Sponge boundary condition for frequency-domain modeling

Several techniques have been developed to get rid of edge reflections from artificial boundaries. One of them is to use paraxial approximations of the scalar and elastic wave equations. The other is to attenuate the seismic waves inside the artificial boundary by a gradual reduction of amplitudes. These techniques have been successfully applied to minimize unwanted seismic waves for time-domain seismic modeling. Unlike time-domain seismic modeling, suppression of edge reflections from artificial boundaries has not been successful in frequency-domain seismic modeling. Rayleigh waves caused by coupled motions of P- and S-waves near the surface have been a particularly difficult problem to overcome in seismic modeling. In this paper, I design a damping matrix for frequencydomain modeling that damps out seismic waves by adding a diffusion term to the wave equation. This technique can suppress unwanted seismic waves, including Rayleigh waves and P- and S-waves from an artificial boundary

Headwave Stacking in Terms of Partial Derivative Wavefield

Head wave stacking and velocity analysis are used to image the shallow subsurface, while CMP stacking and velocity analysis are used to image deep structures of the earth. I relate these concepts to partial derivative seismograms, which gives stacking straight line of head waves. The stacking straight line can be described kinematically by partial derivative seismograms, resulting in an interesting seismic imaging relationship

Understanding CMP stacking hyperbola in terms of partial derivative wavefield

Common midpoint (CMP) stacking and velocity analysis are fundamental seismic imaging concepts based on a layered velocity model. We relate these concepts to partial derivative seismograms, which give seismic amplitude variations as a function of layer coordinates. The CMP stacking hyperbola can be described kinematically by partial derivative seismograms, resulting in an interesting seismic imaging relationship

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).To overcome this disadvantage inherent in space-frequency domain modeling, we propose a new weighted average finite-difference operator by approximating the spatial derivative and the mass acceleration term of the wave equation. We use 25 grid points around the collocation. In this way, we can reduce the number of grid points so that G is now 2.5. This approaches the Nyquist sampling limit in terms of the normalized phase velocity

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. ABSTRACT 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 secondorder approximation formula when a band type solver is used on a scalar machine

Wave equation calculation of most energetic traveltimes and amplitudes for Kirchhoff prestack migration

This work was conceived during a visit by Kurt Marfurt to Seoul National University, sponsored by the Korean Ministry of Science andTechnology.This work was financially supported by the Brain Korea 21 Project of the Ministry of Education of Korea and the National Research Laboratory project of the Ministry of Science and Technology. The authors acknowledge the support of the Korea Institute of Science and Technology Information (KISTI) under the Grand Challenge Support Program and the use of the Supercomputing Center

Refraction traveltime tomography using damped monochromatic wavefield

For complicated earth models, wave-equation–based refraction-traveltime tomography is more accurate than ray-based tomography but requires more computational effort. Most of the computational effort in traveltime tomography comes from computing traveltimes and their Fr´echet derivatives, which for ray-based methods can be computed directly. However, in most wave-equation traveltime-tomography algorithms, the steepest descent direction of the objective function is computed by the backprojection algorithm, without computing a Fr ´echet derivative directly. We propose a new wave-based refraction-traveltime– tomography procedure that computes Fr´echet derivatives directly and efficiently. Our method involves solving a damped-wave equation using a frequency-domain, finite-element modeling algorithm at a single frequency and invoking the reciprocity theorem. A damping factor, which is commonly used to suppress wraparound effects in frequency-domain modeling, plays the role of suppressing multievent wavefields. By limiting the wavefield to a single first arrival, we are able to extract the first-arrival traveltime from the phase term without applying a time window. Computing the partial derivative of the damped wave-equation solution using the reciprocity theorem enables us to compute the Fr ´echet derivative of amplitude, as well as that of traveltime, with respect to subsurface parameters. Using the Marmousi-2 model, we demonstrate numerically that refraction traveltime tomography with large-offset data can be used to provide the smooth initial velocity model necessary for prestack depth migration.This work was financially supported by the National Laboratory Project of the Ministry of Science and Technology and the Brain Korea 21 project of the Ministry of Education. We are also grateful to Prof. K. J. Marfurt of the University of Houston and Dr. M. Schoenberger for editing our manuscript

Prevalence of Allergic Diseases among Korean School-age Children: A Nationwide Cross-Sectional Questionnaire Study

The purpose of this study was to investigate the nationwide prevalence of childhood asthma, eczema and other allergic diseases in Korean school-age children (8-11 yr old) and to assess the difference between residential areas. Among 6,279 elementary schools, 427 schools were randomly selected according to residential area (metropolitan, provincial, rural, and industrial area) by the cluster sampling method. Parents of students completed a modified Korean version of a questionnaire formulated by the International Study of Asthma and Allergies in Childhood (ISAAC). Among 50,200 subjects, 31,026 (61.8%) responded, and 30,893 (99.6%) were analyzed. The 12-month prevalence of wheeze, flexural rash, and allergic rhinitis symptoms were 4.8%, 15.3%, and 32.9%, respectively. The prevalence of diagnosis of allergic diseases in boys was higher than that in girls, with the exception of eczema. In both boys and girls, the difference of the prevalence of allergic diseases among industrial, metropolitan and provincial areas was not statistically significant, but the differences between rural area and other areas were significant. Our results support the importance of contextual effect associated with residential area as causative agents of allergic diseases among Korean school-age children

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 secondorder 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