upwind finite difference calculation of traveltimes seismic traveltimes can be computed efficiently on a regular grid by an upwind finite difference method the method solves a conservation law that describes changes in the gradient components of the traveltime field the traveltime field itself is easily obtained from the solution of the conservation law by numerical integration the conservation law derives from the eikonal equation and its solution depicts the first arrival time field the upwind finite difference scheme can be implemented in fully vectorized form in contrast to a similar scheme proposed recently by vidale the resulting traveltime field is useful both in kirchhoff migration and modeling and in seismic tomography many reliable methods exist for the numerical solution of conservation laws which appear in fluid mechanics as statements of the conservation of mass momentum etc a first order upwind finite difference scheme proves accurate enough for seismic applications upwind schemes are stable because they mimic the behavior of flu

multi fractional generalized cauchy process and its application to teletraffic abstract the contributions given in this paper are in two aspects the first is to introduce a novel random function which we call the multi fractional generalized cauchy mgc process the second is to dissertate its application to network traffic for studying the multi fractal behavior of traffic on a point by point basis the introduced mgc process is with the time varying fractal dimension d t and the time varying hurst parameter h t the representations of the autocorrelation function acf and the power spectrum density psd of the mgc process are proposed besides the asymptotic expressions of the acf and psd of the mgc process are presented the computation formula of d t is given the mgc model may be a new tool to describe the multi fractal behavior of traffic precisely it may be used to reveal the local irregularity or local self similarity lss which is a small time scale behavior of traffic and global long term persistence or long range dependence lrd which is a large time scale behavior of traffic on a point by point basis the cast study with real traffic traces exhibits that the variance of d t is much greater than that of h t thus the present mgc model may provide a novel way to explain the fact that traffic has highly local irregularity while its lrd is robust

generalized cauchy model of sea level fluctuations with long range dependence abstract this article suggests the contributions with two highlights one is to propose a novel model of sea level fluctuations sea level for short which is called the generalized cauchy gc process it provides a new outlook for the description of local and global behaviors of sea level from a view of fractal in that the fractal dimension d that measures the local behavior of sea level and the hurst parameter h which characterizes the global behavior of sea level are independent of each other the other is to show that sea level appears multi fractal in both spatial and time such a meaning of multi fractal is new in the sense that a pair of fractal parameters d h of sea level is varying with measurement sites and time this research exhibits that the ranges of d and h of sea level in general are 1 d 2 and 0 5 h 1 respectively but d is independent of h with respect to the global behavior of sea level we shall show that h 0 96 for all data records at all measurement sites implying that strong lrd may be a general phenomenon of sea level on the other side regarding with the local behavior we will reveal that there appears d 1 or d 1 for data records at a few stations and at some time but d 0 96 at most stations and at most time meaning that sea level may appear highly local irregularity more frequently than weak local one

shortest path calculation of seismic rays like the traveling salesman who wants to find the shortest route from one city to another in order to minimize his time wasted on traveling one can find seismic raypaths by calculating the shortest traveltime paths through a network that represents the earth the network consists of points that are connected with neighboring points by connections as long as the traveltime of a seismic wave along it the shortest traveltime path from one point to another is an approximation to the seismic ray between them by fermat s principle the shortest path method is an efficient and flexible way to calculate the raypaths and traveltimes of first arrivals to all points in the earth simultaneously there are no restrictions of classical ray theory diffracted raypaths and paths to shadow zones are found correctly there are also no restrictions to the complexity or the dimensionality of the velocity model furthermore there are no problems with convergence of trial raypaths toward a specified receiver nor with ray

modeling network traffic using generalized cauchy process abstract processes with long range dependence lrd have gained wide applications in many fields of science and technologies ranging from hydrology to network traffic two key properties of such processes are lrd that is characterized by the hurst parameter h and self similarity ss that is measured by the fractal dimension d however in the popular traffic model using fractional gaussian noise fgn these two parameters are linearly related this may be regarded as a limitation of fgn in traffic modeling from the point of view of either accurately fitting real traffic or appropriately explaining the particular multi fractal phenomena of traffic in this paper we discuss recent results in traffic modeling from a view of the generalized cauchy gc process the gc process is indexed by two parameters d and h the parameter d in the gc model is independent of h hence it provides a more flexible way to describe the multi fractal phenomena of traffic in addition to accurately modeling traffic for both short term lags and long term ones

