almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks stability of numerical solutions to stochastic delay differential equations have received an increasing attention but there has been so far little work on the stability analysis of numerical solutions to stochastic delay hopfield neural networks the aim of this paper is to study the almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks by using two approaches the euler method and the backward euler method under some reasonable conditions both the euler scheme and the backward euler scheme are proved to be almost sure exponential stability in particular the euler method and the backward euler method are mainly based on the semimartingale convergence theorem

convergence and stability of numerical solutions to sddes with markovian switching a class of linear stochastic delay differential equations with markovian switching is considered the main aim of this paper is to investigate the convergence and stability of the euler method of the equations it is proved that the euler method is convergent with strong order p 1 2 the ms stable properties of the euler scheme are also studied

stability analysis of split step θ milstein method for a class of n dimensional stochastic differential equations abstract in this paper we introduce a split step theta milstein sstm method for n dimensional stochastic delay differential equations sddes the exponential mean square stability of the numerical solutions is analyzed and in accordance with previous findings we prove that the method is exponentially mean square stable if the employed time step is smaller than a given and easily computable upper bound in particular according to our investigation larger time steps can be used in the case 1 2 1 than in the case 0 1 2 numerical results are presented which reveal that the sstm method is conditionally mean square stable and that in the case 1 2 1 the interval of time steps for which the sstm method is theoretically shown to be mean square stable is significantly larger than in the case 0 1 2 it is worth mentioning that the sstm method has never been employed or analyzed for the numerical approximation of sddes at least to the very best of our knowledge

inverses of q distance matrices of a tree the determinant and the inverse of the distance matrix of a tree have been investigated in the literature following the classical formulas due to graham and pollak for the determinant and due to graham and lovasz for the inverse we consider two q analogs of the distance matrix of a tree and obtain formulas for the inverses of the two distance matrices yan and yeh have previously obtained expressions for the determinants of the two distance matrices some related results are proved

nonlinear multichannel impedance inversion by total variation regularization abstractthe analysis of acoustic impedance ai allows for the mapping of seismic reflection data to lithology and hence it plays an important role in the interpretation of poststack seismic data the ai is obtainable from the inversion of the earth reflectivity series efficient deconvolution methods have been developed for recovering the reflectivity series from band limited poststack data which are multiple free zero offset and migrated however calculation of the ai from the reflectivity when considering the spatial correlation of the impedance parameters demands the solution of a constrained nonlinear inverse problem two efficient algorithms are proposed for solving the nonlinear impedance problem in multichannel form with the total variation tv constraint to recover impedance maps with blocky structures the first uses the continuous earth model for reflectivity which allows linearizing the problem in the logarithm domain the second uses the discrete layered earth model for reflectivit

the αth moment stability for the stochastic pantograph equation in this paper we investigate the ath moment asymptotical stability of the analytic solution and the numerical methods for the stochastic pantograph equation by using the razumikhin technique especially the linear stochastic pantograph equations and the semi implicit euler method applying them are considered the convergence result of the semi implicit euler method is obtained the stability conditions of the analytic solution of those equations and the numerical method are given finally some experiments are given

numerical solution of stochastic differential problems in the biosciences stochastic differential equations sdes models play a prominent role in many application areas including biology epidemiology and population dynamics mostly because they can offer a more sophisticated insight through physical phenomena than their deterministic counterparts do so suitable numerical methods must be introduced to simulate the solutions of the resulting stochastic differential systems in this work we take into account both euler taylor expansion and runge kutta type methods for stochastic ordinary differential equations sodes and the euler maruyama method for stochastic delay differential equations sddes focusing on the most relevant implementation issues the corresponding matlab codes for both sodes and sddes problems are tested on mathematical models arising in the biosciences math comput simulation numerical analysis of a campbell like stochastic delay model preprint

