level spacing distributions and the bessel kernel scaling models of randomn n hermitian matrices and passing to the limitn leads to integral operators whose fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order for the gaussian unitary ensemble and for many others as well the kernel one obtains by scaling in the bulk of the spectrum is the sine kernel frac sin pi x y pi x y rescaling the gue at the edge of the spectrum leads to the kernel frac ai x ai y ai x ai y x y where ai is the airy function in previous work we found several analogies between properties of this airy kernel and known properties of the sine kernel a system of partial differential equations associated with the logarithmic differential of the fredholm determinant when the underlying domain is a union of intervals a representation of the fredholm determinant in terms of a painleve transcendent in the case of a single interval and also in this case asymptotic expansions for these determinants and related quantities achieved with the help of a differential operator which commutes with the integral operator in this paper we show that there are completely analogous properties for a class of kernels which arise when one rescales the laguerre or jacobi ensembles at the edge of the spectrum namely frac j alpha sqrt x sqrt y j alpha sqrt y sqrt x j alpha sqrt x j alpha sqrt y 2 x y wherej z is the bessel function of order in the cases 1 2 these become after a variable change the kernels which arise when taking scaling limits in the bulk of the spectrum for the gaussian orthogonal and symplectic ensembles in particular an asymptotic expansion we derive will generalize ones found by dyson for the fredholm determinants of these kernels

correlated wishart ensembles and chaotic time series we study the correlated wishart ensembles in the context of time series analysis we are interested in the statistics of eigenlevels viz variables associated with independent eigenmodes in the system the motivation of this work is to study the effect of time series correlations on the wishart ensembles in this connection we derive the level density and the two point function for the correlated wishart ensembles by using the binary correlation method using our analytic results we analyze spectra of autocovariance matrices derived from single variable stationary time series we consider the stochastic time series of gaussian variables with exponentially decaying correlations and time series of chaotic maps viz the arnold map the standard map and the stadium billiard map in both cases correlated time series are encountered and analyzed under the framework of random matrix theory it is shown that the eigenlevel statistics for the chaotic maps follow closely those of correlated wishart ensembles it is indicated that the presence of collective modes in the spectra of autocovariance matrices is related to the integrability of the system

equations for finite difference time domain simulation of sound propagation in moving inhomogeneous media and numerical implementation finite difference time domain fdtd calculations are typically performed with partial differential equations that are first order in time equation sets appropriate for fdtd calculations in a moving inhomogeneous medium with an emphasis on the atmosphere are derived and discussed in this paper two candidate equation sets both derived from linearized equations of fluid dynamics are proposed the first which contains three coupled equations for the sound pressure vector acoustic velocity and acoustic density is obtained without any approximations the second which contains two coupled equations for the sound pressure and vector acoustic velocity is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure it is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere practical fdtd implementation of the second set of equations is discussed results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform high mach number flow and with fast field program calculations of sound propagation in a stratified moving atmosphere

complex wishart matrices and conductance in mesoscopic systems exact results it is noted that the hypothesis of independent random complex elements for the off diagonal blocks say m2 and m3 of the transfer matrix describing conductance in a mesoscopic wire allows the eigenvalue distribution of the matrix product m3 m3 or m2 m2 to be computed exactly exact expressions in terms of double wronskian and toeplitz determinants are derived for the distribution of the smallest and second smallest eigenvalue of this and similar random matrix products

attenuation compensation in anisotropic least squares reverse time migration abstractanisotropic and attenuating properties of subsurface media cause amplitude loss and waveform distortion in seismic wave propagation resulting in negative influence on seismic imaging to correct the anisotropy effect and compensate amplitude attenuation a compensated amplitude vertical transverse isotropic vti least squares reverse time migration lsrtm method is adopted in this method the attenuation term of an attenuated acoustic wave equation is extended to a vti quasi differential wave equation which takes care of effects from anisotropy and attenuation the finite difference method is used to solve the equation in which attenuation terms are solved in the wavenumber domain and other terms are solved in the space or wavenumber domain stable regularization operators are derived and introduced to the equations to eliminate severe numerical noise in high frequency components during backward propagation meanwhile a demigration operator migration operator and gradient formula for att

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

3d rotated and standard staggered finite difference solutions to biot s poroelastic wave equations stability condition and dispersion analysis a fourth order in space and second order in time 3d staggered sg and rotated staggered grid rsg method for the solution of biot s equation are presented the numerical dispersion and stability conditions are derived using a von neumann analysis the exact stability condition is calculated from the roots of a 12th order polynomial and therefore no nontrivial expression exists to overcome this a 1d stability condition is usually generalized to three dimensions it is shown that in certain cases the 1d approximate stability condition is violated by a 3d sg method the rsg method obeys the approximate 1d stability condition for the material properties and spatiotemporal scales in the examples shown both methods have been verified against an analytical solution for an infinite homogeneous porous medium with a misfit error of less than 0 5 a free surface has been implement ed to test the accuracy of this boundary condition it also serves as a test of the methods to include high material contrasts th

compensating q effects in viscoelastic media by adjoint based least squares reverse time migration low values of p and s wave quality factors qp and qs result in strong intrinsic seismic attenuation in both seismic modeling and imaging we use a linearized waveform inversion approach by generalizing least squares reverse time migration lsrtm for viscoelastic media q lsrtm to compensate the attenuation loss for both p and s images we use the first order particle velocity stress and memory variable equations with explicit q in the formulations based on the generalized standard linear solid gsls as the forward modeling operator the linearized two way viscoelastic modeling operator is obtained with modulus perturbations introduced for the relaxed p and s moduli the viscoelastic adjoint operator and the p and s imaging conditions for modulus perturbations are derived using the adjoint state method and an augmented lagrangian functional q lsrtm solves the viscoelastic linearized modeling operator for generating synthetic data and the adjoint operator is used for back propagating the data re

