Tomostatic Waveform Tomography on Near-surface Refraction Data

Tomostatic Waveform Tomography on Near-surface Refraction Data Jianming Sheng, Alan Leeds, and Konstantin Osypov ChevronTexas WesternGeco February 18, 23 ABSTRACT The velocity variations and static shifts caused by near-surface effects and positional uncertainties can be solved using constrained tomography. The waveform tomography method minimizes the firstarrival waveform by waveform inversion with an initial model obtained by traveltime tomography. A better velocity with higher resolution is possible because we are not restricted by high-frequency assumptions. In an earlier report I showed that for synthetic data this method can enhance the resolution of the tomogram significantly compared to a ray-based tomography method and has good convergence properties. In this report, tomostatic waveform tomography was applied to synthetic data for a blind test and to 2D marine field data. The blind test results suggested that waveform tomography can provide a more accurate velocity model and thus a better migration section. In the raw stack section of the marine data, some time sags can be observed which are caused by shallow gas clouds and it can be treated as a static problem. A traveltime velocity tomogram was used to do static correction and also migration, and the stacked section and migration image were improved. To improve further, a waveform tomogram was used which fits the data better than the traveltime tomogram. However, the static corrected stack section and the depth migrated image show little 1

improvements. Further work is required to investigate the factors that influece the results, refine the waveform tomogram code and improve the data preprocessing. NUMERICAL TESTS Tomostatic waveform tomography was applied to two data sets: 1). synthetic data from WesternGeco; 2). 2D marine data from WesternGeco and ChevronTexas. Synthetic Data from WesternGeco Depth (km).2.4.6.8 1. Surface Location (km) 5 1 15 2 25 recording surface Figure 1: The true velocity model for the 2-D synthetic data courtesy of Konstantin Osypov from WesternGeco. The shots and geophones were located on the surface. Recording geometry is split-spread with the first shot at 3 km, and the last shot at 23 km. The shot spacing is 5 m, and the group interval is 25 m. The peak frequency of the wavelet in the data is 17 Hz. This 2D synthetic data set, courtesy of Konstantin Osypov from WesternGeco, was generated by a 2-D acoustic finite-difference code. Figures 1 and 2 show the true velocity and density models. The shallowest layer is the weathered zone. The base of the weathering is horizontal until lateral position 7 km where the weathering base becomes 2

Depth (km).2.4.6.8 1. Surface Location (km) 5 1 15 2 25 recording surface Figure 2: The true density model corresponds to the velocity model shown in Figure 1. Three horizontal reflectors due to the density contrasts are at depths 3 m, 65 m and 1 m which are intersected by a two sets of dipping reflectors. Offset (m) -2 2 Time (sec.) 1 2 Figure 3: The 15th common shot gather from the WesternGeco synthetic data set (model 1). The shot is located at horizontal distance 1.45 km on the surface. 3

quasi-sinusoidal with a wavelength that is chirped with a linear variation. In the region where the weathered base varies most rapidly, the wavelength variation is as small as 15 m. The amplitude on the chirp is 5 m. Three later reflections are attributable entirely to density contrasts at depths 3 m, 65 m and 1 m. Here, the major concern of the tomostatic waveform tomography is the shallowest weathered layer. The shots and geophones were located on the surface. Recording geometry is split-spread with the first shot at 3 km, and the last shot at 23 km. The shot spacing is 5 m, and the group interval is 25 m. The peak frequency of the wavelet in the data is 17 Hz. The record length was 2. seconds with a sample interval of 4 milliseconds.figure 3 shows the 15th common shot gather for which the shot point is located at the horizontal distance 1.45 km. Figure 4 shows the ray-based traveltime velocity tomogram (horizontal distance from 1524 m to 4572 m). Taking the traveltime velocity tomogram as the velocity model, the source wavelet was first inverted by backprojecting the waveform residuals (Zhou et al., 1997). Here, the density was set by the experimental formula: density = 21 ( ) velocity.5. 1981.2 Figure 5 shows the original and modeled seismograms for the near-offset traces. It can be seen that the wavelets were fitted quite well. Figure 6 shows the inverted source wavelet. Using this source wavelet and taking the traveltime tomogram as the initial model, the waveform tomogram was obtained shown in Figure 7 (horizontal distance from 5 m to 875 m). Compared with the ray-based traveltime tomogram shown in Figure 8, the waveform tomogram was much better resolved especially for the higher wavelength part. However, some edge effects showed up and some artifacts appeared in the waveform tomogram, and some artifacts at the lower part were due to density errors in my guessed model. Using the obtained waveform velocity tomogram as the migration velocity model, the depth migration section was obtained and is shown in Figure 9. The flatness of the 3 m reflector and proper positioning of steep dips for the most part of the image indicate a sufficient quality of the near-surface reconstruction for depth imaging. However, beneath the near-surface variations with wavelengths comparable to the seismic 4

