing seismic data we have developed an interferometric interpolation method for filling in trace gaps in common shot gathers there are two steps for implementation first virtual traces are created in the trace gaps by crosscorrelating recorded traces in a shot gather followed by summing correlated trace pairs over all shot positions second a 1d matching filter is applied to the predicted events to correct for wavelet and amplitude distortions by using a 1d assumption assuming a layered medium around the midpoint in a common midpoint cmp gather the interferometric interpolation method can be applied to cmp gathers it is a fully data driven method that requires only the original data results with synthetic and field data empirically show that the near offset traces can be interpolated but because of the approximations introduced by a limited recording aperture there are still some artifacts for comparison a 2d nonstationary prediction error filter pef was also used instead of a 1d matching filter in the se

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

test non inferiority and equivalence based on the odds ratio under a simple crossover trial for testing the non inferiority or equivalence of a generic drug to a standard drug the odds ratio or of patient response rates has been recommended to measure the relative treatment efficacy on the basis of a random effects logistic regression model we develop asymptotic test procedures for testing non inferiority and equivalence with respect to the or of patient response rates under a simple crossover design we further derive exact test procedures which are especially useful for the situations in which the number of patients in a crossover trial is small we address sample size calculation for testing non inferiority and equivalence based on the asymptotic test procedures proposed here we also discuss estimation of the or of patient response rates for both the treatment and period effects finally we include two examples one comparing two solution aerosols in treating asthma and the other one studying two inhalation devices for asthmatics to illustrate the use of the proposed test procedures and estimators

new criteria for the oscillation and existence of monotone solutions of second order nonlinear difference equations we obtain sufficient conditions for the oscillation of the perturbed difference equation d a n 1 dy n 1 s f n y n g n y n dy n n 1 as well as for the existence of monotone solutions of the nonlinear difference equation d a n 1 dy n 1 s k nf y r n 0 n 1 where 0 s p q with p even and q odd integers and some incorrect results in a recent paper are pointed out examples which illustrate the importance of our results are also included

oscillation of second order perturbed nonlinear difference equations using the riccati transformation techniques we will establish some new oscillation criteria for the second order perturbed nonlinear difference equation d a n 1 dx n 1 c f n x n g n x n dx n n 1where c 0 is a quotient of odd positive integers some comparison between our theorems and those previously known results are indicated examples are interested in the text to illustrate the relevance of our results

minimum weighted norm interpolation of seismic records in seismic data processing we often need to interpolate and extrapolate data at missing spatial locations the reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired we propose a wavefield reconstruction scheme for spatially band limited signals the method entails solving an inverse problem where a wavenumber domain regularization term is included the regularization term constrains the solution to be spatially band limited and imposes a prior spectral shape the numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix vector multiplications implemented via the fast fourier transform fft is adopted the algorithm can be used to perform multidimensional reconstruction in any spatial domain

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

a simple analysis of a simple crossover trial with a dichotomous outcome measure for the two treatment two period crossover trial with a dichotomous outcome measure a simple and straightforward analysis is proposed compute the treatment difference for each of the treatment sequences ab and ba and then average over the sequence groups the mean difference is used in the statistical test and in the computation of the 95 per cent confidence interval the method is generalized to the case of a crossover trial including more than two treatments

oscillation of two dimensional difference systems abstract the authors consider the nonlinear two dimensional difference system x n b n g y n y n 1 a n f x n n n o no no 1 where n 0 n 1 2 a n and b n n n n 0 are real sequences and f g r r are continuous with uf u 0 and ug u 0 for u 0 a solution x n y n of the system is oscillatory if both components are oscillatory the authors obtain sufficient conditions for all solutions of the system to be oscillatory some of their results allow a n to oscillate examples to illustrate the results are included

multiple periodic solutions for superquadratic second order discrete hamiltonian systems abstract some multiplicity results are obtained for periodic solutions of the nonautonomous superquadratic second order discrete hamiltonian systems 2 u t 1 f t u t 0 t z by using critical point theory especially a three critical points theorem proposed by brezis and nirenberg

oscillation criteria for second order nonlinear difference equations with damped term abstract several oscillation criteria are established for the second order damped nonlinear difference equation a n 1 y n 1 p n 1 y n 1 q n y n 0 n n 0 0 where 0 is any quotient of odd integers p n and q n are real sequences and f c r r such that x f x 0 for x 0 several examples which dwell upon the importance of our results are also included

oscillation criteria for a nonlinear difference equation abstract essential and nontrivial improvements and extensions of several recent oscillation criteria are obtained for the nonlinear difference equation 1 below

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