a simplified lax wendroff correction for staggered grid fdtd modeling of electromagnetic wave propagation in frequency dependent media the lax wendroff correction is an elegant method for increasing the accuracy and computational efficiency of finite difference time domain fdtd solutions of hyperbolic problems however the conventional approach leads to implicit solutions for staggered grid fdtd approximations of maxwell s equations with frequency dependent constitutive parameters to overcome this problem we propose an approximation that only retains the purely acoustic i e lossless terms of the lax wendroff correction this modified lax wendroff correction is applied to an o 2 4 accurate staggered grid fdtd approximation of maxwell s equations in the radar frequency range 10 mhz 10 ghz the resulting pseudo o 4 4 scheme is explicit and computationally efficient and exhibits all the major numerical characteristics of an o 4 4 accurate fdtd scheme even for strongly attenuating and dispersive media the numerical properties of our approach are constrained by classical numerical dispersion and von neumann routh stability

dynamic modeling of gene expression data we describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time we deduce the time translational matrix for previously published dna microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition the resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution we show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix this finding suggests that the number of essential connections among the genes is small

applying finite element analysis to the memory variable formulation of wave propagation in anelastic media finite element methods are applied to solution of seismic wave motion in linear viscoelastic media using the memory variable formalism the displacements are represented as a superposition of a set of basis functions it is shown that if memory variables are represented using the spatial derivatives of those basis functions rather than the basis functions themselves the equations to be solved are simpler and require less computer memory using this formulation results for sh waves in one and two dimensions are calculated using a simple explicit finite element in space finite difference in time scheme these results agree with those found with a method of lines solution results in a homogeneous medium also agree with the frequency domain solutions of kjartansson s constant q method

quick and accurate q parameterization in viscoelastic wave modeling we introduce a procedure for including the attenuation factor q in a consistent manner in seismic modeling and show 3d examples the q fitting over a chosen frequency band involves two algorithms the first creates starting values of relaxation times and the second does nonlinear inversion using the results of the first as initial values the resulting q function gives a good approximation to a constant q over the chosen frequency band the algorithm is combined with a finite difference f d code that includes topographies in 3d seismic media the velocity stress formulation for viscoelastic wave modeling is used with an arbitrary number of relaxation mechanisms to model a desired q behavior these equations are discretized by high order f ds in the interior of the medium and we gradually reduce the f d order to two at the stress free surface where we implement our free surface boundary conditions the seismic f d algorithm is applied to a marine seismic experiment with and without viscoelasticity to emphasize the importance of including physical attenuation and dispersion in seismic modeling their inclusion even for marine surveys is clearly important for lossy ocean bottoms our procedure for more accurate modeling of physical dispersion and attenuation may increase future motivation to include viscoelasticity in seismic inversion

finite difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid we describe the application of the rotated staggered grid rsg finite difference technique to the wave equations for anisotropic and viscoelastic media the rsg uses rotated finite difference operators leading to a distribution of modeling parameters in an elementary cell where all components of one physical property are located only at one single position this can be advantageous for modeling wave propagation in anisotropic media or complex media including high contrast discontinuities because no averaging of elastic moduli is needed the rsg can be applied both to displacement stress and to velocity stress finite difference fd schemes whereby the latter are commonly used to model viscoelastic wave propagation with a von neumann style anlysis we estimate the dispersion error of the rsg scheme in general anisotropic media in three different simulation examples all based on previously published problems we demonstrate the application and the accuracy of the proposed numerical approach

not all that glitters is rmt in the forecasting of risk of portfolios in the brazilian stock market abstract using stocks of the brazilian stock exchange bm f bovespa we build portfolios of stocks based on markowitz s theory and test the predicted and realized risks this is done using the correlation matrices between stocks and also using random matrix theory in order to clean such correlation matrices from noise we also calculate correlation matrices using a regression model in order to remove the effect of common market movements and their cleaned versions using random matrix theory this is done for years of both low and high volatility of the brazilian stock market from 2004 to 2012 the results show that the use of regression to subtract the market effect on returns greatly increases the accuracy of the prediction of risk and that although the cleaning of the correlation matrix often leads to portfolios that better predict risks in periods of high volatility of the market this procedure may fail to do so the results may be used in the assessment of the true risks when one builds a portfolio of stocks during periods of crisis

recursion for the smallest eigenvalue density of β wishart laguerre ensemble the statistics of the smallest eigenvalue of wishart laguerre ensemble is important from several perspectives the smallest eigenvalue density is typically expressible in terms of determinants or pfaffians these results are of utmost significance in understanding the spectral behavior of wishart laguerre ensembles and among other things unveil the underlying universality aspects in the asymptotic limits however obtaining exact and explicit expressions by expanding determinants or pfaffians becomes impractical if large dimension matrices are involved for the real matrices beta 1 edelman has provided an efficient recurrence scheme to work out exact and explicit results for the smallest eigenvalue density which does not involve determinants or matrices very recently an analogous recurrence scheme has been obtained for the complex matrices beta 2 in the present work we extend this to beta wishart laguerre ensembles for the case when exponent alpha in the associated laguerre weight function lambda alpha e beta lambda 2 is a non negative integer while beta is positive real this also gives access to the smallest eigenvalue density of fixed trace beta wishart laguerre ensemble as well as moments for both cases moreover comparison with earlier results for the smallest eigenvalue density in terms of certain hypergeometric function of matrix argument results in an effective way of evaluating these explicitly exact evaluations for large values of n the matrix dimension and alpha also enable us to compare with tracy widom density and large deviation results of katzav and castillo we also use our result to obtain the density of the largest of the proper delay times which are eigenvalues of the wigner smith matrix and are relevant to the problem of quantum chaotic scattering

critical correlations in a z invariant inhomogeneous ising model abstract we study the critical spin spin correlation function in the z invariant inhomogeneous ising model which includes the rectangular triangular honeycomb and checkerboard lattices as special cases using quadratic difference equations we derive various explicit representations for the correlation function confirming and simplifying also a miraculous result of baxter