selecting an optimal aperture in kirchhoff migration using dip angle images we present a method for selecting a migration aperture in kirchhoff migration we first split migrated data into constant dip angle partial images then in every partial image we estimate the consistency between each event and the constant dip of the analyzed section we filter out events whose slope is far from the corresponding dip stacking of the filtered partial images corresponds to migration having an optimal aperture synthetic and real data examples demonstrate that the proposed approach to migration aperture optimization is able to reduce migration noise while preserving diffraction energy which characterizes small geologic objects and brings additional resolution to the image

finite difference solution of the eikonal equation along expanding wavefronts we show that a scheme to solve the 2 d eikonal equation by a finite difference method can violate causality for moderate to large velocity contrasts v2 v1 2 as an alternative we present a finite difference scheme in which the solution region progresses outward from an expanding wavefront rather than an expanding square and therefore honors causality our method appears to be stable and reasonably accurate for a variety of velocity models with moderate to large velocity contrasts the penalty is a large increase in computational cost and programming effort

record length requirement of long range dependent teletraffic abstract this article contributes the highlights mainly in two folds on the one hand it presents a formula to compute the upper bound of the variance of the correlation periodogram measurement of teletraffic traffic for short with long range dependence lrd for a given record length t and a given value of the hurst parameter h theorems 1 and 2 on the other hand it proposes two formulas for the computation of the variance upper bound of the correlation periodogram measurement of traffic of fractional gaussian noise fgn type and the generalized cauchy gc type respectively corollaries 1 and 2 they may constitute a reference guideline of record length requirement of traffic with lrd in addition record length requirement for the correlation periodogram measurement of traffic with either the schuster type or the bartlett one is studied and the present results about it show that both types of periodograms may be used for the correlation measurement of traffic with a pre desired variance bound of correlation estimation moreover real traffic in the internet archive by the special interest group on data communication under the association for computing machinery of us acm sigcomm is analyzed in the case study in this topic

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

fast phase space computation of multiple arrivals we present a fast general computational technique for computing the phase space solution of static hamilton jacobi equations starting with the liouville formulation of the characteristic equations we derive escape equations which are static time independent eulerian pdes they represent all arrivals to the given boundary from all possible starting configurations the solution is numerically constructed through a one pass formulation building on ideas from semi lagrangian methods dijkstra like methods for the eikonal equation and ordered upwind methods to compute all possible trajectories corresponding to all possible boundary conditions the technique is of computational order o n log n where n is the total number of points in the computational phase space domain any particular set of boundary conditions then is extracted through rapid post processing suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance as an application we apply the technique to the problem of computing first multiple and most energetic arrivals to the eikonal equation

testing non existence of input output relationships by estimating fractal dimensions our aim is to propose tests for non existence of nonlinear relationships between signals which after passing a test can be interpreted as input and output signals of a certain system if its characteristic is sufficiently smooth the proposed tests are based on the theoretical results on equality of fractal dimensions of these signals as well as on estimation of fractal dimensions from observations they are applicable when at least one of these signals has the fractal dimensions strictly larger than one i e it is rough enough the tests are then verified on simulated data their applicability is illustrated by two sets of real data namely observations of two financial time series and samples of displacement force signals in a magneto hydrological damper

