Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Enhancing the resolution of seismic data based on the generalized S-transform

Enhancing the resolution of seismic data based on the generalized S-transform generalized S-transform combined with spectrum modeling. Without assuming that the reflection coeffi cients are random white noise as in the conventional resolution-enhanced techniques, the wavelet which changes with time and frequency was simulated and eliminated. After using the inverse S-transform for the processed instantaneous spectrum, the signal in the time domain was obtained again with a more balanced spectrum and broader frequency band. The quality of seismic data was improved without additional noise. Time-frequency domain, generalized S-transform, spectrum modeling, instantaneous Key words: spectrum, balanced spectrum 2000a; Li et al, 2007; Li et al, 2005), which make the 1 Introduction processed section approach the actual interfaces underground. Conventional techniques for enhancing seismic Spectrum modeling is an effective and stable technique. resolution, such as deconvolution, usually assume that This method considers that the amplitude spectrum of the the reflection coefficients are white noise, so the auto- wavelet is smooth and that of the reflection coefficients correlation of the wavelet is equivalent to the auto-correlation is vibratory without the assumption of random reflection of the seismic record (Yu and Zhao, 2002). However, the coeffi cients. The wavelet can be simulated approximately as reflection coefficient is not a random sequence because of a specifi c curve from the amplitude spectrum of the seismic the thin interbeds and the multi-period sedimentary cycles. record and then is eliminated. The residual part is considered Accordingly, it is inaccurate to broaden the spectrum of to be the amplitude spectrum of the reflection coefficients the seismic record as that of wavelet (Zhao et al, 1996), (Sun, 2000b). and it also cannot satisfy the technical requirements for the With regard to the wavelet, Ricker deduced the amplitude prospecting for thin interbeds and lithologic reservoirs. spectrum of the Ricker wavelet (Ricker, 1977): This paper started from enhancing the resolution through eliminating the wavelet, and discussed the validity of 22 2 f f (1) Wf()  ( )( )exp( ) spectrum modeling on wavelet simulation. Considering the f f cc time variant characteristics of the wavelet, it is more accurate and effective to use spectrum modeling deconvolution in the Rosa tested and summarized the empirical mathematical time-frequency domain after the generalized S-transform expression of the amplitude spectrum of the seismic wavelet instead of spectrum modeling deconvolution in the one- (Rosa and Ulrych, 1991): dimensional frequency domain. This analysis process agrees with the seismic propagation underground and the result provides high quality seismic data for accurate interpretation. k (2) Wf() f exp( a f ) ¦ n n 0 2 Extraction and elimination of seismic wavelet where k is a constant, a is the coeffi cient of the multinomial of f. The reflection coefficient section is the perfect high In this way, the amplitude spectrum of the wavelet is resolution section. The seismic section can be considered simulated by using the least-square fi tting method based on as the reflection coefficient section which is influenced by the amplitude spectrum of seismic record (as shown in Fig. 1). wavelet. There are many wavelet extraction techniques to Within the analyzed frequency band, the amplitude reduce the effect of wavelet (Yun and Ding, 2005; Sun, spectrum of the seismic record divided by that of the wavelet is the amplitude spectrum of the reflection coefficient. *Corresponding author. email: tianjh13579@eyou.com Keeping the phase of the seismic record invariable, we Received October 28, 2008 154 Pet.Sci.