wavelength the quality of the image is significantly deteriorated. This could be explained by limitations of ray tracing in Kirchhoff migration. 1 2 26 24 3 22 4 5 6 7 8 2 18 16 14 9 12 1.5 1 1.5 2 2.5 Horizontal Distance (m) x 1 4 1 (m/s) Figure 4: The ray-based traveltime velocity tomogram for the WesternGeco synthetic data set (model 1). 2D marine data from WesternGeco and ChevronTexas This 2D marine data set, courtesy of Alan Leeds from ChevronTexas, consists of 99 shots with a shot interval of 25 meters, time sample interval of 4 milliseconds, trace length of 8188 milliseconds and 18 channels. The receiver spacing is 25 meters with the nearest offset of 173 m and the farthest offset of 4648 m. Figure 1 shows the brute stack section from CDP 45 to CDP 68 with the CDP interval of 12.5 m. From the brute stack section, it can be seen that some velocity variation caused by shallow gas clouds causes time sags and false structures. It can be solved by tomostatic methods (Zhu et al, 1992) in which tomograms are used to compute field statics. Using refraction traveltimes from CDP 55 to 65, traveltime tomography was carried out. Source and receiver static corrections were calculated vertically from the surface downward to a datum of 2 meters using the traveltime velocity tomogram and then upward to the surface using a 5

1 (a) 1.2.4.6.8.1.12.14.16.18 1 1.2.4.6.8.1.12.14.16.18 (b) Amplitude 2 2.2.4.6.8.1.12.14.16.18 (c) 1 1.2.4.6.8.1.12.14.16.18 1 (d) (e) 1.2.4.6.8.1.12.14.16.18 Traveltime (sec.) Figure 5: The comparison between the original and modeled seismograms of the nearoffset traces for the WesternGeco synthetic data. (a) offset=-5. m; (b) offset=-25. m; (c) offset= m;(d) offset=25. m; (e) offset=5. m. 4 3 2 1 Amplitude 1 2 3 4 5 6.5.1.15.2.25 Time (sec.) Figure 6: The inverted source wavelet for the synthetic data from WesternGeco. 6

5 1 26 24 22 15 2 2 18 25 16 3 14 35 12 4 5 55 6 65 7 75 8 85 Horizontal Distance (m) 1 (m/s) Figure 7: The waveform velocity tomogram for the WesternGeco synthetic data (horizontal distance from 5 m to 875 m). 24 5 22 1 2 15 2 25 18 16 3 14 35 12 4 5 55 6 65 7 75 8 85 Horizontal Distance (m) 1 (m/s) Figure 8: The ray-based traveltime tomogram for the WesternGeco synthetic data (horizontal distance from 5 m to 875 m). 7

Horizontal Distance (m) 5 6 7 8 1 2 3 4 Figure 9: The Kirchhoff depth migration section using the obtained waveform velocity tomogram as the migration velocity model (distance from 5 m to 875 m). constant substitute velocity. After the source and receiver statics were corrected, a new stacked image was obtained using the same NMO velocity. A total of 49 177 = 8673 first-arrival traveltimes were picked using an automatic picking code and were inverted by traveltime tomography. Figure 11 shows the gather from shot 663 with the solid curve indicating the picked traveltimes. Figure 12 to 13 shows the traveltime velocity tomogram, ray density distribution and the RMS traveltime residual vs. iteration plot. The tomogram resolved some shallow low velocity zones at about CDP 64, 614, 625 and 634, and four major refractors, which can be seen more clearly in Figure 15, the migration image, and in Figure 16, the refraction migration image. Compared to the migration image (shown in Figure 17) obtained from NMO velocity, the migration image was improved. Figure 18 shows the Common Image Gather (CIG) at CDP 6 which indicates the velocity tomogram was a good approximation. Using the traveltime tomogram, source and receiver 8

2 Time (sec.) 4 6 8 5 CDP # 55 6 65 Brute stack section Figure 1: The brute stack section for the Gulf of Mexico seismic line. 9

