an inverse scattering series method for attenuating multiples in seismic reflection data we present a multidimensional multiple attenuation method that does not require any subsurface information for either surface or internal multiples to derive these algorithms we start with a scattering theory description of seismic data we then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering these include 1 the idea that the inversion process can be viewed as a series of steps each with a specific task 2 the realization that the inverse scattering series provides an opportunity for separating out subseries with specific and useful tasks 3 the recognition that these task specific subseries can have different and more favorable data requirements convergence and stability conditions than does the original complete inverse series and most importantly 4 the development of the first method for physically interpreting the contribution that individual terms and pieces of terms in the inv

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

an optimal 9 point finite difference frequency space 2 d scalar wave extrapolator in this study a new finite difference technique is designed to reduce the number of grid points needed in frequency space domain modeling the new algorithm uses optimal nine point operators for the approximation of the laplacian and the mass acceleration terms the coefficients can be found by using the steepest descent method so that the best normalized phase curves can be obtained this method reduces the number of grid points per wavelength to 4 or less with consequent reductions of computer memory and cpu time that are factors of tens less than those involved in the conventional second order approximation formula when a band type solver is used on a scalar machine

dependence structure of the korean stock market in high frequency data abstract this paper analyzes the evolution of the dependence structure for various time window intervals known as epps effect using the trade and quote data of 663 actively traded stocks in korean stock market it is found that the random matrix theory analysis could not represent the dependence structure of the stock market in the microstructure regime the cook johnson copula is introduced as a parsimonious alternative method to handle this problem and the existence of the epps effect is confirmed for the 663 stocks using high frequency data it was also found that large capitalization companies tend to have a stronger dependence structure except for the largest capitalization group since the phenomenon of price level resistance leads to the weak dependence structure in the largest capitalization group in addition grouping the industry as a sub portfolio is an appropriate approach for hour interval traders whereas this approach is not a strategy recommended for high frequency traders

feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band limited reflection data abstractbecause seismic reflection data are band limited acoustic impedance profiles derived from them are nonunique the conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients by making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data drawing only on first principles the zoeppritz equation in this case the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band limited data the local layer cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness provided that the objective is to reconstruct a smooth version

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

quantifying and interpreting collective behavior in financial markets firms having similar business activities are correlated we analyze two different cross correlation matrices c constructed from i 30 min price fluctuations of 1000 us stocks for the two year period 1994 95 and ii one day price fluctuations of 422 us stocks for the 35 year period 1962 96 we find that the eigenvectors of c corresponding to the largest eigenvalues allow us to partition the set of all stocks into distinct subsets these subsets are similar to business sectors and are stable for extended periods of time we find that price fluctuations of these subsets are characterized by power law decaying time correlations reminiscent of strongly interacting systems the internal structure of a complex system manifests itself in correlations among its constituents in complex physical systems interactions between constituents cause collective modes having special statistical properties which reflect the underlying dynamics can we quantify collective movement of stock prices in analogous terms to address this question we analyze the equal time correlation matrix c constructed from the price fluctuations of a large number of stocks first we find that the collective modes for the stock market problem partition the set of all stocks studied into distinct subsets typically these subsets are formed by combinations of related industries and in some cases they go beyond grouping by industry due to company diversification the traditional partitioning of firms into subsets by products and services is difficult and sometimes arbitrary and thus our results could be viewed as a statistical alternative to traditional industry classification 1 furthermore we find that the price fluctuations of the collective modes display long range power law time correla

random matrix theory and fund of funds portfolio optimisation abstract the proprietary nature of hedge fund investing means that it is common practise for managers to release minimal information about their returns the construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise in this paper random matrix theory rmt is applied to a cross correlation matrix c constructed using hedge fund returns data the analysis reveals a number of eigenvalues that deviate from the spectrum suggested by rmt the components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers the inverse participation ratio is used to quantify the number of components that participate in each eigenvector finally the correlation matrix is cleaned by separating the noisy part from the non noisy part of c this technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio leading to an improved risk profile for a fund of hedge funds

