Influence of the self2organization of the Earth interior upon the traveltime and amplitude of seismic wave

Transcription

1 CHINESE JOURNAL OF GEOPHYSICS Vol. 50, No. 4 Jul., 2007,,..,2007,50 (4) : Xu T,Ning J R,Liu C C,et al. Influence of the self2organization of the Earth interior upon the traveltime and amplitude of seismic wave. Chinese J. Geophys. (in Chinese),2007,50 (4) : , 1,2, 1,3, 1,4 1,, , , , ;,, von Karman ; ;,, ;, ; von Karman,,.,,,,, (2007) P , Influence of the self2organization of the Earth interior upon the traveltime and amplitude of seismic wave XU Tao 1,NINGJun2Rui 1,2,LIU Chun2Cheng 1,3,LI Shou2Lin 1,4 1 State Key Laboratory of Lithosphere Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing , China 2 Exploration and Production Research Institute, SINOPEC, Beijing , China 3 China National Offshore Oil Corporation. Tian Jin, Tianjin , China 4 International Exploration Corporation, China Petroleum & Chemical Corporation, Beijing , China Abstract We utilize random media to describe small2scale inhomogeneity and self2organized structure in the Earth interior. A block model is adopted to describe the self2organized structure instead of traditional grids in 22D. Gaussian, exponential, and von Karman autocorrelation functions are used to represent the isotropic and anisotropic self2organized structure. We use numerical methods to perform ray tracing and rectify amplitudes by dynamic ray tracing, furthermore, analyze the influence upon the kinematic and dynamic characteristics of seismic waves. The results indicate that seismic ray trajectories probably generate significant aberrances and the amplitudes of seismic rays may weaken or enlarge at different offsets for the existence of the self2organized structure in the earth interior ; from Gaussian to von Karman, amplitudes present more obvious statistic characters. Keywords Self2organized structure, Block model, Seismic wave, Ray trajectory, Traveltime, Seismic amplitude ( , , ) 973 (2002CB412604).,,1978,,2004,,. E2mail : iggcas. ac. cn

2 4 : ,,,, [1 8 ].,, ( ),. : (1),,,, ; (2) ; (3) (, ).,.,,,,,., [9 11 ].,..,, [12,13 ].,,,.,, [14 21 ] [9 12,22 29 ],,,. ;,, ; ; von Karman [9 14,16,17,22,23,30 ]., v ( x) = v 0 ( x) + v ( x), (1) v 0, ; v,. v ( x) = v 0 ( x) (1 + ), (2), = ( x), ( ) ( ). ( x) = 0, (3) 2 ( x) = 2, (4) ( x) ( x ) = R ( r), (5), 2, R ( r), r = x - x. 212 ( ).,, von Karman ( ) Kummer [9 14,16,17,22,23,30 ], [11,30 ]., ( x) R ( r) ^F ( k) [31, 32 ]. 1 2., K 0, 2 a b x z. ^f ( k),. 1 Table 1 Isotropic autocorrelation functions and associated power spectrums ( ) e r2 Πa 2 e - a2 k 2 Π4 ( ) e - a2 k 2 r Π4 e rπa ( a k 2 ) - 1 ( a k 2 r) - 3Π2 von Karman K 0 ( rπa) ( a k 2 ) - 1Π2 ( a k 2 r) - 1

