Estimation of Q and inverse Q filtering for prestack ... - Springer Link

APPLIED GEOPHYSICS, Vol.6, No.1 (March 2009), P. 59 - 69, 16 Figures. DOI:10.1007/s11770-009-0009-y

Estimation of Q and inverse Q filtering for prestack reflected PP- and converted PS-waves* Yan Hongyong1, 2 and Liu Yang1, 2♦ Abstract: Multi-component seismic exploration technology, combining reflected PP- and converted PS-waves, is an effective tool for solving complicated oil and gas exploration problems. The improvement of converted wave resolution is one of the key problems. The main factor affecting converted wave resolution is the absorption of seismic waves in overlying strata. In order to remove the effect of absorption on converted waves, inverse Q filtering is used to improve the resolution. In this paper, we present a method to estimate the S-wave Q values from prestack converted wave gathers. Furthermore, we extend a stable and effective poststack inverse Q filtering method to prestack data which uses wave field continuation along the ray path to compensate for attenuation in prestack common shot PPand PS-waves. The results of theoretical modeling prove that the method of estimating the S-wave Q values has high precision. The results from synthetic and real data prove that the stable inverse Q filtering method can effectively improve the resolution of prestack PP- and PS-waves. Keywords: reflected PP-wave, reflected converted PS-wave, prestack, Q, inverse Q filtering

Introduction Multi-component seismic exploration combining reflected PP- and converted PS-waves has been applied extensively and good results have been obtained in oil-gas and coal field exploration. However, with the continuous development of research and practice, the difficulties and problems have been gradually exposed. Compared to the PP-wave, the PS-wave has a lower propagation velocity when their main frequency and bandwidth are the same. In theory, PS-waves should have higher vertical resolution. However, practice shows that the effective high frequency energy components in the PS-wave data are weaker than in the PP-wave data since rocks exhibit stronger absorption for S-waves than

for P-waves. In other words, the converted wave seismic exploration usually fails to show the advantage of high resolution. Therefore, to compensate for the absorption attenuation of converted PS-waves, an effective inverse Q filter is essential to improve the data resolution in multi-component seismic exploration. The key to the inverse Q filtering compensation method is estimating relatively accurate P- and S-wave Q values. There are many methods for estimating Q values and the most common is estimating Q values from VSP data. Seven methods for Q estimation were investigated by Tonn (1991): (1) the amplitude decay method, (2) rise-time discrimination, (3) wavelet modeling, (4) the analytic signal method in the time domain, (5) the spectral ratio method, (6) the matching technique, and (7) spectral modeling in the frequency

Manuscript received by the Editor December 26, 2008; revised manuscript received February 4, 2009. *The study was supported by the 863 Program (Grant No.2007AA06Z218). 1. State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, 102249, China. 2. CNPC Key Laboratory of Geophysical Exploration, China University of Petroleum, Beijing, 102249, China. ♦ Corresponding author (Liu yang, email: [email protected]).

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Prestack reflected PP- and converted PS-waves domain. His study showed that none of the methods can be applied to every situation and their effects are dependent on record quality. Quan and Harris (1997) made use of a mass centroid frequency shift to estimate the Q values from VSP data. Rickett (2006, 2007) and Gao and Yang (2007) developed a high-precision method to estimate the Q values from VSP data. In terms of estimating the Q values from surface seismic data, Dasgupta and Clark (1998) made use of the spectral ratio method to estimate the Q values from prestack reflected wave gathers. Zhang and Ulrych (2002) presented a new method to estimate the Q values from prestack CMP gathers using peak frequency. The methods have been further developed by Liu and Wei (2005a; 2005b). As for estimating Q values from converted waves, Carderon-Macias et al. (2004) presented a method to estimate the Q values from converted wave seismic data. The estimated converted wave Q values are related to the P-wave to S-wave velocity ratio. In this paper, we derive a method based on the spectral ratio principle to estimate converted wave Q values and introduce the interval velocity computation method into Q estimation. Thus, a new method to estimate P- and S-wave Q values from prestack PP- and PS-wave gathers was obtained. Many researchers have studied inverse Q filtering compensation. Hale (1981) presented an inverse Q filtering method based on the Futterman mathematical model. Bickel and Natarajan (1985) presented an inverse Q filtering method from the point of view of plane wave propagation. It describes plane wave propagation using complex numbers and the inverse Q filtering operator is time variant. McCarley (1985) proposed an autoregressive model based on a constant Q filter. Hargreaves and Calvert (1991) presented a phase inverse Q filtering method based on a constant Q formation model which used a wave field inverse extrapolation to compensate for phase but the method neglected the impact of amplitude. Bano (1996) presented a phase inverse Q filtering method based on a constant interval Q value formation model, which can effectively and stably compensate for phase distortion. He also neglected the impact of amplitude. Liu et al. (2005) presented an inverse Q filtering method based on divided time window absorption compensation in the frequency domain. Wang (2002; 2003; and 2006) presented a full inverse Q filtering method for constant interval Q formation models with continuously variable Q values. This method can effectively and stably compensate for amplitude and phase. Zhang and Tadeusz (2007) introduced the least squares principle and Bayasian theory into the inverse Q filtering method to counter instability of inverse Q filtering and obtained good 60

