rayleigh marchenko redatuming for target oriented true amplitude imaging abstractmarchenko redatuming is a revolutionary technique to estimate green s functions from virtual sources in the subsurface using only data measured at the earth s surface without having to place either sources or receivers in the subsurface this goal is achieved by crafting special wavefields so called focusing functions that can focus energy at a chosen point in the subsurface despite its great potential strict requirements on the reflection response such as knowledge and accurate deconvolution of the source wavelet including absolute scaling factor and co location of sources and receivers have so far challenged the application of marchenko redatuming to real world scenarios i combine the coupled marchenko equations with a one way version of the rayleigh integral representation to obtain a new redatuming scheme that handles internal as well as free surface multiples using dual sensor band limited seismic data with an unknown source signature from any acquisition system that presents arbit

nonparametric quantile estimations for dynamic smooth coefficient models in this article quantile regression methods are suggested for a class of smooth coefficient time series models we use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework we establish the asymptotic properties of both the local polynomial and local constant estimators for mixing time series also a bandwidth selector based on the nonparametric version of the akaike information criterion is suggested together with a consistent estimate of the asymptotic covariance matrix furthermore the asymptotic behaviors of the estimators at boundaries are examined a comparison of the local polynomial quantile estimator with the local constant estimator is presented a simulation study is carried out to illustrate the performance of estimates an empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

generalized bremmer series with rational approximation for the scattering of waves in inhomogeneous media the bremmer series solution of the wave equation in generally inhomogeneous media requires the introduction of pseudodifferential operators in this paper sparse matrix representations of these pseudodifferential operators are derived the authors focus on designing sparse matrices keeping the accuracy high at the cost of ignoring any critical scattering angle phenomena such matrix representations follow from rational approximations of the vertical slowness and the transverse laplace operator symbols and of the vertical derivative as they appear in the parabolic equation method sparse matrix representations lead to a fast algorithm an optimization procedure is followed to minimize the errors in the high frequency limit for a given discretization rate the bremmer series solver consists of three steps directional decomposition into up and downgoing waves one way propagation and interaction of the counterpropagating constituents each of these steps is represented by a sparse matrix equation the resulting algorithm provides an improvement of the parabolic equation method in particular for transient wave phenomena and extends the latter method systematically for backscattered waves

flux normalized wavefield decomposition and migration of seismic data separation of wavefields into directional components can be accomplished by an eigenvalue decomposition of the accompanying system matrix in conventional pressurenormalized wavefield decomposition the resulting one way wave equations contain an interaction term which depends on the reflectivity function applying directional wavefield decomposition using flux normalized eigenvalue decomposition and disregarding interaction between up and downgoing wavefields these interaction terms were absent by also applying a correction term for transmission loss the result was an improved estimate of the up and downgoing wavefields in the wave equation angle transform a crosscorrelation function in local offset coordinates was fourier transformed to produce an estimate of reflectivity as a function of slowness or angle we normalized this wave equation angle transform with an estimate of the planewave reflection coefficient the flux normalized oneway wave propagation scheme was applied to imaging and to the normalized wave equation angle transform on synthetic and field data this proved the effectiveness of the new methods

application of unsplit convolutional perfectly matched layer for scalar arbitrarily wide angle wave equation abstracta classical split perfectly matched layer pml method has recently been applied to the scalar arbitrarily wide angle wave equation awwe in terms of displacement however the classical split pml obviously increases computational cost and cannot efficiently absorb waves propagating into the absorbing layer at grazing incidence our goal was to improve the computational efficiency of awwe and to enhance the suppression of edge reflections by applying a convolutional pml cpml we reformulated the original awwe as a first order formulation and incorporated the cpml with a general complex frequency shifted stretching operator into the renewed formulation a staggered grid finite difference fd method was adopted to discretize the first order equation system for wavefield depth continuation the first order awwe with the cpml saved memory compared with the original second order awwe with the conventional split pml with the help of numerical examples we verified the correctness of the staggered

target oriented wave equation least squares migration inversion with phase encoded hessian prestack depth migration produces blurred images resulting from limited acquisition apertures complexities in the velocity model and band limited characteristics of seismic waves this distortion can be partially corrected using the model space least squares migration inversion approach where a target oriented wave equation hessian operator is computed explicitly and then inverse filtering is applied iteratively to deblur or invert for the reflectivity however one difficulty is the cost of computing the explicit hessian operator which requires storing a large number of green s functions making it challenging for large scale applications a new method to compute the hessian operator for the wave equation based least squares migration inversion problem modifies the original explicit hessian formula enabling efficient computation of this operator an advantage is that the method eliminates disk storage of green s functions the modifications however also introduce undesired crosstalk artifacts two different phase encoding schemes plane wave phase encoding and random phase encoding suppress the crosstalk when the randomly phase encoded hessian operator is applied to the sigsbee2a synthetic data set an improved subsalt image with more balanced amplitudes is obtained

reducing two way splitting error of ffd method in dual domains the fourier finite difference ffd method is very popular in seismic depth migration but its straightforward 3d extension creates two way splitting error due to ignoring the cross terms of spatial partial derivatives traditional correction schemes either in the spatial domain by the implicit finite difference method or in the wavenumber domain by phase compensation lead to substantially increased computational costs or numerical difficulties for strong velocity contrasts we propose compensating the two way splitting error in dual domains alternately in the spatial and wavenumber domains via fourier transform first we organize the expanded square root operator in terms of two way splitting ffd plus the usually ignored cross terms second we select a group of optimized coefficients to maximize the accuracy of propagation in both inline and crossline directions without yet considering the diagonal directions finally we further optimize the constant coefficient of the compensation part to further improve the overall accuracy of the operator in implementation the compensation terms are similar to the high order corrections of the generalized screen method but their functions are to compensate the two way splitting error rather than the expansion error numerical experiments show that optimized one term compensation can achieve nearly perfect circular impulse responses and the propagation angle with less than 1 error for all azimuths is improved up to 60 from 35 compared with traditional single domain methods our scheme can handle lateral velocity variations even for strong velocity contrasts much more easily with only one additional fourier transform based on the two way splitting ffd method which helps retain the computational efficiency

