1. Wave Modeling, Tomography, Geostatistics and Edge Detection Youli Quan

2. Modeling Waves in a Borehole First Topic

3. Modeling Waves in a Borehole Borehole models Mathematical description Examples Conclusions

4.  Borehole models Mathematical description Examples Conclusions Modeling Waves in a Borehole

5. BOREHOLE RELATED SEISMIC MEASUREMENTS o o Vertical seismic profiling o Cross- borehole profiling Single borehole profiling o Sonic logging Fluid-filled borehole x Source Fluid-filled borehole

8. Borehole models  Mathematical description Examples Conclusions Modeling Waves in a Borehole

13. Borehole models Mathematical description  Examples Conclusions Modeling Waves in a Borehole

17. o Source Receivers 100 m 150 m 10 m Formation I Formation II Borehole xxxxxxxxxxxxxxxxxxxx REFLECTION DUE TO AN OUTER-CYLINDRICAL FORMATION Model Vp=3 km/s Vs=1.8 km/s Vp=1.9 km/s Vs=1.4 km/s

18. Seismograms (f o = 800 Hz) 10 150 1050 100150 Time (ms) source - receiver offset (m)

19. A SYNTHETIC CROSSWELL SURVEY oooooooooooooooooooooooooooooo 30 m Receivers Sources Cased borehole Vp=5 km/s Vs=2.9 km/s Vp=5.8 km/s Vs=3.3 km/s 100 m Formation (a) Model. There is a fault in the formation(b) A common receiver gather xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 30 m 10 20 30 40 0 Time (ms) 0 S-R offset (m) 100

20. Borehole models Mathematical description Examples  Conclusions Modeling Waves in a Borehole

21. A new wave modeling method based on the generalized R/T coefficients is developed for complex borehole simulations. This method is efficient, robust, and accurate. It has been applied to sonic logging, crosswell profiling, and single borehole profiling.

22. Attenuation Tomography Second Topic

23. Acoustic Sources Acoustic Receivers Lower Absorption Higher Absorption Higher frequency Waveform Lower frequency Waveform Waveform and Attenuation

24. Measure Attenuation from Waveform Medium Response H(f) Incident Wave S(f) Transmitted Wave R(f)=S(f)H(f) H(f)  exp[  f  o dl] 

25. xxxxxxxxxxxxxxxxxxxxxxxx oooooooooooooooooooooooooooo Sources Receivers Vf=5 kft/s Qf=20 70 ft 100 ft Vp=11.8 kft/s Vs=6.9 kft/s Qp=30 Vp=12 kft/s Vs=7 kft/s Qp=60 2565 (a) Original model (b) Reconstruction SYNTHETIC EXAMPLE ON ATTENUATION TOMOGRAPHY Crosswell geometry, RT method for modeling

26. Geostatistics Third Topic

27. Geostatistics Introduction Variogram Kriging

28.  Introduction Variogram Kriging Geostatistics

29. Geostatistics is the study of phenomena that fluctuate in space. It offers tools aimed at understanding and modeling spatial variability. These tools include histogram, covariance, variogram, kriging, simulation, and etc.

30. Introduction  Variogram Kriging Geostatistics

31. x x x x x x x x x x x x x x x x x x x x x x x x vivi vjvj h ij Experimental Models:

32. Theoretical Models: Exponential Model Spherical Model

33. Introduction Variogram  Kriging Geostatistics

34. x x x x x x x x x x x x x x x x x x x x o Kriging is a linear estimator with following features: vivi (a)Weighting factors are solved based on the selected variogram. (b)It has minimum variance of the estimation errors. (c)The estimation is unbiased. (d)Estimated values has the same statistical properties as given data