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

simultaneous multitrace impedance inversion with transform domain sparsity promotion abstractthe impedance inversion technique plays a crucial role in seismic reservoir properties prediction however most existing impedance inversion methods often suffer from spatial discontinuities and instability because each vertical profile is processed independently in the inversion we tested a transform domain sparsity promotion simultaneous multitrace impedance inversion method to address this issue the approach was implemented through minimizing a data misfit term and a transform domain sparsity constraint term that incorporates the 2d or 3d structural information into the inversion processing a 2d synthetic data example was applied to mainly explain the roles of the transform domain sparsity constraint we determined that the transform domain sparsity constraint can help in stabilizing the inversion reducing the influence of high wavenumber noise on the inverted result and exploring spatial continuities of structures furthermore a 3d field data example was used to examine the effectiven

mean square stability of analytic solution and euler maruyama method for impulsive stochastic differential equations from the view of algebra the mean square stability of analytic solutions and numerical solutions for impulsive stochastic differential equations are considered by the logarithmic norm the conditions under which the analytic and numerical solutions for a linear impulsive stochastic differential equation are mean square stable ms stable respectively are obtained the conditions are simple and easy to use some numerical experiments are given to illustrate the results

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

resolution in seismic trace inversion by parameter estimation an alternative to the conventional time series approach to single trace modeling and inversion by convolution and inverse filtering is a parametric approach to obtain insight into the potential of the parametric approach the solution of the single trace forward problem is formulated in matrix terms for the nonlinear reflector lag time parameters this is achieved by linearization which is shown to be a valid approximation over a sufficiently large region the matrix forward operators are analyzed by means of the singular value decomposition svd the svd can be considered a generalization of the fourier transform of convolution operators on the basis of the svd analysis inverse operators are designed which combine stability with high resolving power a method to determine the resolving power of the parametric inverse operators is presented several examples show how wavelet bandwidth data noise level and model complexity influence the resolving power of the data for the reflection coefficient and

using waveform relaxation methods to approximate neutral stochastic functional differential equation systems this paper extends the waveform relaxation wr method to neutral stochastic functional differential equations the linear convergence theory of the continuous time wr method is established in the mean square sense when the coefficients of stochastic differential equation systems satisfy the lipschitz condition and the contractive mapping the discrete time wr method based on the euler scheme which is used in an actual implementation was also studied it turns out that the sequence produced by this method converges linearly to the euler approximate solution which is convergent in addition we prove that the preceding methods are convergent superlinearly if the neutral term does not been split finally the theory is applied to a one dimensional model problem and checked against results obtained by numerical experiments

convergence of numerical solutions to neutral stochastic delay differential equations with markovian switching recently numerical solutions of stochastic differential equations have received a great deal of attention it is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet in the paper the euler maruyama method for neutral stochastic delay differential equations is developed the key aim is to show that the numerical solutions will converge to the true solutions under the local lipschitz condition

a fast automatic multichannel blind seismic inversion for high resolution impedance recovery abstractthe inversion of seismic reflection data for acoustic impedance ai is a common and accepted method for the interpretation of poststack seismic data the original mathematical problem is nonlinear due to the nonlinearity of relation between the ai and the earth reflectivity series and also the insufficiency of information about the source wavelet furthermore the problem is ill posed due to the lack of low and high frequencies in the data we have developed a multichannel blind inversion and solved it for obtaining the ai model and the wavelet directly from seismic reflection data we found a solution to the overall problem by alternating between two subproblems corresponding to the ai and wavelet recovery having an estimation of the wavelet the algorithm directly inverts multichannel data for a high resolution ai model having blocky structures in the sense of total variation tv regularization while satisfying a priori low frequency information the advantages of the split bregman techniq

multichannel spatially correlated reflectivity inversion using block sparse bayesian learning abstractthe reflectivity inversion approach based on a variety of regularization terms was extensively developed and applied to image subsurface structure in recent years in addition multichannel reflectivity inversion or deconvolution considering the lateral continuity of reflection interfaces or reflectivity in adjacent channels has been developed however these processing operations seldom adaptively judge the stratal continuity or automatically alter the parameters of the corresponding algorithm to use the special correlation of the reflection information contained in the seismic data a multichannel spatially correlated reflectivity inversion using block sparse bayesian learning bsbl is introduced the method adopts a covariance matrix that describes the spatial relationship of reflectivity and simultaneously controls the temporal sparsity with an expectation maximization algorithm we can obtain the parameters of the multichannel reflectivity model including the mean i e the estimated mul

identities for minors of the laplacian resistance and distance matrices it is shown that if l and d are the laplacian and the distance matrix of a tree respectively then any minor of the laplacian equals the sum of the cofactors of the complementary submatrix of d up to sign and a power of 2 an analogous more general result is proved for the laplacian and the resistance matrix of any graph a similar identity is proved for graphs in which each block is a complete graph on r vertices and for q analogues of such matrices of a tree our main tool is an identity for the minors of a matrix and its inverse