(2009)6:153-157 Mansinha, 2003). Gao summarized the previous expressions, and the basis function is normalized as follows (Gao et al, 2003): g ()t exp( i2ʌ fft)e A f xp(DE(ft ) i2ʌ fft) (5) () f 0 0 where A is the amplitude of the basic wavelet, α is the 0 20 40 60 80 100 120 140 160 attenuation rate of the energy, β is the time-lag factor of t, ms energy, f is the apparent frequency of the basic wavelet. The GST provides better time and frequency resolution than Fig. 1 Simulated smooth amplitude spectrum of the wavelet on the the S-transform while maintaining the advantages of the basis of the amplitude spectrum of the seismic record S-transform. The solid line in Fig. 2(a) is a Ricker wavelet whose performed the reverse FFT (Fast Fourier Transform) and dominant frequency is 30 Hz, and sampling interval is 1 ms. obtained the record in the time domain. Fig. 2(b) is the signal after inverse S-transform. Fig. 2(c) Due to the time-variant characteristics of the seismic shows the error curve and the average absolute error is 3.16 -5 record, the amplitude at a specific frequency changes with 10 . We can draw a conclusion that the GST can reconstruct time. Considering the absorption characteristics of rocks, the the signal without loss. This provides the feasibility of dominant frequency was reduced because of the propagation processing signal in time-frequency domain and then of the seismic wave (Fan and Zeng, 1995). Thus simulation transforming back to time domain. in the frequency domain could not consider the instantaneous variation adequately (Fig. 1). We could analyze the seismic signal within the time window to overcome this deficiency. 0.5 However, the frequency variation may be great between two adjacent layers, and the spectrum analysis in the time window which reflects the average effect of frequencies affects the -0.5 0 50 100 150 200 250 300 350 400 450 500 processing result. It is necessary to transform the seismic t, ms record into the two-dimensional time-frequency domain, and the spectrum modeling may be more feasible and effective. (a) Ricker wavelet 3 Spectrum modeling in time-frequency 0.5 domain 3.1 S-transform and generalized S-transform -0.5 0 50 100 150 200 250 300 350 400 450 500 The S-transform of time series h(t) is defi ned by: t, ms (b) Signal after inverse generalized S-transform f 22 () W  tf Sf (,W ) h(t)˜ ˜ exp( ˜ ) exp( i2ʌ ft)dt (3) 2ʌ -3 f ×10 where f is frequency, and τ is the midpoint of the time 0 window, thus it also denotes the location of the window -5 0 50 100 150 200 250 300 350 400 450 500 function in the time axis. t, ms The S-transform is the combination and improvement of (c) Error curve the short time Fourier Transform and the continuous wavelet Characteristics of reconstruction without loss of GST Fig. 2 transform (Stockwell et al, 1996). It has the characteristics of frequency-dependent resolution which the short time Fourier 3.2 Wavelet spectrum in time-frequency domain Transform does not have. It indeed provides the global signal based on the generalized S-transform in the time-frequency domain compared with the time-scale domain analysis of the continuous wavelet transform. GST is a perfect time-frequency analysis tool, and we can The inverse S-transform is defi ned by: simulate the wavelet spectrum which changes with time and frequency. f f Fig. 3(a) shows a seismic reflection sequence from a ht ( ) ( S (WW , f )d ) exp(i2ʌ ft)df (4) ³³ thin interbedded model. Fig. 3(b) is the seismic response f f using a Ricker wavelet whose primary dominant frequency One problem of the S-transform in practical application is is 30Hz. Fig. 3(c) is the 3D plot of the wavelet changing the fi xed Gaussian window, and the generalized S-transform with time and frequency, which shows specific movements (GST) is designed to resolve this problem (Pinnegar and in time-frequency domain. Fig. 3(d) shows the signal after Amplitude Amplitude Amplitude Amplitude Pet.Sci.