functional coefficient instrumental variables models we consider estimation of nonparametric structural models under a functional coefficient representation for the regression function under this representation models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables a nonparametric generalization of random coefficient models the functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed and partially linear models over which they have appreciable flexibility we propose two step estimators that use local linear approximations in both steps the first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors our large sample results include consistency and asymptotic normality of the proposed estimators the high practical power of estimators is illustrated via both a monte carlo simulation study and an application to returns to education

a spatial temporal point process model with a continuous distribution of storm types 1 a point process rainfall model is further developed that has storm origins occurring in space time according to a poisson process where each storm origin has a random radius so that storms occur as circular regions in two dimensional space where the storm radii are taken to be independent exponential random variables each storm origin is of random type z where z follows a continuous probability distribution cell origins occur in a further spatial poisson process and have arrival times that follow a neyman scott point process each cell origin has a radius so that cells form discs in two dimensional space where the cell radii are independent exponential random variables each cell has a random lifetime and an intensity that remains constant over both the cell lifetime and cell disk area statistical properties up to third order are given for the model using these properties the model is fitted to 10 min series taken from 23 sites across the rome region italy distributional properties of the observed annual maxima are compared to equivalent values sampled from series that are simulated using the fitted model the results indicate that the model will be of use in urban drainage projects for the rome region

wide angle fd and ffd migration using complex pade approximations seismic migration by downward continuation using the one way wave equation approximations has two shortcomings imaging steep dip reflectors and handling evanescent waves complex pade approximations allow a better treatment of evanescent modes stabilizing finite difference migration without requiring special treatment for the migration domain boundaries imaging of steep dip reflectors can be improved using several terms in the pade expansion we discuss the implementation and evaluation of wide angle complex pade approximations for finite difference and fourier finite difference migration methods the dispersion relation and the impulsive response of the migration operator provide criteria to select the number of terms and coefficients in the pade expansion this ensures stability for a prescribed maximum propagation direction the implementations are validated on the marmousi model data set and seg eage salt model data

reciprocity properties of one way propagators acoustic reciprocity is a fundamental property of the wave equation for the total acoustic wavefield rayleigh 1878 in its most elementary form the reciprocity principle states that an acoustic response remains the same when the source and receiver are interchanged in terms of green s functions this reciprocity principle reads g r2 r1 g r1 r2 with r x y z for more general expressions and their seismic applications see fokkema and van den berg 1993

migration of primaries and multiples using an imaging condition for amplitude normalized separated wavefields abstractmigration of primary and multiple reflections leads to enhanced subsurface illumination and to increased image resolution a joint migration approach using the complete wavefield requires properly imaged primaries and multiples of all orders in recent works primaries and multiples have therefore been imaged separately using the upgoing and downgoing pressure wavefields obtained by decomposing dual sensor streamer data the matches between the corresponding depth images are still not found to be sufficiently accurate so new and more appropriate imaging conditions need to be found we reviewed the classical imaging approach used in one way wave equation migration with the aim of extending it for simultaneous migration of primaries and all orders of multiples based on rayleigh s reciprocity theorem and well known theoretical developments we derived a new imaging condition described in terms of the upgoing pressure wavefield and a filtered version of the downgoing vertical velocity wavefield t

a semiparametric quantile panel data model with an application to estimating the growth effect of fdi abstract this paper estimates the impact of foreign direct investment on economic growth by proposing a new semiparametric quantile panel data model with correlated random effects in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant a three stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated a simple and easily implemented procedure for making inferences is proposed monte carlo simulation is conducted to examine the finite sample performance of the proposed estimators finally using the cross country panel data we find a strong empirical evidence of the existence of the absorptive capacity hypothesis together with another new finding that fdi has much stronger growth effects for countries with fast economic growth than for those with slow economic growth

quantile regression under misspecification with an application to the u s wage structure quantile regression qr fits a linear model for conditional quantiles just as ordinary least squares ols fits a linear model for conditional means an attractive feature of ols is that it gives the minimum mean squared error linear approximation to the conditional expectation function even when the linear model is misspecified empirical research using quantile regression with discrete covariates suggests that qr may have a similar property but the exact nature of the linear approximation has remained elusive in this paper we show that qr minimizes a weighted mean squared error loss function for specification error the weighting function is an average density of the dependent variable near the true conditional quantile the weighted least squares interpretation of qr is used to derive an omitted variables bias formula and a partial quantile regression concept similar to the relationship between partial regression and ols we also present asymptotic theory for the qr process under misspecification of the conditional quantile function the approximation properties of qr are illustrated using wage data from the u s census these results point to major changes in inequality from 1990 to 2000

fourier finite difference migration many existing migration schemes cannot simultaneously handle the two most important problems of migration imaging of steep dips and imaging in media with arbitrary velocity variations in all directions for example phase shift k migration is accurate for nearly all dips but it is limited to very simple velocity functions on the other hand finite difference schemes based on one way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events we propose a new hybrid migration method named fourier finite difference migration wherein the downward continuation operator is split into two downward continuation operators one operator is a phase shift operator for a chosen constant background velocity and the other operator is an optimized finite difference operator for the varying component of the velocity function if there is no variation of velocity then only a phase shift operator will be applied automatically on the other hand if there is a strong variatio