multichannel matching pursuit for seismic trace decomposition the technique of matching pursuit can adaptively decompose a seismic trace into a series of wavelets however the solution is not unique and is also strongly affected by data noise multichannel matching pursuit mcmp exploiting lateral coherence as a constraint might improve the uniqueness of the solution it extracts a constituent wavelet that has an optimal correlation coefficient to neighboring traces instead of to a single trace only according to linearity theory a wavelet shared by neighboring traces is the best match to the average of multiple traces and therefore it might effectively suppress the data noise and stabilize the performance it is found that the mcmp scheme greatly improves spatial continuity in decomposition and can generate a plausible time frequency spectrum with high resolution for reservoir detection

delay dependent stability of stochastic split step θ methods for stochastic delay differential equations abstract in this paper the delay dependent asymptotic mean square stability of the stochastic split step method for a scalar linear stochastic delay differential equation with real coefficients is studied the full stability region of this method is given by using root locus technique the necessary and sufficient condition with respect to the equation coefficients time stepsize and method parameter is derived it is proved that the stochastic split step backward euler can preserve the asymptotic mean square stability of the underlying system completely in addition the numerical stability regions of the stochastic split step method and the stochastic method are compared with each other at last we validate our conclusions by numerical experiments

discretisation of stochastic control problems for continuous time dynamics with delay as a main step in the numerical solution of control problems in continuous time the controlled process is approximated by sequences of controlled markov chains thus discretising time and space a new feature in this context is to allow for delay in the dynamics the existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls weak convergence of the approximating extended markov chains to the original process together with convergence of the associated optimal strategies is established

mixed phase deconvolution and wavelet estimation the seismic convolutional model describes seismic wave propagation as a linear system a seismic trace then consists of a wavelet or pulse convolved with the reflection response or reflectivity series plus additive noise an important problem in seismic data processing is the removal of the effect of the wavelet spiking deconvolution or inverse filtering in order to estimate the reflectivity series when the wavelet is known designing an optimal spiking filter by a least squares approach is straightforward for a mixed delay wavelet we must delay the position of the desired output spike this delay can later be removed so that the effective filter is no longer causal but operates on both past and future input data values with respect to the output position when the wavelet is unknown we must determine both the wavelet and the reflectivity series from the input data solving this ambiguous problem requires additional assumptions about the wavelet the reflectivity series and the noise common assumptions are that the reflectivity series is a stationary random process and that it is uncorrelated to the stationary random noise furthermore if it is assumed that the signal to noise ratio is large the autocorrelation function acf of the seismic trace can be used as an estimate of the acf of the wavelet if in addition it is assumed as it commonly is that the wavelet is minimum delay meaning that all roots of its associated polynomial have amplitude greater than 1 an optimal least squares inverse filter can be computed by solving the normal equations using a levinson algorithm the normal equations are also called the yule walker yw equations however problems can arise with minimum phase inverse filtering when the wavelet is not minimum delay in a tutorial on spiking deconvolution tle 1995 leinbach showed that applying a minimum phase filter to an air gun

inversion of normal incidence seismograms the well known instability of kunetz s 1963 inversion algorithm can be explained by the progressive manner in which the calculations are done descending from the surface and by the fact that completely different impedances can yield indistinguishable synthetic seismograms those difficulties can be overcome by using an iterative algorithm for the inversion of the one dimensional 1 d wave equation together with a stabilizing constraint on the sums of the jumps of the desired impedance for computational efficiency the synthetic seismogram is computed by the method of characteristics and the gradient of the error criterion is computed by optimal control techniques adjoint state equation the numerical results on simulated data confirm the expected stability of the algorithm in the presence of measurement noise tests include noise levels of 50 percent the inversion of two field sections demonstrates the practical feasibility of the method and the importance of taking into account all internal a

discrete time approximations of stochastic delay equations the milstein scheme in this paper we develop a strong milstein approximation scheme for solving stochastic delay differential equations sddes the scheme has convergence order 1 in order to establish the scheme we prove an infinite dimensional ito formula for tame functions acting on the segment process of the solution of an sdde it is interesting to note that the presence of the memory in the sdde requires the use of the malliavin calculus and the anticipating stochastic analysis of nualart and pardoux given the nonanticipating nature of the sdde the use of anticipating calculus methods in the context of strong approximation schemes appears to be novel

