proportional means regression for censored medical costs summary the semiparametric proportional means model specifies that the mean function for the cumulative medical cost over time conditional on a set of covariates is equal to an arbitrary baseline mean function multiplied by an exponential regression function we demonstrate how to estimate the vector valued regression parameter using possibly censored lifetime costs the estimator is consistent and asymptotically normal with an easily estimable covariance matrix simulation studies show that the proposed methodology is appropriate for practical use an application to aids is provided

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

improved frequency domain elastic wave modeling using weighted averaging difference operators we develop a new finite difference scheme that reduces the number of grid points per wavelength required in frequency domain elastic modeling our approach computes weighted averages of the spatial second order derivative and the mass acceleration terms using a 25 point computational stencil by determining the weighting coefficients to minimize numerical dispersion and numerical anisotropy we reduce the number of grid points to 3 3 per shear wavelength with a resulting error in velocities smaller than 1 our choice of grid points reduces the computer memory needed to store the complex impedance matrix to 4 of that for a conventional second order scheme and to 54 of that for a combined second order scheme the 25 point weighted averaging scheme of this paper makes it possible to accurately simulate realistic models numerical examples show that this technique can achieve the same accurate solutions with fewer grid points than those from previous frequency domain second order schemes our technique can be extended directly to 3 d elastic modeling the computational efficiency will be even greater than that realized for 2 d models

a mass redistributed finite element method mr fem for acoustic problems using triangular mesh the accuracy of numerical results using standard finite element method fem in acoustic problems will deteriorate with increasing frequency due to the dispersion error such dispersion error depends on the balance between the stiffness and mass of discretization equation systems this paper reports an improved finite element method fem for solving acoustic problems by re distributing the mass in the mass matrix to tune the balance aiming to minimize the dispersion errors this is done by shifting the integration point locations when computing the entries of the mass matrix while ensuring the mass conservation the new method is verified through the detailed numerical error analysis and a strategy is also proposed for the best mass redistribution in terms of minimizing dispersion error the relative dispersion error of present mass redistributed finite element method mr fem is found to be much smaller than the fem solution in both theoretical prediction and numerical examination the present mr fem works well by using the linear triangular elements that can be generated automatically which enables automation in computation and saving computational cost in mesh generation numerical examples demonstrate the advantages of mr fem in comparison with the standard fem using the same triangular meshes and quadrilateral meshes

temporal process regression summary we consider regression for response and covariates which are temporal processes observed over intervals a functional generalised linear model is proposed which includes extensions of standard models in multi state survival analysis simple nonparametric esti mators of time indexed parameters are developed using working independence estimating equations and are shown to be uniformly consistent and to converge weakly to gaussian processes the procedure does not require smoothing or a markov assumption unlike approaches based on transition intensities the usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy the estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters providing novel goodness of fit tests the methodology s practical utility is illustrated in a data analysis

simultaneous multifrequency inversion of full waveform seismic data we present a simultaneous multifrequency inversion approach for seismic data interpretation this algorithm inverts all frequency data components simultaneously a data weighting scheme balances the contributions from different frequency data components so the inversion process does not become dominated by high frequency data components which produce a velocity image with many artifacts a gauss newton minimization approach achieves a high convergence rate and an accurate reconstructed velocity image by introducing a modified adjoint formulation we can calculate the jacobian matrix efficiently allowing the material properties in the perfectly matched layers pmls to be updated automatically during the inversion process this feature ensures the correct behavior of the inversion and implies that the algorithm is appropriate for realistic applications where a priori information of the background medium is unavailable two different regularization schemes an l2 norm and a weighted l2 norm function a

infinite boundary element absorbing boundary for wave propagation simulations in the boundary element be solution of wave propagation infinite absorbing elements are introduced to minimize diffractions from truncated edges of models this leads to a significant simplification and reduction of computational effort especially for 3 d problems the infinite be absorbing boundary condition has a general form for both 2 d and 3 d problems and for both acoustic and elastic cases its implementation is facilitated by the introduction of the corresponding shape functions numerical experiments illustrate a nearly perfect absorption of unwanted diffractions the approach overcomes some of the difficulties encountered in conventional absorbing techniques and takes less memory space and less computing time

3d finite difference modeling of elastic wave propagation in the laplace fourier domain abstractwith the recent interest in the laplace fourier domain full waveform inversion we have developed new heterogeneous 3d fourth and second order staggered grid finite difference schemes for modeling seismic wave propagation in the laplace fourier domain our approach is based on the integro interpolation technique for the velocity stress formulation in the cartesian coordinate system five averaging elastic coefficients and three averaging densities are necessary to describe the heterogeneous medium with harmonic averaging of the bulk and shear moduli and arithmetic averaging of density in the fourth order approximation we improved the accuracy of the scheme using a combination of integral identities for two elementary volumes small and large around spatial gridpoints where the wave variables are defined two solution approaches are provided both of which are solved with iterative krylov methods in the first approach the stress variables are eliminated and a linear system for the veloc

numerical dispersion analysis of discontinuous galerkin method with different basis functions for acoustic and elastic wave equations the discontinuous galerkin method dgm has been applied to investigate seismic wave propagation recently however few studies have examined the dispersion property of dgm with different basis functions therefore three common basis functions legendre polynomial lagrange polynomial with equidistant nodes and lagrange polynomial with gauss lobatto legendre gll nodes are employed for numerical approximation the numerical dispersion and anisotropy numerical behavior of acoustic and elastic waves are compared and the numerical errors of different order methods are analyzed the result shows that the dispersion errors for all basis functions reduce generally with increasing interpolation orders but with large differences in different directions specifically the legendre basis function and lagrange basis function with gll nodes have attractive advantages over the lagrange polynomial with equidistant nodes for numerical computation we verify the dispersion properties by theoretical and numerical ana

