地震背景噪声互相关函数的面波理论表达形式
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摘要
基于弹性动力学面波激发公式推导出地震背景噪声互相关函数(简称为NCF)的理论表达形式.证明了NCF等价于面波的震源激发公式,其中一个台站为等价震源的位置,另一个台站为接收点.本文提出的最重要的概念是等价震源相位,它直接影响群速度与相速度的测量误差.在噪声源均匀分布的条件下,等价震源相位等于-π/4.一般情况下,等价震源相位与噪声源分布有关,而不是简单的常数.在大信噪比的条件下,等价震源相位的最大可能取值等于信噪比的倒数.本文详细讨论了利用三台法测量相速度的可能性,并且给出了估算等价震源相位以及相速度测量误差的公式.
The present study derives the surface-wave theoretical expression of the noise cross-correlation function (NCF).We demonstrate that the NCF is equivalent to the surface-wave excitation,in which the equivalent source is at one of the two stations.The most important concept of this paper is the equivalent source s phase function,which directly influences the accuracy of group and phase velocity measurements.Under a homogenous source distribution assumption the equivalent source's phase is —π/4.In general,it is dependent on the distribution of noise sources,instead of being a constant.Under the condition of large signal to noise ratios (SNR) ,the possible maximal value of the equivalent source phase is equal to SNR's reciprocal. This paper also tries to study the possibility of using three stations to measure phase velocities and to estimate the equivalent source's phase function and then gives the measurement errors.
The present study derives the surface-wave theoretical expression of the noise cross-correlation function (NCF).We demonstrate that the NCF is equivalent to the surface-wave excitation,in which the equivalent source is at one of the two stations.The most important concept of this paper is the equivalent source s phase function,which directly influences the accuracy of group and phase velocity measurements.Under a homogenous source distribution assumption the equivalent source's phase is —π/4.In general,it is dependent on the distribution of noise sources,instead of being a constant.Under the condition of large signal to noise ratios (SNR) ,the possible maximal value of the equivalent source phase is equal to SNR's reciprocal. This paper also tries to study the possibility of using three stations to measure phase velocities and to estimate the equivalent source's phase function and then gives the measurement errors.
引文
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[4] Shapiro N M, Campillo M. Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise.Geophys. Res. Lett., 2004, 31: L07614, doi: 10． 1029/2004GL019491
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[6] Sabra K G, Gerstoft P, Roux P, et al. Extracting time-domain Greens function estimates from ambient seismic noise. Geophys. Res. Lett., 2005, 32: L03310, doi: 10． 1029/2004GL021862
[7] Sabra K G, Gerstoft P, Roux P, et al. Surface wave tomography from microseisms in Southern California.Geophys. Res. Lett., 2005, 32: L14311, doi: 10． 1029/2005GL023155
[8] Shapiro N M, Campillo M, Stehly L, et al. High-resolution surface-wave tomography from ambient seismic noise.Science, 2005, 307(5715) : 1615-1618
[9] Campillo M, Paul A. Long-Range correlations in the diffuse seismic coda. Science, 2003, 299(5606) : 547-549
[10] Paul A, Campillo M, Margerin L, et al. Empirical synthesis of time-asymmetrical Green functions from the correlation of coda waves. J. Geophys. Res., 2005, 110: B08302, doi:10． 1029/2004JB003521
[11] Yang Y J, Ritzwoller M H, Levshin A L, et al. Ambient noise Rayleigh wave tomography across Europe. Geophys.J. Int. , 2007, 168: 259-274
[12] Yao H J, van der Hilst R D, de Hoop M V. Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis; ⅠI-Phase velocity maps. Geophys. J.Int. , 2006, 166(2) : 732-744
[13] Snieder R. Extracting the Green' s function from the correlation of coda waves: a derivation based on stationary phase. Phys. Rev. E, 2004, 69(4) : 046610． 1-046610． 8