domain limited solution of the wave equation in riemannian coordinates we propose to solve the two way time domain acoustic wave equation in a generalized riemannian coordinate system via finite differences the coordinate system is defined in such a way that one of its independent variables conforms to the primary wavefront for example using a ray coordinate system with the traveltime being one of the coordinates at each finite difference time step the solution domain is limited to a narrow corridor around the primary wavefront leading to an increase in the computational performance a new finite difference scheme is introduced to stabilize the solution and facilitate its implementation this new scheme is a blend of the simple explicit and the stable implicit schemes as a proof of concept the proposed method is compared to the classical explicit finite difference scheme performed in cartesian coordinates on two synthetic velocity models with varying complexities at a reduced cost the proposed method produces similar results to the classical one however some amplitude differences arise due to various implementation issues the most direct application for the proposed method is the source side of reverse time migration

traveltime and amplitude estimation using wavefront construction we have developed and implemented a new method for estimating traveltimes and amplitudes in a general smooth two dimensional 2 d model the basic idea of this wavefront wf construction approach is to use ray tracing to estimate a new wf from the old one the wf is defined as a curve in 2 d of constant traveltime from the source the ray direction and amplitude will then be a function of s the distance along the front to maintain a sufficiently small sampling distance along the wf it is scanned at every time step and new rays are interpolated whenever the distance between two rays becomes larger than a predefined limit as the wavefronts are constructed the data i e traveltimes amplitude coefficients etc are transferred to the receivers by interpolation within the ray cells advantages of the wf construction method are its flexibility robustness and accuracy first second and later arrivals may be found at any point in the model any shape of the initial wavefront is possible the drawb

3 d traveltime computation using huygens wavefront tracing traveltime computation is widely used in seismic modeling imaging and velocity analysis the two most commonly used methods are ray tracing and numerical solutions to the eikonal equation eikonal solvers are fast and robust but are limited to computing only the first arrival traveltimes ray tracing can compute multiple arrivals but lacks the robustness of eikonal solvers we propose a robust and complete method of traveltime computation it is based on a system of partial differential equations which is equivalent to the eikonal equation but formulated in the ray coordinates system we use a first order discretization scheme that is interpreted very simply in terms of the huygens s principle our explicit finite difference solution to the eikonal equation solved in the ray coordinates system delivers both computational speed and stability since we use more than one point on the current wavefront at every time step the finite difference method has proven to be a robust alternative to conventional ray tracing while being faster and having a better ability to handle rough velocity media and penetrate shadow zones

improving autocorrelation regression for the hurst parameter estimation of long range dependent time series based on golden section search abstract this article presents an improved autocorrelation correlation function acf regression method of estimating the hurst parameter of a time series with long range dependence lrd by using golden section search gss we shall show that the present method is substantially efficient than the conventional acf regression method of h estimation our research uses fractional gaussian noise as a data case but the method introduced is applicable to time series with lrd in general

periodogram based estimators of fractal properties we suggest an estimator based on the periodogram of the fractal index and fractal dimension of a continuous stationary gaussian process we argue that the cosine part of the periodogram is more appropriate than the full periodogram for this application the term semiperiodogram is used to describe the cosine component and our estimator is based on simple linear regression of the logarithm of the semiperiodogram on the algorithm of frequency theoretical properties of the estimator including its bias variance and asymptotic distribution are derived consistency is possible using only a small trace of the process recorded over a fixed interval we do not need to model the covariance function parametrically and assume only mild conditions on the behaviour of the covariance in the neighbourhood of the origin the issue of aliasing is discussed in both theoretical and numerical terms and the numerical properties of the estimator are assessed in a simulation study

fractal analysis of surface roughness by using spatial data summary we develop fractal methodology for data taking the form of surfaces an advantage of fractal analysis is that it partitions roughness characteristics of a surface into a scale free component fractal dimension and properties that depend purely on scale particular emphasis is given to anisotropy where we show that for many surfaces the fractal dimension of line transects across a surface must either be constant in every direction or be constant in each direction except one this virtual direction invariance of fractal dimension provides another canonical feature of fractal analysis complementing its scale invariance properties and enhancing its attractiveness as a method for summarizing properties of roughness the dependence of roughness on direction may be explained in terms of scale rather than dimension and can vary with orientation scale may be described by a smooth periodic function and may be estimated nonparametrically our results and techniques are applied to analyse data on the surfaces of soil and plastic food wrapping for the soil data interest centres on the effect of surface roughness on retention of rain water and data are recorded as a series of digital images over time our analysis captures the way in which both the fractal dimension and the scale change with rainfall or equivalently with time the food wrapping data are on a much finer scale than the soil data and are particularly anisotropic the analysis allows us to determine the manufacturing process which produces the smoothest wrapping with least tendency for micro organisms to adhere