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

a dispersion minimizing compact finite difference scheme for the 2d helmholtz equation in this paper we present a dispersion minimizing compact finite difference scheme for solving the 2d helmholtz equation which is a fourth order scheme the error between the numerical wavenumber and the exact wavenumber is analyzed and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters

high accuracy wave simulation revised derivation numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic wave equation the nearly analytic integration discrete naid method for solving the two dimensional acoustic wave equation has been fully mathematically revised analyzed and tested the naid method is an alternative numerical modeling method for generating synthetic seismograms the acoustic wave equation is first transformed into a system of first order ordinary differential equations odes with respect to time variable t and then directly integrated at a small time interval of tn tn 1 to obtain semi discrete ordinary differential equations the integral kernel is expanded into a truncated taylor series to which the integration operator is explicitly applied the high order temporal derivatives involved in the integral kernel are replaced by high order spatial derivatives which then are approximately calculated as a weighted linear combination of the displacement the particle velocity and their spatial gradients in this article we investigate the theoretical properties of the revised naid method including the discrete error and the stability criteria numerical results for constant and layered velocity models show that comparing to the lax wendroff correction lwc scheme and the staggered grid finite difference method the naid method can effectively suppress the numerical dispersion and source noises caused by the discretization of the acoustic wave equation with too coarse spatial grids or when models have strong velocity contrasts between adjacent layers the proposed naid method has been applied in computing the acoustic wavefields for two heterogeneous models the corner edge model and the marmousi model promising numerical results illustrate that the naid method provides an encouraging tool for large scale and complex wave simulation and inversion problems based on the acoustic equation

comparison of source independent methods of elastic waveform inversion in this paper we investigate several source independent methods of nonlinear full waveform inversion of multicomponent elastic wave data this includes iterative estimation of source signature ies standard trace normalization stn and average trace normalization atn inversion methods all are based on the finite element method in the frequency domain one synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature kss inversion method the numerical experiments show that the ies method is superior to both stn and atn methods in two component elastic wave inversion in the frequency domain when the source signature is unknown the stn and atn methods have limitations associated with near zero amplitudes or polarity reversals in traces from one of the components which destroy the energy balance in the normalized traces and cause a loss of frequency information but the atn method is somewhat superior to the stn method in suppressing random noise and improving stability as the developed formulas and the numerical experiments show we suggest the ies method as a practical procedure for multicomponent seismic inversion

a bayesian approach to estimate uncertainty for full waveform inversion using a priori information from depth migration abstractfull waveform inversion fwi enables us to obtain high resolution subsurface images however estimating model uncertainties associated with this technique is still a challenging problem we have used a bayesian inference framework to estimate model uncertainties associated with fwi the uncertainties were assessed based on an a posteriori covariance operator evaluated at the maximum a posteriori model for the prior distribution we have used a spatially nonstationary covariance operator based on a plane wave construction with local dips measured from migrated images preconditioned frequency domain fwi was used to estimate the maximum a posteriori model efficient manipulation of the posterior covariance was based on a low rank approximation of the data misfit hessian preconditioned by the prior covariance operator the strong decay of the singular values indicated that data were mostly informative about a low dimensional subspace of model parameters to reduce computational cost of the random

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

semiparametric modeling and estimation of the terminal behavior of recurrent marker processes before failure events abstractrecurrent event processes with marker measurements are mostly and largely studied with forward time models starting from an initial event interestingly the processes could exhibit important terminal behavior during a time period before occurrence of the failure event a natural and direct way to study recurrent events prior to a failure event is to align the processes using the failure event as the time origin and to examine the terminal behavior by a backward time model this article studies regression models for backward recurrent marker processes by counting time backward from the failure event a three level semiparametric regression model is proposed for jointly modeling the time to a failure event the backward recurrent event process and the marker observed at the time of each backward recurrent event the first level is a proportional hazards model for the failure time the second level is a proportional rate model for the recurrent events occurring before the failure event and the thi

a frequency space 2 d scalar wave extrapolator using extended 25 point finite difference operator finite difference frequency domain modeling for the generation of synthetic seismograms and crosshole tomography has been an active field of research since the 1980s the generation of synthetic seismograms with the time domain finite difference technique has achieved considerable success for waveform crosshole tomography and for wider applications in seismic reverse time migration this became possible with the rapid development of high performance computers however the space frequency x finite difference modeling technique is still beyond the capability of the modern supercomputer in terms of both cost and computer memory therefore finite difference time domain modeling is much more popular among exploration geophysicists a limitation of the space frequency domain is that the recently developed nine point scheme still requires that g the number of grid points per wavelength be 5 this value is greater than for most other numerical modeling techniques for example the pseudospectral scheme