an analysis of stability of milstein method for stochastic differential equations with delay this paper deals with the adapted milstein method for solving linear stochastic delay differential equations it is proved that the numerical method is mean square ms stable under suitable conditions the obtained result shows that the method preserves the stability property of a class of linear constant coefficient problems this is also verified by several numerical examples

spectra of digraph transformations let d be a directed graph without loops or multiple arcs with vertex set v d v and arc set e d e let d0 be the digraph with vertex set v and with no arcs d1 the complete digraph with vertex set v d d and d the complement dc of d for e x y e let x t e and y h e let t d tcb d be the digraph with vertex set v e and such that v e is an arc in t d resp in tcb d if and only if v v e e and vertex v t e resp v t e in d similarly let h d hcb d be the digraph with vertex set v e and such that e v is an arc in h d resp in hcb d if and only if v v e e and vertex v h e resp v h e in d given a digraph d and three variables x y z 0 1 the xyz transformation of d is the digraph dxyz such that dxy0 dx dl y and dxyz dxy0 w where w t d h d if z w tcb d hcb d if z and w is the complete bipartite digraph with parts v and e if z 1 in this paper we obtain the adjacency characteristic polynomials of some xyz transformations of an r regular digraph d in terms of r the number of vertices and the adjacency spectrum of d similar results are obtained for some non regular digraphs named digraph functions we also give various constructions of non isomorphic cospectral digraphs using xyz transformations our notion of xyz transformation is also valid for digraphs with multiple arcs and loops if x y z 0 and z 0 1 we also extend the notion of xyz transformation to digraphs v e with loops and no multiple arcs

convergence and stability of the semi implicit euler method for a linear stochastic differential delay equation the paper deals with convergence and stability of the semi implicit euler method for a linear stochastic differential delay equation it is proved that the semi implicit euler method is convergent with strong order p the conditions under which the method is ms stable and gms stable are determined and the numerical experiments are given

mean square convergence of one step methods for neutral stochastic differential delay equations this paper deals with strong approximations of the solutions of neutral stochastic differential delay equations nsddes in ito sense a general framework for the strong convergence of a class of drift implicit one step schemes to the solutions of nsddes is established two examples to illustrate the applicability of our results are provided

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

the existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and levy jumps in this paper we consider a class of stochastic pantograph differential equations with levy jumps spdewljs by using the burkholder davis gundy inequality and the kunita s inequality we prove the existence and uniqueness of solutions to spdewljs whose coefficients satisfying the lipschitz conditions and the local lipschitz conditions meantime we establish the p th exponential estimations and almost surely asymptotic estimations of solutions to spdewljs

zeta functions of line middle total graphs of a graph and their coverings we consider the ihara zeta functions of line graphs middle graphs and total graphs of a regular graph and their regular or irregular covering graphs let l g m g and t g denote the line middle and total graph of g respectively we show that the line middle and total graph of a regular and irregular respectively covering of a graph g is a regular and irregular respectively covering of l g m g and t g respectively for a regular graph g we express the zeta functions of the line middle and total graph of any regular or irregular covering of g in terms of the characteristic polynomial of the covering also the complexities of the line middle and total graph of any regular or irregular covering of g are computed furthermore we discuss the l functions of the line middle and total graph of a regular graph g

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

ms stability of the euler maruyama method for stochastic differential delay equations the aim of this paper is to investigate the stability of the euler maruyama method for the stochastic differential equations with time delay the definition of ms stability of numerical methods is established the condition of the mean square stability of analytical solution is obtained for a linear scalar system with multiplicative noise and the ms stability of the numerical scheme is proved

introduction to the numerical analysis of stochastic delay differential equations abstract we consider the problem of the numerical solution of stochastic delay differential equations of ito form d x t f x t x t d t g x t x t d w t t 0 t and x t t for t 0 with given f g wiener noise w and given 0 with a prescribed initial function we indicate the nature of the equations of interest and give a convergence proof for explicit single step methods some illustrative numerical examples using a strong euler maruyama scheme are provided

zeta functions of several corona type graphs abstract in this paper we present the decomposition formulae for the zeta functions of families of graphs obtained through corona type construction furthermore we construct some families of graphs with the same zeta function by the spectra of these graphs