(2009)6:153-157 155 0.5 0.5 -0.5 -0.5 0 50 100 150 200 250 300 0 50 100 150 200 250 300 t, ms t, ms (b) Synthetic seismic record (a) Refl ection sequence model 0.8 0.5 0.6 0.4 0.2 -0.5 f, Hz 0 50 100 150 200 250 300 150 200 t, ms t, ms (c) 3D time-variant wavelet spectrum (d) Seismic record after deconvolution Model experiment of spectrum modeling in the time-frequency domain Fig. 3 inverse S-transform. We can see that the adjacent events are actual seismic data, it is necessary to analyze the seismic distinguished, and the shape of signal after processing is record in the time-frequency domain before spectrum closer to the refl ection sequence. modeling. The distribution of amplitude in the time-frequency domain reflects the characteristics of the sedimentary cycle 4 Actual seismic data processing of formation (Wang et al, 2008), thus we should consider the geological signifi cance and choose reasonable instantaneous Fig. 4(a) shows a post-stack seismic section. Fig. 4(b) is frequency bands, within which we can simulate the seismic the result after processing by spectral whitening. Fig. 4(c) is wavelet (Liu et al, 2006a; 2006b). Fig. 4(d) shows one the section after deconvolution in the time-frequency domain seismic trace and the wavelet distribution in the time- by using GST. Compared with Fig. 4(a), both Fig. 4(b) and frequency domain. Fig. 4(e) is the comparison of spectrum Fig. 4(c) improve the resolution but Fig. 4(c) reveals more analysis, from which we can see that the processed result has details than Fig. 4(b). a broader frequency band and higher dominant frequency. Because of the plentiful frequency components in the (a) Seismic section before processing (b) Seismic section processed by conventional method Amplitude Amplitude Amplitude Amplitude Pet.Sci.(2009)6:153-157 157 Ros a A L and Ulrych T J. Processing via spectral modeling. Geophysics. References 1991. 56(8): 1244-1251 Fan X D and Zeng H. Time-space variant spectrum whitening of Sto ckwell R G, Mansinha L and Lowe R P. Localization of the complex seismic data. Oil Geophysical Prospecting. 1995. 30(4): 550-555 (in spectrum: the S transform. IEEE Transactions on Signal Processing. Chinese) 1996. 44(4): 998-1001 Gao J H, Chen W C, Li Y M, et al. Generalized S transform and seismic Sun C Y. Study on the extraction of spatial varied seismic wavelets. response analysis of thin interbeds. Geophysics. 2003. 46(4): 526- Journal of China University of Petroleum (Edition of Natural Science). 2000a. 24(1): 77-84 (in Chinese) Li D W, Yin C, Zhao W K, et al. Seismic wavelet extraction based on Sun C Y. Spectrum modeling method and its application to seismic phase scan. Journal of Southwest Petroleum University. 2007. 29(3): resolution improvement. Oil Geophysical Prospecting. 2000b. 35(1): 17-19 (in Chinese) 27-35 (in Chinese) Li G F , Peng S P, Gao R S, et al. Method of mixed phase wavelet Wan g P, Li G F, Zhang L Q, et al. Thin-layer reservoir prediction in the extraction in spectrum domain. Natural Gas Industry. 2005. 25(1): 85- lower Es_1 of the western ramp of Qikou Depression. Journal of 87 (in Chinese) China University of Petroleum (Edition of Natural Science). 2008. Liu X W, Liu H, Li Y M, et al. Study on characteristics of seismic 32(2): 28-33 (in Chinese) stratigraphy by generalized S-transform. Progress in Geophysics. Yun M H and Ding W. Analysis of seismic wavelet frequency. 2006. 21(2): 440-451 (in Chinese) Geophysical Prospecting for Petroleum. 2005. 44(6): 578-581 (in Liu X W, Nian J B and Liu H. Generalized S-transform based seismic Chinese) attenuation analysis. Progress in Geophysics. 2006. 29(1): 20-24 (in Yu P and Zhao Z Y. Three techniques of deconvolution in seismic data Chinese) processing. Global Geology. 2002. 21(2): 181-184 (in Chinese) Pin negar C R and Mansinha L. The S-transform with windows of Zha o B, Yu S P, Nie X B, et al. Spectral-modeled deconvolution and its arbitrary and varying shape. Geophysics. 2003. 68(1): 381-385 application. Oil Geophysical Prospecting. 1996. 31(1): 101-116 (in Ric ker N H. Transient Waves in Visco-elastic Media. Amsterdam: Chinese) Elsevier Science & Technology Publishing Company. 1977 (Edited by Hao Jie) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Petroleum Science Springer Journals