3 1176 (Chinese J. Geophys. ) 50 2 Table 2 Elliptical anisotropic autocorrelation functions and associated power spectrums ( ) ( ) e x2 Πa 2 + z 2 Πb 2 e - ( a2 k 2 x + b2 k 2 z )Π4 e x 2 Πa 2 + z 2 Πb 2 (1 + a 2 k 2 x + b 2 k 2 z) - 3Π2 von Karman K 0 ( x 2 Πa 2 + z 2 Πb 2 ) (1 + a 2 k 2 x + b 2 k 2 z) - 1 ^F ( k) ^f ( k) : : ^F ( k) = ^f 3 ( k) ^f ( k) ; (6) ^f ( k) = ^f ( k) ; (7), k = ( k T k) 1Π2 ;, k = ( k T Lk) 1Π2, L. [30 ] : ^f ( k) = ^f S ( k) ^f a ( k) ^f ag ( k), (8),^f S ( k), ^f a ( k), ^f S ( k) = k - dπ2- N, (9) ^f a ( k) = (1 + ( ak) - 2 ) - dπ4- NΠ2, (10) ^f ag ( k) ^f ag ( k) = e - a2 G k2 Π8. (11) (9) (11), d ; N Hurst ; a a G von Karman ;.,.,N = - dπ2, ; a G = 0 von Karman, N = 0, N = 1Π2 ; a G = 0, a =, [30]. 1 ^f a ( k) ^f ag ( k), a, k a G, k. 1 ^f a ( k) ^f ag ( k). (10) (11). Fig. 1 Product of high2pass filter ^f a ( k) and low2pass Gaussian filter ^f ag ( k) against a logarithmic wave2number k, : (1) W ( x), ^W ( k) ; (2), ^U ( k) = ^f ( k) ^W ( k) ; (3) ^U ( k), U ( x) ; (4) U ( x) ;. 2 (2a) (2b) von Karman ( ) (2c). 20 km,.,, von Karman,. 213., :,,,,,.,. [15,18 ] ( [ NlgN ], N ).,.,, [19,20 ]. [18,21 ],,,,. ( ) [18 ]. 3, 7, ( 5a), ( 3 4 )., ( 3 4) : (1) 4,, ; (2) ; (3),,, 4,,, ( 5b 5d).

4 4 : new Fig. 4 New incidence angle new updated by an initial incidence angle 1 and an increment 3 2 (a) ; (b) ; (c) von Karman ( ). ( ), ( ). Fig. 2 Three self2organized media (a) Gassian ; (b) Exponential ; (c) Zero von Karman. Blue colors denote fast regions and red colors denote slow regions. 3, 4 Fig. 3 The representation of a self2organized media in a complex block structure. Block # 4 denotes a Gaussian random media 311, [14,16,17 ]., [33 ] : 9 t x = vsin, 9 t z = vcos, 9 t = - cos 9 v 9 x + sin 9 v 9 z. (12), Eluer Runge2Kutta., [21 ] [18 ]. ( 4 ),,,. new 312 = 1 + ( x rcvr - x 1 ) x. (13),. : ; ( ), ; [33,34 ]. 4,.,

5 1178 (Chinese J. Geophys. ) 50 5 (a) ; (b) ; (c) ; (d) ; (e) c, ; (f) d, ; (g) c,von Karman ; (h) d,von Karman ; (i) (d,f,h) (b) Fig. 5 (a) Initial shooting trajectories based on the background velocity model ; (b) Tracing results based on the background velocity model ; (c) Initial shooting trajectories based on a superimposed Gaussian random perturbation velocity model ; (d) Tracing results based on the velocity model as (c) ; (e) Same as (c) with an exponential random perturbation ; (f) Tracing results based on (e) ; (g) Same as (c) with a von Karman random perturbation ; (h) Tracing results based on (g) ; (i) Traveltime error of tracing trajectories in (d), (f) and (h) to background traveltime (b)

6 4 : 1179 [35 37 ], 5, 400 km 90 km ; 7., 4,. : ( 5a 5b) ( 5c 5d) ( 5e 5f) von Karman ( 5g 5h)., : 2 km, 8 km,, 1 %( 3 %) ;, ( 5c 5h), von Karman,. 5a 5b ;5c 5h (, ) ; 5i ( 5d 5f 5h) ( 5b). 200 km,,, km km,,.,, von Karman,, von Karman,. 6a, ; 6b,., km, km. von Karman,,,,,. 6 (a) (5b) (5d) (5f) von Karman (5h) ; (b) Fig. 6 (a) From the top down, the synthetic seismograms of dynamic tracing based on background (5b), Gaussian (5d), Exponential (5f) and von Karman (5h) velocity models ; (b) Three random amplitude relative errors to the background

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