大延伸非均匀介质中地震波全弹性散射理论Ⅰ——弹性波单次散射理论
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摘要
所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究.应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解.这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础.在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论.该理论可包容小尺度非均匀体、大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论.
The focal point of the work described in this paper is the investigation of elastic seismic scattering by heterogeneous continua of large extent. For mathematical convenience, the incident waves are considered as time harmonic waves and the study works in the frequency domain. Elastic scattering from a continuous and laterally unbounded heterogeneous layer is formulated using the Born approximation. A general solution for the scattered waves for the above-stated medium is given in terms of a Fourier integral over plane waves. On this basis, far-field asymptotic expressions for weak elastic scattering by a finite, continuous and inhomogeneous layer are presented which agree with earlier results. For the case where perturbations of the two elastic parameters and the density have the same form of spatial variation, the spectrum of plane waves scattered from a heterogeneous layer is expressed as a product of an "elastic scattering factor" and a "distribution factor". As in earlier results for small-scale heterogeneity, the scattering pattern depends on various combinations of perturbations of elastic parameters and density. The work described in this paper is a basis for solving the problem of multiple scattering of elastic seismic waves for extended and heterogeneous media.In this paper, a theory of full elastic scattering for heterogeneous media of large extent has been established, which can be considered as a more general and unitive theory of weak scattering that can contain the theory of full elastic scattering for heterogeneous media of large extent, the theory of full elastic scattering for small-scale heterogeneities and the theory of scattering of scalar waves in the case of weak and single scattering.
The focal point of the work described in this paper is the investigation of elastic seismic scattering by heterogeneous continua of large extent. For mathematical convenience, the incident waves are considered as time harmonic waves and the study works in the frequency domain. Elastic scattering from a continuous and laterally unbounded heterogeneous layer is formulated using the Born approximation. A general solution for the scattered waves for the above-stated medium is given in terms of a Fourier integral over plane waves. On this basis, far-field asymptotic expressions for weak elastic scattering by a finite, continuous and inhomogeneous layer are presented which agree with earlier results. For the case where perturbations of the two elastic parameters and the density have the same form of spatial variation, the spectrum of plane waves scattered from a heterogeneous layer is expressed as a product of an "elastic scattering factor" and a "distribution factor". As in earlier results for small-scale heterogeneity, the scattering pattern depends on various combinations of perturbations of elastic parameters and density. The work described in this paper is a basis for solving the problem of multiple scattering of elastic seismic waves for extended and heterogeneous media.In this paper, a theory of full elastic scattering for heterogeneous media of large extent has been established, which can be considered as a more general and unitive theory of weak scattering that can contain the theory of full elastic scattering for heterogeneous media of large extent, the theory of full elastic scattering for small-scale heterogeneities and the theory of scattering of scalar waves in the case of weak and single scattering.
引文
1 Wu RS, Aki K. Elastic wave scattering by a random medium and the small-scale inhomogeneities in the litho-sphere. J Geophys Res, 1985, 90: 10261～10273
2 Aki K. Analysis of the seismic coda of local earthquakes as scattered waves. J Geophys Res, 1969, 74: 615～631
3 Wu RS, Aki K. Multiple scattering and energy transfer of seismic waves-separation of scattering effect fromintrinsic attenuation——II. Application of the theory to Hindu Kush Region. Pure Appl Geophys, 1988, 128(1):49～80
4 Hudson JA. The scattering of elastic waves by granular media. Qu J Mech Appl Math, 1968, 21: 487～502