a new time space domain high order finite difference method for the acoustic wave equation a new unified methodology was proposed in finkelstein and kastner 2007 39 to derive spatial finite difference fd coefficients in the joint time space domain to reduce numerical dispersion the key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies we develop this new time space domain fd method further for 1d 2d and 3d acoustic wave modeling using a plane wave theory and the taylor series expansion new spatial fd coefficients are frequency independent though they lead to a frequency dependent numerical solution we prove that the modeling accuracy is 2nd order when the conventional 2m th order space domain fd and the 2nd order time domain fd stencils are directly used to solve the acoustic wave equation however under the same discretization the new 1d method can reach 2m th order accuracy and is always stable the 2d method can reach 2m th order accuracy along eight directions and has better stability similarly the 3d method can reach 2m th order accuracy along 48 directions and also has better stability than the conventional fd method the advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models in addition we study the influence of the fd stencil length on numerical modeling for 1d inhomogeneous media and derive an optimal fd stencil length required to balance the accuracy and efficiency of modeling a new time space domain high order staggered grid fd method for the 1d acoustic wave equation with variable densities is also developed which has similar advantages demonstrated by dispersion analysis stability analysis and modeling experiments the methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering

seismic modeling in viscoelastic media anelasticity is usually caused by a large number of physical mechanisms which can be modeled by different microstructural theories a general way to take all these mechanisms into account is to use a phenomenologic model such a model which is consistent with the properties of anelastic media can be represented mechanically by a combination of springs and dash pots a suitable system can be constructed by the parallel connection of several standard linear elements and is referred to as the general standard linear solid rheology two relaxation functions that describe the dilatational and shear dissipation mechanisms of the medium are needed this model properly describes the short and long term behaviors of materials with memory and is the basis for describing viscoelastic wave propagation this work presents two dimensional 2 d and three dimensional 3 d forward modeling in linear viscoelastic media the theory implements boltzmann s superposition principle based on a spectrum of relaxation mechanisms

guaranteed quality all quadrilateral mesh generation with feature preservation in this paper a quadtree based mesh generation method is described to create guaranteed quality geometry adapted all quadrilateral meshes with feature preservation for arbitrary planar domains given point cloud our method generates all quad meshes with these points as vertices and all the angles are within 45 135 for given planar curves quadtree based spatial decomposition is governed by the curvature of the boundaries and narrow regions 2 refinement templates are chosen for local mesh refinement without creating any hanging nodes a buffer zone is created by removing elements around the boundary to guarantee the mesh quality the angles facing the boundary are improved via template implementation and two buffer layers are inserted in the buffer zone it is proved that all the elements of the final mesh are quads with angles between 45 e and 135 e e 5 with the exception of badly shaped elements that may be required by the specified geometry sharp features and narrow regions are detected and preserved furthermore boundary layer meshes are generated by splitting elements of the second buffer layer we have applied our algorithm to a set of complicated geometries including the lake superior map and the air foil with multiple components

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

viscoacoustic waveform inversion of velocity structures in the time domain abstractbecause of the conversion of elastic energy into heat seismic waves are attenuated and dispersed as they propagate the attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results using a viscoacoustic model consisting of a single standard linear solid we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation we derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion the wave equations were numerically solved by high order finite difference methods on centered grids to extrapolate seismic wavefields the finite difference methods were implemented satisfying stability conditions which are also presented numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude

a k space operator based least squares staggered grid finite difference method for modeling scalar wave propagation abstracttwo staggered grid finite difference sgfd schemes with fourth and sixth order accuracies in time have been developed recently based on new sgfd stencils the sgfd coefficients of the two schemes are determined by a taylor series expansion te approach which is accurate only near a zero wavenumber we have adopted the same sgfd stencils and determined the sgfd coefficients by minimizing the errors between the wavenumber responses of the sgfd operators and the first order k wavenumber space operator in a least squares ls sense we solved the ls problems by performing a weighted pseudoinverse of nonsquare matrices to obtain the sgfd coefficients and to yield ls based sgfd methods we have developed an efficient ls implementation by using a small number of representative wavenumbers which makes the computational time for estimating the coefficients negligible dispersion analysis and numerical examples demonstrate that our ls based sgfd methods can preserve the original temporal accuracy and

application of the τ function theory of painleve equations to random matrices pv piii the lue jue and cue with denoting an average with respect to the eigenvalue pdf for the laguerre unitary ensemble the object of our study is e n i a x l i l 0 i l for i 0 s and i s where x i l 1 for l i and x i l 0 other wise using okamoto s development of the theory of the painleve v equation it is shown that e n i a is a function associated with the hamiltonian therein and so can be characterized as the solution of a certain second order second degree differential equation or in terms of the solution of certain difference equations the cases 0 and 2 are of particular interest because they correspond to the cumulative distribution and density function respectively for the smallest and largest eigenvalue in the case i s e n i a is simply related to an average in the jacobi unitary ensemble and this in turn is simply related to certain averages over the orthogonal group the unitary symplectic group and the circular unitary ensemble the latter integrals are of interest for their combinatorial content also considered are the hard edge and soft edge scaled limits of e n i a in particular in the hard edge scaled limit it is shown that the limiting quantity e hard 0 s a can be evaluated as a function associated with the hamiltonian in okamoto s theory of the painleve iii equation

q compensated least squares reverse time migration using low rank one step wave extrapolation abstractattenuation of seismic waves needs to be taken into account to improve the accuracy of seismic imaging in viscoacoustic media reverse time migration rtm can be performed with q compensation which is also known as q rtm least squares rtm lsrtm has also been shown to be able to compensate for attenuation through linearized inversion however seismic attenuation may significantly slow down the convergence rate of the least squares iterative inversion process without proper preconditioning we have found that incorporating attenuation compensation into lsrtm can improve the speed of convergence in attenuating media obtaining high quality images within the first few iterations based on the low rank one step seismic modeling operator in viscoacoustic media we have derived its adjoint operator using nonstationary filtering theory the proposed forward and adjoint operators can be efficiently applied to propagate viscoacoustic waves and to implement attenuation compensation recognizing that