Offset (m) 125 25 375.5 Traveltime (sec.) 1. 1.5 2. 2.5 3. Figure 11: The CSG for shot 663. The solid curve indicates the picked traveltimes. statics were calculated and shown in Figure 19, and the stacked section after the application of tomostatics is shown in Figure 2. The key reason the migration image and the stack section could be improved is that a more accurate velocity was used, and this motivated us to do waveform tomography and do tomostatics correction using the waveform tomogram. Before waveform tomography, some data preprocessing steps are necessary: 1. The field data were transformed from 3-D to 2-D format by applying a filter i ω in the frequency domain and scaling the data by t to approximate geometrical spreading (Barton, 1989; Zhou et al, 1995); 2. According to Liao and McMechan (1997), the attenuation transfer function T (f) about frequency f can be expressed as T (f) = exp{ f πt }, (1) Q 1

1 2 3 21 2 19 4 5 6 18 17 16 7 8 9 1 55 56 57 58 59 6 61 62 63 64 65 CDP NUMBER 15 14 13 Figure 12: The traveltime velocity tomogram for the 2D marine data. CDP NUMBER 55 6 65 Student Version of MATLAB 5 2 1 Figure 13: The ray density distribution for the traveltime tomography. 11

.18 RMS Traveltime Residual vs Iterations RMS Traveltime Residual(sec).16.14.12.1.8.6.4.2 5 1 15 2 25 3 Iterations Figure 14: The RMS traveltime residual Vs. iterations for the traveltime tomography. CDP NUMBER 56 58 6 62 64 2 4 6 8 1 Figure 15: The reflection migration image using the traveltime tomogram. 12

1 2 3.6.4.2 4 5 6 7 8 9.2.4.6.8 1 55 56 57 58 59 6 61 62 63 64 65 Distance (m) 1 Figure 16: The refraction migration image using the traveltime tomogram. CDP NUMBER 56 58 6 62 64 2 4 6 8 1 Figure 17: The reflection migration image using the NMO velocity. 13

Offset (m) 1 2 3 4 5 2 4 6 8 1 Figure 18: The CIG at CDP 6 for the reflection migration using the traveltime tomogram..45.4.35.3 Statics (sec.).25.2.15.1.5.5 55 56 57 58 59 6 61 62 63 64 65 CDP NUMBER Figure 19: The calculated statics using the traveltime tomogram. 14

CDP NUMBER 56 58 6 62 64 1 Traveltime (sec.) 2 3 4 Figure 2: The stacked section after tomostatics correction using the traveltime tomogram. 15

CDP NUMBER 56 58 6 62 64 1 Traveltime (sec.) 2 3 4 Figure 21: The stacked section using NMO velocity. 16

where the attenuation factor Q is assumed to be constant, and t denotes the traveltime. The Q is also related with the centroid frequency as f r = f s 2πσ2 s t, (2) Q where f r and f s denote the centroid frequecies at the receiver and the source, seperately, and σs 2 denotes the variance of the source spectrum. After f r and σs 2 were calculated and the traveltimes t were picked, the Q value can be estimated by line-fit. Figure 22 shows the plot of f r vs. traveltime t, and the Q value was estimated 1 to be about 325. Now, the correction T (f) was applied to the spectrum to take the absorption effects into account; 3. The data was then normalized and every thing was muted outexcept the first arrivals. Figure 23 and 24 show the amplitude vs. offset with and without amplitude correction, separately. These Log Log plots indicate that the amplitude correction is essential to matching the observed and computed seismograms. Figure 25 shows the CSG 663 after preprocessing. Using the traveltime velocity tomogram as the initial model, the source wavelets were inverted, shown in Figure 26, by back-projecting the near-offset waveform residuals. The waveform tomogram was obtained after 14 iterations, shown in Figure 27. Figure 28 shows the plot of waveform residual vs. iterations. Figure 29 shows the amplitude comparison between the calculated amplitudes with the traveltime and waveform tomogram; it can be seen that the waveform tomogram matches the data better than the traveltime tomogram, and this explains why the waveform tomogram seems more noisy compared to the traveltime tomogram in Figure 12. Figures 3 and 31 show the calculated seismograms for the waveform and traveltime tomograms, seperately. Figures 32 and 33 show the migrated image and the CIG at CDP 6; compared to the corresponding results for the traveltime tomogram, they are quite similar. The calculated statics are shown in Fig- 17

45 4 fr= 2.594*trt+35.1948 Sigma=11.5758Hz Qp=325 Centroid frequency (Hz.) 35 3 25 2.5 1 1.5 2 2.5 3 Traveltime (sec.) Figure 22: The centroid frequency vs. traveltime. The attenuation factor Q was estimated to 325 by line-fit. 18