results. In general, these methods only compensate zero offset seismic. For prestack seismic data, reasonable compensation methods should be performed along ray paths, since the actual wave attenuation occurs along the propagation path. Based on this idea, we introduce a full inverse Q filtering algorithm with the continuously variable Q values presented by Wang (2006) into prestack common shot gathers. This method uses wave field continuation along the ray path to perform inverse Q filtering compensation on prestack PP- and PS-wave data. The results are relatively perfect.

Method Estimation of Q Taking into account the absorption formation attenuation, the seismic wave amplitude spectrum can be expressed approximately by the following equation (Zhang and Ulrych, 2002):

B( f , t )

§ S ft · A(t ) B ( f , t0 ) exp ¨  ¸, © Q ¹

(1)

where f is the frequency, B(f,t) is the seismic wave amplitude spectrum at travel time t, Q is the medium quality factor, B(f,t 0) is the seismic wave amplitude spectrum at the initial time t 0, and A(t) is a factor independent of frequency. At times t1 and t2,

B ( f , t1 )

§ S ft1 · A(t1 ) B ( f , t0 ) exp ¨  ¸, © Q ¹

(2)

B ( f , t2 )

§ S ft2 · A(t2 ) B( f , t0 ) exp ¨  ¸. © Q ¹

(3)

When equation (3) is divided by equation (2), we obtain

B ( f , t2 ) B( f , t1 )

§ S ft2 · A(t2 ) exp ¨  ¸ © Q ¹. § S ft1 · A(t1 ) exp ¨  ¸ © Q ¹

(4)

After taking the logarithm of both sides of equation (4), we have

§ B ( f , t2 ) · S f (t2  t1 ) ln ¨ , ¸ C Q © B ( f , t1 ) ¹ where C

(5)

§ A(t2 ) · ln ¨ ¸ is considered a constant, and f and © A(t1 ) ¹

Yan et al. B are considered unknowns. Here, we assume that Q is independent of frequency. For each frequency value, we can obtain the logarithm of the spectral ratio using equation (5), which is a function of frequency with a § t t · slope of S ¨ 2 1 ¸ . Each frequency corresponds to one © Q ¹ 200

1

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Q value. We can estimate the Q values from prestack common shot point gathers (CSP gathers), for a single layer (see Figure 1) using any two traces of the prestack CSP gather and equation (5).

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Fig. 1 Attenuated PP-wave CSP gather (a) and attenuated PS-wave CSP gather (b).

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Fig. 2 Amplitude spectra corresponding to the CSP gathers in Figure 1. (Here, [0] represents the original wavelet, [1] and [40] represent the reflection amplitude spectra of trace 1 and 40, respectively.)