waveform inversion including well constraints anisotropy and attenuation the goal of full waveform inversion wfi is to derive high fidelity earth models for seismic imaging from the full waveforms of the acquired seismic data the attractiveness of wfi lies mainly in its limited number of approximations at least in a theoretical sense in contrast to other model determination techniques such as semblance or ray based tomography despite this various methodologies must be utilized to make the technique viable with today s computing technology and restrictions of seismic acquisition these are collectively referred to as waveform inversion strategies and in this article we discuss mainly regularization and preconditioning strategies as the wavefields need to be accurately modeled to represent the kinematics of all the waves during wfi iterations the inclusion of anisotropy often helps to improve the wfi results in the first section of this article we introduce forward modeling and its adjoint based on acoustic wave equations in vertical transversely isotropic vti med

maximizing the cfl number of stable time space domain explicit finite difference modeling abstract the time space domain explicit finite difference fd method numerically solves wave equation by applying fd to approximate its spatial and temporal derivatives this method always faces the stability problem i theoretically analyze stability condition of this method for the acoustic wave equation and find that the maximum courant friedrichs lewy cfl number of stable modeling depends on the maximum value of the spatial fd dispersion relation the conventional method commonly determines spatial fd coefficients by approximating the spatial fd dispersion to the exact relation within the given wavenumber area however outside this area the dispersion relation and hence the maximum cfl number is uncontrollable to make it controllable i propose to simultaneously approximate the spatial fd dispersion relation to a given function outside this area further i develop an algorithm to maximize the maximum cfl number stability analysis and modeling examples demonstrate that the proposed method has better stability than the conventional method especially when the maximum effective wavenumber frequency is small for the 2d case the conventional method performs stable simulation using a cfl number of no more than 0 707 but the new method can perform stable simulation using a large cfl number for example 1 6 4 8 and 9 0 and non long spatial fd stencils

comparison of two algorithms for isotropic elastic p and s vector decomposition the research leading to this paper is supported by the sponsors of the ut dallas geophysical consortium a portion of the computations was done at the texas advanced computing center this paper is contribution no 1270 from the department of geosciences at the university of texas at dallas special thanks go to j brown a shabelansky and two anonymous reviewers for their useful comments and encouragements

time space domain implicit finite difference methods for modeling acoustic wave equations it was proved that the implicit spatial finite difference fd method can obtain a higher accuracy than the explicit fd by using even a smaller operator length however when only second order fd in time is used the combined fd is prone to temporal dispersion and easily becomes unstable when a relatively large time step is used the time space domain fd can suppress the temporal dispersion however because the spatial derivatives are solved explicitly the method suffers from spatial dispersion and a large spatial operator length has to be adopted we propose two effective time space domain implicit fd methods for modeling 2d and 3d acoustic wave equations the high order fd is first incorporated into the discretization for the second order temporal derivative and is combined with the implicit spatial fd the plane wave analysis method is used to derive the time space domain dispersion relations and two novel methods are proposed to determine the spatial and temporal fd coefficients in the joint time

lowrank seismic wave extrapolation on a staggered grid we evaluated a new spectral method and a new finite difference fd method for seismic wave extrapolation in time using staggered temporal and spatial grids we derived a wave extrapolation operator using a lowrank decomposition for a first order system of wave equations and designed the corresponding fd scheme the proposed methods extend previously proposed lowrank and lowrank fd wave extrapolation methods from the cases of constant density to those of variable density dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion the method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors tests on 2d synthetic examples demonstrated that the proposed method is highly accurate and stable the proposed methods can be used for seismic modeling or reverse time migration

full waveform static corrections using blind channel identification near surface wavefield perturbations can be very complex and completely mask the target reflections despite this complexity conventional methods rely on parameterizations characterized by simple time and amplitude anomalies to compensate for these perturbations determining and compensating for time shifts is generally referred to as residual static corrections whereas surface consistent deconvolution techniques deal with amplitude anomalies we present an approach that uses the full waveform to parameterize near surface perturbations therefore we refer to this method as waveform statics important differences from conventional static corrections are that this approachallowstimeshiftstovarywithfrequencyandtakesamplitudevariationsdirectlyintoaccount furthermore theprocedure is fully automated and does not rely on near surface velocity information the waveform static corrections are obtained using blind channel identification and applied to the recordings using multichannel deconvolution as a result the method implicitly incorporates array forming the developed method is validated onsyntheticdataandappliedtopartofafielddatasetacquiredin an area with significant near surface heterogeneity the source and receiver responses obtained are strongly correlated to the near surfaceconditionsandshowchanges bothinphaseandfrequency content along the spread the application of the waveform statics demonstrates that they not only correct for near surface wavefield perturbations but also strongly reduce coherent noise this results in substantial improvements both in trace totrace coherency and in depth resolution in addition the procedure delineates reflection events that are difficult to detect prior to our proposed correction based on these results we conclude that complex near surface perturbations can be successfully dealt with using the multichannel full waveform static correctionprocedure

the distribution and moments of the smallest eigenvalue of a random matrix of wishart type abstract given a random rectangular m n matrix with elements from a normal distribution what is the distribution of the smallest singular value to pose an equivalent question in the language of multivariate statistics what is the distribution of the smallest eigenvalue of a matrix from the central wishart distribution in the null case we give new results giving the distribution as a simple recursion this includes the more difficult case when n m is an even integer without resorting to zonal polynomials and hypergeometric functions of matrix arguments with the recursion one can obtain exact expressions for the density and the moments of the distribution in terms of functions usually no more complicated than polynomials exponentials and at worst ordinary hypergeometric functions we further elaborate on the special cases when n m 0 1 2 and 3 and give a numerical table of the expected values for 2 m 25 and 0 n m 25

robust geometrically based automatic two dimensional mesh generation a technical description of the algorithms employed in the modified quadtree mesh generator is given although the basis of the mesh generator is the same as the original version developed by yerry and shephard 1 2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique as demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach but introduce additional algorithmic difficulties the solutions of which are also presented in addition to examples showing the capability of the mesh generator the linear computational growth rate of the mesh generator is demonstrated