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

locally solving fractional laplacian viscoacoustic wave equation using hermite distributed approximating functional method abstractaccurate seismic modeling in realistic media serves as the basis of seismic full waveform inversion and imaging recently viscoacoustic seismic modeling incorporating attenuation effects has been performed by solving a fractional laplacian viscoacoustic wave equation in this equation attenuation being spatially heterogeneous is represented partially by the spatially varying power of the fractional laplacian operator previously approximated by the global fourier method we have developed a local spectral approach based on the hermite distributed approximating functional hdaf method to implement the fractional laplacian in the viscoacoustic wave equation our approach combines local methods simplicity and global methods accuracy several numerical examples are developed to evaluate the feasibility and accuracy of using the hdaf method for the frequency independent q fractional laplacian wave equation

from classical reflectivity to velocity inversion to full waveform inversion using phase modified and deconvolved reverse time migration images abstractto obtain a physical understanding of gradient based descent methods in full waveform inversion fwi we find a connection between the fwi gradient and the image provided by reverse time migration rtm the gradient uses the residual data as a virtual source and rtm uses the observed data directly as the boundary condition so the fwi gradient is similar to a time integration of the rtm image using the residual data which physically converts the phase of the reflectivity to the phase of the velocity therefore gradient based fwi can be connected to the classical reflectivity to velocity impedance inversion rvi we have developed a new fwi scheme that provides a self contained and physically intuitive derivation which naturally establishes a connection among the amplitude preserved rtm the zoeppritz equations amplitude variation with angle inversion and rvi and combines them into a single framework to produce a preconditioned inversion formula in this scheme the relative velocity upd

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

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

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

high resolution prestack seismic inversion using a hybrid fista least squares strategy abstracta new inversion method to estimate high resolution amplitude versus angle attributes ava attributes such as intercept and gradient from prestack data is presented the proposed technique promotes sparse spike reflectivities that when convolved with the source wavelet fit the observed data the inversion is carried out using a hybrid two step strategy that combines fast iterative shrinkage thresholding algorithm fista and a standard least squares ls inversion fista which can be viewed as an extension of the classical gradient algorithm provides sparse solutions by minimizing the misfit between the modeled and the observed data and the l1 norm of the solution fista is used to estimate the location in time of the main reflectors then ls is used to retrieve the appropriate reflectivity amplitudes that honor the data fista like other iterative solvers for l1 norm regularization does not require matrices in explicit form making it easy to apply economic in computational terms and ad

efficient interval estimation of a ratio of marginal probabilities in matched pair data non iterative method matched pair designs have been commonly employed in diagnostic epidemiologic and laboratory studies for estimation of a ratio of two marginal probabilities in matched pair data a wald type logarithmic method is computationally simple but an actual coverage rate is known to be smaller than a nominal one and a length of the confidence interval is shorter than it should be the fieller type method based on constrained maximum likelihood cml estimators possesses asymptotically optimum statistical properties and a coverage rate is close to a nominal one however hitherto the limits have been obtained by numerical iterations in this paper we derive the efficient confidence limits based on cml as analytical solutions of a quartic equation and present the confidence limits in a closed form

cross correlation dynamics in financial time series abstract the dynamics of the equal time cross correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows empirical results for the s p 500 and the dow jones euro stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross correlation matrix over these time windows oppose those of the largest eigenvalue this behaviour is shown to be independent of the size of the time window and the number of stocks examined a basic one factor model is then proposed which captures the main dynamical features of the eigenvalue spectrum of the empirical data through the addition of perturbations to the one factor model leading to a market plus sectors model additional sectoral features are added resulting in an inverse participation ratio comparable to that found for empirical data by partitioning the eigenvalue time series we then show that negative index returns drawdowns are associated with periods where the largest eigenvalue is greatest while positive index returns drawups are associated with periods where the largest eigenvalue is smallest the study of correlation dynamics provides some insight on the collective behaviour of traders with varying strategies

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

temporal windowing and inverse transform of the wavefield in the laplace fourier domain temporal windowing is a valuable process which can help us to focus on a specific event in a seismogram however applying the time window is difficult outside the time domain we suggest a windowing method which is applicable in the laplace fourier domain the window function we adopt is defined as a product of a gain function and an exponential damping function the fourier transform of a seismogram windowed by this function is equivalent to the partial derivative of the laplace fourier domain wavefield with respect to the complex damping constant therefore we can obtain a windowed seismogram using the partial derivatives of the laplace fourier domain wavefield we exploit the time windowed wavefield which is modeled directly in the laplace fourier domain to reconstruct subsurface velocity model by waveform inversion in the laplace fourier domain we present the windowed seismograms by introducing an inverse laplace fourier transform technique and demonstrate the effect of temporal windowing in a synthetic laplace fourier domain waveform inversion example