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

mimetic seismic wave modeling including topography on deformed staggered grids abstractfinite difference methods for modeling seismic waves are known to be inaccurate when including a realistic topography due to the large dispersion errors that appear in the modelled surface waves and the scattering introduced by the staircase approximation to the topography as a consequence alternatives to finite difference methods have been proposed to circumvent these issues we present a new numerical scheme for 3d elastic wave propagation in the presence of strong topography this finite difference scheme is based upon a staggered grid of the lebedev type or fully staggered grid fsg it uses a grid deformation strategy to make a regular cartesian grid conform to a topographic surface in addition the scheme uses a mimetic approach to accurately solve the free surface condition and hence allows for a less restrictive grid spacing criterion in the computations the scheme can use high order operators for the spatial derivatives and obtain low dispersion results with as few as six points pe

traveltime and amplitude calculations using the damped wave solution because of its computational efficiency prestack kirchhoff depth migration remains the method of choice for all but the most complicated geological depth structures further improvement in computational speed and amplitude estimation will allow us to use such technology more routinely and generate better images to this end we developed a new accurate and economical algorithm to calculate first arrival traveltimes and amplitudes for an arbitrarily complex earth model our method is based on numerical solutions of the wave equation obtained by using well established finite difference or finite element modeling algorithms in the laplace domain where a damping term is naturally incorporated in the wave equation we show that solving the strongly damped wave equation is equivalent to solving the eikonal and transport equations simultaneously at a fixed reference frequency which properly accounts for caustics and other problems encountered in ray theory using our algorithm we can easily calculate first arrival traveltimes for given models we present numerical examples for 2 d acoustic models having irregular topography and complex geological structure using a finite element modeling code

grid dispersion and stability criteria of some common finite element methods for acoustic and elastic wave equations purely numerical methods based on finite element approximation of the acoustic or elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms we present formulas for the grid dispersion and stability criteria for some popular finite element methods fem for wave propagation namely classical and spectral fem we develop an approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of these fems for acoustic or elastic wave propagation that overcomes difficulties caused by irregular node spacing within the element and the use of high order polynomials as is the case for spectral fem analysis reveals that for spectral fem of order four or greater dispersion is less than 0 2 at four to five nodes per wavelength and dispersion is not angle dependent new results can be compared with grid dispersion results of some classical finite difference methods fdm used for acoustic or elastic wave propagation analysis reveals that fdm and classical fem require a larger sampling ratio than a spectral fem to obtain results with the same degree of accuracy the staggered grid fdm is an efficient scheme but the dispersion is angle dependent with larger values along the grid axes on the other hand spectral fem of order four or greater is isotropic with small dispersion making it attractive for simulations with long propagation times

dispersion optimized quadratures for isogeometric analysis abstract we develop and analyze quadrature blending schemes that minimize the dispersion error of isogeometric analysis up to polynomial order seven with maximum continuity in the span the schemes yield two extra orders of convergence superconvergence on the eigenvalue errors while the eigenfunction errors are of optimal convergence order both dispersion and spectrum analysis are unified in the form of a taylor expansion for eigenvalue errors the resulting schemes increase the accuracy and robustness of isogeometric analysis for wave propagation as well as the differential eigenvalue problems we also derive an a posteriori error estimator for the eigenvalue error based on the superconvergence result we verify with numerical examples the analysis of the performance of the proposed schemes

estimating medical costs from incomplete follow up data estimation of the average total cost for treating patients with a particular disease is often complicated by the fact that the survival times are censored on some study subjects and their subsequent costs are unknown the naive sample average of the observed costs from all study subjects or from the uncensored cases only can be severely biased and the standard survival analysis techniques are not applicable to minimize the bias induced by censoring we partition the entire time period of interest into a number of small intervals and estimate the average total cost either by the sum of the kaplan meier estimator for the probability of dying in each interval multiplied by the sample mean of the total costs from the observed deaths in that interval or by the sum of the kaplan meier estimator for the probability of being alive at the start of each interval multiplied by an appropriate estimator for the average cost over the interval conditional on surviving to the start of the interval the resultant estimators are consistent if censoring occurs solely at the boundaries of the intervals in addition the estimators are asymptotically normal with easily estimated variances extensive numerical studies show that the asymptotic approximations are adequate for practical use and the biases of the proposed estimators are small even when censoring may occur in the interiors of the intervals an ovarian cancer study is provided

accurate and efficient seismic modeling in random media the optimum method for seismic modeling in random media must 1 be highly accurate to be sensitive to subtle effects of wave propagation 2 allow coarse sampling to model media that are large compared to the scale lengths and wave propagation distances which are long compared to the wavelengths this is necessary to obtain statistically meaningful overall attributes of wavefields high order staggered grid finite difference algorithms and the pseudospectral method combine high accuracy in time and space with coarse sampling investigations for random media reveal that both methods lead to nearly identical wavefields the small differences can be attributed mainly to differences in the numerical dispersion this result is important because it shows that errors of the numerical differentiation which are caused by poor polynomial interpolation near discontinuities do not accumulate but cancel in a random medium where discontinuities are numerous the differentiator can be longer than the medium scale leng

semi parametric regression models for cost effectiveness analysis improving the efficiency of estimation from censored data in a cost effectiveness analysis using clinical trial data estimates of the between treatment difference in mean cost and mean effectiveness are needed several methods for handling censored data have been suggested one of them is inverse probability weighting and has the advantage that it can also be applied to estimate the parameters from a linear regression of the mean such regression models can potentially estimate the treatment contrast more precisely since some of the residual variance can be explained by baseline covariates the drawback however is that inverse probability weighting may not be efficient using existing results on semi parametric efficiency this paper derives the semi parametric efficient parameter estimates for regression of mean cost mean quality adjusted survival time and mean survival time the performance of these estimates is evaluated through a simulation study applying both the new estimators and the inverse probability weighted estimators to the results of the evaluate trial showed that the new estimators achieved a halving of the variance of the estimated treatment contrast for cost some practical suggestions for choosing an estimator are offered

source independent full waveform inversion of seismic data a set of seismic trace data is collected in an input data set that is first fourier transformed in its entirety into the frequency domain a normalized wavefield is obtained for each trace of the input data set in the frequency domain normalization is done with respect to the frequency response of a reference trace selected from the set of seismic trace data the normalized wavefield is source independent complex and dimensionless the normalized wavefield is shown to be uniquely defined as the normalized impulse response provided that a certain condition is met for the source this property allows construction of the inversion algorithm disclosed herein without any source or source coupling information the algorithm minimizes the error between data normalized wavefield and the model normalized wavefield the methodology is applicable to any 3 d seismic problem and damping may be easily included in the process

