GNGTS – Atti del 20° Convegno Nazionale / 08.02

G. Bernasconi

Dipartimento di Elettronica e Informazione, Politecnico di Milano

3D SEISMIC MIGRATION “WHILE DRILLING”

Abstract. This paper addresses the theory and the practical implementation of 3D pre-stack Kirchhoff depth migration of SWD data. We found that the separation of upgoing and downgoing waves can be avoided by focusing the migration operator below the source (bit): in this way the downgoing waves interact destructively without corrupting the final image. Original solutions are presented to equalize the illumination of the migration target, to reduce the migration artefacts and to control the alias. The procedure is tested on a real data set, kindly furnished by ENI-AGIP Division and OGS. The result is compared with the seismic section obtained from surface reflection data. The overall features are similar.

MIGRAZIONE SISMICA 3D “WHILE DRILLING”

Riassunto. In questo lavoro si analizzano i problemi teorici ed implementativi della migrazione pre-stack alla Kirchhoff per dati SWD 3D. Abbiamo verificato che la separazione degli arrivi discendenti e risalenti può essere ottenuta mediante la focalizzazione verso il basso dell’operatore di migrazione. Si presentano inoltre soluzioni originali per equalizzare l’illuminazione del pannello migrato, per ridurre gli artefatti di migrazione e per analizzare gli effetti dell’alias. Le procedure sono verificate su un dataset SEISBIT® reale, gentilmente fornito da ENI-AGIP ed OGS. Il confronto tra il pannello migrato e la linea sismica di riferimento mostra notevoli somiglianze.

INTRODUCTION SWD technique uses the drill-bit vibrations as a source of seismic energy

(Rector, 1992). The seismic signal is recorded by sensors on the surface and it is processed in order to obtain a RVSP equivalent dataset (Rector et al., 1991; Miranda et al., 1996).

The signal contains the waves that propagate directly from the bit to the receivers (downgoing waves in VSP recordings) and the reflected waves coming from discontinuities ahead of the bit (upgoing waves). The migration process aims at focusing the reflected waves in the correct depth position. The direct waves are usually cancelled during a pre-processing step. It requires the picking of the first breaks and the application of median filters (Hardage, 1983), and it becomes difficult with low signal to noise ratio.

Since VSP (RVSP-SWD) datasets tend to be small (hundreds of traces), the speed and the efficiency of a migration scheme are not as important as its robustness and flexibility, features associated with Kirchhoff summation (Bicquart, 1988; Dillon, 1988). The Kirchhoff solution can handle virtually any configuration of sources and receivers and it can be compensated for irregular spatial sampling of the array elements (receivers and sources). Propagation through complex velocity fields can be introduced via external modelling procedures.

In this paper we present an implementation of a prestack Kirchhoff depth migration for 3D-SWD data and its application to a real dataset. We focus the migration operator below the source (bit): we found that this can replace the separation of upgoing and downgoing waves, as the downgoing waves interact destructively without corrupting the final image.

GNGTS – Atti del 20° Convegno Nazionale / 08.02

As the source (bit) penetrates into the target, it produces an irregular illumination. Moreover, limited observation geometry and aperture produces migration artefacts or false images. We show practical solutions to equalize the illumination of the migration target, to reduce the migration artefacts and to control the alias. The procedure is tested on a SEISBIT® 3D SWD data set, acquired by ENI-AGIP Division and OGS. The result compares satisfactorily with the seismic section obtained from surface reflection data.

3D SWD DATASET ENI-AGIP Division and OGS run a SEISBIT® 3D SWD acquisition in Italy

(Bertelli et al., 1998; Poletto et al., 2001) to obtain detailed information in the well area and to demonstrate the reliability of the 3D SWD technique. Surface receivers were set down along two orthogonal lines crossing at the well and along two circles centered on the well. The internal circle had a radius of approximately 1100 m and the external circle had a radius of 2200 m. They used a saw-toothed shaped circular disposition to facilitate the separation of the surface arrivals (noise) from the deep arrivals (signal from the bit). The total number of receivers was 391 (Fig. 1).

Fig. 1 - 3D SWD acquisition. Position of sources (bit) and receivers on the surface.

The acquisition started at a depth of 428 m and was completed at a depth of

3060 m, for a total count of 159 levels. ENI-AGIP Division and OGS provided the processed data (equivalent RVSP survey) and the velocity model.

METHOD AND RESULTS We use a standard Kirchhoff migration summation (Claerbout, 1984)

dSdUetAAjm RS

o

ttjRs

Sr ),,(),(),()( sr

)(sr ωω

πω ω

ω

xxnxxxxx +∇⋅= ∫ ∫ (1)

with

GNGTS – Atti del 20° Convegno Nazionale / 08.02

m(x): migrated image at position x, Ar(xr,x), tr: amplitude and travel time of the Green function from the image point at position x to the receiver at position xr, As(x,xs), ts: amplitude and travel time of the Green function from the source (bit) at position xs to the image point at position x, U(xr, xs, ω): spectral component at frequency ω of the wavefield recorded by the receiver in xr due to a source in xs.

Fig. 2 - Migration process for RVSP geometry.

We compute traveltimes, amplitudes, departing and arrival angles, with a gridded rays method (Bernasconi and Drufuca, 2000). The input data are the velocity model, the coordinates of sources and receivers, and the position of the target. The velocity model is given on a 3D rectangular grid.