For the multi-layer case, we use the equivalent Q principle. Assuming that the strata consists of n layers, quality factor in each layer is Q1, Q2…Qn, and the two way seismic travel time in each layer is t1, t2…tn, the equivalent Q in each layer Q 1,eff, Q 2,eff…Q n,eff can be estimated from equation (5). Zhang and Ulrych (2002) suggested a similar RMS velocity approach to compute Q of each layer from prestack gathers. This method takes the equivalent Q as the RMS Q of layer n, so the Q value Qn of layer n can be obtained:

Qn

(Qn2, eff t0, n  Qn21, eff t0, n 1 ) /(t0, n  t0, n 1 ) ,

(6)

where t0,1, t0,2…t0,n are the zero offset travel times. For the computation of S-wave Q values using the PSwave, we use the seismic waves at t1 and t2 along the PSwave propagation direction. Their amplitude spectra can be expressed as:

B ( f , t1 )

§ S ft1 p A(t1 ) B( f , t0 ) exp ¨ ¨ Qp ©

· § S ft1s ¸¸ exp ¨ © Qs ¹

· ¸ , (7) ¹ 61

Prestack reflected PP- and converted PS-waves

B ( f , t2 )

§ S ft2 p A(t2 ) B( f , t0 ) exp ¨ ¨ Qp ©

· § S ft2 s ¸¸ exp ¨ © Qs ¹

· ¸ ,(8) ¹

where Qp is the P-wave Q value, Qs is the S-wave Q value, t1p and t1s are the P- and S-wave one way travel times at t1, and t2p and t2s are the P- and S-wave one way travel times at t2. Here, t1=t1p+t1s and t2=t2p+t2s. When equation (8) is divided by equation (7), we obtain

to the highest frequency within the seismic bandwidth and Qr is the Q value at any reference frequency. Continuing the wave field downward from the surface τ0=0 to the time τ, we obtain the stable wave field expression:

U W , Z

ª W § · J W ' º ª W § · J Z Z '» «i ¨ Z ¸ U  0, Z exp « ³ ¨ ¸ d W exp u « 0 © Zh ¹ » « ³0 © Zh ¹ 2Q(W ' ) ¬ ¼ ¬

J W ' º ª W § · J W ' º § S ft2 p · § S ft2 s ·ª W § Z ·  Z ' '» » u exp «i ¨ Z ¸ Z exp ¸« ³ ¨ ¸ A(t2 ) exp ¨U W , Z ¸ exp (15) U 0, d W Z d W ,  ¨ ¨ Qp ¸ » « ³0 © Zh ¹ » 2Q(W ' ) B ( f , t2 ) © Qs ¹« 0 © Zh ¹ © ¹ ¬ . (9) ¼ ¬ ¼ B( f , t1 ) § S ft1 p · § S ft1s · that is, exp ¨  A(t1 ) exp ¨  ¸ ¨ Q p ¸¸ Q s © ¹ © ¹ ª W § · J W ' º Z After taking the logarithm of both sides of equation (9), E W , Z U W , Z U  0, Z exp «i ³ ¨ ¸ Z dW ' » , « 0 © Zh ¹ » we have ¬ ¼ § · t t  § B ( f , t2 ) · § A(t2 ) · t t (16) 2p 1p ln ¨  2 s 1s ¸ . ¸ ln ¨ ¸  S f ¨¨ ¸ where Qs ¹ © B( f , t1 ) ¹ © A(t1 ) ¹ © Qp

(10) We compute the equivalent Q value of each layer from the PS-wave using equation (10) and then estimate the Q value of each layer using equation (6).

Inverse Q filtering method

E W , Z

ª W § · J W ' º Z Z '» exp «  ³ ¨ ¸ d W . « 0 © Zh ¹ » 2Q W ' ¬ ¼

Solving equation (16), we have the stable equation:

ª W § · J W ' º Z '» « U W , Z U  0, Z / (W , Z ) exp i ³ ¨ ¸ Z dW , After propagating a distance of Δx, the plane wave « 0 © Zh ¹ » U(x,ω) can be expressed by ¬ ¼ (17) (11) U  x  'x, Z U  x, Z exp  ik Z 'x , where σ2 is the stability factor (Wang, 2006). where ω is the radial frequency, i is the imaginary After applying every frequency value to equation (17) number unit, and k(ω) is the wave number. and summing the obtained plane wave, we obtain the Q is introduced in k(ω) to express the Q attenuation effect: seismic record in the time domain. J ª W § · J W ' º § i ·Z § Z · f 1 Z '» k Z ¨1  « (12) ¸ ¨ ¸ . u W U  0, Z / W , Z u exp i ³ ¨ ¸ Z dW d Z. « 0 © Zh ¹ » S ³0 © 2Qr ¹ vr © Zh ¹ ¬ ¼ '  J W ª W§ ·  º where Qr and vr are the Q factor and phase velocity 1at f Z (18) u W and³ U  0, Z / W , Z u exp «i ³ ¨ ¸ Z dW ' » d Z. any reference frequency, γ=(1/π)Qr-1 (Kolsky, 1956), « 0 © Zh ¹ » S 0 ωh is the tuning frequency (Wang and Guo, 2004). The ¬ ¼ inverse Q filtering expression is This equation is the stable full inverse Q filtering expression (Wang, 2006). (13) U  x  'x, Z U  x, Z exp  ik Z 'x . Wang (2006) compensated single trace data and postSubstituting equation (12) and the travel time stack data using this full inverse Q filtering method, increment Δτ for Δx into equation (13), we have compensating zero offset seismic data and ª§ Z · J Z'W º ª § Z · J namely, º horizontal layers. Because up-going and down-going » u exp «i ¨ ¸ Z'W » . U W  'W , Z U W , Z exp «¨ ¸ Z 2 Q Z «© h ¹ « © h¹ »¼ have the same propagation path, he compensated waves J » ª§ Z · J Z'¬W º ª § Z¼ · J ¬ º only the continuation of the up-going wave field with » u exp «i ¨ ¸ Z'W » . U W  'W , Z U W , Z exp «¨ ¸ a double absorption and attenuation effect. However, Z 2 Q Z «¬© h ¹ «¬ © h ¹ »¼ J » ¼ actually the wave attenuation process occurs along (14) the propagation path, so it’s necessary to perform Q 1 where J W , ωh is the tuning frequency related compensation for prestack traces along the ray path. S Q W 62

Yan et al.

1 ­ m ª   § Z · S Qp , j §Z ·S 1 f ° We apply this inverse Q filtering method to prestack « u W U  0, Z / W , Z u exp ®i ¦ ¨ ¸ Ztd , j  ¨ ¸ « records and compensate along the seismic wave propagation S ³0 © Zh ¹ ° j 1 «© Zh ¹ ¬ ¯ path. The key point is to determine the corresponding 1 1 ­ m ª   º½ propagation path at each time point in the original f § Z · S Qp , j § Z · S Qs , j 1 records. ° ° « u Ware U  0, Z Ztd , j  ¨ ¸ Z tu , j » ¾ d Z , horizontal, Assuming that the subsurface layers we / W , Z u exp ®i ¦ «¨ ¸ ³ 0 » S © Zh ¹ ° j 1 «© Zh ¹ ° subdivide the major layers, whose velocities are known, ¬ ¼» ¿ ¯ into many virtual thin layers. Based on the geometry, we (20) simulate the PP- and PS-wave ray paths by ray tracing where through each thin layer for each trace (see Figure 3) to E W , Z  V 2 determine the ray path in each thin layer for each offset / W , Z , E 2 W , Z  V 2 and obtain the up- and down-going propagation times for each receiver time point. Then, we make a template and of propagation paths and interpolate each corresponding 1 1 ­ m ª   propagation path at each time point in the original records § Z · S Qp , j Z § Z · S Qs , j Z ° « E W , Z exp ®¦ ¨ ¸ td , j  ¨ ¸ based on the template. Finally, we obtain all the travel times « 2Q p , j 2Qs , j j 1 © Zh ¹ © Zh ¹ ° «¬ in each layer corresponding to each time point in the records. ¯

S

E W , Z

1 1 ­R m ª   º½ § Z · S Qp , j Z § Z · S Qs , j Z ° ° « exp ®¦ ¨ ¸ td , j  ¨ ¸ tu , j » ¾ , « » Z Z 2 Q 2 Q p, j s, j © h¹ ° j 1 «© h ¹ »¼ °¿ ¬ ¯

where Qp, j and Qs, j are the P- and S-wave Q factors in layer j, respectively.