source receiver compression scheme for full waveform seismic inversion we have developed a source receiver compression approach for reducing the computational time and memory usage of the acoustic and elastic full waveform inversions by detecting and quantifying the extent of redundancy in the data we assembled a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers used in the survey because the numbers of these simultaneous sources and receivers could be significantly less than those of the physical sources and receivers the computational time and memory usage of any gradient type inversion method such as steepest descent nonlinear conjugate gradient contrast source inversion and quasi newton methods could be reduced the scheme is based on decomposing the data into their principal components using a singular value decomposition approach and the data reduction is done through the elimination of the small eigenvalues consequently this would suppress the effect of noise in the data moreover taking advantage

regression analysis of incomplete medical cost data the accumulation of medical cost over time for each subject is an increasing stochastic process defined up to the instant of death the stochastic structure of this process is complex in most applications the process can only be observed at a limited number of time points furthermore the process is subject to right censoring so that it is unobservable after the censoring time these special features of the medical cost data especially the presence of death and censoring pose major challenges in the construction of plausible statistical models and the development of the corresponding inference procedures in this paper we propose several classes of regression models which formulate the effects of possibly time dependent covariates on the marginal mean of cost accumulation in the presence of death or on the conditional means of cost accumulation given specific survival patterns we then develop estimating equations for these models by combining the approach of generalized estimating equations for longitudinal data with the inverse probability of censoring weighting technique the resultant estimators are shown to be consistent and asymptotically normal with simple variance estimators simulation studies indicate that the proposed inference procedures behave well in practical situations an application to data taken from a large cancer study reveals that the medicare enrollees who are diagnosed with less aggressive ovarian cancer tend to accumulate medical cost at lower rates than those with more aggressive disease but tend to have higher lifetime costs because they live longer

estimating mean cost using auxiliary covariates we study the estimation of mean medical cost when censoring is dependent and a large amount of auxiliary information is present under missing at random assumption we propose semiparametric working models to obtain low dimensional summarized scores an estimator for the mean total cost can be derived nonparametrically conditional on the summarized scores we show that when either the two working models for cost survival process or the model for censoring distribution is correct the estimator is consistent and asymptotically normal small sample performance of the proposed method is evaluated via simulation studies finally our approach is applied to analyze a real data set in health economics

on the construction and efficiency of staggered numerical differentiators for the wave equation finite difference fd techniques have established themselves as viable tools for the numerical modeling of wave propagation the accuracy and the computational efficiency of numerical modeling can be enhanced by using high order spatial differential operators dablain 1986

a recursive green s function technique for acoustic scattering from heterogeneous objects a fast efficient algorithm for computing acoustic fields scattered by inhomogeneous objects in an otherwise homogeneous space is presented the algorithm called the recursive green s function method rgfm constructs the domain green s function by recursively combining known green s functions from smaller subdomains the fields on the scatterer surface are then computed using a boundary integral formulation proper implementation of the rgfm results in a storage requirement of o n and computational costs of o n3 2 and o n2 for two and three dimensional problems respectively where n is the total number of discrete points in the inhomogeneous region results are compared with those obtained from exact solutions to show the accuracy of the method

full wave directional illumination analysis in the frequency domain directional illumination analysis based on one way wave equations has been studied extensively however its inherent limitations e g one way propagation wide angle error and amplitude inaccuracy can severely hinder its applications for accurate survey design and true reflection imaging corrections in complex media we have analyzed the illumination in the frequency domain using full two way wave propagators considering the extensive computation and huge storage required for time domain methods and the fact that the illumination is frequency dependent this full wave analysis can provide frequency dependent full angle true amplitude illumination not only for the downgoing waves but also for the upgoing waves including turning waves and reflected waves two methods were considered to decompose the full wavefield into the local angle domain a direct full dimensional decomposition and more efficient split step decomposition composed of three lower dimensional decompositions the results of illumination analysis demonstrated the advantages of this method the two decomposition methods produced similar results

a new 3 d numerical approach to the solution of pdes with optimal accuracy on irregular domains and cartesian meshes abstract a new 3 d numerical approach for the time dependent wave and heat equations as well as for the time independent laplace equation on irregular domains with the dirichlet boundary conditions has been developed trivial cartesian meshes and simple 27 point uniform and nonuniform stencil equations are used for 3 d irregular domains the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique very small distances 0 1 h 1 0 9 h where h is the grid size between the grid points of a cartesian mesh and the boundary do not worsen the accuracy of the new technique at similar 27 point stencils the accuracy of the new approach is two orders higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the fifth order tetrahedral finite elements with much wider stencils the wave and heat equations can be uniformly treated with the new approach the order of the time derivative in these equations does not affect the coefficients of the stencil equations of the semi discrete systems the new approach can be directly applied to other partial differential equations

