Ma Zaitian (1930- ) is a native of Faku, Liaoning Province. He graduated from Geophysics Department, Leningrad Mining College in 1957. He is now academician of Chinese Academy of Sciences and professor, and post-doctorate tutor of Shanghai Tongji University.

Ma originated many creative principles and technologies on the reflection seismology method, which played a key role in developing seismic prospecting in China. In the 1950s and 1960s, Ma advanced a series of seismic prospecting methods, including the "seismic reflection standard stratum method," which helped the finding of oil fields in the North China Basin. In the 1970s, as the director of the method and program research office of the most important geophysical computer center, he led and participated in the building of a giant-powered computer data handling system for seismic prospecting in China.

In the 1980s, Ma focused on the study of seismic migration imaging and 3-D seismic prospecting methods and obtained the most important achievements in the study of migration imaging principle and methods. Later, he undertook the key project of the National Natural Science Fund of "seismic wave spread and wave field imaging", and developed new theories and new technologies in depth migration methods and multiple component seismic data handling. In recognition of his outstanding achievements, he was awarded several local and national prizes, including Shanghai Science and Technology Progress Prize, First Class (1990); State Science and Technology Progress Award, Second Class (1991), and so on.

DEVELOPMENT OF SEISMIC MIGRATION THEORY AND PRACTICE

Ma Zaitian

(Tongji University, Shanghai)

Abstract

None of the large and middle oii fields in the world has been discovered without using the technique of seismic prospecting after the World War II The main work of studying the subsurface structures is the seismic migration processing with large computer. The modern seismic migration technique was pioneered by J.F. Claerbout at the Stanford University in the 1970s.His equation adapts to only single geological structure with dip angles 0o  --  15o.

To break out the dip limitation of Claerbout's equation we put forward a new theory, method and technique, which are playing an important role in the completion of modern seismic imaging technique. The idea and method described here have been popularized in China and abroad.

For the best imaging seismic observation data we worked out a new higher-order partial differential equation and its solution. The solution was obtained by using our 'order-splitting' method. The higher-order partial differential equation used in seismic migration was derived as follows:

 (1)

where n is the order number of the equation; i=1, 2, 3？？？, r[r=(n+1)/2),if n is odd; r=n/2, if n is even];  =n-1, n-2, n-3, ？？？ , r; k=0,2,4, ？？？ , r;  j=1, 2, 3, ？？？ , s (s=n-r); m =1, 3, 5, ？？？ , if n is odd; m=0, 2, 4, ？？？ , if n is even ; q=2,4,6, ？？？.

The equation (1) is a new type of partial differential equation; it cannot be solved by conventional method. We proposed a new scheme called order-splitting method to solve it. In numerical mathematics, the dimension-splitting method has been used, but the order-splitting method is not existed before. By the order-splitting method the high-order equation (1) can be transformed into a system of second-order partial differential equations:

 (2)

j=1,2,3, ？？？ , n-1.

Each equation in (2) is a parabolic-type equation. We have proved that it is well- posed and stable in computation. The system of equations (2) is equivalent to the original equation (1).

The method was tested by theoretical and practical seismic data, and the results show that the order-splitting method is excellent in seismic migration. The research has scientific and practical useful value. It has been playing an important role in the study of complex geological subsurface structures for exploration and production of oil and gas in every region where they exist.