dithering of absorbers for efficient finite difference modeling of viscoelastic wave propagation viscoelastic modeling traditionally uses multiple relaxation mechanisms absorbers per wave type in each cell of the numerical grid we show that one absorber per cell suffices when the absorbers of different relaxation frequencies and absorption strengths are dithered in a supercell i e a very small area of several nearby cells the relaxation frequencies used in a supercell can be preselected to cover the bandwidth required in the modeling and distributed locally in a random manner to minimize numerical scattering the absorption strengths however must be found iteratively to yield an average absorption that matches the desired medium over the bandwidth we have tested the dithered absorber method for modeling a variety of 2 d media using a staggered grid finite difference scheme for a uniform medium our result agrees well with the exact analytic solution for inhomogeneous models the dithered absorber solution agrees well with the finite difference solution computed with five absorbers per cel

variance calculations and the bessel kernel in the laguerre ensembleof n xn hermitian matrices it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic denoted varnf asn furthermore this statistic often contains an additional parameter a for which the limit is most interesting and most difficult to compute numerically we derive exact expressions for both limn varnf and lim limn varnf

accelerating full waveform inversion with attenuation compensation abstractthe calculation of the gradient in full waveform inversion fwi usually involves crosscorrelating the forward propagated source wavefield and the back propagated data residual wavefield at each time step in the real earth propagating waves are typically attenuated due to the viscoelasticity which results in an attenuated gradient for fwi replacing the attenuated true gradient with a q compensated gradient can accelerate the convergence rate of the inversion process we have used a phase dispersion and an amplitude loss decoupled constant q wave equation to formulate a viscoacoustic fwi we used this wave equation to generate a q compensated gradient which recovers amplitudes while preserving the correct kinematics we construct an exact adjoint operator in a discretized form using the low rank wave extrapolation technique and we implement the gradient compensation by reversing the sign of the amplitude loss term in the forward and adjoint operators this leads to a q dependent gradient prec

time space domain mesh free finite difference based on least squares for 2d acoustic wave modeling abstractfinite difference fd methods approximate derivatives through a weighted summation of function values from neighboring nodes traditionally these neighboring nodes are assumed to be distributed regularly such as in square or rectangular lattices to improve geometric flexibility one option is to develop fd in a mesh free discretization in which scattered nodes can be placed suitably with respect to irregular boundaries or arbitrarily shaped anomalies without coordinate transformation or forming any triangles or tetrahedra etc these mesh free fds have had successful applications especially in computational geoscience however they are all space domain fd schemes in which fd coefficients are derived by approximating spatial derivatives individually in the space domain for acoustic wave modeling it has been proven that space domain fd methods normally have higher dispersion error than time space domain fd methods which determine fd coefficients by approximating the time space domain disp

modeling of a constant q methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique linear anelastic phenomena in wave propagation problems can be well modeled through a viscoelastic mechanical model consisting of standard linear solids in this paper we present a method for modeling of constant q as a function of frequency based on an explicit closed formula for calculation of the parameter fields several standard linear solids connected in parallel can be tuned through a single parameter to yield an excellent constant q approximation the proposed method enables substantial savings in computations and memory requirements experiments show that the new method also yields higher accuracy in the modeling of q than e g the pade approximant method

asymptotic form of the kullback leibler divergence for multivariate asymmetric heavy tailed distributions abstract an asymptotic expression for the kullback leibler kl divergence measure of multivariate skew t distributions mst is derived this novel class of flexible family distributions incorporates a shape and degree of freedom parameters in order to manipulate the skewness and heavy tail presence of the data respectively the quadratic form expressions of mst models are used to provide asymptotic measures additional inequalities for mst entropy and simulation studies are reported finally the expected values of the kl divergence of a sample correlation matrix obtained by pearson s correlation coefficient are discussed

two efficient modeling schemes for fractional laplacian viscoacoustic wave equation abstractrecently a decoupled fractional laplacian viscoacoustic wave equation has been developed based on the constant q model to describe wave propagation in heterogeneous media we have developed two efficient modeling schemes to solve the decoupled fractional laplacian viscoacoustic wave equation both schemes can cope with spatial variable order fractional laplacians conveniently and thus are applicable for modeling viscoacoustic wave propagation in heterogeneous media both schemes are based on fast fourier transform and have a spectral accuracy in space the first scheme solves a modified wave equation with constant order fractional laplacians instead of spatial variable order fractional laplacians due to separate discretization of space and time the first scheme has only first order accuracy in time differently the second scheme is based on an analytical wave propagator and has a higher accuracy in time to increase computational efficiency of the second modeling scheme we have adopted the

nonlinear scattering based imaging in elastic media theory theorems and imaging conditions with the more widespread introduction of multicomponent recording devices in land and marine ocean bottom seismic acquisition elastic imaging may become mainstream in coming years we have derived new nonlinear elastic imaging conditions a correlation type representation theorem for perturbed elastic media commonly used in seismic interferometry to explain how a scattered wave response between two receivers sources may be predicted given a boundary of sources receivers can be considered as a starting point for the derivation here we use this theorem to derive and interpret imaging conditions for elastic migration by wavefield extrapolation e g elastic reverse time migration some approximations lead to a known heuristically derived imaging condition that crosscorrelates p and s wave potentials that are separated in the subsurface after full wavefield extrapolation this formal connection reveals that the nonapproximated correlation type representation theorem can be interpreted as a nonlinear imaging condition that accounts also for multiply scattered and multiply converted waves properly focusing such energy at each image point we present a synthetic data example using either an ideal acquisition on a full closed boundary or a real partial boundary seismic exploration survey and we demonstrate the importance of nonlinearities in pure and converted mode imaging in pp imaging they result in better illumination and artifact reduction whereas in ps imaging they show how zero time lag and zero space lag crosscorrelation imaging conditions are not ideal for imaging of converted mode waves because no conversion arises from zero offset experiments

triangular and quadrilateral surface mesh quality optimization using local parametrization a procedure is presented to improve the quality of surface meshes while maintaining the essential characteristics of the discrete surface the surface characteristics are preserved by repositioning mesh vertices in a series of element based local parametric spaces such that the vertices remain on the original discrete surface the movement of the mesh vertices is driven by a non linear numerical optimization process two optimization approaches are described one which improves the quality of elements as much as possible and the other which improves element quality but also keeps the new mesh as close as possible to the original mesh