Enhancing the resolution of seismic data based on the generalized S-transform

Tian, Jianhua; Song, Wei; Yang, Feizhou
Petroleum Science , Volume 6 (2) – May 8, 2009
Download PDF
5 pages

Loading next page...
 
/lp/springer-journals/enhancing-the-resolution-of-seismic-data-based-on-the-generalized-s-ozBOu0QIYz

References (29)

Publisher
Springer Journals
Copyright
Copyright © 2009 by China University of Petroleum (Beijing) and Springer-Verlag GmbH
Subject
Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
ISSN
1672-5107
eISSN
1995-8226
DOI
10.1007/s12182-009-0024-x
Publisher site
See Article on Publisher Site

Abstract

generalized S-transform combined with spectrum modeling. Without assuming that the reflection coeffi cients are random white noise as in the conventional resolution-enhanced techniques, the wavelet which changes with time and frequency was simulated and eliminated. After using the inverse S-transform for the processed instantaneous spectrum, the signal in the time domain was obtained again with a more balanced spectrum and broader frequency band. The quality of seismic data was improved without additional noise. Time-frequency domain, generalized S-transform, spectrum modeling, instantaneous Key words: spectrum, balanced spectrum 2000a; Li et al, 2007; Li et al, 2005), which make the 1 Introduction processed section approach the actual interfaces underground. Conventional techniques for enhancing seismic Spectrum modeling is an effective and stable technique. resolution, such as deconvolution, usually assume that This method considers that the amplitude spectrum of the the reflection coefficients are white noise, so the auto- wavelet is smooth and that of the reflection coefficients correlation of the wavelet is equivalent to the auto-correlation is vibratory without the assumption of random reflection of the seismic record (Yu and Zhao, 2002). However, the coeffi cients. The wavelet can be simulated approximately as reflection coefficient is not a random sequence because of a specifi c curve from the amplitude spectrum of the seismic the thin interbeds and the multi-period sedimentary cycles. record and then is eliminated. The residual part is considered Accordingly, it is inaccurate to broaden the spectrum of to be the amplitude spectrum of the reflection coefficients the seismic record as that of wavelet (Zhao et al, 1996), (Sun, 2000b). and it also cannot satisfy the technical requirements for the With regard to the wavelet, Ricker deduced the amplitude prospecting for thin interbeds and lithologic reservoirs. spectrum of the Ricker wavelet (Ricker, 1977): This paper started from enhancing the resolution through eliminating the wavelet, and discussed the validity of 22 2 f f (1) Wf()  ( )( )exp( ) spectrum modeling on wavelet simulation. Considering the f f cc time variant characteristics of the wavelet, it is more accurate and effective to use spectrum modeling deconvolution in the Rosa tested and summarized the empirical mathematical time-frequency domain after the generalized S-transform expression of the amplitude spectrum of the seismic wavelet instead of spectrum modeling deconvolution in the one- (Rosa and Ulrych, 1991): dimensional frequency domain. This analysis process agrees with the seismic propagation underground and the result provides high quality seismic data for accurate interpretation. k (2) Wf() f exp( a f ) ¦ n n 0 2 Extraction and elimination of seismic wavelet where k is a constant, a is the coeffi cient of the multinomial of f. The reflection coefficient section is the perfect high In this way, the amplitude spectrum of the wavelet is resolution section. The seismic section can be considered simulated by using the least-square fi tting method based on as the reflection coefficient section which is influenced by the amplitude spectrum of seismic record (as shown in Fig. 1). wavelet. There are many wavelet extraction techniques to Within the analyzed frequency band, the amplitude reduce the effect of wavelet (Yun and Ding, 2005; Sun, spectrum of the seismic record divided by that of the wavelet is the amplitude spectrum of the reflection coefficient. *Corresponding author. email: tianjh13579@eyou.com Keeping the phase of the seismic record invariable, we Received October 28, 2008 154 Pet.Sci.