globally optimized finite difference extrapolator for strongly vti media implicit finite difference fd migration is unconditionally stable and is popular in handling strong velocity variations but its extension to strongly transversely anisotropic media with vertical symmetric axis media is difficult traditional local optimizations generate the optimized coefficients for each pair of thomsen anisotropy parameters independently which can degrade results substantially for large anisotropy variations and lead to a huge table we developed an implicit fd method using the analytic taylor series expansion and used a global optimization scheme to improve its accuracy for wide phase angles we first extended the number of the constant coefficients then we relaxed the coefficient of the time delay extrapolation term by tuning a small factor such that error is less than 0 1 finally we optimized the constant coefficients using a simulated annealing algorithm by constraining that all the error functions on a fine grid of the whole anisotropic region did not exceed 0 5 simultaneously the extended number of the constant coefficients and the relaxed coefficient greatly enhanced the flexibility of matching the dispersion relation and significantly improved the ability of handling strong anisotropy over a much wider range compared with traditional local optimization our scheme does not need any table and table lookup for each order of the fd method only one group of optimized coefficients is enough to handle strong variations in velocity and anisotropy more importantly our global optimization scheme guarantees the accuracy for various possible ranges of anisotropy parameters no matter how strong the anisotropy is for the globally optimized second order fd method the accurate phase angle is up to 58 and the increase is about 18 22 for the globally optimized fourth order fd method the accurate phase angle is up to 77 and the increase is about 22 27

riemannian wavefield extrapolation riemannian spaces are described by nonorthogonal curvilinear coordinates we generalize one way wavefield extrapolation to semiorthogonal riemannian coordinate systems that include but are not limited to ray coordinate systems we obtain a one way wavefield extrapolation method that can be used for waves propagating in arbitrary directions in contrast to downward continuation which is used for waves propagating mainly in the vertical direction ray coordinate systems can be initiated in many different ways for example from point sources or from plane waves incident at various angles since wavefield propagation happens mostly along the extrapolation direction we can use inexpensive finite difference or mixed domain extrapolators to achieve high angle accuracy the main applications of our method include imaging of steeply dipping or overturning reflections

migration of seismic data by phase shift plus interpolation under the horizontally layered velocity assumption migration is defined by a set of independent ordinary differential equations in the wavenumber frequency domain the wave components are extrapolated downward by rotating their phases this paper shows that one can generalize the concepts of the phase shift method to media having lateral velocity variations the wave extrapolation procedure consists of two steps in the first step the wave field is extrapolated by the phase shift method using l laterally uniform velocity fields the intermediate result is l reference wave fields in the second step the actual wave field is computed by interpolation from the reference wave fields the phase shift plus interpolation pspi method is unconditionally stable and lends itself conveniently to migration of three dimensional data the performance of the methods is demonstrated on synthetic examples the pspi migration results are then compared with those obtained from a finite difference method

wave equation based seismic illumination analysis we present a wave equation based method for seismic illumination analysis a one way wave equation based generalized screen propagator is used to extrapolate the wavefields from sources and receivers to the subsurface target a local plane wave analysis is used at the target to calculate localized directionalenergyfluxesforbothsourceandreceiver wavefields we construct an illumination matrix using these energy fluxes to quantify the target illumination conditions the target geometry information is used to manipulate the illumination matrix and generate different types of illumination measures the wave equation based approach can properly handle forward multiple scattering phenomena including focusing defocusing diffraction and interference effects itcanbedirectlyappliedtocomplexvelocitymodels velocity model smoothing and fresnel zone smoothing are not required different illumination measurements derived from this method can be applied to target oriented or volumetric illumination analyses this new method is flexible and practical for illumination analysis in complex 2d and 3d velocity models with nontrivial acquisition and target

adaptive varying coefficient linear models varying coefficient linear models arise from multivariate nonparametric regression nonlinear time series modelling and forecasting functional data analysis longitudinal data analysis and others it has been a common practice to assume that the vary coefficients are functions of a given variable which is often called an index a frequently asked question is which variable should be used as the index in this paper we explore the class of the varying coefficient linear models in which the index is unknown and is estimated as a linear combination of regression and or other variables this will enlarge the modelling capacity substantially we search for the index such that the derived varying coefficient model provides the best approximation to the underlying unknown multi dimensional regression function in the least square sense the search is implemented through the newly proposed hybrid backfitting algorithm the core of the algorithm is the alternative iteration between estimating the index through a one step scheme and estimating coefficient functions through a one dimensional local linear smoothing the generalised cross validation method for choosing bandwidth is efficiently incorporated into the algorithm the locally significant variables are selected in terms of the combined use of t statistic and akaike information criterion we further extend the algorithm for the models with two indices simulation shows that the proposed methodology has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers the methods are further illustrated through the canadian mink muskrat data in 1925 1994 and the pound dollar exchange rates in 1974 1983

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

on additive conditional quantiles with high dimensional covariates we investigate the estimation of the conditional quantile when many covariates are involved in particular we model the conditional quantile of a response as a nonlinear additive function of relevant covariates for this setup we propose a nonparametric smoother to estimate the unknown functions the estimator provides direct computation of the nonlinear functions because it does not require any iteration the estimator allows fast and routine data analysis on the theoretical front we also show asymptotic properties of the estimator including mean squared error and limiting distribution the theory confirms that for moderate dimension of the covariates the estimator escapes the curse of dimensionality problem both simulated and real data examples are provided to illustrate the methodology

theory of true amplitude one way wave equations and true amplitude common shot migration one way wave operators are powerful tools for forward modeling and migration here we describe a recently developed true amplitude implementation of modified one way operators and present some numerical examples by true amplitude one way forward modeling we mean that the solutions are dynamically correct as well as kinematically correct that is ray theory applied to these equations yields the upward and downward traveling eikonal equations of the full wave equation and the amplitude satisfies the transport equation of the full wave equation the solutions of these equations are used in the standard wave equation migration imaging condition the boundary data for the downgoing wave is also modified from the one used in the classic theory because the latter data is not consistent with a point source for the full wave equation when the full wave form solutions are replaced by their ray theoretic approximations the imaging formula reduces to the common shot kirchhoff inversion formula in this sense