2d frequency domain elastic full waveform inversion using time domain modeling and a multistep length gradient approach abstractto decouple the parameters in elastic full waveform inversion fwi we evaluated a new multistep length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction to perform wavefield extrapolations for the inversion we used parallelized high precision finite element fe modeling in the time domain the inversion was implemented in the frequency domain the data were obtained at every subsurface grid point using the discrete fourier transform at each time domain extrapolation step we also used frequency selection to reduce cycle skipping time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data and source wavelet estimation at the receivers over the full frequency spectrum by using a fast fourier transform in the inversion the velocity and density reconstructions behaved differently as a low wavenumber tomography for v

efficient calculation of the steepest descent direction for source independent seismic waveform inversion an amplitude approach in seismic waveform inversion if we have no information on source signature we need to invert seismic data and source signature either simultaneously or successively in order to avoid the iterative update of the source signature in waveform inversion based on classical local optimization techniques we propose two source independent objective functions using amplitude spectra of fourier transformed wavefields one is constructed by normalizing the amplitude spectra of observed data and modeled data with respect to the respective reference amplitudes the other is achieved by cross multiplying the amplitude spectra of observed data and modeled data with the respective reference amplitudes in the computation of the steepest descent direction we circumvent explicitly computing the jacobian by employing a matrix formalism of the wave equation in the frequency domain through numerical examples for the marmousi model we demonstrate that our inversion algorithms can reproduce the subsurface velocity structure without estimating source signature

grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics summary the spatial discretisation of a continuum by the fem introduces dispersion errors to the numerical solution of stress wave propagation errors of phase and group velocities and the scatter of wave propagation are induced when these propagating phenomena are modelled by the fem the speed of a single harmonic wave depends on its frequency parasitic effects do not exist in an ideal unbounded continuum with higher order finite elements there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts in principle the dispersion errors and the spurious oscillations cannot be removed from these solutions but can be suppressed to a certain extent for reliable numerical solutions by the fem the dispersion errors should be analysed and determined the dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one dispersion analysis is carried out for the consistent and lumped mass matrices a dispersive improved lumped mass matrix for biquadratic serendipity elements is proposed the paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes copyright 2013 john wiley sons ltd

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

a numerical homogenization method for heterogeneous anisotropic elastic media based on multiscale theory the development of reliable methods for upscaling finescale models of elastic media has long been an important topic for rock physics and applied seismology several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures in such cases the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation however such theories cannot be applied directly to homogenize elastic media with more complex arbitrary spatial heterogeneity therefore we have proposed a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous anisotropic elastic media specifically our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions homogenized effective medium parameters were then computed using these basis functions and the approach applied a numerical discretization that was similar to the rotated staggered grid finite difference scheme comparisons of the results from our method and from conventional analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry additional tests examined anisotropic models with arbitrary spatial heterogeneity in which the average size of the heterogeneities ranged from several centimeters to several meters and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100 comparisons to finite difference simulations proved that the numerical homogenization was equally accurate for these complex cases

dispersion minimizing quadrature rules for c1 quadratic isogeometric analysis abstract we develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation the rules are optimal in the sense that they only require two quadrature points per element to minimize the dispersion error barto et al 2017 1 and they are equivalent to the optimized blending rules we recently described our approach further simplifies the numerical integration instead of blending two three point standard quadrature rules we construct directly a single two point quadrature rule that reduces the dispersion error to the same order for uniform meshes with periodic boundary conditions also we present a 2 5 point rule for both uniform and non uniform meshes with arbitrary boundary conditions consequently we reduce the computational cost by using the proposed quadrature rules various numerical examples demonstrate the performance of these quadrature rules

an improved optimal nearly analytical discretized method for 2d scalar wave equation in heterogeneous media based on the modified nearly analytical discrete operator abstractconventional finite difference methods will encounter strong numerical dispersion on coarse grids or when higher frequencies are used the nearly analytic discrete method nadm and its improved version developed recently can suppress numerical dispersion efficiently however the nadm is imperfect especially in long time seismic wave propagation simulation to overcome this limitation by minimizing the energy error function we have developed a modified optimal nearly analytical discretized mnad method the stencil of mnad for the 2d wave equation is a novel diamond stencil mnad has two major advantages the first one is that mnad can suppress numerical dispersion effectively on coarse grids which significantly improved computational efficiency and reduced memory demands the second advantage is that the energy error of mnad is much smaller after long time simulation the numerical dispersion analysis shows that the maximum phase velocity error was 5 92 even if only two sampling points w

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

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

a consistent estimator for the distribution of quality adjusted survival time summary quality adjusted survival analysis is a new approach to therapy evaluation in clinical trials it has received much attention recently because of its ability to take patients quality of life into consideration in this paper we present a method that enables us to calculate the survival distribution of quality adjusted lifetime using martingale theory for counting processes we can show that our estimator is asymptotically consistent normally distributed and its asymptotic variance estimate can be obtained analytically simulation experiments are conducted to compare our estimator with the true underlying distribution for two cases that are of practical importance

iterative finite difference solution analysis of acoustic wave equation in the laplace fourier domain we have investigated numerical characteristics of iterative solutions to the acoustic wave equation in the laplacefourier lf domain we transformed the time domain acoustic wave equation into the lf domain the transformed equation was discretized with finite differences and was solved with iterative methods finite difference modeling experiments demonstrate that iterative methods require an infinitesimal stopping tolerance to accurately compute the pressure field especially at long offsets to understand the requirement for such infinitesimal tolerance values we analyzed the evolution of intermediate solution vectors residual vectors and search direction vectors during the iteration the analysis showed that the requirement arises from the fact that in the solution space the amplitude of the pressure field varies more than sixty orders of magnitude on the common log scale accordingly we propose a rule of thumb for choosing a proper stopping tolerance value we also examined numerical dispersion errors in terms of the grid sampling resolutions per skin depth and wavelength we found that despite the similarity of the form of the acoustic wave and electromagnetic diffusion equations the former is different from the latter due to the fact that in the lf domain the skin depth of the acoustic wave equation is decoupled from its wavelength this aspect requires that in the lf domain its grid size be determined by considering the minimum grid sampling resolutions based not only the wavelength but also the skin depth

on estimation of the wavelet variance summary the wavelet variance decomposes the variance of a time series into components associated with different scales we consider two estimators of the wavelet variance the first based upon the discrete wavelet transform and the second called the maximal overlap estimator based upon a filtering interpretation of wavelets we determine the large sample distribution for both estimators and show that the maximal overlap estimator is more efficient for a class of processes of interest in the physical sciences we discuss methods for determining an approximate confidence interval for the wavelet variance we demonstrate through monte carlo experiments that the large sample distribution for the maximal overlap estimator is a reasonable approximation even for the moderate sample size of 128 observations we apply our proposed methodology to a series of observations related to vertical shear in the ocean

