Writing Kirchhoff migration/modelling in a matrix form

Abdolnaser Yousefzadeh and John C. Bancroft

ABSTRACT

Kirchhoff prestack migration and modelling are linear operators. Therefore, it is possible to apply them to the earth model and seismic data as a matrix-vector multiplication instead of using an operator. A visual technique for creating Kirchhoff modelling, G, migration, G T , and inversion, G T G,matrices is shown without requirement of going to the deep mathematics of Kirchhoff migration or Green functions. Construction of the modelling/migration matrices goes to the most internal loop of the Kirchhoff modelling/migration algorithms. Once they are calculated, they can be easily repeated just by multiplication of the matrix to the model or data vector.

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