growth and convergence a profile of distribution dynamics and mobility in this paper we focus primarily on the dynamic evolution of the world distribution of growth rates in per capita gdp we propose new concepts and measures of convergence or divergence that are based on entropy distances and dominance relations between groups of countries over time we update the sample period to include the most recent decade of data available and we offer traditional parametric and new nonparametric estimates of the most widely used growth regressions for two important subgroups of countries oecd and non oecd traditional parametric models are rejected by the data however using robust nonparametric methods we find strong evidence in favor of polarization and within group mobility

migration with arbitrarily wide angle wave equations we develop a new scalar migration technique that is highly accurate for imaging steep dips in heterogeneous media this method is based on arbitrarily wide angle wave equations awwes that are highly accurate space domain one way wave equations and have a form similar to the 15 equation the accuracy of the proposed method is increased by introducing auxiliary variables as well as adjusting the parameters of the approximation poststack migration is carried out by downward continuation using the awwe for which we have developed a stable explicit double marching scheme up to 80 accuracy is achieved by second order awwe migration with only 2 3 times the computational effort of the 15 equation and requiring almost the same storage we illustrate the performance of awwe migration using impulse response graphs a single dipping reflector and a slice of the seg eage salt model

arbitrarily wide angle wave equations for complex media by combining various ideas related to one way wave equations owwes half space stiffness relation special finite element discretization and complex coordinate stretching a systematic procedure is developed for deriving a series of highly accurate space domain versions of owwes the resulting procedure is applicable to complex media where the governing equation full wave equation is a second order differential system making the procedure applicable for general heterogeneous anisotropic porous viscoelastic media owing to their high accuracy in representing waves propagating in an arbitrarily wide range of angles the resulting equations are named arbitrarily wide angle wave equations awwes in order to illustrate the proposed procedure awwes are derived for one way propagation in acoustic as well as elastic media while acoustic awwes can be considered as modified versions of well known space domain owwes based on rational approximations of the square root operator the elastic awwes are significantly different from the existing elastic owwes unlike the existing elastic owwes elastic awwes are displacement based and are applicable to general anisotropic media furthermore awwes are simple in their form and appear amenable to easy numerical implementation

a stable one way wave propagator for vti media for the purpose of one way wave equation imaging a pseudoscreen propagator is developed for transversely isotropic media with vertical axes of symmetry the phase shift for propagation through a depth slice is decomposed into three terms a gazdag phase shift for propagation in a laterally homogeneous reference medium a correction for lateral variability of vertical propagation and a remaining wide angle term for oblique directions of propagation based on rational function approximation for this remaining wide angle term a fourier finite difference ffd approach with four way splitting is applied fourth order pade approximation is unsatisfactory in anelliptic media for large propagation angles with respect to the vertical direction therefore a method of coefficient optimization is developed in conjunction with a method of choosing an adequate homogeneous reference medium in a depth slice by symmetrizing the finite difference operators and because of the choice of the optimized coefficients the propagator is stable in the sense that the least squares norm of the wavefield measured for a frequency depth slice does not grow with increasing depth of propagation a small amount of artificial damping is applied to suppress artifacts that appear at the critical angle defined by the velocities in the reference medium and the actual medium synthetic examples confirm that good kinematic accuracy is achieved for a wide range of propagation angles typically up to 60

anisotropic complex pade hybrid finite difference depth migration standard real valued finite difference fd and fourier finite difference ffd migrations cannot handle evanescent waves correctly which can lead to numerical instabilities in the presence of strong velocity variations a possible solution to these problems is the complex pade approximation which avoids problems with evanescent waves by rotating the branch cut of the complex square root we have applied this approximation to the acoustic wave equation for vertical transversely isotropic media to derive more stable fd and hybrid fd ffd migrations for such media our analysis of the dispersion relation of the new method indicates that it should provide more stable migration results with fewer artifacts and higher accuracy at steep dips our studies lead to the conclusion that the rotation angle of the branch cut that should yield the most stable image is 60 for fd migration as confirmed by numerical impulse responses and work with synthetic data

optimized chebyshev fourier migration a wide angle dual domain method for media with strong velocity contrasts a wide angle propagator is essential when imaging complex media with strong lateral velocity contrasts in one way waveequation migration we have developed a dual domain one way propagator using truncated chebyshev polynomials and a globally optimized scheme our method increases the accuracy of the expanded square root operator by adding two high order terms to the traditional split step fourier propagator first we approximate the square root operator using taylor expansion around the reference background velocity then we apply the first kindchebyshevpolynomialstoeconomizetheresultsofthe taylor expansion finally we optimize the constant coefficients using the globally optimized scheme which are fixed and feasible for arbitrary velocity models theoretical analysis and numericalexperimentshavedemonstratedthatthemethodhasvery highaccuracyandexceedstheunoptimizedfourierfinite difference propagator for the entire range of practical velocity contrasts the accurate propagation angle of the method is always about 60 under the relative error of 1 for complex media with weak moderate and even strong lateral velocity contrasts the method allows us to handle wide angle propagations and strong lateral velocity contrast simultaneously by using fourier transform alone only four 2d fourier transforms are required for each step of 3d wavefield extrapolation and the computing cost is similar to that of the fourier finite difference method compared with the finite difference method our method has no twowaysplittingerrori e azimuthal anisotropyerrorfor3dcases and almost no numerical dispersion for coarse grids in addition it has strong potential to be accelerated when an enhanced fast fouriertransformalgorithmemerges