We migrate a vertical panel of 1000 m in the horizontal direction and 1700 m in the vertical direction, centered around the well (Fig. 3a). Surface seismic data is available in the position of the target (Figg. 3c and 3d).

The migration operator is focused ahead of the bit: in this way we found that cancellation of downgoing waves is not required, as they interact destructively without corrupting the final image.

Geometrical spreading and obliquity weighting factors are applied during the summation based on source, receiver and migration point positions.

As the source (bit) penetrates into the subsurface, the limited aperture of the migration operator produces an irregular illumination of the target. For each point in the target image we compute a “source counter”. It contains the number of sources that enlighten the point and it permits the equalization of the final image (Fig. 4).

The receiver positions are used to create a mosaic of Voronoi polygons in the acquisition surface (Fig. 5). Each seismic trace is multiplied by the area of the corresponding polygon, so to compensate the irregular sampling of the recording surface and to describe correctely the areal element dS of eq. (1).

GNGTS – Atti del 20° Convegno Nazionale / 08.02

Fig. 3 - (a) Migration target. (b) Vertical slice of the velocity field and target. (c) Position of the surface seismic line (blue line). (d) Time section from seismic data; the box corresponds to the position of the migration target.

Fig. 4 - Irregular illumination of the target due to the bit penetration (left) and source counter (right). The discretization of the Kirchhoff summation causes aliasing noise. Antialias

conditions are formulated looking at the full pre-stack 5D domain (2D position of receivers on the surface, 3D position of sources in the subsurface) of neighbouring sources and receivers (Mazzucchelli and Rocca, 2001). Fig. 6 shows the grouping of receivers and the final result of antialias analysis for our target. It reveals that the maximum non aliased frequency is greater than 100 Hz. This procedure allows to better preserve the seismic content of seismic data.

GNGTS – Atti del 20° Convegno Nazionale / 08.02

0.05

1.0

0.05

1.0

Fig. 5 - Area computation for the equalization of the receiver footprint.

Fig. 6 - Antialias analysis. Grouping of receivers (left) and result of the analysis on the migration target (right).

Limited observation angles, narrow zones of illumination and variable fold

produce artefacts and false images in the final result. We control these effects by constraining the migration summation around an expected dip (Fig. 7), using the information from the incident angles of the source wave and of the receiver wave (van der Poel and Cassel, 1989; Nemeth et al., 2000).

We validated the overall procedure on synthetic data for a horizontally layered medium, with sources and receivers in the same position as in the real case. Fig. 8 shows the result for the sinthetic case

The application to the real data is shown in Fig. 8. The output image in depth has been converted in time, and it is compared with the surface seismic section. The overall features are similar. The migrated panel exhibits a higher resolution than surface seismic.

GNGTS – Atti del 20° Convegno Nazionale / 08.02

Fig. 7 - The migration summation is limited around an expected dip.

Fig. 8 - Synthetic data for horizontal reflectors. Left: acquisition geometry, target position and reflectors position. Center: migration without dip limitation. Right: migration with dip limitation.

CONCLUSIONS We produced relatively good results with our 3D-SWD Kirchhoff depth migration

in a real data sets: they compare favorably with surface seismic sections. We show practical solutions to control migration artifacts and to reduce footprint effects. We demonstrate that SWD data is useful in obtaining time and depth images in the well vicinity.

GNGTS – Atti del 20° Convegno Nazionale / 08.02

Fig. 9 - Surface seismic section (upper). Migrated panel over the surface seismic section (lower).

Acknowledgments. I acknowledge ENI-AGIP and OGS for providing the dataset and the

velocity model. Thanks to Prof. F. Rocca for helpful discussions and to D. Buglione for tuning the migration code with RVSP geometries.

REFERENCES Bernasconi, G., Drufuca, G., 2001: 3-D traveltimes and amplitudes by gridded rays. Geophysics, 66,

277–282. Bertelli, L., Miranda, F., Poletto, F., Rocca, F., 1998: Design of SWD 3D RVSP using Seisbit®

technology. Extended Abstracts, EAGE Internat. Mtg., Paper 10-49. Bicquart, P., 1998, Application of Kirchhoff depth migration to 3D-VSP. SEG Internat. Mtg., Expanded

Abstracts, 389 –392. Dillon, P.B., 1990, A comparison between Kirchhoff and GRT migration on VSP data: Geophysical

Prospecting, 38, 757-777. Claerbout, J.F., 1984: Imaging the earth interior. SEP, Stanford. Hardage, B. A., 1983: Vertical Seismic profiling, Geophysical Press, London. Mazzucchelli, P., Rocca, F., 2001: Antialiasing for n-D Kirchhoff operators. Extended Abstracts, EAGE

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Miranda, M., Aleotti, L., Abramo, F., Poletto, F., Craglietto, A., Persoglia, S., Rocca, F., 1996: Impact of the Seismic ‘While Drilling’ technique on exploration wells. First Break, 14, 55–68.

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Rector, J.W., Marion, B. P., 1991: The use of drill-bit energy as a downhole seismic source. Geophysics, 56, 628-634.

Van der Poel, N. J., Cassell, B. R., 1989: Borehole seismic surveys for fault delineation in the Dutch North Sea. Geophysics, 54, 1091-1100.