a robust 2 refinement algorithm in octree or rhombic dodecahedral tree based all hexahedral mesh generation in this paper we present a novel 2 refinement algorithm for adaptive all hexahedral mesh generation based on two tree structures octree and rhombic dodecahedral tree given a smooth boundary surface we first use a pre defined error function to detect the main surface features and build a strongly balanced octree then a novel 2 refinement algorithm is developed to eliminate all hanging nodes in the octree which is robust for any unstructured meshes and induces a smooth transition with very little propagation later all elements outside and around the boundary are removed to create the octree core mesh and a buffer zone the boundary points on the core mesh are projected onto the surface and form the final mesh motivated from nature a new tree structure based on rhombic dodecahedron is introduced sharp features are also detected and preserved during mesh generation finally pillowing geometric flow and optimization based smoothing are applied to improve quality of the constructed meshes

recurrence equations for the computation of correlations in the 1 r 2 quantum many body system in a previous paper the two particle distribution function and one particle density matrix for the quantum many body system with the 1 r2 pair potential have been expressed as limiting cases of selberg correlation integrals recurrence equations are derived which allow rapid evaluation of these multidimensional integrals the exact results for the two particle distribution are compared with the harmonic approximation

an accurate and efficient scheme for wave propagation in linear viscoelastic media the problem of wave propagation in a linear viscoelastic medium can be described mathematically as an exponential evolution operator of the form em t acting on a vector representing the initial conditions where m is a spatial operator matrix and t is the time variable techniques like finite difference for instance are based on a taylor expansion of this evolution operator we propose an optimal polynomial approximation of em t based on the powerful method of interpolation in the complex plane in a domain which includes the eigenvalues of the matrix m the new time integration technique is implemented to solve the isotropic viscoacoustic equation of motion the algorithm is tested for the problem of wave propagation in a homogeneous medium and compared with second order temporal differencing and the spectral chebychev method the algorithm solves efficiently and with machine accuracy the problem of seismic wave propagation with a dissipation mechanism in the sonic band a characteristic of sedimen

3d frequency domain finite difference viscoelastic wave modeling using weighted average 27 point operators with optimal coefficients abstractexperimental data suggest that the viscoelastic behavior of rocks is more easily and accurately described in the frequency domain than in the time domain supporting the idea of simulating seismic wave propagation in the frequency domain we evaluated weighted averaged 27 point finite difference operators for 3d viscoelastic wave modeling in the frequency domain within the proposed framework we developed general equations for normalized phase velocities that can be used with arbitrary finite difference operators three sets of weighting coefficients for second order central finite difference operators that minimize the numerical dispersion for up to five grid points per wavelength were found using a damped least squares ls criterion as well as a global optimization scheme based on l1 and l2 norm criteria the three sets produced very similar dispersion curves and improvement provided by global optimization appeared marginal in this respect we also evaluated a discrete form for the heterogen

accurate viscoelastic modeling by frequency domain finite differences using rotated operators the viscoelastic wave equation is an integro differential equation that requires special methods when using time domain numerical finite difference methods in the frequency domain the integral terms are easily represented by complex valued elastic media properties there are further significant advantages to using the frequency domain if the forward or the inverse problem requires modeling or inverting a large number of prestack source gathers numerical modeling is expensive for seismic data because of the large number of wavelenghths typically separating sources from receivers which results in a need for a large number of grid points a major obstacle to using frequency domain methods is the consequent storage requirements to reduce these we maximize the accuracy and simultaneously minimize the spatial extent of the numerical operators we achieve this by extending earlier published methods introduced for the viscoacoustic case to the viscoelastic case this requires the formulation of two new nume

optimal fourth order staggered grid finite difference scheme for 3d frequency domain viscoelastic wave modeling we investigate an optimal fourth order staggered grid finite difference scheme for 3d frequency domain viscoelastic wave modeling an anti lumped mass strategy is incorporated to minimize the numerical dispersion the optimal finite difference coefficients and the mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity an iterative damped least squares method the levenberg marquardt algorithm is utilized for the optimization dispersion analysis shows that the optimal fourth order scheme presents less grid dispersion and anisotropy than the conventional fourth order scheme with respect to different poisson s ratios moreover only 3 7 grid points per minimum shear wavelength are required to keep the error of the group velocities below 1 the memory cost is then greatly reduced due to a coarser sampling a parallel iterative method named carp cg is used to solve the large ill conditioned linear system for the frequency domain modeling validations are conducted with respect to both the analytic viscoacoustic and viscoelastic solutions compared with the conventional fourth order scheme the optimal scheme generates wavefields having smaller error under the same discretization setups profiles of the wavefields are presented to confirm better agreement between the optimal results and the analytic solutions

numerical modeling of transient two dimensional viscoelastic waves this paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids dissipation mechanisms are described using the generalized zener model no time convolutions are required thanks to the introduction of memory variables that satisfy local in time differential equations by appropriately choosing the relaxation parameters it is possible to accurately describe a large range of materials such as solids with constant quality factors the evolution equations satisfied by the velocity the stress and the memory variables are written in the form of a first order system of pdes with a source term this system is solved by splitting it into two parts the propagative part is discretized explicitly using a fourth order ader scheme on a cartesian grid and the diffusive part is then solved exactly jump conditions along the interfaces are discretized by applying an immersed interface method numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this numerical modeling for dealing with challenging problems such as multiple scattering configurations

a constant fractional order viscoelastic wave equation and its numerical simulation scheme abstractefficient modeling schemes currently exist to handle the spatially variable order fractional laplacians in the fractional laplacian viscoacoustic wave equation the simplest approach is to change the spatially variable order fractional laplacians into a linear combination of several constant fractional order laplacians we generalize the constant fractional order scheme to a spatially variable fractional order viscoelastic wave equation and develop an almost equivalent constant fractional order viscoelastic wave equation our constant fractional order scheme avoids the simulation error introduced by directly averaging the spatially varying fractional order thus our scheme simulates seismic wave propagation in viscoelastic media with sharp q contrasts well the fast fourier transform is used in the approximation of the fractional laplacians which improves the spectral accuracy in space several simulation examples are performed to verify that the numerical solution of a homogeneous q model obtai