semiparametric quantile regression estimation in dynamic models with partially varying coefficients national science foundation of china 71131008 70871003 70971113 university of north carolina at charlotte chinese ministry of education minjiang scholarship from fujian province china xiamen university boston college

a generalized spatial temporal model of rainfall based on a clustered point process the objective in this paper is to present and fit a relatively simple stochastic spatial temporal model of rainfall in which the arrival times of rain cells occur in a clustered point process in the x y plane rain cells are represented as discs each disc having a random radius the locations of the disc centres being given by a two dimensional poisson process the intensity of each cell is a random variable that remains constant over the area of the disc and throughout the lifetime of the cell the lifetime being an exponential random variable the cells are randomly classified from 1 to n with different parameters for the different cell types so that the random variables of an arbitrary cell e g radius and intensity are correlated multi site second order properties are derived and used to fit the model to hourly rainfall data taken from six sites in the thames basin uk

the hartley transform in seismic imaging phase shift migration techniques that attempt to account for lateral velocity variations make substantial use of the fast fourier transform fft generally the hermitian symmetry of the complex valued fourier transform causes computational redundancies in terms of the number of operations and memory requirements in practice a combination of the fft with the well known real to complex fourier transform is often used to avoid such complications as an alternative means to the fourier transform we introduce the inherently real valued non symmetric hartley transform into phase shift migration techniques by this we automatically avoid the hermitian symmetry resulting in an optimized algorithm that is comparable in efficiency to algorithms based on the real to complex fft we derive the phase shift operator in the hartley domain for migration in two and three dimensions and formulate phase shift plus interpolation split step migration and split step double square root prestack migration in terms of the

stable wide angle fourier finite difference downward extrapolation of 3 d wavefields i present an unconditionally stable implicit finite difference operator that corrects the constant velocity phase shift operator for lateral velocity variations the method is based on the fourier finite difference ffd method contrary to previous results my correction operator is stable even when the medium velocity has sharp discontinuities and the reference velocity is higher than the medium velocity the stability of the new correction enables the definition of a new downward continuation method based on the interpolation of two wavefields the first wavefield is obtained by applying the ffd correction starting from a reference velocity lower than the medium velocity the second wavefield is obtained by applying the ffd correction starting from a reference velocity higher than the medium velocity the proposed fourier finite difference plus interpolation ffdpi method combines the advantages of the ffd technique with the advantages of interpolation a simple and economical procedure for defining

directional illumination analysis using the local exponential frame we have developed an efficient method of directional illuminationanalysisinthelocalangledomainusinglocalexponential frame beamlets the space domain wavefields with different shot receiver geometries are decomposed into the local angle domain by using the local exponential beamlets which form a tight frame with the redundancy ratio two and are implemented by a linear combination of local cosine and localsinetransforms becauseofthefastalgorithmsofthelocal cosine sine transforms this method is much more efficient than the previously used decomposition methods in directional illumination analysis such as the local slant stackingmethodandthegabor daubechiesframemethod theresults of directional illumination di maps and the acquisitiondipresponsesadrforthe2dseg eagesaltmodel and the 45 shot 3d seg eage model demonstrated the validity and feasibility of our method compared with the illumination results using local slant stacking decomposition thenewmethodproducesilluminationmapsofsimilarquality but it does so a few times faster furthermore because of its high computational efficiency and saving in memory usage the new method makes the 3d directional illumination analysisreadilyapplicableintheindustry

nonparametric estimation of an additive quantile regression model this article is concerned with estimating the additive components of a nonparametric additive quantile regression model we develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n r 2r 1 when the additive components are r times continuously differentiable for some r 2 this result holds regardless of the dimension of the covariates and thus the new estimator has no curse of dimensionality in addition the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function the numerical performance and usefulness of the estimator are illustrated by monte carlo experiments and an empirical example

fourier finite difference wave propagation we introduce a novel technique for seismic wave extrapolation in time the technique involves cascading a fourier transform operator and a finite difference operator to form a chain operator fourier finite differences ffd we derive the ffd operator from a pseudoanalytical solution of the acoustic wave equation two dimensional synthetic examples demonstrate that the ffd operator can have high accuracy and stability in complex velocity media applying the ffd method to the anisotropic case overcomes some disadvantages of other methods such as the coupling of qp waves and qsv waves the ffd method can be applied to enhance accuracy and stability of seismic imaging by reverse time migration

prestack migration by split step dsr the double square root dsr prestack migration equation though defined for depth variable velocity can be used to image media with strong velocity variations using a phase shift plus interpolation pspi or split step correction the split step method is based on applying a phase shift correction to the extrapolated wavefield a correction that attempts to compensate for the lateral velocity variations i show how to extend dsr prestack migration to lateral velocity media and exemplify the method by applying the new algorithm to the marmousi data set the split step dsr migration is very fast and offers excellent imaging results

shot profile true amplitude crosscorrelation imaging condition the u d imaging condition for shot profile migration can be used to estimate the angle dependent reflection coefficient but is difficult to implement numerically because of the spectral division involved most techniques for stabilizing the division require a damping factor which might be difficult to estimate and which also introduces bias into the final result a stable result can be achieved by approximating the imaging condition with a crosscorrelation of the up and downgoing wavefields at zero time lag but this will lead to incorrect amplitudeversus angle ava behavior of the estimated reflection coefficient we use a simple model for wave propagation of primary reflections in the wavenumber frequency domain and invert the model with respect to the reflection coefficient by using the properties of wavefield extrapolators it can then be shown that the reflection coefficients can be estimated by crosscorrelation of the upgoing wavefield and a downgoing wavefield where the initial wavefield is the inverse of the wavefield generated by a point source the new imaging condition gives the correct ava behavior for horizontal reflectors for dipping reflectors it is shown that a postmigration correction factor can be used to recover the correct angle behavior of the reflection coefficient the new imaging condition is numerically stable does not involve damping factors is simple to implement numerically and is a simple modification of the classical crosscorrelation imaging condition numerical examples confirm the correct ava behavior of the new imaging condition