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided

dispersion minimized mass for isogeometric analysis abstract we introduce the dispersion minimized mass for isogeometric analysis to approximate the structural vibration which we model as a second order differential eigenvalue problem the dispersion minimized mass reduces the eigenvalue error significantly from the optimum order of 2 p to the superconvergence order of 2 p 2 for the p th order isogeometric elements with maximum continuity which in return leads to a more accurate method we first establish the dispersion error where the leading error term is explicitly written in terms of the stiffness and mass entries for arbitrary polynomial order isogeometric elements we derive the dispersion minimized mass in one dimension by solving a p dimensional local matrix problem for the p th order approximation and then extend it to multiple dimensions on tensor product grids we show that the dispersion minimized mass can also be obtained by approximating the mass matrix using optimally blended quadratures we generalize the lower order quadrature blending results to arbitrary polynomial order isogeometric approximations as well as to arbitrary quadrature rules various numerical examples validate the eigenvalue and eigenfunction error estimates

waveform inversion using a logarithmic wavefield although waveform inversion has been studied extensively since its beginning 20 years ago applications to seismic field data have been limited and most of those applications have been for global seismology or engineering seismology scale problems not for exploration scale data as an alternative to classical waveform inversion we propose the use of a new objective function constructed by taking the logarithm of wavefields allowing consideration of three types of objective function namely amplitude only phase only or both in our waveform inversion we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function we compute the steepest descent directions by using a matrix formalism derived from a frequency domain finite element finite difference modeling technique our numerical algorithms are similar to those of reverse time migration and waveform inversion based on the adjoint state of the wave equation in order to demonstrate the practical applicability of our algorithm we use a synthetic data set from the marmousi model and seismic data collected from the korean continental shelf for noisefree synthetic data the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion when random noise is added the inverted velocity model is also close to the true marmousi model but when frequencies below 5 hz are removed from the data the velocity structure is not as good as those for the noise free and noisy data for field data we compare the time domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short period features of the subsurface although we use wrapped phases in our examples we still obtain reasonable results we expect that if we were to use correctly unwrapped phases in the inversion algorithm we would obtain better results

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

accelerating hessian free gauss newton full waveform inversion via l bfgs preconditioned conjugate gradient algorithm abstractfull waveform inversion fwi has emerged as a powerful strategy for estimating subsurface model parameters by iteratively minimizing the difference between synthetic data and observed data the hessian free hf optimization method represents an attractive alternative to newton type and gradient based optimization methods at each iteration the hf approach obtains the search direction by approximately solving the newton linear system using a matrix free conjugate gradient cg algorithm the main drawback with hf optimization is that the cg algorithm requires many iterations in our research we develop and compare different preconditioning schemes for the cg algorithm to accelerate the hf gauss newton gn method traditionally preconditioners are designed as diagonal hessian approximations we additionally use a new pseudo diagonal gn hessian as a preconditioner making use of the reciprocal property of green s function furthermore we have developed an l bfgs inverse hessian preconditioning

efficient laplace domain modeling and inversion using an axis transformation technique abstractwe tested an axis transformation technique for modeling wave propagation in the laplace domain using a finite difference method this technique enables us to use small grids near the surface and large grids at depth accordingly we can reduce the number of grids and attain computational efficiency in modeling and inversion in the laplace domain we used a dispersion analysis and comparisons between modeled wavefields obtained on the regular and transformed axes we demonstrated in a synthetic laplace domain inversion technique shows that this method is efficient and yields a result comparable to that of a laplace domain inversion using a regular grid in a synthetic inversion example the memory usage reduced to less than 33 and the computation time reduced to 39 of those required for the regular grid case using a logarithmic transformation function

empirical likelihood based confidence intervals for mean medical cost with censored data in this paper we propose empirical likelihood methods based on influence function and jackknife techniques for constructing confidence intervals for mean medical cost with censored data we conduct a simulation study to compare the coverage probabilities and interval lengths of our proposed confidence intervals with that of the existing normal approximation based confidence intervals and bootstrap confidence intervals the proposed methods have better finite sample performances than existing methods finally we illustrate our proposed methods with a relevant example

dispersion optimized quadrature rules for isogeometric analysis modified inner products their dispersion properties and optimally blended schemes abstract this paper introduces optimally blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations to quantify the approximation errors when we modify the inner products we generalize the pythagorean eigenvalue theorem of strang and fix the proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non uniform meshes as well as for different polynomial orders and continuity of the basis the optimally blended schemes improve the convergence rate of the method by two orders with respect to the fully integrated galerkin method the proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems

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

perturbational and nonperturbational inversion of rayleigh wave velocities the inversion of rayleigh wave dispersion curves is a classic geophysical inverse problem we have developed a set of matlab codes that performs forward modeling and inversion of rayleigh wave phase or group velocity measurements we describe two different methods of inversion a perturbational method based on finite elements and a nonperturbational method based on the recently developed dix type relation for rayleigh waves in practice the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method although the perturbational method is well known we solve the forward problem using an eigenvalue eigenvector solver instead of the conventional approach of root finding features of the codes include the ability to handle any mix of phase or group velocity measurements combinations of modes of any order the presence of a surface water layer computation of partial derivatives due to changes in material properties and layer boundaries and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of rayleigh waves

