A B S T R A C TSeismic migration can be formulated in terms of two consecutive downward extrapolation steps: refocusing the receivers and refocusing the sources. Applying only the first focusing step with an estimate of the focusing operators results in a common focal point (CFP) gather for each depth point at a reflecting boundary. The CFP gathers, in combination with the estimates of the focusing operators, can be used in an iterative procedure to obtain the correct operators. However, current 3D seismic data acquisition geometries do not contain the dense spatial sampling required for calculation of full 3D CFP gathers. We report on the construction of full 3D CFP gathers using a non-full 3D acquisition geometry. The proposed method uses a reflector-orientated data infill procedure based on the azimuthal redundancy of the reflection data. The results on 3D numerical data in this paper show that full 3D CFP gathers, which are kinematically and dynamically correct for the target event, can be obtained. These gathers can be used for iterative updating of the 3D focusing operators. I N T R O D U C T I O NMost migration techniques use a velocity model to correct for two-way wave propagation in the medium. These two-way propagation operators are constructed from one-way propagation operators, forward modelled in the velocity model. After the correction for two-way wave propagation, the result obtained is analysed and the velocity model is updated until a certain criterion is satisfied, e.g. a flat common-image gather (Al-Yahya 1989). Owing to the complex nature of two-way wave propagation, this updating can be difficult and in addition, due to the fact that the updating is not performed directly on the one-way operators but on a parametrization of the velocity model, a restriction to the one-way operator solution space is imposed.To overcome these problems a new migration methodology was introduced by Berkhout (1997a,b), which is called the common focal point (CFP) method. In this method, the correction for two-way wave propagation is split into two separate steps, both correcting for one-way wave propagation. This correction is performed by means of applying focusing operators, which can be seen as time-reversed Green's functions that describe one-way wave propagation in the medium. These operators are simpler in nature than operators that describe two-way wave propagation. Besides this simplification, a very elegant updating criterion can also be derived in which the update is directly performed on the one-way propagation operators without the need for a velocity model (Berkhout 1997b;Bolte, Verschuur and Hegge 1999). While this so-called CFP technology was initially introduced as a migration tool, a number of other applications have been developed since then, including: the inversion of the focusing operators to obtain a velocity model of the subsurface (Hegge, Fokkema and Duijndam 1998;Kabir and Verschuur 2000;Cox and Verschuur 2003); estimating the angle-dependent reflectivities in the twice-focused domain (Ber...

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