ASSESSMENT OF 3-D SEISMIC ACQUISITION GEOMETRIES BY FOCAL BEAM ANALYSIS Arno W.F. Volker (Ph.D. student) Subfaculty of Applied Physics Laboratory of Seismics and Acoustics, The objective of this research is to develop a scheme for designing 3-D data acquisition geometries. Three quality criteria are defined by which acquisition geometry are characterised. These criteria are: resolution, true amplitude (allows extraction of angle dependent reflection information) and noise suppression. The analysis of the acquisition geometry is based on the CFP-technology. For the analysis focused beams are defined. The focused beams describe the focusing properties of the source and receiver geometry. Introduction The concept of focused beams was introduced by Berkhout (1997). These beams describe the focusing properties of the source and receiver arrays at a certain subsurface grid point. The focused beams are used to analyse the acquisition footprint of 3-D data acquisition geometries. The focusing properties of the separate beams (source and receiver beams) can be analysed in the Radon domain. Optimally, the beams should have a unit amplitude within the desired spatial frequency band. This property ensures optimal resolution and true amplitude images. In case of a stationary acquisition geometry the focused beams can be combined to the resolution function, i.e., the final image. The resolution function is in this case simply the space frequency domain product of the separate source and receiver beams (Berkhout, 1997). In case of bifocal migration, the result is given by the ray-parameter-frequency domain product of the source beam, the reflectivity and the receiver beam. The Radon domain product of the source and receiver beam is called the AVP-function. Note that in this case a unit angle independent reflector is modelled. Optimally the Radon domain product of the source and receiver beam should be unity within the desired spatial bandwidth. Any deviation is caused by the acquisition geometry. This condition is quite severe and will not be met in general. This project started in September 1997 and should be finished in September 2001. Results in 2001 The design of a 3-D seismic survey can be split in several steps. First of all the objectives of the survey are identified and all the information about the survey area is gathered. After these very important steps a basic template design is made. Note that the objectives of the survey and specific problems for the survey area affect the geometry design. This template is a characteristic pattern of sources and receivers, which will be moved along the earth’s surface in order to cover the whole survey area. The choice of the roll along distance greatly affects the quality of the final results and the costs of a survey. The effect of roll along has been analysed. In order to perform this analysis approximate expressions for the computation of the focal beams have been derived. It has been shown that the focal beam in homogeneous media can be computed using a Fourier transform of the source and receiver sampling function. The sampling function is given in terms of the wavenumbers kx and ky with respect to the target point. In an area around the focal point the approximation is very accurate. Figure 1 shows an example of a cross-section of the receiver beam in the xy-plane using the exact equation and the derived approximation. The effect of source or receiver arrays can also be included in the computation of the focal beam. The focal beam can also beam computed along an arbitrary dipping plane. The wavenumbers are redefined to incorporate the dip of the plane. These expressions are exact for a plane, which only is dipping along one direction. For a plane with a dip in both x- and y-direction the expressions are sufficiently accurate for a dip up to 30°. A similar expression can be derived for inhomogeneous media, in that case the sampling functions are written in terms of the slowness components at the target. The focal beam is then given by a Radon transform of the source or receiver sampling function. This enables a very efficient way of computation of the focal beam. Furthermore this method gives a lot of insight about how the final image is formed based on the source-receiver geometry and the roll along of the basic template. The noise suppression capabilities of acquisition geometries can be analysed similary as the focusing properties. Focusing operators are applied to the noise. Analysis of the remaining apparent velocities after one focusing step shows how well the noise can be suppressed by the source or receiver geometry. Figure 1: Receiver beam computed using the derived approximation and the exact equation. In an area around the focal point difference between the exact result and the approximation is negligible. Publications and presentations in 2001 Berkhout, A.J., O. Ongkiehong, A.W.F. Volker, G. Blacquiere; (2001) Comprehensive assessment of seismic acquisition geometries by focal beams—Part I: Theoretical considerations: Geophysics, Soc. of Expl. Geophys., 66, pp. 911-917. Volker, A.W.F., G. Blacquiere, A.J. Berkhout, O. Ongkiehong; (2001) Comprehensive assessment of seismic acquisition geometries by focal beams -- Part II: Practical aspects and examples: Geophysics, Soc. of Expl. Geophys., 66, pp. 918-931. Drijkoningen, G.G., D. Draganov, H. van der Meer, A. Volker, A.K.T. Wever; (2001) A very shallow (0100m) 3D land seismic survey near Boulogne-sur-Mer, N-France, 63rd Mtg.: Eur. Assn. of Expl. Geophys., Session: P131. Blacquiere, G., A.W.F. Volker; (2001) 3D Physical modelling, 63rd Mtg.: Eur. Assn. of Expl. Geophys., Session: P007. Volker, A.W.F., G. Blacquiere, A.J. Berkhout; (2001) Analysis of 3D acquisition geometries with focal beams, 63rd Mtg.: Eur. Assn. of Expl. Geophys., Session: A-16. Volker, A., G. Blacquiere, A.J. Berkhout; (2001) Acquisition design for optimum amplitude accuracy, 71st Ann. Internat. Mtg: Soc. of Expl. Geophys., 60-63. Volker, A.W.F.; Assessment of 3-D seismic acquisition geometries by focal beam analysis, Ph.D thesis, Delft University of Technology Completed graduate courses Does not apply.