• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.51-56
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• 2008

The waveform inversion for isotropic media has ever been studied since the 1980s, but there has been few studies for anisotropic media. We present a seismic waveform inversion algorithm for 2-D heterogeneous transversely isotropic structures. A cell-based finite difference algorithm for anisotropic media in time domain is adopted. The steepest descent during the non-linear iterative inversion approach is obtained by backpropagating residual errors using a reverse time migration technique. For scaling the gradient of a misfit function, we use the pseudo Hessian matrix which is assumed to neglect the zero-lag auto-correlation terms of impulse responses in the approximate Hessian matrix of the Gauss-Newton method. We demonstrate the use of these waveform inversion algorithm by applying them to a two layer model and the anisotropic Marmousi model data. With numerical examples, we show that it's difficult to converge to the true model when we assumed that anisotropic media are isotropic. Therefore, it is expected that our waveform inversion algorithm for anisotropic media is adequate to interpret real seismic exploration data.

• Nuclear Engineering and Technology
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• v.5 no.1
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• pp.38-43
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• 1973

The spin-rotation constants of the proton and tile fluorine nucleus in C $H_4$, Si $H_4$, Ge $H_4$, C $F_4$, Si $F_4$ and Ge $F_4$ were determined experimentally by the molecular beam magnetic resonance method. From the Hamiltonian and the high field approximation, the quantized energy level is given by the following equation. W $m_{I}$ $m_{J}$=- $g_{I}$ $m_{I}$H- $g_{J}$ $m_{J}$H- $C_{av}$ $m_{I}$ $m_{J}$, where $c_{av}$ is one third of the trace of the C tensor. In the nuclear resonance experiment, the proton and the fluorine nuclear resonance curves consist of many unresolved lines given by v=- $g_{J}$H- $C_{av}$ $m_{I}$, and a Gaussian approximation is made to correlate $c_{av}$ to the experimentally obtained half-width of the resonance curve. In the rotational resonance experiment, the five resonance peaks as predicted by v=- $g_{I}$H- $c_{av}$ $m_{I}$, $m_{I}$=0, $\pm$1 and $\pm$2, were all observed. The magnitude of car was determined by measuring the frequency distance between two adjacent peaks. The sign of $c_{av}$ was determined by the side peak suppression technique. The technique is described, and the sign and magnitude of the spin-rotation constant cav are summarized as following: for C $H_4$ -10.3$\pm$0.4tHz(from the rotational resonance), for SiH +3.71$\pm$0.08kHz(from the nuclear resonance), for Ge $H_4$+3.79$\pm$0.13kHz(from the nuclear resonance), for C $F_4$, -6.81$\pm$0.08kHz(from the rotational resonance), for Si $F_4$, -2.46$\pm$0.06kHz(from the rotational resonance), and finally for Ge $F_4$-1.84$\pm$0.04kHz(from the rotational resonance).onal resonance).esonance).