an efficient seismic modeling in viscoelastic isotropic media abstractenergy is absorbed and attenuated when seismic waves propagate in real earth media hence the viscoelastic medium needs to be considered there are many ways to construct the viscoelastic body in which the generalized standard linear viscoelastic body is the most representative one for viscoelastic wave propagation and imaging it is very important to obtain a compact and efficient viscoelastic equation because of this we derived a set of simplified viscoelastic equations in isotropic media on the basis of the standard linear solid body and the constitutive relation for a linear viscoelastic isotropic solid the simplified equations were composed of the linear equations of momentum conservation the stress strain relations and the memory variable equations during the derivation of the equations the lame differentiation matrix which has a similar form to the stiffness matrix and indicates the relations between viscoelastic and elastic stiffness matrices was introduced to simplify the memo

wishart and anti wishart random matrices we provide a compact exact representation for the distribution of the matrix elements of the wishart type random matrices for any finite number of rows and columns of without any large n approximations in particular we treat the case when the wishart type random matrix contains redundant non random information which is a new result this representation is of interest for a procedure for reconstructing the redundant information hidden in wishart matrices with potential applications to numerous models based on biological social and artificial intelligence networks

a new approach to the development of automatic quadrilateral mesh generation a methodology for the automatic mesh generation of quadrilateral elements is proposed the methodology is based on the facts that i a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides ii a quadrilateral can be formed by two triangles which share a common side by taking advantage of the techniques developed in an existing automatic triangular mesh generator quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest in particular an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described techniques to improve the quality of the generated quadrilateral meshes are introduced the robustness and versatility of the mesh generator are demonstrated by a variety of examples

finite difference modeling of electromagnetic wave propagation in dispersive and attenuating media realistic modeling of electromagnetic wave propagation in the radar frequency band requires a full solution of maxwell s equations as well as an adequate description of the material properties we present a finite difference time domain fdtd solution of maxwell s equations that allows accounting for the frequency dependence of the dielectric permittivity and electrical conductivity typical of many near surface materials this algorithm is second order accurate in time and fourth order accurate in space conditionally stable and computationally only marginally more expensive than its standard equivalent without frequency dependent material properties empirical rules on spatial wavefield sampling are derived through systematic investigations of the influence of various parameter combinations on the numerical dispersion curves since this algorithm intrinsically models energy absorption efficient absorbing boundaries are implemented by surrounding the computational domain by a thin 2 dominant waveleng

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

3d weak dispersion reverse time migration using a stereo modeling operator reliable 3d imaging is a required tool for developing models of complex geologic structures reverse time migration rtm as the most powerful depth imaging method has become the preferred imaging tool because of its ability to handle complex velocity models including steeply dipping interfaces and large velocity contrasts finite difference methods are among the most popular numerical approaches used for rtm however these methods often encounter a serious issue of numerical dispersion which is typically suppressed by reducing the grid interval of the propagation model resulting in large computation and memory requirements in addition even with small grid spacing numerical anisotropy may degrade images or worse provide images that appear to be focused but position events incorrectly recently stereo operators have been developed to approximate the partial differential operator in space these operators have been used to develop several weak dispersion and efficient stereo modeling methods that have been found to be superior to conventional algorithms in suppressing numerical dispersion and numerical anisotropy we generalized one stereo modeling method fourth order nearly analytic central difference nacd from 2d to 3d and applied it to 3d rtm the rtm results for the 3d seg eage phase a classic data set 1 and the seg advanced modeling project model demonstrated that even when using a large grid size the nacd method can handle very complex velocity models and produced better images than can be obtained using the fourth order and eighth order lax wendroff correction lwc schemes we also applied 3d nacd and fourth order lwc to a field data set and illustrated significant improvements in terms of structure imaging horizon layer continuity and positioning we also investigated numerical dispersion and found that not only does the nacd method have superior dispersion characteristics but also that the angular variation of dispersion is significantly less than for lwc

time space domain dispersion relation based finite difference method with arbitrary even order accuracy for the 2d acoustic wave equation high order finite difference fd methods have been widely used for numerical solution of acoustic wave equations it has been reported that the modeling accuracy is of 2nd order when the conventional 2m th order space domain fd and the 2nd order time domain fd stencils are directly used to solve the acoustic wave equation under the same discretization the present version of time space domain dispersion relation based fd method can improve the accuracy from 2nd order to 2m th order along eight directions for the 2d acoustic wave equation to increase the accuracy further we propose a new fd stencil for 2d acoustic wave equation modeling this new time space domain dispersion relation based fd stencil can reach the same arbitrary even order accuracy along all directions and is more accurate and more stable than the conventional one for the same m dispersion analysis and modeling examples demonstrate its advantages

finite difference modeling with adaptive variable length spatial operators most finite difference simulation algorithms use fixed length spatial operators to compute spatial derivatives the choice of length is dictated by computing cost stability and dispersion criteria that are satisfied globally we propose finite difference schemes with adaptive variable length spatial operators to decrease computing costs significantly without reducing accuracy these schemes adopt long operators in regions of low velocity and short operators in regions of high velocity two methods automatically determine variable operator lengths dispersion analysis along with 1d and 2d modeling demonstrates the validity and efficiency of our schemes in addition a hybrid absorbing boundary condition helps reduce unwanted reflections from model boundaries our scheme is more efficient than those based on variable grid methods for modeling migration and inversion of models with complex velocity structures because the latter require local grid refinement which usually increases memory requirements

a novel scheme to generate meshes with hexahedral elements and poly pyramid elements the carving technique abstract a novel scheme for three dimensional mesh generation termed the carving technique is proposed with the aid of poly pyramid elements soaking the geometry information of a given model into a regular reference mesh with brick elements the reference mesh is trimmed by the surface of the model using the marching cube algorithm the trimmed elements are reconstructed by the proposed elements which here are termed the poly pyramid elements therefore the finite element mesh is automatically generated from the surface information shape functions of the poly pyramid elements are constructed by moving least square mls approximation numerical results are presented to examine the performance of the poly pyramid elements and to demonstrate the effectiveness of the proposed scheme