existence and uniqueness of the solutions and convergence of semi implicit euler methods for stochastic pantograph equations abstract in this paper the sufficient conditions of existence and uniqueness of the solutions for stochastic pantograph equation are given i e the local lipschitz condition and the linear growth condition under the lipschitz condition and the linear growth condition it is proved that the semi implicit euler method is convergence with strong order 1 2

on the rate of convergence of finite difference approximations for bellmans equations with variable coefficients the estimates presented here for parabolic bellman s equations with variable coefficients extend the ones earlier obtained for constant coefficients

multitrace impedance inversion with lateral constraints abstractwe have developed a lateral constraint to the inversion of 1d seismic impedance models to suppress the effect of data noise and improve the fidelity of formation boundaries in 2d models for situations with dips of less than 20 typical inversion frameworks rely on a 1d forward model with each 1d trace being inverted independently adjacent inversion models are combined together to form a 2d impedance model adding a lateral constraint improves the fidelity of the 2d impedance models while retaining much of the advantage of the low computational cost associated with typical 1d inversion schemes solving the 1d lateral constraint inversion 1d lci problem involves the simultaneous inversion of multiple 1d traces producing layered sections with lateral smoothed transition in addition to enforcing lateral continuity in the inversion model this algorithm allows for the inclusion of a priori knowledge from boreholes we determined the effectiveness of this algorithm on two synthetic models as well

mean square exponential stability for stochastic control systems with discrete time state feedbacks and their numerical schemes in simulation aiming at the qualitative numerical simulation this article concerns the mean square exponential stability mses of the stochastic systems with discrete time state feedbacks and their numerical schemes a time delay dependent stability criterion is obtained for the underlying system the euler maruyama and backward euler maruyama schemes are established and their mses are proved under the same criterion which means that the numerical schemes preserve the stability of the continuous model the illustrative example at the end of this letter shows that the theoretical upper bound for the sampling period limited in the stability criterion is much greater than that obtained by the stability criteria from the literature

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

multichannel blind deconvolution of seismic signals a new algorithm for simultaneous wavelet estimation and deconvolution of seismic reflection signals is given to remove the inherent ambiguity in this blind deconvolution problem we introduce relevant a priori information our major assumption is sparseness of the reflectivity which corresponds to a layered earth model this allows nonminimum phase wavelets to be recovered reliably and closely spaced reflectors to be resolved to combine a priori knowledge and data we use a bayesian framework and derive a maximum a posteriori estimate computing this estimate is a difficult optimization problem solved by a suboptimal iterative procedure the procedure alternates steps of wavelet estimation and reflectivity estimation the first step only requires a simple least squares fit while the second step is solved by the iterated window maximization algorithm proposed by kaaresen this enables better efficiency and optimality than established alternatives the resulting optimization method can easily handle multichannel models with only a moderate increase of the computational load lateral continuity of the reflectors is achieved by modeling local dependencies between neighboring traces major improvements in both wavelet and reflectivity estimates are obtained by taking the wavelet to be invariant across several traces the practicality of the algorithm is demonstrated on synthetic and real seismic data an application to multivariate well log segmentation is also given

tutorial spectral bandwidth extension invention versus harmonic extrapolation abstractvarious postprocessing methods can be applied to seismic data to extend the spectral bandwidth and potentially increase the seismic resolution frequency invention techniques including phase acceleration and loop reconvolution produce spectrally broadened seismic sections but arbitrarily create high frequencies without a physical basis tests in extending the bandwidth of low frequency synthetics using these methods indicate that the invented frequencies do not tie high frequency synthetics generated from the same reflectivity series furthermore synthetic wedge models indicate that the invented high frequency seismic traces do not improve thin layer resolution frequency invention outputs may serve as useful attributes but they should not be used for quantitative work and do not improve actual resolution on the other hand under appropriate circumstances layer frequency responses can be extrapolated to frequencies outside the band of the original data using spectral periodicities determined