generalization of the bremmer coupling series an operator formalism is developed to expand the acoustic wave field in a multi dimensionally smoothly varying medium generated by a source localized in space and time into a sum of constituents each of which can be interpreted as a wave that has traveled up and down with respect to a direction of preference a definite number of times this expansion is a generalization of the bremmer coupling series the condition of smoothness of the medium relates to the width of the signature of the source in the configuration both the existence and the convergence in the weak sense of the expansion are discussed the operator calculus involved leads to a natural generalization of the concept of slowness surface to multi dimensionally smoothly varying media the operator associated with the corresponding generalized vertical slowness induces the full one way wave operator in the type of media under consideration in addition a wavefield decomposition operator as well as an interaction operator that couples the decomposed constituents are derived

sample splitting and threshold estimation threshold models have a wide variety of applications in economics direct applications include models of separating and multiple equilibria other applications include empirical sample splitting when the sample split is based on a continuously distributed variable such as firm size in addition threshold models may be used as a parsimonious strategy for nonparametric function estimation for example the threshold autoregressive model tar is popular in the nonlinear time series literature threshold models also emerge as special cases of more complex statistical frameworks such as mixture models switching models markov switching models and smooth transition threshold models it may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures despite the large number of potential applications the statistical theory of threshold estimation is undeveloped it is known that threshold estimates are super consistent but a distribution theory useful for testing and inference has yet to be provided this paper develops a statistical theory for threshold estimation in the regression context we allow for either cross section or time series observations least squares estimation of the regression parameters is considered an asymptotic distribution theory for the regression estimates the threshold and the regression slopes is developed it is found that the distribution of the threshold estimate is nonstandard a method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic it is shown that this yields asymptotically conservative confidence regions monte carlo simulations are presented to assess the accuracy of the asymptotic approximations the empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of durlauf and johnson 1995

accounting for free surface multiples in marchenko imaging imagine placing a receiver at any location in the earth and recording the response at that location to sources on the surface in such a world we could place receivers around our reservoir to better image the reservoir and understand its properties realistically this is not a feasible approach for understanding the subsurface we have developed an alternative and realizable approach to obtain the response of a buried virtual receiver for sources at the surface our method is capable of retrieving the green s function for a virtual point in the subsurface to the acquisition surface in our case a physical receiver is not required at the subsurface point instead we require the reflection measurements for sources and receivers at the surface of the earth and a macromodel of the velocity no small scale details of the model are necessary we can interpret the retrieved green s function as the response to sources at the surface for a virtual receiver in the subsurface we obtain this green s function by solving the marchenko equation an integral equation pertinent to inverse scattering problems our derivation of the marchenko equation for the green s function retrieval takes into account the free surface reflections present in the reflection response previous work considered a response without free surface multiples we decompose the marchenko equation into up and downgoing fields and solve for these fields iteratively the retrieved green s function not only includes primaries and internal multiples as do previous methods but it also includes freesurface multiples we use these up and downgoing fields to obtain a 2d image of our area of interest in this case below a synclinal structure

wide angle one way wave equations a one way wave equation also known as a paraxial or parabolic wave equation is a differential equation that permits wave propagation in certain directions only such equations are used regularly in underwater acoustics in geophysics and as energy absorbing numerical boundary conditions the design of a one way wave equation is connected with the approximation of 1 s2 1 2 on 1 1 by a rational function which has usually been carried out by pade approximation this article presents coefficients for l2 l and other alternative classes of approximants that have better wide angle behavior for theoretical results establishing the well posedness of these wide angle equations see the work of trefethen and halpern well posedness of one way wave equations and absorbing boundary conditions math comput 47 421 435 1986

recursive integral time extrapolation methods for waves a comparative review abstractwe compared several families of algorithms for recursive integral time extrapolation rite algorithms for waves in isotropic and anisotropic media these methods allow simulating accurate wave extrapolation with little numerical dispersion even when using larger time steps than are usually possible for conventional finite difference methods these various rite algorithms all share the use of mixed space wavenumber domain operators derived from fourier integral solutions of single mode wave equations we evaluated a taxonomy for rite methods based on how they approximated the influence of medium heterogeneity one family of methods uses mixed domain series expansions to provide accurate approximations to heterogeneous extrapolators even for large time steps we compared several methods for deriving coefficients for such series approximations another family of methods uses interpolation between different homogeneous extrapolations to approximate heterogeneous time extrapolation such methods can b

a born wkbj inversion method for acoustic reflection data density and bulk modulus variations in an acoustic earth are separately recoverable from standard reflection surveys by utilizing the amplitude versus offset information present in the observed wave fields both earth structure and a variable background velocity can be accounted for by combining the born and wkbj approximations in a before stack migration with two output sections one for density variations and the other for bulk modulus variations for the inversion the medium is considered to be composed of a known low spatial frequency variation the background plus an unknown high spatial frequency variation in bulk modulus and density the reflectivity the division between the background and the reflectivity depends upon the frequency content of the source for constant background parameters computations are done in the fourier domain where the first part of the algorithm includes a frequency shift identical to that in an f k migration the modulus and density variations are then determined by observing in a least squares sense amplitude versus offset wavenumber for a spatially variable background wkbj green s operators that model the direct wave in a medium with a smoothly varying background are used a downward continuation with these operators removes the effects of variable velocity from the problem and consequently the remainder of the inversion essentially proceeds as if the background were constant if the background is strictly depth dependent the inversion can be expressed in closed form the method neglects multiples and surface waves and it is restricted to precritical reflections density is distinguishable from bulk modulus only if a sufficient range of precritical incident angles is present in the data

