A. J. Berkhout

Acoustic control by wave field synthesis

The acoustics in auditoria are determined by the properties of both the direct sound and the later arriving reflections. If electroacoustic means are used to repair disturbing deficiencies in the acoustics, one has to cope with unfavorable side effects such as localization problems and artificial impressions of the reverberant field (electronic flavor). To avoid those side effects, the concept of electroacoustic wave front synthesis is introduced. The underlying theory is based on the Kirchhoff–Helmholtz integral. In this new concept the wave fields of the sound sources on stage are measured by directive microphones; next they are electronically extrapolated away from the stage, and finally they are re‐emitted in the hall by one or more loudspeaker arrays. The proposed system aims at emitting wave fronts that are as close as possible to the real wave fields. Theoretically, there need not be any differences between the electronically generated wave fields and the real wave fields. By using the image source...

Adaptive surface‐related multiple elimination

The major amount of multiple energy in seismic data is related to the large reflectivity of the surface. A method is proposed for the elimination of all surface‐related multiples by means of a process that removes the influence of the surface reflectivity from the data. An important property of the proposed multiple elimination process is that no knowledge of the subsurface is required. On the other hand, the source signature and the surface reflectivity do need to be provided. As a consequence, the proposed process has been implemented adaptively, meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple‐free data equals the inversion residue. Results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion.

Estimation of multiple scattering by iterative inversion; Part 1, Theoretical considerations

A review has been given of the surface-related multiple problem by making use of the so-called feedback model. From the resulting equations it has been concluded that the proposed solution does not require any properties of the subsurface. However, source-detector and reflectivity properties of the surface need be specified. Those properties have been quantified in a surface operator and this operator is estimated as part of the multiple removal problem. The surface-related multiple removal algorithm has been formulated in terms of a Neumann series and in terms of an iterative equation. The Neumann formulation requires a nonlinear optimization process for the surface operator; while the iterative formulation needs a number of linear optimizations. The iterative formulation also has the advantage that it can be integrated easily with another multiple removal method. An algorithm for the removal of internal multiples has been proposed as well. This algorithm is an extension of the surface-related method. Removal of internal multiples requires knowledge of the macro velocity model between the surface and the upper boundary of the multiple generating layer. In Part II (also published in this issue) the success of the proposed algorithms has been demonstrated on numerical experiments and field data examples.

Changing the mindset in seismic data acquisition

Seismic acquisition surveys are designed such that the time intervals between shots are sufficiently large to avoid the tail of the previous source response interfering with the next one (zero overlap in time). To economize on survey time and processing effort, the current compromise is to keep the number of shots to some acceptable minimum. The result is that in current practice the source domain is poorly sampled.

Estimation of multiple scattering by iterative inversion; Part II, Practical aspects and examples

A surface-related multiple-elimination method can be formulated as an iterative procedure: the output of one iteration step is used as input for the next iteration step (part I of this paper). In this paper (part II) it is shown that the procedure can be made very efficient if a good initial estimate of the multiple-free data set can be provided in the first iteration, and in many situations, the Radon-based multiple-elimination method may provide such an estimate. It is also shown that for each iteration, the inverse source wavelet can be accurately estimated by a linear (least-squares) inversion process. Optionally, source and detector variations and directivity effects can be included, although the examples are given without these options. The iterative multiple elimination process, together with the source wavelet estimation, are illustrated with numerical experiments as well as with field data examples. The results show that the surface-related multiple-elimination process is very effective in time gates where the moveout properties of primaries and multiples are very similar (generally deep data), as well as for situations with a complex multiple-generating system.

Angle‐dependent reflectivity by means of prestack migration

Most present day seismic migration schemes determine only the zero‐offset reflection coefficient for each grid point (depth point) in the subsurface. In matrix notation, the zero‐offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source‐wave field into a reflected‐wave field. However, angle dependent reflectivity information is contained in the full reflectivity matrix. Our objective is to obtain angle‐dependent reflection coefficients from seismic data by means of prestack migration (multisource, multioffset). After downward extrapolation of source and reflected wave fields to one depth level, the rows of the reflectivity matrix (representing angle‐dependent reflectivity information for each grid point at that depth level) are recovered by deconvolving the reflected wave fields with the related source wave fields. This process is carried out in the space‐frequency domain. In order to preserve the angle‐dependent reflectivity in the im...

Pushing the limits of seismic imaging, Part I: Prestack migration in terms of double dynamic focusing

In this paper, the author proposes to extend the synthesis of areal sources (controlled emission) to the synthesis of areal detectors (controlled detection) such that the concept of numerical focusing can be formulated as a special version of target‐oriented synthesis. As a consequence, the insight in the complex prestack migration process can be improved significantly by making use of the concepts “focusing in emission” and “focusing in detection.” Focusing in emission transforms shot records into so‐called common focus‐point (CFP) gathers. Focusing in detection transforms CFP gathers into the prestack migration result. If structural information is sought, the focus point in emission is chosen equal to the focus point in detection: confocal version of CFP migration. If rock and pore information is required as well, the focus point in emission is chosen different from the focus point in detection: bifocal version of CFP migration. Errors in the underlying macro velocity model can be better analysed than b...

Pushing the limits of seismic imaging, Part II: Integration of prestack migration, velocity estimation, and AVO analysis

The author proposes an operator‐driven prestack migration scheme that is based on the synthesis of common focus‐point (CFP) gathers. Each CFP gather represents the response of a synthesized source array that aims at the illumination of one subsurface gridpoint (focus point). The involved synthesis operator is referred to as the focusing operator. If the time‐reversed focusing operator and its related focus‐point response have equal traveltimes, then the underlying macro velocity model is correct and the focus‐point response in the CFP gather is stacked by weighted addition along the common traveltime curve (CFP‐stacking), yielding the prestack migration result at the subsurface grid point under consideration. If the time‐reversed focusing operator and its related focus‐point response have different traveltimes, then the underlying macro velocity model is incorrect and the correct focusing operator can be derived from the two traveltime curves. A simple updating procedure is proposed. The total CFP migrati...

Seismic migration of blended shot records with surface-related multiple scattering

This paper focuses on the concept of using blended data and multiple scattering directly in the migration process, meaning that the blended input data for the proposed migration algorithm includes blended surface-related multiples. It also means that both primary and multiple scattering contribute to the seismic image of the subsurface. Essential in our approach is that multiples are not included in the Greens functions but are part of the incident wavefields, utilizing the so-called double illumination property. We find that complex incident wavefields, such as blended primaries and/or blended multiples, require a reformulation of the imaging principle in order to provide broadband angle-dependent reflection properties.

Imaging of multiple reflections

Current multiple-removal algorithms in seismic processing use either differential moveout or predictability. If the differential moveout between primaries and multiples is small, prediction is the only option available. In the last decade, multidimensional prediction-error filtering by weighted convolution, such as surface-related multiple elimination (SRME), have proved to be very successful in practice. So far, multiples have been considered as noise and have been discarded after the removal process. In this paper, we argue that multiple reflections contain a wealth of information that can be used in seismic processing to improve the resolution of reservoir images beyond current capability. In the near future, one may expect that the so-called weighted-crosscorrelation (WCC) concept may offer an attractive alternative in approaching the multiple problem. WCC creates an option to avoid the adaptive subtraction process as applied in prediction-error algorithms. Moreover, it allows the transformation of multiples into primaries. The latter means that seismic imaging with primaries and multiples (nonlinear process) can be implemented by a sequence of linear processes, including the transformation of multiples into primaries and the imaging of primaries.