有限差分法合成地震图中的网格频散
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摘要: 用有限差分法合成地震图时, 有限大小的地球模型必须分成许多小网格。如果和源信号的波长相比, 格子太大, 那么随着走时的增加, 波将产生频散。这一现象被称为网格频散, 也就是不同频率的波速度也不相同, 频率较高的信号比频率较低的信号速度慢。此时, 随着走时的增加, 信号将产生一个显着的尾区。这一现象将在如下情况发生：①网格间距太大: ②采样率太大: 或③震源波长和网格大小相比太短。换言之, 用有限差分法合成地震图的一个重要参数是, 每个震源信号波长上网格的点数。本文的工作表明：当P-SV波对经有限差分的弹性模型传播时, 源函数的频率对网格频散有很大的影响。文中所用的二维弹性模型包括：①正断层: ②半空间上单层模型。结果表明：用有限差分法合成地震图时, 如果对于介质的最低速度, 与震源信号的半功率频率相应的一个波长和格点间距之比超过10时, 网格频散将减小到满意的水平。
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[1] Alford, R. M., Kelly, K. R. and Boore, D. M., 1974. Accuracy of finite——difference modeling of the acoustic wave equation. Geophysics, 39, 834——842.
[2] Alterman, Z. S and Loewenthal, D., 1970. Seismic waves in a quarter and three quarter plane. Geophys. J. R. astr. Soc., 20, 101——126.
[3] Boore, D. M., 1969. Finite——Difference Solutions to the Equatirnu of Elastic Wave Propagation, with Applications to Lone Waves (?uer Ih'pping Interfaces. Ph. D., Thesis, M. I. T., Mass.
[4] Boore, D. M., 1970. Love waves in nonuniform wave guides: Finite——difference calculations. J. Geophys. Res., 75, 1512——1527.
[5] Boore, D. M., 1972. Finite——difference methods for seismic wave propagation in heterogeneous materials. In: Alder, B., Fernback, S. and Rotenberg, M. (editors), Methods in Computational Physics, Vol. if, Academic Press.
[6] Clayton. R. and Engquist, B., 1977. Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Sei.s. Soc. Amer., 67, 1529——1540.
[7] Javaherian, A., 1982. Eliminatirm of Spuriatts Re_flecti}na from Finite——Difference Synthetic Seismograms with Applicutitnts to the San Andrews Fault Zone. Ph. D. Thesis, University of Texas at Dallas.
[8] Kelly, K. R., Ward. R. W., Treitlel, S. and Alford, M., 1976. Synthetic seismograms: A finite——difference approach. Geophysics, 41, 2——27.[1] Alford, R. M., Kelly, K. R. and Boore, D. M., 1974. Accuracy of finite——difference modeling of the acoustic wave equation. Geophysics, 39, 834——842.
[2] Alterman, Z. S and Loewenthal, D., 1970. Seismic waves in a quarter and three quarter plane. Geophys. J. R. astr. Soc., 20, 101——126.
[3] Boore, D. M., 1969. Finite——Difference Solutions to the Equatirnu of Elastic Wave Propagation, with Applications to Lone Waves (?uer Ih'pping Interfaces. Ph. D., Thesis, M. I. T., Mass.
[4] Boore, D. M., 1970. Love waves in nonuniform wave guides: Finite——difference calculations. J. Geophys. Res., 75, 1512——1527.
[5] Boore, D. M., 1972. Finite——difference methods for seismic wave propagation in heterogeneous materials. In: Alder, B., Fernback, S. and Rotenberg, M. (editors), Methods in Computational Physics, Vol. if, Academic Press.
[6] Clayton. R. and Engquist, B., 1977. Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Sei.s. Soc. Amer., 67, 1529——1540.
[7] Javaherian, A., 1982. Eliminatirm of Spuriatts Re_flecti}na from Finite——Difference Synthetic Seismograms with Applicutitnts to the San Andrews Fault Zone. Ph. D. Thesis, University of Texas at Dallas.
[8] Kelly, K. R., Ward. R. W., Treitlel, S. and Alford, M., 1976. Synthetic seismograms: A finite——difference approach. Geophysics, 41, 2——27.
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