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

confidence intervals for a ratio of binomial proportions based on paired data four interval estimation methods for the ratio of marginal binomial proportions are compared in terms of expected interval width and exact coverage probability two new methods are proposed that are based on combining two wilson score intervals the new methods are easy to compute and perform as well or better than the method recently proposed by nam and blackwelder two sample size formulas are proposed to approximate the sample size required to achieve an interval estimate with desired confidence level and width

the reaction of stock markets to crashes and events a comparison study between emerging and mature markets using wavelet transforms abstract we study here the behaviour of the first three eigenvalues 1 2 3 and their ratios 1 2 1 3 2 3 of the covariance matrices of the original return series and of those rebuilt from wavelet components for emerging and mature markets it has been known for some time that the largest eigenvalue 1 contains information on the risk associated with the particular assets of which the covariance matrix is comprised here we wish to ascertain whether the subdominant eigenvalues 2 3 hold information on the risk of the stock market and also to measure the recovery time for emerging and mature markets to do this we use the discrete wavelet transform which gives a clear picture of the movements in the return series by reconstructing them using each wavelet component our results appear to indicate that mature markets respond to crashes differently to emerging ones in that emerging markets may take up to two months to recover while major markets take less than a month to do so in addition the results appears to show that the subdominant eigenvalues 2 3 give additional information on market movement especially for emerging markets and that a study of the behaviour of the other eigenvalues may provide insight on crash dynamics

cluster structure in the correlation coefficient matrix can be characterized by abnormal eigenvalues abstract in a large number of previous studies the researchers found that some of the eigenvalues of the financial correlation matrix were greater than the predicted values of the random matrix theory r m t here we call these eigenvalues as abnormal eigenvalues in order to reveal the hidden meaning of these abnormal eigenvalues we study the toy model with cluster structure and find that these eigenvalues are related to the cluster structure of the correlation coefficient matrix in this paper model based experiments show that in most cases the number of abnormal eigenvalues of the correlation matrix is equal to the number of clusters in addition empirical studies show that the sum of the abnormal eigenvalues is related to the clarity of the cluster structure and is negatively correlated with the correlation dimension

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

inverse scattering theory inverse scattering series method for one dimensional non compact support potential the reversion of the born neumann series of the lippmann schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem one limitation of the current inversion methods based on the reversion of the born neumann series is that the velocity potential should have compact support however this assumption cannot be satisfied in certain cases especially in seismic inversion based on the idea of distorted wave scattering we explore an inverse scattering method for velocity potentials without compact support the strategy is to decompose the actual medium as a known single interface reference medium which has the same asymptotic form as the actual medium and a perturbative scattering potential with compact support after introducing the method to calculate the green s function for the known reference potential the inverse scattering series and volterra inverse scattering series are derived for the perturbative potential analytical and numerical examples demonstrate the feasibility and effectiveness of this method besides to ensure stability of the numerical computation the lanczos averaging method is employed as a filter to reduce the gibbs oscillations for the truncated discrete inverse fourier transform of each order our method provides a rigorous mathematical framework for inverse acoustic scattering with a non compact support velocity potential

seismic sparse spike deconvolution via toeplitz sparse matrix factorization abstractwe have developed a new sparse spike deconvolution ssd method based on toeplitz sparse matrix factorization tsmf a bilinear decomposition of a matrix into the product of a toeplitz matrix and a sparse matrix to address the problems of lateral continuity effects of noise and wavelet estimation error in ssd assuming the convolution model a constant source wavelet and the sparse reflectivity a seismic profile can be considered as a matrix that is the product of a toeplitz wavelet matrix and a sparse reflectivity matrix thus we have developed an algorithm of tsmf to simultaneously deconvolve the seismic matrix into a wavelet matrix and a reflectivity matrix by alternatively solving two inversion subproblems related to the toeplitz wavelet matrix and sparse reflectivity matrix respectively because the seismic wavelet is usually compact and smooth the fused lasso was used to constrain the elements in the toeplitz wavelet matrix moreover due to the limitations of computer memory large