finite difference modeling of wave propagation in a fluid solid configuration finite difference fd techniques are widely used to model wave propagation through complex structures two main sources of error can be identified 1 from numerical dispersion and numerical anisotropy and 2 by modeling the response of internal grid boundaries conventional discretization criteria to reduce the effects of numerical dispersion and numerical anisotropy have long been established 5 8 gridpoints per wavelength for a fourth order accurate fd scheme we analyze the second source of errors comparing different staggered grid fd solutions to the cagniard de hoop solution in models with fluid solid contacts our results confirm that it is sufficient to rely on conventional discretization criteria if the fluid solid interface is aligned with the grid if accurate modeling of the scholte wave is required then a new imaging method we propose should be used to allow for conventional sampling of the wavefield to minimize numerical dispersion however for an interface not aligned with the grid irregular interfaces a spatial sampling of at least 15 gridpoints per minimum wavelength is required to obtain acceptable results particularly in seismic seabed applications where scholte waves may need to be modeled more accurately

viscoelastic finite difference modeling real earth media disperse and attenuate propagating mechanical waves this anelastic behavior can be described well by a viscoelastic model we have developed a finite difference simulator to model wave propagation in viscoelastic media the finite difference method was chosen in favor of other methods for several reasons finite difference codes are more portable than for example pseudospectral codes moreover finite difference schemes provide a convenient environment in which to define complicated boundaries a staggered scheme of second order accuracy in time and fourth order accuracy in space appears to be optimally efficient because of intrinsic dispersion no fixed grid points per wavelength rule can be given instead we present tables which enable a choice of grid parameters for a given level of accuracy since the scheme models energy absorption natural and efficient absorbing boundaries may be implemented merely by changing the parameters near the grid boundary the viscoelastic scheme is

exact results and universal asymptotics in the laguerre random matrix ensemble for various values of the parameters in the laguerre random matrix ensemble the distribution of the smallest eigenvalue and the scaled n level distribution function are calculated exactly in terms of generalized hypergeometric functions in certain cases these functions are expressed as multidimensional integrals from which asymptotic formulas are calculated and predictions of universal behavior verified

viscoacoustic modeling and imaging using low rank approximation abstracta constant q wave equation involving fractional laplacians was recently introduced for viscoacoustic modeling and imaging this fractional wave equation has a convenient mixed domain space wavenumber formulation which involves the fractional laplacian operators with a spatially varying power we have applied the low rank approximation to the mixed domain symbol which enables a space variable attenuation specified by the variable fractional power of the laplacians using the proposed approximation scheme we formulated the framework of the q compensated reverse time migration q rtm for attenuation compensation numerical examples using synthetic data demonstrated the improved accuracy of using low rank wave extrapolation with a constant q fractional laplacian wave equation for seismic modeling and migration in attenuating media low rank q rtm applied to viscoacoustic data is capable of producing images comparable in quality with those produced by conventional rtm from acoustic data

hexagon based all quadrilateral mesh generation with guaranteed angle bounds in this paper we present a novel hexagon based mesh generation method which creates all quadrilateral all quad meshes with guaranteed angle bounds and feature preservation for arbitrary planar domains given any planar curves an adaptive hexagon tree structure is constructed by using the curvature of the boundaries and narrow regions then a buffer zone and a hexagonal core mesh are created by removing elements outside or around the boundary to guarantee the mesh quality boundary edges of the core mesh are adjusted to improve their formed angles facing the boundary and two layers of quad elements are inserted in the buffer zone for any curve with sharp features a corresponding smooth curve is firstly constructed and meshed and then another layer of elements is inserted to match the smooth curve with the original one it is proved that for any planar smooth curve all the element angles are within 60 e 120 e e 5 we also prove that the scaled jacobians defined by two edge vectors are in the range of sin 60 e sin90 or 0 82 1 0 furthermore the same angle range can be guaranteed for curves with sharp features with the exception of small angles in the input curve in addition all the elements in the final mesh are grouped into five types and most elements only need a few flops to construct the stiffness matrix for finite element analysis this will significantly reduce the computational time and the required memory during the stiffness matrix construction we have applied our algorithm to a set of complicated geometries including the lake superior map and a three component air foil with sharp features

acoustic and elastic modeling by optimal time space domain staggered grid finite difference schemes abstractstaggered grid finite difference sfd methods are widely used in modeling seismic wave propagation and the coefficients of finite difference fd operators can be estimated by minimizing dispersion errors using taylor series expansion te or optimization we developed novel optimal time space domain sfd schemes for acoustic and elastic wave equation modeling in our schemes a fourth order multiextreme value objective function with respect to fd coefficients was involved to yield the globally optimal solution with low computational cost we first used variable substitution to turn our optimization problem into a quadratic convex one and then used least squares ls to derive the optimal sfd coefficients by minimizing the relative error of time space domain dispersion relations over a given frequency range to ensure the robustness of our schemes a constraint condition was imposed that the dispersion error at each frequency point did not exceed a given threshold moreover the hybrid absorbin

kullback leibler distance as a measure of the information filtered from multivariate data we show that the kullback leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data for correlation matrices of multivariate gaussian variables we analytically determine the expected values of the kullback leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown we propose to make use of the kullback leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures we also show how to use this distance to measure the stability of filtering procedures with respect to statistical uncertainty we explain the effectiveness of our method by comparing four filtering procedures two of them being based on spectral analysis and the other two on hierarchical clustering we compare these techniques as applied both to simulations of factor models and empirical data we investigate the ability of these filtering procedures in recovering the correlation matrix of models from simulations we discuss such ability in terms of both the heterogeneity of model parameters and the length of data series we also show that the two spectral techniques are typically more informative about the sample correlation matrix than techniques based on hierarchical clustering whereas the latter are more stable with respect to statistical uncertainty