5 Haddon RAW. Scattering of seismic body waves by small random inhomogeities in the earth. NORSAR Sci Rep, Norw. Seismic Array, Oslo, 1978, 3-77/78
6 Sato H. Attenuation of body waves and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. J Geophys, 1984, 89: 1221～1241
7 Wu RS. The perturbation method in elastic scattering. Pure Apll Geophys, 1989, 131(4): 605～637
8 Sato H. Unified approach to amplitude attenuation and coda excitation in the randomly inhomogeneous litho-sphere. Pure Apll Geophys, 1990, 132: 93～122
9 Li XF, Hudson JA. Elastic scattered waves from a continuous and heterogeneous layer. Geophys J Int, 1995, 121: 82～102
10 Li XF. Elastic scattering of P and S wave from a continuous and heterogeneous layer. R R University of Cambridge, 1993, 8: 1～61
11 Wu RS. Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method. J Geophys Res, 1994, 94: 751～761
12 Ellison TH. The propagation of sound waves through a medium with very small random variationa in refractive index. J Atmosph and Terres Phys, 1951, 2: 14～21
13 Hudson JA. Scattering waves in the coda of P. J Geophys, 1977, 43: 359～374
14 Kennett BLN. Seimic waves in laterally in inhomogeneous media. Geophys J R Astron Soc, 1972, 27: 301～325
15 Cisternas A, Jobert G. Extension of matrix methods to structures with slightly irregular stratification. J Geophys, 1977, 43: 59～74
16 Saastanmoinen PR. Model approach to wave propagation in layered media with lateral inhomogeneities. J Geophys, 1977, 43: 75～82
17 Park P, Odom R. The effect of stochastic rough interfaces on coupled-mode elastic waves. Geophys J Int, 1999, 136: 123～143
18 Eason G, Fulton J, Sneddon IN. The generation of waves in an infinite elastic solid by variable forces. Phil Trans Roy Soc London, 1955-1956, 248. A: 575～607
19 Ishimaru A. Wave propagation and scattering in random media, 2, Acadimic Press, New York, San Francisco, London, 1978
20 Hudson JA. Scattering waves in the coda of P. J Geophys, 1977, 43: 359～374
2 Aki K. Analysis of the seismic coda of local earthquakes as scattered waves. J Geophys Res, 1969, 74: 615～631
3 Wu RS, Aki K. Multiple scattering and energy transfer of seismic waves-separation of scattering effect fromintrinsic attenuation——II. Application of the theory to Hindu Kush Region. Pure Appl Geophys, 1988, 128(1):49～80
4 Hudson JA. The scattering of elastic waves by granular media. Qu J Mech Appl Math, 1968, 21: 487～502
5 Haddon RAW. Scattering of seismic body waves by small random inhomogeities in the earth. NORSAR Sci Rep, Norw. Seismic Array, Oslo, 1978, 3-77/78
6 Sato H. Attenuation of body waves and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. J Geophys, 1984, 89: 1221～1241
7 Wu RS. The perturbation method in elastic scattering. Pure Apll Geophys, 1989, 131(4): 605～637
8 Sato H. Unified approach to amplitude attenuation and coda excitation in the randomly inhomogeneous litho-sphere. Pure Apll Geophys, 1990, 132: 93～122
9 Li XF, Hudson JA. Elastic scattered waves from a continuous and heterogeneous layer. Geophys J Int, 1995, 121: 82～102
10 Li XF. Elastic scattering of P and S wave from a continuous and heterogeneous layer. R R University of Cambridge, 1993, 8: 1～61
11 Wu RS. Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method. J Geophys Res, 1994, 94: 751～761
12 Ellison TH. The propagation of sound waves through a medium with very small random variationa in refractive index. J Atmosph and Terres Phys, 1951, 2: 14～21
13 Hudson JA. Scattering waves in the coda of P. J Geophys, 1977, 43: 359～374
14 Kennett BLN. Seimic waves in laterally in inhomogeneous media. Geophys J R Astron Soc, 1972, 27: 301～325
15 Cisternas A, Jobert G. Extension of matrix methods to structures with slightly irregular stratification. J Geophys, 1977, 43: 59～74
16 Saastanmoinen PR. Model approach to wave propagation in layered media with lateral inhomogeneities. J Geophys, 1977, 43: 75～82
17 Park P, Odom R. The effect of stochastic rough interfaces on coupled-mode elastic waves. Geophys J Int, 1999, 136: 123～143
18 Eason G, Fulton J, Sneddon IN. The generation of waves in an infinite elastic solid by variable forces. Phil Trans Roy Soc London, 1955-1956, 248. A: 575～607
19 Ishimaru A. Wave propagation and scattering in random media, 2, Acadimic Press, New York, San Francisco, London, 1978
20 Hudson JA. Scattering waves in the coda of P. J Geophys, 1977, 43: 359～374
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