1. Seismic Reflection Data Processing and Interpretation A Workshop in Cairo 28 Oct. – 9 Nov. 2006 Cairo University, Egypt Dr. Sherif Mohamed Hanafy Lecturer Title: Migration (1)

2. Solving Migration Problem In matrix notation, we can write And the error is given by; Minimizing the error by Lease square gives and;

3. Solving Migration Problem Solving Give us (from previous lecture) the least square solution (known also as migration) is given by; Since (L T L) -1 is very expensive, we assume it equals to identity

4. Complete the solution from the word document

5. Solving Migration Problem

6. This equation smeared the energy along the ellipse that verifies it. And reflection point could be any point along this ellipse.

7. Solving Migration Problem This is called prestack migration. Since the source and receiver locations are not the same, migration will form semi ellipse. The post stack migration, where both source and receiver has the same position, known also as zero-offset data migration, will smear the data along semi circles. Its center is at the source-receiver location, and its radius given from;

8. Solving Migration Problem Post-stack migration data smeared along circles.

9. Solving Migration Problem We will not be able to determine the exact source of reflection events using only one source/receiver point. Adding one more source/receiver point will decrease the probability

10. Resolution Let dx be the horizontal resolution and dz is the vertical resolution. At any point the horizontal and vertical resolutions can be shown in figure

11. Resolution To reduce dx ambiguity, we use far offset geophones. To reduce dz ambiguity we use near offset geophones

12. Resolution

13. Synthetic and real examples

14. End of this lecture Thank You for you attention All examples on this lecture is based on my work