Seismic modelling in 3D for migration testing

Gary F. Margrave, Joanna Kathleen Cooper

A 3D modelling technique, called Rayleigh-Sommerfeld modelling, is described as an alternative to Kirchhoff modelling. Rayleigh-Sommerfeld modelling, when applied using a forward Born approximation, is shown to be the familiar phase-shift migration running in reverse. Compared to the Kirchhoff method, Rayleigh-Sommerfeld is much faster, especially on large datasets, but produces a similar response. Rayleigh-Sommerfeld is used to create an exhaustive 3D synthetic dataset which will be used for 3D migration testing. Such an exhaustive dataset, defined as having no spatial aliasing in either source or receiver gathers, can be extremely large and the efficiency of Rayleigh-Sommerfeld modelling is required to create one. The model created is the response of three horizontal reflectors embedded in a v(z) medium. Consisting of 1681 source gathers, each having 1681 receivers, it is shown to be very high frequency and to contain both specular reflections and diffractions. Example 3D shot record migrations demonstrate the fidelity of the model and the high resolution of prestack migration.