emergence of correlations between securities at short time scales abstract the correlation matrix is the key element in optimal portfolio allocation and risk management in particular the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode sectors and style factors we investigate how these eigenvalues depend on the time scale of securities returns in the u s market for this purpose one minute returns of the largest 533 u s stocks are aggregated at different time scales and used to estimate the correlation matrix and its spectral properties we reveal the emergence of several dominant eigenvalues as the time scale increases a simple lead lag factor model is proposed to capture and reproduce the observed time scale dependence of eigenvalues using this model the relaxation time of the eigenvalues emergence is estimated to be around one minute for all the dominant eigenmodes including the market mode as a consequence the use of five minute returns time series for inferring correlations between stocks turns out to be a good compromise between statistical abundance of data points and well established correlations our findings evidence that the underlying economic and financial mechanisms determining the correlation structure of securities depend as well on time scales

random matrix theory analysis of cross correlations in the us stock market evidence from pearson s correlation coefficient and detrended cross correlation coefficient abstract in this study we first build two empirical cross correlation matrices in the us stock market by two different methods namely the pearson s correlation coefficient and the detrended cross correlation coefficient dcca coefficient then combining the two matrices with the method of random matrix theory rmt we mainly investigate the statistical properties of cross correlations in the us stock market we choose the daily closing prices of 462 constituent stocks of s p 500 index as the research objects and select the sample data from january 3 2005 to august 31 2012 in the empirical analysis we examine the statistical properties of cross correlation coefficients the distribution of eigenvalues the distribution of eigenvector components and the inverse participation ratio from the two methods we find some new results of the cross correlations in the us stock market in our study which are different from the conclusions reached by previous studies the empirical cross correlation matrices constructed by the dcca coefficient show several interesting properties at different time scales in the us stock market which are useful to the risk management and optimal portfolio selection especially to the diversity of the asset portfolio it will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix r for the dcca coefficient because it does not obey the marcenko pastur distribution

signal and noise in correlation matrix using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator this relation can be used in practice to compute eigenvalue invariants of the covariance correlation matrix results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom like for instance those in statistical physics lattice measurements of field theory genetics quantitative finance and other applications of multivariate statistics

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

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

comparing the structure of an emerging market with a mature one under global perturbation a b s t r a c t in this paper we investigate the tehran stock exchange tse and dow jones industrial average djia in terms of perturbed correlation matrices to perturb a stock market there are two methods namely local and global perturbation in the local method we replace a correlation coefficient of the cross correlation matrix with one calculated from two gaussian distributed time series whereas in the global method we reconstruct the correlation matrix after replacing the original return series with gaussian distributed time series the local perturbation is just a technical study we analyze these markets through two statistical approaches random matrix theory rmt and the correlation coefficient distribution by using rmt we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks we find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with gaussian distributed time series the mean values of correlation coefficients the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the rmt prediction fall sharply in both markets by comparing these two markets we can see that the djia is more sensitive to global perturbations these findings are crucial for risk management and portfolio selection

on the analysis of cross correlations in south african market data we report briefly on an application of random matrix theory to the analysis of sa financial market data an analysis of cross correlations in south african financial market data e print cond mat 0402389 correlation matrices c are constructed from 10 years of daily data for stocks listed on the johannesburg stock exchange from january 1993 to december 2002 spectral properties of c are tested against random matrix predictions we highlight some quantitative differences which arise when treating prices as existing only when measured as opposed to interpolating missing or illiquid trading days with a zero order hold

wavelet radon domain dealiasing and interpolation of seismic data spatial aliasing is unavoidable in some seismic data and has serious effects on the performance of multichannel data processing and migration antialias filtering produces distortion of the signal through the removal of high frequency information in contrast dealiasing produces an unaliased estimate of the signal at all frequencies present in the original time series a new dealiasing algorithm is developed by exploiting the properties of seismic wavefields in the wavelet radon transform domain specifically the overlap of information between wavelet scales at the same frequency the effectiveness of the wavelet radon dealiasing algorithm is demonstrated through the processing of both synthetic and field seismic data

a helmholtz iterative solver for 3d seismic imaging problems a preconditioned iterative solver for the 3d frequency domain wave equation applied to seismic problems is evaluated the preconditioner corresponds to an approximate inverse of a heavily damped wave equation deduced from the undamped wave equation the approximate inverse is computed with one multigrid cycle numerical results show that the method is robust and that the number of iterations increases roughly linearly with frequency when the grid spacing is adapted to keep a constant number of discretization points per wavelength to evaluate the relevance of this iterative solver the number of floating point operations required for two imaging problems are roughly evaluated this rough estimate indicates that the time domain migration approach is more than one order of magnitude faster the full wave form tomography based on a least squares formulation and a scale separation approach has the same complexity in both domains