(2009)6:153-157 Mansinha, 2003). Gao summarized the previous expressions, and the basis function is normalized as follows (Gao et al, 2003): g ()t exp( i2ʌ fft)e A f xp(DE(ft ) i2ʌ fft) (5) () f 0 0 where A is the amplitude of the basic wavelet, α is the 0 20 40 60 80 100 120 140 160 attenuation rate of the energy, β is the time-lag factor of t, ms energy, f is the apparent frequency of the basic wavelet. The GST provides better time and frequency resolution than Fig. 1 Simulated smooth amplitude spectrum of the wavelet on the the S-transform while maintaining the advantages of the basis of the amplitude spectrum of the seismic record S-transform. The solid line in Fig. 2(a) is a Ricker wavelet whose performed the reverse FFT (Fast Fourier Transform) and dominant frequency is 30 Hz, and sampling interval is 1 ms. obtained the record in the time domain. Fig. 2(b) is the signal after inverse S-transform. Fig. 2(c) Due to the time-variant characteristics of the seismic shows the error curve and the average absolute error is 3.16 -5 record, the amplitude at a specific frequency changes with 10 . We can draw a conclusion that the GST can reconstruct time. Considering the absorption characteristics of rocks, the the signal without loss. This provides the feasibility of dominant frequency was reduced because of the propagation processing signal in time-frequency domain and then of the seismic wave (Fan and Zeng, 1995). Thus simulation transforming back to time domain. in the frequency domain could not consider the instantaneous variation adequately (Fig. 1). We could analyze the seismic signal within the time window to overcome this deficiency. 0.5 However, the frequency variation may be great between two adjacent layers, and the spectrum analysis in the time window which reflects the average effect of frequencies affects the -0.5 0 50 100 150 200 250 300 350 400 450 500 processing result. It is necessary to transform the seismic t, ms record into the two-dimensional time-frequency domain, and the spectrum modeling may be more feasible and effective. (a) Ricker wavelet 3 Spectrum modeling in time-frequency 0.5 domain 3.1 S-transform and generalized S-transform -0.5 0 50 100 150 200 250 300 350 400 450 500 The S-transform of time series h(t) is defi ned by: t, ms (b) Signal after inverse generalized S-transform f 22 () W  tf Sf (,W ) h(t)˜ ˜ exp( ˜ ) exp( i2ʌ ft)dt (3) 2ʌ -3 f ×10 where f is frequency, and τ is the midpoint of the time 0 window, thus it also denotes the location of the window -5 0 50 100 150 200 250 300 350 400 450 500 function in the time axis. t, ms The S-transform is the combination and improvement of (c) Error curve the short time Fourier Transform and the continuous wavelet Characteristics of reconstruction without loss of GST Fig. 2 transform (Stockwell et al, 1996). It has the characteristics of frequency-dependent resolution which the short time Fourier 3.2 Wavelet spectrum in time-frequency domain Transform does not have. It indeed provides the global signal based on the generalized S-transform in the time-frequency domain compared with the time-scale domain analysis of the continuous wavelet transform. GST is a perfect time-frequency analysis tool, and we can The inverse S-transform is defi ned by: simulate the wavelet spectrum which changes with time and frequency. f f Fig. 3(a) shows a seismic reflection sequence from a ht ( ) ( S (WW , f )d ) exp(i2ʌ ft)df (4) ³³ thin interbedded model. Fig. 3(b) is the seismic response f f using a Ricker wavelet whose primary dominant frequency One problem of the S-transform in practical application is is 30Hz. Fig. 3(c) is the 3D plot of the wavelet changing the fi xed Gaussian window, and the generalized S-transform with time and frequency, which shows specific movements (GST) is designed to resolve this problem (Pinnegar and in time-frequency domain. Fig. 3(d) shows the signal after Amplitude Amplitude Amplitude Amplitude Pet.Sci.