.2.4.6 Log1 Amplitude.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 Log1 offset (m) Figure 23: The Log1 amplitude vs. Log1 offset for shot 663. The solid curve represents the amplitude after correction, and the circled one represents the synthetic amplitude using the waveform velocity tomogram. Student Version of MATLAB 19

.5 1 Log1 Amplitude 1.5 2 2.5 3 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 Log1 offset (m) Figure 24: The Log1 amplitude vs. Log1 offset for shot 663. The solid curve represents the amplitude before correction, and the circled one represents the synthetic amplitude using the waveform velocity tomogram. Offset (m) 1 2 3 4 1 2 3 Figure 25: The CSG 663 after preprocessing. 2

4 x 1 6 3 2 1 Amplitude 1 2 3 4.2.4.6.8.1.12 Time (sec.) Figure 26: The inverted source wavelet for shot 663. 1 21 2 2 3 19 4 5 6 7 8 9 1 55 56 57 58 59 6 61 62 63 64 65 CDP NUMBER 18 17 16 15 14 13 Figure 27: The waveform tomogram after 14 iterations. 21

4 3.9 3.8 Log1 Residual 3.7 3.6 3.5 3.4 3.3 3.2 2 4 6 8 1 12 Iterations Figure 28: The waveform waveform residual vs. iterations..5 Solid Data Star Waveform Triangle Traveltime Log1 Amplitude.5 1 1.5 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 Log1 offset (m) Figure 29: The amplitude comparison between the calculated amplitudes with the traveltime and waveform tomograms for shot 663. The solid, triangled and stared curves represent the amplitudes for the corrected data, the calculated mplitudes using the waveform and traveltime tomograms, separately. 22

Offset (m) 1 2 3 4 1 2 3 Figure 3: The calculated seismogram for shot 663 with the waveform tomogram. Offset (m) 1 2 3 4 1 2 3 Figure 31: The calculated seismogram for shot 663 with the traveltime tomogram. 23

ure 34, which indicates that the differences of the statics calculated with the waveform and traveltime tomogram were quite small almost less than one sample point (4 millisends), and this results in little improvement in the stacked section shown in Figure 35. CDP NUMBER 56 58 6 62 64 2 4 6 8 1 Figure 32: The reflection migration section using the waveform tomogram. Some factors might prevent us from getting an expected better result, such as, the data preprocessing, waveform inversion algorithm and the way to calculate the statics and to do the correction. The autopicked traveltimes might also have errors. Further work is required to refine the method. DISCUSSION The waveform tomogram for the synthetic data from WesternGeco shows that a better resolved tomogram can be obtained by waveform tomography. However, the result for the field data shows little improvement. Further work is required to understand better the factors which might influence the results, refine the waveform inversion method and 24

Offset (m) 1 2 3 4 5 2 4 6 8 1 Figure 33: The CIG at CDP 6 using the waveform tomogram. 1 x 1 3 8 6 Statics (sec.) 4 2 2 56 57 58 59 6 61 62 63 64 CDP NUMBER Figure 34: The comparison of the statics calculated using the waveform and traveltime tomogram. The solid and dash dotted curves represent the statics calculated using the waveform and traveltime tomograms, separately. 25

56 58 6 62 64 1 CDP NUMBER 2 3 4 Figure 35: The stacked section using the waveform tomogram. 26

improve the data preprocessing. ACKNOWLEDGEMENTS I am grateful for the financial support from the members of the 22 University of Utah Tomography and Modeling/Migration (UTAM) Consortium. REFERENCES Barton, G., 1989. Elements of Green s functions and propagation, Oxford University Press. Liao, Q. and McMechan, G. A., 1997. Tomographic imaging of velocity and Q with application to crosswell seismic data from the Gypsy Pilot Site, Oklahoma, Geophysics, 62, 184 1811. Zhou, C., Cai, W., Luo, Y., Schuster, G. T., & Hassanzadeh, S., 1995. Acoustic wave-equation traveltime and waveform inversion of crosshole seismic data, Geophysics, Vol. 6, 765 773. Zhou, C., Schuster, G. T., Hassanzadeh, S., & Harris, J. M., 1997. Elastic wave equation traveltime and waveform inversion of crosswell data, Geophysics, Vol. 62, 853 868. Zhu, X., Sixta, D. P., and Angstman, B. G., 1992. Tomo-statics: Turning-ray tomography + static corrections, The Leading Edge, 11, No. 12, 15 23. 27