a regionalization method based on a cluster probability model 1 a regionalization method based on a cluster probability model a mixed multivariate gaussian model is proposed for grouping sites into nonoverlapping contiguous homogeneous regions defined by a voronoi tessellation theisson polygons the cluster probability model is applied to second order standardized annual sample properties mean coefficient of variation and autocorrelation evaluated at the daily level of aggregation taken from each of 234 daily rainfall records with positions located in the basque country spain using the bayesian information criterion four clusters of sites are identified which do not fall into contiguous regions the distances between all neighboring pairs of sites connected by edges from the delaunay planar graph are found the probability that a site belongs to each of the four clusters is extracted from the fitted gaussian model and multiplied into the probability that the neighboring site belongs to the same cluster these products are divided by the squared distance between the sites and are summed to give an overall measure of a site belonging to a cluster that takes into account the classification of neighboring sites regions from the voronoi tessellation of the points are classed on the basis of this measure and according to whether they are spatially isolated from other regions of the same class points that have the least influence on the variance of residual errors of the fitted model are found using a criterion based on wilks lambda for multivariate analysis of variance and the classes of the least influential points are adjusted to ensure the overall regions are contiguous

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

target oriented wave equation inversion a target oriented strategy can be applied to estimate a wave equation least squares inverse lsi image by explicitly computing the wave equation hessian the lsi image is obtained as the solution of a nonstationary least squares inverse filtering problem the rows of the hessian are the nonstationary filters containing information about the acquisition geometry the velocity model and the band limited characteristics of the seismic data by exploiting the sparsity and the structure of the hessian matrix a large number of iterations necessary to achieve convergence can be computed cheaply the results on a structurally complex model show the improvements of the lsi image versus the migrated image

optimization of the parameters in complex pade fourier finite difference migration abstractcomplex pade fourier finite difference migration is a stable one way wave equation technique that allows for better treatment of evanescent modes than its real counterpart in this way producing fewer artifacts as for real fourier finite difference ffd migration its parameters can be optimized to improve the imaging of steeply dipping reflectors the dip limitation of the ffd operator depends on the variation of the velocity field we have developed a wide angle approximation for the one way continuation operator by means of optimization of the pade coefficients and the most important velocity dependent parameter we have evaluated the achieved quality of the approximate dispersion relation in dependence on the chosen function of the ratio between the model and reference velocities under consideration of the number of terms in the pade approximation and the branch cut rotation angle the optimized parameters are chosen based on the migration results and the computational cost we found that by

subsurface reflectivity estimation from imaging of primaries and multiples using amplitude normalized separated wavefields abstractseveral studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors however to characterize the reflector properties there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples from this perspective and based on the wave equation and rayleigh s reciprocity theorem recent works have suggested computing the subsurface image from the green s function reflection response or reflectivity by inverting a fredholm integral equation in the frequency space domain by following claerbout s imaging principle and assuming locally reacting media the integral equation may be reduced to a trace by trace deconvolution imaging condition for a complex overburden and considering that the structure of the subsurface is angle dependent this trace by trace deconvolution does not properly solve the fredholm integral equation we

source receiver marchenko redatuming obtaining virtual receivers and virtual sources in the subsurface abstractby solving the marchenko equations one can retrieve the green s function marchenko green s function between a virtual receiver in the subsurface and points at the surface no physical receiver is required at the virtual location we extend the idea behind these equations to retrieve the green s function between any two points in the subsurface i e between a virtual source and a virtual receiver no physical source or physical receiver is required at either of these locations this green s function is called the virtual green s function and it includes all primary internal and free surface multiples similar to the marchenko green s function this virtual green s function requires the reflection response at the surface single sided illumination and an estimate of the first arrival traveltime from the virtual locations to the surface these green s functions can be used to image the interfaces from above and below

one way wave equation migration in log polar coordinates we obtained acoustic wave and wavefield extrapolation equations in log polar coordinates lpcs and tried to enhance the imaging to achieve this goal it was necessary to decrease the angle between the wavefield extrapolation axis and wave propagation direction in the one way wave equation migration wem if we were unable to carry it out more reflection wave energy would be lost in the migration process it was concluded that the wavefield extrapolation operator in lpcs at low frequencies has a large wavelike region and at high frequencies it can mute the evanescent energy in these coordinate systems an extrapolation operator can readily lend itself to high order finitedifference schemes therefore even with the use of inexpensive operators wem in lpcs can clearly image varied horizontal and vertical events in complex geologic structures using wide angle and turning waves in these coordinates we did not encounter any problems with reflections from opposing dips dispersion played important roles not only as a filter operator but also as a gain function prestack and poststack migration results were obtained with extrapolation methods in different coordinate systems and it was concluded that migration in lpcs can image steeply dipping events in a much better way when compared with other methods

gaussian parsimonious clustering models gaussian clustering models are useful both for understanding and suggesting powerful criteria banfield and raftery 1993 have considered a parametrization of the variance matrix ek of a cluster pk in terms of its eigenvalue decomposition ek lkdkakd k lk where lk defines the volume of pk dk is an orthogonal matrix which defines its orientation and ak is a diagonal matrix with determinant 1 which defines its shape this parametrization allows us to propose many general clustering criteria from the simplest one spherical cluster with equal volumes which leads to the classical k means criterion to the most complex one unknown and different volumes orientations and shapes for all clusters methods of optimization to derive the maximum likelihood estimates as well as the practical usefulness of these models are discussed we especially analyze the influence of the volumes of clusters we report monte carlo simulations and an application on stellar data which dramatically illustrated the relevance of allowing clusters to have different volumes