Synthetic data processing Fig. 3 Ray paths of PP-wave (solid line) and PS-wave (dashed line) at each time for one trace in the CSP gather.

We can get the propagation path at time τ for one trace in the record based on this method, namely, estimating the down-going travel times td,1, td,2…td,m and the up-going travel times tu,1, tu,2…tu,m in each layer. Using equation (18), we have the compensation expression at time τ. The compensation expression for PP-waves is: 1 ­ m ª  § Z · S Qp , j 1 f ° « u W U  0, Z / W , Z u exp ®i ¦ ¨ ¸ Z (td , j « S ³0 ° j 1 «© Z h ¹ ¬ ¯ 1 ­ m ª  º½ S Qp , j § · 1 f Z ° ° « U  0, Z / W , Z u exp ®i ¦ ¨ ¸ Z (td , j  tu , j ) » ¾ dZ , (19) « » S ³0 Z ° j 1 «© h ¹ »¼ °¿ ¬ ¯ where E W , Z  V 2 / W , Z , E 2 W , Z  V 2 and 1 ­ m ª  º½ S Qp , j § · Z Z ° ° « E W , Z exp ®¦ ¨ ¸ (td , j  tu , j ) » ¾ ., « » 2Q p , j ° j 1 «© Zh ¹ »¼ °¿ ¬ ¯ The compensation expression for PS-waves is:

Estimating Q from CSP gathers The equivalent Q values are computed based on the spectral ratio method using the amplitude spectrum of the seismic section wavelet. The equivalent Q values have an RMS relationship with the interval Q values. Therefore, we can estimate the P- and S-wave Q values in each layer. Using this method, the computed Q value at each layer is close to the true value. When estimating the Q values by º½ the spectral ratio method, we should compare adjacent °  tu , j ) » ¾ d Z , trace»pairs. It not only eliminates the source effect during »¼ °¿ the computation but also effectively suppresses the error propagation and accumulation. It also suppresses the error caused by sudden wavelet distortion. When estimating of S-wave Q values using the PS-wave, the P-wave Q value precision may affect those of the S-wave. To verify the Q value estimation method using prestack multi-component seismic data, we designed a horizontal layered model 1 (shown in Table 1). The parameters used by synthetic data are: 100 m offset, 100 m trace interval, and there are 20 receivers. A 40 Hz Ricker wavelet is the source. Since the Q value estimation using the spectral ratio method has nothing to do with the change of reflection coefficient with offset, we don’t consider the change of reflection coefficient with offset in model 1. 63

Prestack reflected PP- and converted PS-waves Table 1 Parameters of the horizontally layered model 1

We compute the PP- and PS-wave travel times using ray tracing and then obtain the PP- and PS-wave synthetic seismic records shown in Figure 4. For the synthetic PP- and PS-wave seismic records, we computed the Q values using the method described above for each layer. P-wave Q values are 31.2, 49.5, 65.0, and 79.0 and the S-wave Q values are 20.5, 41.2, 56.6, and 75.8. As shown in Figure 5, the estimated and the theoretic Q values coincide well. 5

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Fig. 4 PP-wave (a) and PS-wave (b) synthetic CSP attenuation gathers computed from model 1 (without considering the variation of reflection coefficient with offset). Theorical Q Estimated Q

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Fig. 5 Comparison between the theoretical and the estimated Q values for P-waves (a) and S-waves (b) using the data from Figure 4.