reconstruction of the velocity and density in a stratified acoustic half space using a short pulse point source the reconstruction of the velocity and density in a stratified half space using the reflection data generated by a short pulse point source is considered transverse spatial hankel transform is applied to the transient reflected and incident pressures on the surface the reflection kernel in the hankel transformed space is obtained through a deconvolution the time domain green function approach based on the wave splitting is then used to reconstruct the parameters this time domain approach to the inverse problem is exact and noniterative numerical results for some synthetical examples are presented to illustrate the hankel transform deconvolution and the reconstruction the finite difference time domain method is used to generate the transient reflection data in the physical space in a numerical simulation the reconstruction using obliquely incident plane waves is also considered in an appendix

signal and noise in financial correlation matrices abstract using random matrix theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator experimentally measured correlation matrix these relations will be used to analyze a particular case of the correlations in financial series and to show that contrary to earlier claims correlations can be measured also in the random part of the spectrum implications for the portfolio optimization are briefly discussed

inverse scattering theory renormalization of the lippmann schwinger equation for acoustic scattering in one dimension the most robust treatment of the inverse acoustic scattering problem is based on the reversion of the born neumann series solution of the lippmann schwinger equation an important issue for this approach to inversion is the radius of convergence of the born neumann series for fredholm integral kernels and especially for acoustic scattering for which the interaction depends on the square of the frequency by contrast it is well known that the born neumann series for the volterra integral equations in quantum scattering are absolutely convergent independent of the strength of the coupling characterizing the interaction the transformation of the lippmann schwinger equation from a fredholm to a volterra structure by renormalization has been considered previously for quantum scattering calculations and electromagnetic scattering in this paper we employ the renormalization technique to obtain a volterra equation framework for the inverse acoustic scattering series proving that this series also converges absolutely in the entire complex plane of coupling constant and frequency values the present results are for acoustic scattering in one dimension but the method is general the approach is illustrated by applications to two simple one dimensional models for acoustic scattering

accuracy of finite difference and finite element modeling of the scalar and elastic wave equations numerical solutions of the scalar and elastic wave equations have greatly aided geophysicists in both forward modeling and migration of seismic wave fields in complicated geologic media and they promise to be invaluable in solving the full inverse problem this paper quantitatively compares finite difference and finite element solutions of the scalar and elastic hyperbolic wave equations for the most popular implicit and explicit time domain and frequency domain techniques in addition to versatility and ease of implementation it is imperative that one choose the most cost effective solution technique for a fixed degree of accuracy to be of value a solution technique must be able to minimize 1 numerical attenuation or amplification 2 polarization errors 3 numerical anisotropy 4 errors in phase and group velocities 5 extraneous numerical parasitic modes 6 numerical diffraction and scattering and 7 errors and transmission coefficients this paper shows that in homogeneous media the

reconstruction of two dimensional permittivity distribution using the distorted born iterative method the distorted born iterative method dbim is used to solve two dimensional inverse scattering problems thereby providing another general method to solve the two dimensional imaging problem when the born and the rytov approximations break down numerical simulations are performed using the dbim and the method proposed previously by the authors int j imaging syst technol vol 1 no 1 p 100 8 1989 called the born iterative method bim for several cases in which the conditions for the first order born approximation are not satisfied the results show that each method has its advantages the dbim shows faster convergence rate compared to the bim while the bim is more robust to noise contamination compared to the dbim

a parallel multigrid based preconditioner for the 3d heterogeneous high frequency helmholtz equation we investigate the parallel performance of an iterative solver for 3d heterogeneous helmholtz problems related to applications in seismic wave propagation for large 3d problems the computation is no longer feasible on a single processor and the memory requirements increase rapidly therefore parallelization of the solver is needed we employ a complex shifted laplace preconditioner combined with the bi cgstab iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator a 3d multigrid method with 2d semi coarsening is employed we show numerical results for large problems arising in geophysical applications

dynamics of implied volatility surfaces from random matrix theory abstract we analyze the dynamics of the implied volatility surface of kospi 200 futures options from random matrix theory to extract the informative data we use random matrix criteria implied volatility data have a colossal eigenvalue and the order of eigenvalues in a noisy regime is distinguishably smaller than a random matrix theory prediction we discern the marketwide knowledge of the implied volatility surface movement such as the level skew and smile effect these dynamics has the ergodic property and long range autocorrelation we also study the relationship between the three implied volatility surface dynamics and the underlying asset dynamics and confirm the existence of leverage effect even in the short time interval