(2009)6:153-157 155 0.5 0.5 -0.5 -0.5 0 50 100 150 200 250 300 0 50 100 150 200 250 300 t, ms t, ms (b) Synthetic seismic record (a) Refl ection sequence model 0.8 0.5 0.6 0.4 0.2 -0.5 f, Hz 0 50 100 150 200 250 300 150 200 t, ms t, ms (c) 3D time-variant wavelet spectrum (d) Seismic record after deconvolution Model experiment of spectrum modeling in the time-frequency domain Fig. 3 inverse S-transform. We can see that the adjacent events are actual seismic data, it is necessary to analyze the seismic distinguished, and the shape of signal after processing is record in the time-frequency domain before spectrum closer to the refl ection sequence. modeling. The distribution of amplitude in the time-frequency domain reflects the characteristics of the sedimentary cycle 4 Actual seismic data processing of formation (Wang et al, 2008), thus we should consider the geological signifi cance and choose reasonable instantaneous Fig. 4(a) shows a post-stack seismic section. Fig. 4(b) is frequency bands, within which we can simulate the seismic the result after processing by spectral whitening. Fig. 4(c) is wavelet (Liu et al, 2006a; 2006b). Fig. 4(d) shows one the section after deconvolution in the time-frequency domain seismic trace and the wavelet distribution in the time- by using GST. Compared with Fig. 4(a), both Fig. 4(b) and frequency domain. Fig. 4(e) is the comparison of spectrum Fig. 4(c) improve the resolution but Fig. 4(c) reveals more analysis, from which we can see that the processed result has details than Fig. 4(b). a broader frequency band and higher dominant frequency. Because of the plentiful frequency components in the (a) Seismic section before processing (b) Seismic section processed by conventional method Amplitude Amplitude Amplitude Amplitude Pet.Sci.(2009)6:153-157 157 Ros a A L and Ulrych T J. Processing via spectral modeling. Geophysics. References 1991. 56(8): 1244-1251 Fan X D and Zeng H. Time-space variant spectrum whitening of Sto ckwell R G, Mansinha L and Lowe R P. Localization of the complex seismic data. Oil Geophysical Prospecting. 1995. 30(4): 550-555 (in spectrum: the S transform. IEEE Transactions on Signal Processing. Chinese) 1996. 44(4): 998-1001 Gao J H, Chen W C, Li Y M, et al. Generalized S transform and seismic Sun C Y. Study on the extraction of spatial varied seismic wavelets. response analysis of thin interbeds. Geophysics. 2003. 46(4): 526- Journal of China University of Petroleum (Edition of Natural Science). 2000a. 24(1): 77-84 (in Chinese) Li D W, Yin C, Zhao W K, et al. Seismic wavelet extraction based on Sun C Y. Spectrum modeling method and its application to seismic phase scan. Journal of Southwest Petroleum University. 2007. 29(3): resolution improvement. Oil Geophysical Prospecting. 2000b. 35(1): 17-19 (in Chinese) 27-35 (in Chinese) Li G F , Peng S P, Gao R S, et al. Method of mixed phase wavelet Wan g P, Li G F, Zhang L Q, et al. Thin-layer reservoir prediction in the extraction in spectrum domain. Natural Gas Industry. 2005. 25(1): 85- lower Es_1 of the western ramp of Qikou Depression. Journal of 87 (in Chinese) China University of Petroleum (Edition of Natural Science). 2008. Liu X W, Liu H, Li Y M, et al. Study on characteristics of seismic 32(2): 28-33 (in Chinese) stratigraphy by generalized S-transform. Progress in Geophysics. Yun M H and Ding W. Analysis of seismic wavelet frequency. 2006. 21(2): 440-451 (in Chinese) Geophysical Prospecting for Petroleum. 2005. 44(6): 578-581 (in Liu X W, Nian J B and Liu H. Generalized S-transform based seismic Chinese) attenuation analysis. Progress in Geophysics. 2006. 29(1): 20-24 (in Yu P and Zhao Z Y. Three techniques of deconvolution in seismic data Chinese) processing. Global Geology. 2002. 21(2): 181-184 (in Chinese) Pin negar C R and Mansinha L. The S-transform with windows of Zha o B, Yu S P, Nie X B, et al. Spectral-modeled deconvolution and its arbitrary and varying shape. Geophysics. 2003. 68(1): 381-385 application. Oil Geophysical Prospecting. 1996. 31(1): 101-116 (in Ric ker N H. Transient Waves in Visco-elastic Media. Amsterdam: Chinese) Elsevier Science & Technology Publishing Company. 1977 (Edited by Hao Jie)

Journal

Petroleum Science – Springer Journals

Published: May 8, 2009

There are no references for this article.