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

seismic absorption compensation a least squares inverse scheme the problem of instability plagues conventional inverse q filtering we formulate the deabsorption problem as an inverse problem in terms of least squares and impose regularization by means of bayes theorem the solution is iterative and nonparametric and returns a reflectivity that has been constrained to be sparse the inverse scheme is tested on both synthetic and real data and the results obtained demonstrate the viability of the approach

s rock methods for stochastic delay differential equations with one fixed delay abstract we propose stabilized explicit stochastic runge kutta methods of strong order one half for ito stochastic delay differential equations with one fixed delay the family of the methods is constructed by embedding runge kutta chebyshev methods of order one for ordinary differential equations the values of a damping parameter of the methods are determined appropriately in order to obtain excellent mean square stability properties numerical experiments are carried out to confirm their order of convergence and stability properties

zeta functions of finite graphs and coverings iii abstract a graph theoretical analog of brauer siegel theory for zeta functions of number fields is developed using the theory of artin l functions for galois coverings of graphs from parts i and ii in the process we discuss possible versions of the riemann hypothesis for the ihara zeta function of an irregular graph

families of line graphs and their quantization any directed graph g with n vertices and j edges has an associated line graph l g where the j edges form the vertices of l g we show that the non zero eigenvalues of the adjacency matrices are the same for all graphs of such a family ln g we give necessary and sufficient conditions for a line graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions line graphs may therefore serve as models to study the semiclassical limit of large matrix size of a quantum dynamics on graphs with fixed classical behaviour

generalized linear inversion of reflection seismic data generalized linear inversion sometimes known as model perturbation nonlinear regression or inverse modeling is applied to synthetic and real seismic data sets with the objective of obtaining an impedance profile as a function of time the impedances solved for are parameterized in a manner that describes the unknown earth using fewer variables than previous seismic generalized linear inversion techniques in this application only single traces of common midpoint cmp processed data will be inverted the method of generalized linear inversion gli presented here is designed to improve on the shortcomings of recursive inversion with respect to relative and absolute scale of the impedance results resolution of impedance boundaries and distortion from residual wavelet effects in obtaining these goals other advantageous aspects of gli were discovered for example it is insensitive to noise in many cases and it will allow an interpreter to fix the impedance of any number of known lithologies in an in

numerical analysis of semilinear stochastic evolution equations in banach spaces the solution of stochastic evolution equations generally relies on numerical computation here usually the main idea is to discretize the spde spatially obtaining a system of sdes that can be solved by e g the euler scheme in this paper we investigate the discretization error of semilinear stochastic evolution equations in lp spaces resp banach spaces the space discretization may be done by galerkin approximation for the time discretization we consider the implicit euler the explicit euler scheme and the crank nicholson scheme in the last section we give some examples i e we consider an spdes driven by nuclear wiener noise approximated by wavelets and delay equation approximated by finite differences

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

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

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

ihara zeta functions of coronae abstract we derive a factorization formula for the ihara zeta function of the corona of two graphs when the two graphs are regular this factorization formula involves the graphs adjacency spectra as an application we show that if each composing graph of a corona of regular graphs is replaced with a cospectral mate then the ihara zeta function of the corona does not change we also give a formula for the weighted kirchhoff index of the corona of two regular graphs

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

minimum entropy deconvolution with frequency domain constraints a method for reconstructing the reflectivity spectrum using the minimum entropy criterion is presented the algorithm fmed described is compared with the classical minimum entropy deconvolution med as well as with the linear programming lp and autoregressive ar approaches the med is performed by maximizing an entropy norm with respect to the coefficients of a linear operator that deconvolves the seismic trace by comparison the approach presented here maximizes the norm with respect to the missing frequencies of the reflectivity series spectrum this procedure reduces to a nonlinear algorithm that is able to carry out the deconvolution of band limited data avoiding the inherent limitations of linear operators the proposed method is illustrated under a variety of synthetic examples field data are also used to test the algorithm the results show that the proposed method is an effective way to process band limited data the fmed and the lp arise from similar conceptions both methods seek an extremum of a particular norm subjected to frequency constraints in the lp approach the linear programming problem is solved using an adaptation of the simplex method which is a very expensive procedure the fmed uses only two fast fourier transforms ffts per iteration hence the computational cost of the inversion is reduced

the split step backward euler method for linear stochastic delay differential equations in this paper the numerical approximation of solutions of linear stochastic delay differential equations sddes in the ito sense is considered we construct split step backward euler ssbe method for solving linear sddes and develop the fundamental numerical analysis concerning its strong convergence and mean square stability it is proved that the ssbe method is convergent with strong order c 12 in the mean square sense the conditions under which the ssbe method is mean square stable ms stable and general mean square stable gms stable are obtained some illustrative numerical examples are presented to demonstrate the order of strong convergence and the mean square stability of the ssbe method