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Author Geller, Robert J. ♦ Hirabayashi, Nobuyasu ♦ Mizutani, Hiromitsu
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Conventional One-step ♦ Computing Synthetic Seismogram ♦ Dependent Variable ♦ Accurate Finite-difference Scheme ♦ Point Spatial Operator ♦ Accurate Fd Scheme ♦ Sg Scheme ♦ One-step Fd Scheme ♦ Fourth Order ♦ Conventional One-step Fd Scheme ♦ Fd Scheme ♦ 3-d Problem ♦ One-step Scheme ♦ Thus Sg Scheme ♦ Synthetic Seismogram ♦ Common Framework ♦ Non-optimally Accurate One-step Fd Scheme ♦ Second Order ♦ Straightforward Comparison ♦ Various Finite-difference ♦ Cpu Time
Abstract We compare the cost-effectiveness (as quantified by the CPU time required to attain a given level of accuracy) of various finite-difference (FD) schemes for computing synthetic seismograms. Broadly speaking, published FD schemes can be divided into two classes: staggered-grid (SG) schemes, in which velocity and stress are the dependent variables, and schemes in which displacement (or ve-locity) is the only dependent variable. “Displacement only ” schemes can be further divided into conventional one-step FD schemes and optimally accurate FD schemes; the latter have been shown to be about an order of magnitude more cost-effective than the former for one-dimensional (1-D) problems, and two orders of magnitude more efficient for 3-D problems. We show that SG schemes can be transformed into one-step schemes in which velocity is the only dependent variable, thereby allowing a straightforward comparison of SG, conventional one-step, and optimally accurate FD schemes in a common framework. We use this result to show that an SG scheme which is second order in time and fourth order in space, O(2,4), is equivalent to a non-optimally accurate one-step FD scheme with a seven point spatial operator, whereas a conventional O(2,4) one-step FD scheme uses only a five point spatial operator. Thus SG schemes have no advantages in accuracy over con-
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study