frequency wavenumber inversion of acoustic data we describe an inversion procedure for obtaining velocities densities and layer thicknesses from multioffset reflection seismograms generated by a point source excitation in a stratified acoustic medium the reference seismograms are decomposed into cylindrical waves in the frequency wavenumber domain where the inversion is performed by minimizing the difference between the reference data and modeled data using a least squares technique the modeling algorithm is based on the classical reflectivity method we include the effects of limited temporal and spatial apertures by applying a frequency and wavenumber dependent filter in the modeling process this inversion is suited for jacobian matrix methods where the first derivatives of the model generated data with respect to the model parameters are calculated from analytical expressions together with the modeling the numerical examples show that the inversion algorithm recovers with reasonable accuracy the parameters used to generate the reference data the low frequency trends of both the velocity and the density are restored the convergence of the iterative minimization algorithm is fast

true amplitude one way wave equation migration in the mixed domain one way wave equation migration is a powerful imaging tool for locating accurately reflectors in complex geologic structures however the classical formulation of one way wave equations does not provide accurate amplitudes for the reflectors when dynamic information is required after migration such as studies for amplitude variation with angle or when the correct amplitudes of the reflectors in the zero offset images are needed some modifications to the one way wave equations are required the new equations which are called true amplitude one way wave equations provide amplitudes that are equivalent to those provided by the leading order of the ray theoretical approximation through the modification of the transverse laplacian operator with dependence of lateral velocity variations the introduction of a new term associated with the amplitudes and the modification of the source representation in a smoothly varying vertical medium the extrapolation of the wavefields with the true amplitude one way

3d wavefield extrapolation with optimum split step fourier method a one way propagator is proposed for more accurately modeling wide angle wavefields in the presence of severe lateral variations of the velocity the method adds a higher order correction to improve the split step fourier method by directly designing a cascaded operator that matches the exact phase shift operator of a varying velocity using an optimization scheme the coefficients in the cascaded operator are determined according to the local velocity distribution and the prescribed angular range of wavefield propagation the proposed algorithm is implemented alternately in spatial and wavenumber domains using fast fourier transforms as in the split step fourier and generalized screen methods this algorithm can achieve higher accuracy than the generalized screen method for wide angle wavefields although the same numerical scheme is used with comparable computational cost no extra error arises for the proposed algorithm when used for 3d wave propagation in contrast to methods that introduce an implic

instrumental quantile regression inference for structural and treatment effect models we introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference these methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes we describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it we focus our discussion of inference on tests of distributional equality constancy of effects conditional dominance and exogeneity we apply the procedures to characterize the returns to schooling in the u s

robust penalized quantile regression estimation for panel data this paper investigates a class of penalized quantile regression estimators for panel data the penalty serves to shrink a vector of individual specific effects toward a common value the degree of this shrinkage is controlled by a tuning parameter it is shown that the class of estimators is asymptotically unbiased and gaussian when the individual effects are drawn from a class of zero median distribution functions the tuning parameter can thus be selected to minimize estimated asymptotic variance monte carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias

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

review of elastic and electromagnetic wave propagation in horizontally layered media the objective of this paper is to provide a unified treatment of elastic and electromagnetic em wave propagation in horizontally layered media for which the parameters in the partial differential equations are piece wise continuous functions of only one spatial variable by applying a combination of fourier laplace and bessel transforms to the partial differential equations describing the elastic or em wave propagation i obtain a system of 2n linear ordinary differential equations the 2n 2n coefficient matrix is partitioned into 4n n submatrices by a proper choice of variables the diagonal submatrices are zero and the off diagonal submatrices are symmetric all the results in the paper are derived from the symmetry properties of this general equation in the appendices it is shown that three dimensional elastic waves cylindrical p sv waves acoustic waves and electromagnetic waves in isotropic layered media can all be represented by an equation with the same properties the symmetry properties of

testing capital asset pricing models using functional coefficient panel data models with cross sectional dependence abstract this paper proposes a functional coefficient panel data model with cross sectional dependence motivated by re examining the empirical performance of conditional capital asset pricing model in order to characterize the time varying property of assets betas and alpha our proposed model allows the betas to be unknown functions of some macroeconomic and financial instruments moreover a common factor structure is introduced to characterize cross sectional dependence which is an attractive feature under a panel data regression setting as different assets or portfolios may be affected by same unobserved shocks compared to the existing studies such as the classic fama macbeth two step procedure our model can achieve substantial efficiency gains for inference by adopting a one step procedure using the entire sample rather than a single cross sectional regression at each time point we propose a local linear common correlated effects estimator for estimating time varying betas by pooling the data the consistency and asymptotic normality of the proposed estimators are established another methodological and empirical challenge in asset pricing is how to test the constancy of conditional betas and the significance of pricing errors we echo this challenge by constructing an l 2 norm statistic for functional coefficient panel data models allowing for cross sectional dependence we show that the new test statistic has a limiting standard normal distribution under the null hypothesis finally the method is applied to test the model in fama and french 1993 using fama french 25 and 100 portfolios sorted by size and book to market ratio respectively dated from july 1963 to july 2018

bivariate quantile smoothing splines it has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample we introduce bivariate quantile smoothing splines which belong to the space of bilinear tensor product splines as nonparametric estimators for the conditional quantile functions in a two dimensional design space the estimators can be computed by using standard linear programming techniques and can further be used as building blocks for conditional quantile estimations in higher dimensions for moderately large data sets we recommend penalized bivariate b splines as approximate solutions we use real and simulated data to illustrate the methodology proposed

quantile regression for dynamic panel data with fixed effects abstract this paper studies a quantile regression dynamic panel model with fixed effects panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors to reduce the dynamic bias we suggest the use of the instrumental variables quantile regression method of chernozhukov and hansen 2006 along with lagged regressors as instruments in addition we describe how to employ the estimated models for prediction monte carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias and the empirical levels for prediction intervals are very close to nominal levels finally we illustrate the procedures with an application to forecasting output growth rates for 18 oecd countries