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

velocity model building by 3d frequency domain full waveform inversion of wide aperture seismic data we assessed 3d frequency domain fd acoustic fullwaveforminversionfwidataasatooltodevelophigh resolution velocity models from low frequency global offset data the inverse problem was posed as a classic leastsquares optimization problem solved with a steepest descent method inversion was applied to a few discrete frequencies allowing management of a limited subset of the 3d data volume the forward problem was solved with a finite difference frequency domain method based on a massively paralleldirectsolver allowingefficientmultiple shotsimulations the inversion code was fully parallelized for distributedmemory platforms taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver after validation on simple synthetic tests fwi was applied to two targets channel and thrust system of the 3d seg eageoverthrustmodel correspondingto3ddomains of 78 752 25 km and 13 513 54 65 km respectively the maximum inverted frequencies are 15 and 7 hz for the two applications amaximum of 30 dual core biprocessor nodes with 8 gb of shared memory per node were used for the second target the main structures were imaged successfully at a resolution scale consistent with the inverted frequencies our study confirms the feasibility of 3d frequency domain fwi of global offset data on large distributed memory platforms to develop high resolution velocity models these high velocity models may provide accurate macromodelsforwave equationprestackdepthmigration

comments on confidence intervals for a ratio of binomial proportions based on paired data by d g bonett and r m price statistics in medicine 2006 25 3039 3047

seismic waveform inversion in the frequency domain part 1 theory and verification in a physical scale model seismic waveforms contain much information that is ignored under standard processing schemes seismic waveform inversion seeks to use the full information content of the recorded wavefield in this paper i present apply and evaluate a frequency space domain approach to waveform inversion the method is a local descent algorithm that proceeds from a starting model to refine the model in order to reduce the waveform misfit between observed and model data the model data are computed using a full wave equation viscoacoustic frequency domain finite difference method ray asymptotics are avoided and higher order effects such as diffractions and multiple scattering are accounted for automatically the theory of frequency domain waveform wavefield inversion can be expressed compactly using a matrix formalism that uses finite difference finite element frequency domain modeling equations expressions for fast local descent inversion using back propagation techniques then follow naturally implementation of

analysis of the ratio of marginal probabilities in a matched pair setting statistical methods for testing and interval estimation of the ratio of marginal probabilities in the matched pair setting are considered in this paper we are especially interested in the situation where the null value is not one as in one sided equivalence trials we propose a fieller type statistic based on constrained maximum likelihood cml estimation of nuisance parameters for a series of examples the significance level of the cml test is satisfactorily close to the nominal level while a wald type test is anticonservative for reasonable sample sizes we present formulae for approximate power and sample size for the cml and wald tests the matched design is seen to have a clear advantage over the unmatched design in terms of asymptotic efficiency when the two responses of the pair are highly positively correlated we recommend the cml method over the wald method especially for small or moderate sample sizes

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

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

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

spiking band limited traces with a relative entropy algorithm a novel method for the inversion of band limited seismic traces to full bandwidth reflectivity traces is based on a probabilistic spiky model of the reflectivity trace in which position indicators and amplitudes of the spikes occur as random variables and relies on relative entropy inference from information theory first an a priori model for general reflectivity traces in the prospect is derived from nearby wells second the a priori distribution is updated into an a posteriori distribution for the specific trace being studied by the addition of the fourier data of the seismic trace within a passband uncertainty about the fourier coefficients can be accounted for by specification of a noise variance which implicitly is infinite outside the passband the update with relative entropy inference is justified because of its relationship with bayesian inference application of maximum a posteriori map estimation to the a posteriori distribution results in the most likely spiky reflectivity trace of f

a note on rearrangements spectral concentration and the zero order prolate spheroidal wavefunction if the measure of the support of a function f is small its symmetric decreasing rearrangement f is more nearly bandlimited to low frequencies than f while their norms are equal an immediate corollary is that the time limited zero order prolate spheroidal wavefunction is the extremal function for a new optimization problem involving time and bandlimiting the result has an application in exploration seismology