[14] Aki K, Richards P G. Quantitative Seismology. San Francisco: W. H. Freeman, 1980． 314
[15] Yoshizawa K, Kennett B L N. Determination of the influence zone for surface wave paths. Geophys. J. Int. , 2002, 149(2) : 441-454
[16] Spetzler J, Trampert J, Snieder R. The effect of scattering in surface wave tomography. Geophys. J. Int. , 2002, 149(3) :755-767
[17] Zhou Y, Dahlen F A, Nolet G. Three-dimensional sensitivity kernels for surface wave observables. Geophys. J. Int. ,2004, 158(1) : 142-168
[18] Aki K, Richards P G. Quantitative Seismology, vol. 1． San Francisco: W. H. Freeman, 1980． 581
[19] Lin F C, Moschetti M P, Ritzwoller M H. Surface wave tomography of the western United States from ambient seismic noise: Rayleigh and Love wave phase velocity maps.Geophys. J. Int. , 2008, 173(1) : 281-298
[2] Lobkis O I, Weaver R L. On the emergence of the Green's function in the correlations of a diffuse field. J. Acoust. Soc.Am. , 2001, 110(6) : 3011-3017
[3] Weaver R L, Lobkis O I. Diffuse fields in open systems and the emergence of the Green's function (L). J. Acoust. Soc.Am. , 2004, 116(5) : 2731-2734
[4] Shapiro N M, Campillo M. Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise.Geophys. Res. Lett., 2004, 31: L07614, doi: 10． 1029/2004GL019491
[5] Roux P, Sabra K G, Kuperman W A, et al. Ambient noise cross correlation in free space; theoretical approach. J.Acoust. Soc. Am. , 2005, 117(1) : 79-84
[6] Sabra K G, Gerstoft P, Roux P, et al. Extracting time-domain Greens function estimates from ambient seismic noise. Geophys. Res. Lett., 2005, 32: L03310, doi: 10． 1029/2004GL021862
[7] Sabra K G, Gerstoft P, Roux P, et al. Surface wave tomography from microseisms in Southern California.Geophys. Res. Lett., 2005, 32: L14311, doi: 10． 1029/2005GL023155
[8] Shapiro N M, Campillo M, Stehly L, et al. High-resolution surface-wave tomography from ambient seismic noise.Science, 2005, 307(5715) : 1615-1618
[9] Campillo M, Paul A. Long-Range correlations in the diffuse seismic coda. Science, 2003, 299(5606) : 547-549
[10] Paul A, Campillo M, Margerin L, et al. Empirical synthesis of time-asymmetrical Green functions from the correlation of coda waves. J. Geophys. Res., 2005, 110: B08302, doi:10． 1029/2004JB003521
[11] Yang Y J, Ritzwoller M H, Levshin A L, et al. Ambient noise Rayleigh wave tomography across Europe. Geophys.J. Int. , 2007, 168: 259-274
[12] Yao H J, van der Hilst R D, de Hoop M V. Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis; ⅠI-Phase velocity maps. Geophys. J.Int. , 2006, 166(2) : 732-744
[13] Snieder R. Extracting the Green' s function from the correlation of coda waves: a derivation based on stationary phase. Phys. Rev. E, 2004, 69(4) : 046610． 1-046610． 8
[14] Aki K, Richards P G. Quantitative Seismology. San Francisco: W. H. Freeman, 1980． 314
[15] Yoshizawa K, Kennett B L N. Determination of the influence zone for surface wave paths. Geophys. J. Int. , 2002, 149(2) : 441-454
[16] Spetzler J, Trampert J, Snieder R. The effect of scattering in surface wave tomography. Geophys. J. Int. , 2002, 149(3) :755-767
[17] Zhou Y, Dahlen F A, Nolet G. Three-dimensional sensitivity kernels for surface wave observables. Geophys. J. Int. ,2004, 158(1) : 142-168
[18] Aki K, Richards P G. Quantitative Seismology, vol. 1． San Francisco: W. H. Freeman, 1980． 581
[19] Lin F C, Moschetti M P, Ritzwoller M H. Surface wave tomography of the western United States from ambient seismic noise: Rayleigh and Love wave phase velocity maps.Geophys. J. Int. , 2008, 173(1) : 281-298
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