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

wave propagation in heterogeneous media effects of fine scale heterogeneity we study the multiple scattering effects caused by fine scale heterogeneity for this purpose it is unreasonable to rely on a linearization of the dependency of the wavefield in the parameters that describe the medium therefore the only tools that correctly model wave propagation are based on the numerical solution of the two way wave equation by finite differences or finite elements a fine grid provides a straightforward approach to account for fine scale heterogeneity in this situation there is no need for high order schemes variational methods allow us to exhibit a numerical scheme that accounts for heterogeneity and that is by construction stable provided a stability condition is fulfilled this condition is a sufficient stability condition contrary to the classical necessary stability conditions in addition general mathematical results prove the finite difference solution is close to the solution of the wave equation when the grid is fine enough the multiple scattering effects caused by fine scale heterogeneity are very important in particular we observe that imaging the so computed synthetic data by standard migration techniques that assume a linearization of the above mentioned dependency shows a strongly noise corrupted image this illustrates the importance of preprocessing data to remove the effect of multiple scattering we try to improve the signal to noise ratio by removing multiples related to the free surface although significant noise reduction is achieved even more sophisticated preprocessing is required to obtain a clear image of the subsurface

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

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

evaluating utility measurement from recurrent marker processes in the presence of competing terminal events abstractin follow up studies utility marker measurements are usually collected upon the occurrence of recurrent events until a terminal event such as death takes place in this article we define the recurrent marker process to characterize utility accumulation over time for example with medical cost and repeated hospitalizations being treated as marker and recurrent events respectively the recurrent marker process is the trajectory of cumulative cost which stops to increase after death in many applications competing risks arise as subjects are at risk of more than one mutually exclusive terminal event such as death from different causes and modeling the recurrent marker process for each failure type is often of interest however censoring creates challenges in the methodological development because for censored subjects both failure type and recurrent marker process after censoring are unobserved to circumvent this problem we propose a nonparametric framework for the recurrent marker proce

numerical analysis of a narrow angle one way elastic wave equation and extension to curvilinear coordinates in this paper we review the finite difference implementation of a narrow angle one way vector wave equation for elastic 3d media extrapolation is performed in the frequency domain where the second order accurate lateral spatial difference operators are sufficiently accurate for narrow angle propagation we perform a numerical analysis of the finite difference scheme to highlight the stability and dispersion characteristics the von neumann stability criterion indicates that extracting a reference phase during the extrapolation step noticeably improves the forward marching scheme and dispersion analysis shows that numerical grid anisotropy is minimal for the propagation path lengths source pulse spectral content and angular range of forward propagation of interest although the algorithm is reasonable its computational efficiency is limited by the second order accurate extrapolation step therefore the extrapolation scheme can be improved we extend the cartesian narrow angle formulation to curvilinear coordinates where the computational grid tracks the true wavefront in a reference medium and the wavefield derivative normal to the reference wavefront is evaluated locally using the cartesian propagator an example of curvilinear extrapolation for a simple model consisting of a high velocity sphere within a homogeneous background velocity structure shows that the narrow angle propagator is capable of modeling frequency dependent geometric spreading and diffraction effects in curvilinear coordinates

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

dispersion reducing finite elements for transient acoustics this paper focuses on increasing the accuracy of low order four node quadrilateral finite elements for the transient analysis of wave propagation modified integration rules originally proposed for time harmonic problems provide the basis for the proposed technique the modified integration rules shift the integration points to locations away from the conventional gauss or gauss lobatto integration points with the goal of reducing the discretization errors specifically the dispersion error presented here is an extension of the idea to time dependent analysis using implicit as well as explicit time stepping schemes the locations of the stiffness integration points remain unchanged from those in time harmonic case on the other hand the locations of the integration points for the mass matrix depend on the time stepping scheme and the step size furthermore the central difference method needs to be modified from its conventional form to facilitate fully explicit computation the superior performance of the proposed algorithms is illustrated with the help of several numerical examples

optimal blended spectral element operators for acoustic wave modeling spectral element methods based on high order polynomials are among the most commonly used techniques for computing accurate simulations of wave propagation phenomena in complex media however to retain computational efficiency very high order polynomials cannot be used and errors such as numerical dispersion and numerical anisotropy cannot be totally avoided in the present work we devise an approach for reducing such errors by considering modified discrete wave operators we analyze consistent and lumped operators together with blended operators weighted averages of consistent and lumped operators furthermore using the operator blending approach and a novel dispersion analysis method we develop optimal spectral element operators that have increased numerical accuracy without resorting to very high order operators the new operators are faster and computationally more efficient than consistent operators our approach is based on the tensor product decomposition of the element matrices into 1d f

third order symplectic integration method with inverse time dispersion transform for long term simulation the symplectic integration method is popular in high accuracy numerical simulations when discretizing temporal derivatives however it still suffers from time dispersion error when the temporal interval is coarse especially for long term simulations and large scale models we employ the inverse time dispersion transform itdt to the third order symplectic integration method to reduce the time dispersion error first we adopt the pseudospectral algorithm for the spatial discretization and the third order symplectic integration method for the temporal discretization then we apply the itdt to eliminate time dispersion error from the synthetic data as a post processing method the itdt can be easily cascaded in traditional numerical simulations we implement the itdt in one typical exiting third order symplectic scheme and compare its performances with the performances of the conventional second order scheme and the rapid expansion method theoretical analyses and numerical experiments show that the itdt can significantly reduce the time dispersion error especially for long travel times the implementation of the itdt requires some additional computations on correcting the time dispersion error but it allows us to use the maximum temporal interval under stability conditions thus its final computational efficiency would be higher than that of the traditional symplectic integration method for long term simulations with the aid of the itdt we can obtain much more accurate simulation results but with a lower computational cost we use the inverse time dispersion transform to the 3rd order symplectic integration it can greatly reduce the time dispersion error especially for long travel times it is superior to the conventional 2nd and high order finite difference methods it allows the maximum temporal interval under stability conditions thus is efficient we can obtain more accurate simulation results but with a lower computational cost