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

low frequency reflection data augmentation by an inpainting method 1d acoustic media abstractthe augmentation of low frequencies is an important problem for inverting seismic reflection data through an acoustic scattering approach we have characterized how the data down to zero frequency grows in importance with increasing depth and the size of the velocity contrast we have developed a hermite distributed approximation functional hdaf inpainting method that provides a least squares fitting of the acoustic reflection data down to zero frequency the hdaf data fitting is applied to the first born approximation for compact velocity contrasts the top and bottom depth velocities are equal several fitting constraints are derived using a taylor expansion of the reflection data near zero frequency they provide a coupling with the first born approximation of the velocity contrast the method can be extended to the general geophysical case in which the final velocity i e is different from the starting velocity by use of the distorted wave born approximation numerical results for 1d t

random matrix theory for portfolio optimization a stability approach we apply random matrix theory rmt to an empirically measured financial correlation matrix c and show that this matrix contains a large amount of noise in order to determine the sensitivity of the spectral properties of a random matrix to noise we simulate a set of data and add different volumes of random noise having ascertained that the eigenspectrum is independent of the standard deviation of added noise we use rmt to determine the noise percentage in a correlation matrix based on real data from s p500 eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart finally we attempt to separate the noisy part from the non noisy part of c we apply an existing technique to cleaning c and then discuss its associated problems we propose a technique of filtering c that has many advantages from the stability point of view over the existing method of cleaning

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

3d finite difference frequency domain modeling of visco acoustic wave propagation using a massively parallel direct solver a feasibility study we present a finite difference frequency domain method for 3d visco acoustic wave propagation modeling in the frequency domain the underlying numerical problem is the resolution of a large sparse system of linear equations whose right hand side term is the source this system is solved with a massively parallel direct solver we first present an optimal 3d finite difference stencil for frequency domain modeling the method is based on a parsimonious staggered grid method differential operators are discretized with second order accurate staggered grid stencils on different rotated coordinate systems to mitigate numerical anisotropy an antilumped mass strategy is implemented to minimize numerical dispersion the stencil incorporates 27 grid points and spans two grid intervals dispersion analysis shows that four grid points per wavelength provide accurate simulations in the 3d domain to assess the feasibility of the method for frequency domain full waveform inversion we computed simulations in the 3d seg eage overthrust model for frequencies 5 7 and 10 hz results confirm the huge memory requirement of the factorization several hundred figabytes but also the cpu efficiency of the resolution phase few seconds per shot heuristic scalability analysis suggests that the memory complexity of the factorization is o 35n 4 for a n 3 grid our method may provide a suitable tool to perform frequency domain full waveform inversion using a large distributed memory platform further investigation is still necessary to assess more quantitatively the respective merits and drawbacks of time and frequency domain modeling of wave propagation to perform 3d full waveform inversion

2 d bayesian deconvolution inverse problems can be solved in different ways one way is to define natural criteria of good recovery and build an objective function to be minimized if instead we prefer a bayesian approach inversion can be formulated as an estimation problem where a priori information is introduced and the a posteriori distribution of the unobserved variables is maximized when this distribution is a gibbs distribution these two methods are equivalent furthermore global optimization of the objective function can be performed with a monte carlo technique in spite of the presence of numerous local minima application to multitrace deconvolution is proposed in traditional 1 d deconvolution a set of unidimensional processes models the seismic data while a markov random field is used for 2 d deconvolution in fact the introduction of a neighborhood system permits one to model the layer structure that exists in the earth and to obtain solutions that present lateral coherency moreover optimization of an appropriated objective function by simulated annealing allows one to control the fit with the input data as well as the spatial distribution of the reflectors extension to 3 d deconvolution is straightforward

frequency domain acoustic wave modeling and inversion of crosshole data part 1 2 5 d modeling method crosshole experiments usually have sources and receivers confined to a plane and it is assumed that there is negligible variation in the properties of the medium normal to this plane therefore the problem appears two dimensional except for the sources which are 3 d points rather than lines this configuration is denoted as two and one half dimensional we present a frequency domain approach to modeling acoustic wave propagation in such situations which allows correct treatment of point sources but takes advantage of the assumed 2 d nature of the medium to avoid full 3 d simulations the approach uses a fourier transform with respect to the out of plane coordinate to reduce the problem of modeling in 3 d to repeatedly solving a 2 d equation which we accomplish using finite differences the discrete inverse fourier transform from the out of plane wavenumber implies the existence of an infinite number of spurious ghost sources spaced periodically in the out of plane direction these sources generate s