Examples of inverse Q filtering Figures 6a and 6b show the synthetic PP- and PS-wave CSP gathers for a horizontal layered model with three layers. The P-wave Q values of each layer are 40, 50, and 55 and the converted S-wave Q values are 30, 40, and 50. We used a 40 Hz Ricker wavelet. Reflection coefficient variations are ignored because inverse Q filtering has nothing to do with the variation of reflection coefficient. 64

We see that amplitude and frequency gradually decrease and the phase lagged during the propagation of the seismic waves with attenuation absorption. Figure 7 shows the Q values estimated by our method. We applied them to the full inverse Q filtering. After compensating the attenuation records of Figures 6a and b, we obtain the compensated results shown in Figures 8a and b. Comparing the precompensated records (Figure 6) and post-compensated

Yan et al. records (Figure 8), we can see that after the inverse Q filtering compensation strengthened the PP- and PSwave amplitudes, the phases have been recovered, and the resolution of the records has been obviously improved. 200

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From the amplitude spectra of the PP- and PS-waves before and after compensation (Figures 9 and 10), we can see that the energy of the high frequency component has been compensated and the primary frequency moves higher.

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Fig. 6 Attenuated PP-wave (a) and PS-wave (b) CSP synthetic gathers. 60

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Fig. 7 Estimated P-wave (a) and S-wave (b) Q values using the data from Figure 6. 200

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Fig. 8 PP-wave (a) and PS-wave (b) CSP gathers after inverse Q filtering compensation for the data of Figure 6.

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Prestack reflected PP- and converted PS-waves Amplitude vs. Frequency

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Fig. 9 Amplitude spectra of the PP-wave before (a) and after compensation (b). Amplitude vs. Frequency

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Fig. 10 Amplitude spectra of the PS-wave before (a) and after compensation (b).

Real data processing We selected the real multi-wave seismic data from some area of Songliao Basin, which are shown in the Figures 11a and 12a. Our method is used to estimate Q values from prestack gathers. Here, we select four reflection layers from the P-wave data, R pp1,R pp2,R pp3 and Rpp4, which are reflected at 1000 ms, 1500 ms, 2400 ms, and 3200 ms respectively. The estimated P-wave Q value between the surface and Rpp1 is 41.32, between Rpp1 and Rpp2 is 54.73, between Rpp2 and Rpp3 is 66.81, and between R pp3 and R pp4 is 89.21. Accordingly, we select four reflection layers from the converted wave data, Rps1, Rps2, Rps3 and Rps4, which are the reflections at 1200 ms, 2000 ms, 3000 ms, and 3600 ms, respectively. The estimated converted S-wave Q value between the surface and Rps1 is 30.06, between Rps1 and Rps2 is 42.41, 66

between Rps2 and Rps3 is 58.96, and between Rps3 and Rps4 is 74.22. Figures 11b and 12b show the PP- and PS-wave results after inverse Q filtering. Figures 13 and 14 show enlarged portions of Figures 11 and 12. As shown in the figures, after the application of the estimated Q values to the inverse Q filtering, the frequency of main reflector of both PP- and PS-wave resolution have been improved, especially the wave field information in the middle and deep layers are more abundant. Figures 15 and 16 are the amplitude spectra of PP- and PS-waves before and after compensation. We see that the main frequency of both the original PP- and PS-wave data is relatively low, and also the bandwidth is relatively narrow, while after compensation their bandwidth has been broadened, the high frequency component energy has been compensated, the main frequency moves higher, and the resolution has been improved.

Yan et al.

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Fig. 11 PP-wave CSP gathers of real multi-component data before (a) and after compensation (b). Trace No. 25

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Fig. 12 PS-wave CSP gathers of real multi-component data before (a) and after compensation (b).

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Fig.13 Partially enlarged view of Figure 11.

Conclusions The prestack inverse Q filtering compensation to the absorption of seismic wave from the subsurface medium is the f o u n d a t i o n a n d p r e r e q u i s i t e o f poststack data processing, which plays the key role in the improvement of seismic imaging precision, the reasonable interpretation of AVO effect and other

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Fig. 14 Partially enlarged view of Figure 12.

aspects. We estimate the P- and S-wave Q values from prestack PP- and PS-wave gathers and adopt a stable and effective inverse Q filtering method to compensate the CSP gathers. The results of synthetic and real data processing indicate that our method can recover the energy and phase of seismic waves, improve the main seismic signal frequency and broaden the bandwidth, and improve the PP- and PSwave resolution. 67

Prestack reflected PP- and converted PS-waves Amplitude vs. Frequency

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Fig. 15 PP-wave amplitude spectra before (a) and after compensation (b). Amplitude vs. Frequency

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Fig. 16 PS-wave amplitude spectra before (a) and after compensation (b).