a fast sweeping algorithm for accurate solution of the tilted transversely isotropic eikonal equation using factorization abstracttraveltime computation is essential for many seismic data processing applications and velocity analysis tools high resolution seismic imaging requires eikonal solvers to account for anisotropy whenever it significantly affects the seismic wave kinematics moreover computation of auxiliary quantities such as amplitude and take off angle relies on highly accurate traveltime solutions however the finite difference based eikonal solution for a point source initial condition has upwind source singularity at the source position because the wavefront curvature is large near the source point therefore all finite difference solvers even the high order ones show inaccuracies because the errors due to source singularity spread from the source point to the whole computational domain we address the source singularity problem for tilted transversely isotropic tti eikonal solvers using factorization we solve a sequence of factored tilted elliptically anisotropic tea eikonal equations iteratively

3 d traveltime computation using the fast marching method we present a fast algorithm for solving the eikonal equation in three dimensions based on the fast marching method the algorithm is of the order o n log n where n is the total number of grid points in the computational domain the algorithm can be used in any orthogonal coordinate system and globally constructs the solution to the eikonal equation for each point in the coordinate domain the method is unconditionally stable and constructs solutions consistent with the exact solution for arbitrarily large gradient jumps in velocity in addition the method resolves any overturning propagation wavefronts we begin with the mathematical foundation for solving the eikonal equation using the fast marching method and follow with the numerical details we then show examples of traveltime propagation through the seg eage salt model using point source and planewave initial conditions and analyze the error in constant velocity media the algorithm allows for any shape of the initial wavefront while a point source is the most commonly used initial condition initial plane waves can be used for controlled illumination or for downward continuation of the traveltime field from one depth to another or from a topographic depth surface to another the algorithm presented here is designed for computing first arrival traveltimes nonetheless since it exploits the fast marching method for solving the eikonal equation we believe it is the fastest of all possible consistent schemes to compute first arrivals

efficient traveltime solutions of the acoustic ti eikonal equation numerical solutions of the eikonal hamilton jacobi equation for transversely isotropic ti media are essential for imaging and traveltime tomography applications such solutions however suffer from the inherent higher order nonlinearity of the ti eikonal equation which requires solving a quartic polynomial for every grid point analytical solutions of the quartic polynomial yield numerically unstable formulations thus it requires a numerical root finding algorithm adding significantly to the computational load using perturbation theory we approximate in a first order discretized form the ti eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter such perturbation applied to the discretized form of the eikonal equation does not impose any restrictions on the complexity of the perturbed parameter field therefore it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter such as that for the complicated marmousi model the formulation allows for large cost reduction compared to using the direct ti eikonal solver furthermore comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm without any addition to the computational cost

riemannian wavefield extrapolation nonorthogonal coordinate systems riemannian wavefield extrapolation rwe is used to model one way wave propagation on generalized coordinate meshes previous rwe implementations assume that coordinate systems are defined by either orthogonal or semiorthogonal geometry this restriction leads to situations where coordinate meshes suffer from problematic bunching and singularities nonorthogonal rwe is a procedure that avoids many of these problems by posing wavefield extrapolation on smooth but generally nonorthogonal and singularity free coordinate meshes the resulting extrapolation operators include additional terms that describe nonorthogonal propagation these extra degrees of complexity however are offset by smoother coefficients that are more accurately implemented in one way extrapolation operators remaining coordinate mesh singularities are then eliminated using a differential mesh smoothing procedure analytic extrapolation examples and the numerical calculation of 2d and 3d green s functions for cylindrical and near spher