a comparative study of finite element and spectral element methods in seismic wavefield modeling the computational accuracy and efficiency of finite element method and spectral element method sem are investigated thoroughly in time domain elastic wavefield modeling the diagonal mass matrices of the fem and sem free from matrix inversion are compared comprehensively by making full use of the mass lumped technique and quadrature rules we investigate the fem and sem based respectively on quadrilateral with the polynomials of degrees one and two and on triangular grids with the polynomials of degrees one and three generally the numerical solutions based on quadrilateral grids have a higher precision than those computed on triangular grids when the same order of polynomials is used the fem has a comparable accuracy to the sem with the same number of interpolant points in view of the triangular and quadrilateral sems the former suffers from larger computational costs and relatively lower accuracy compared with the latter furthermore the convergence study proves that the triangular sem produces consistently larger errors than the quadrilateral sem for any order and element sizes however the triangular sem can adapt to arbitrary complex geometries effectively in terms of efficiency the fem has an efficiency comparable with the sem on condition that the order of interpolation polynomials is identical in addition a perfectly matched layer pml boundary condition in variational form is deduced by introducing four intermediate variables in frequency domain the pml avoids convolution calculation and obtains an exact solution through inverse fourier transform in time domain the numerical examples verify the validity and effectiveness of the pml

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

an optimal nearly analytic discrete weighted runge kutta discontinuous galerkin hybrid method for acoustic wavefield modeling abstractthe newly developed optimal nearly analytic discrete onad and the weighted runge kutta discontinuous galerkin wrkdg methods can effectively suppress the numerical dispersion caused by discretizing wave equations but it is difficult for onad to implement on flexible meshes whereas the wrkdg has high computational cost for wavefield simulations we have developed a new hybrid algorithm by combining the onad method with the wrkdg method in this hybrid algorithm the computational domain was split into several subdomains in which the subdomain for the onad method used regular cartesian grids whereas the subdomain for the wrkdg method used triangular grids the hybrid method was at least third order spatially accurate we have applied the proposed method to simulate the scalar wavefields for different models including a homogeneous model a rough topography model a fracture model and a cave model the numerical results found that the hybrid method can deal with complicated geometrical struc

an optimal compact sixth order finite difference scheme for the helmholtz equation abstract in this paper we present an optimal compact finite difference scheme for solving the 2d helmholtz equation a convergence analysis is given to show that the scheme is sixth order in accuracy based on minimizing the numerical dispersion a refined optimization rule for choosing the scheme s weight parameters is proposed numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters

optimally blended spectral finite element scheme for wave propagation and nonstandard reduced integration we study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent finite element mass matrix and lumped spectral element mass matrix for the small wave number limit we find and prove that for the optimum blending the resulting scheme a provides 2p 4 order accuracy for p th order method two orders more accurate compared with finite and spectral element schemes b has an absolute accuracy which is mathcal o p 3 and mathcal o p 2 times better than that of the pure finite and spectral element schemes respectively c tends to exhibit phase lag moreover we show that the optimally blended scheme can be efficiently implemented merely by replacing the usual gaussian quadrature rule used to assemble the mass and stiffness matrices by novel nonstandard quadrature rules which are also derived

a high order numerical approach with cartesian meshes for modeling of wave propagation and heat transfer on irregular domains with inhomogeneous materials abstract recently we have developed a new numerical approach for pdes with constant coefficients on irregular domains and cartesian meshes in this paper we extend it to a much more general case of pdes with variable coefficients that have a lot of applications e g the modeling of functionally graded materials the inhomogeneous materials obtained by 3 d printing and many others here we consider the 2 d wave and heat equations for isotropic and anisotropic inhomogeneous materials the idea of the extension to the case of pdes with variable coefficients is based on the representation of the stencil coefficients as functions of the mesh size this leads to the increase in the size of the local system of algebraic equations solved for each grid point of the new approach however this does not change the size of the global system of semidiscrete equations and practically does not increase the computational costs of the proposed technique similar to our previous technique the new 2 d approach with compact 9 point stencils uses trivial cartesian meshes for complex irregular domains and provides the fourth order of accuracy for the wave and heat equations with variable coefficients the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique at similar 9 point stencils the accuracy of the new approach is much higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the third order finite elements with much wider stencils the wave and heat equations are uniformly treated with the new approach

a new family of finite difference schemes to solve the heterogeneous acoustic wave equation equivalent staggered grid scheme esg is a new family of schemes based on the finite difference method fdm the method is applied to acoustic wave propagation in variable density media and the results are compared with those from some classic fdm approaches the main feature of this new family is that it is designed to generate results numerically equivalent to those using the standard staggered grid formulations ssg but with the same memory requirements of simple grid schemes hence it results in a reduction of memory usage by 33 in 2d and 50 in 3d problems compared to the memory usage of ssg the first order system of equations in terms of pressure and velocity is not used here instead the formulation is based on applying new central difference operators to the secondorder acoustic wave equation in terms of pressure obtaining the same level of accuracy and stability as the ssg schemes the equivalence between the esg and ssg is mathematically demonstrated and issues concerning the application of seismic sources and the boundary conditions are addressed