References Bano, M., 1996, Q-phase compensation of seismic records in the frequency domain: Bull. Seis. Soc. Am., 86(4), 1179 – 1186. Bickel, S. H., and Natarajan, R. R., 1985, Plane-wave Q deconvolution: Geophysics, 50(9), 1426 – 1439. Carderon-Macias, C., Ortiz-Osornio, M., and RamosMartinez, J., 2004, Estimation of quality factors from converted-wave PS data: 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts. Dasgupta, R., and Clark, R. A., 1998, Estimation of Q from surface seismic reflection data: Geophysics, 63(6), 2120 – 2128. Gao, J. H., and Yang, S. L., 2007, On the method of quality factors estimation from zero-offset VSP data: Chinese Journal of Geophysics (in Chinese), 50(4), 1198 – 1209. Hale, D., 1981, An inverse Q-filter: SEP Report 26, 231 – 243.

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Hargreaves, N. D., and Calvert, A. J., 1991, Inverse Q filtering by Fourier transform: Geophysics, 56(4), 519 – 527. Kolsky, H., 1956, The propagation of stress pulses in viscoelastic solids: Phil. Mag., 8(1), 673 – 710. Liu, C., Liu, Y., Wang, D., Yang, B. J., Gao, Z. S., and Li, Y. Z., 2005, A method to compensate strata absorption and attenuation in frequency domain: Geophysical Prospecting For Petroleum (in Chinese), 20(4), 1074 – 1082. Liu, Y., and Wei, X. C., 2005, Interval Q inversion from CMP gathers: part I-absorption equation: 75th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1717 – 1720. Liu, Y., and Wei, X. C., 2005, Interval Q inversion from CMP gathers: part II-inversion method: 75th Ann Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1721 – 1724. Ma, Z. J., and Liu, Y., 2005, A summary of research on seismic attenuation: Progress In Geophysics (in Chinese),

Yan et al. 20(4), 1027 – 1082. McCarley, L. A., 1985, An autoregressive filer model for constant Q attenuation: Geophysics, 50(5), 749 – 758. Quan, Y., and Harris, J. M., 1997, Seismic attenuation tomography using the frequency shift method: Geophysics, 62, 895 – 905. Rickett, J., 2006, Integrated estimation of intervalattenuation profiles: Geophysics, 71(4), A19 – A23. Rickett, J., 2007, Estimating attenuation and the relative information content of amplitude and phase spectra: Geophysics, 72(1), R19 – R27. Tonn, R., 1991, The determination of the seismic quality factor Q from VSP data: A comparison of different computational methods: Geophysical Prospecting, 39, 1 – 27. Wang, Y. H., 2002, A stable and efficient approach of inverse Q filtering: Geophysics, 67(2), 657 – 663. Wang, Y. H., 2003, Quantifying the effectiveness of stabilized inverse Q filtering: Geophysics, 68(1), 337 – 345. Wang, Y. H., 2006, Inverse Q-filter for seismic resolution enhancement: Geophysics, 71(3), 51 – 60. Wang, Y. H., and Guo, J., 2004, Modified Kolsky model for seismic attenuation and dispersion: Journal of Geophysics and Engineering, 1(3), 187 – 196.

Zhang, C. J., and Tadeusz, J. U., 2007, Seismic absorption compensation: A least squares inverse scheme: Geophysics, 72(6), 109 – 114. Zhang, C. J., and Ulrych, T. J., 2002, Estimation of quality factors from CMP records: Geophysics, 67(5), 1542 – 1547. Zhang, X. W., Han, L. G., Zhang, F. J., and Shan, G. G., 2007, An inverse Q-filter algorithm based on stable wavefield continuation: Applied Geophysics, 4(4), 263 – 270.

Yan, Hongyong is a Master student at China University of Petroleum(Beijing). He g r a d u a t e d f r o m Ya n g t z e University in 2006. He works mainly on the research of multi-component seismic data processing and seismic wave field numerical simulation. E-mail: yanhongyong@163. com

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