*Oil & Gas Science and Technology - Rev. IFP*Vol. 45 (1990), No.5, pp. 587-603

## Séparation des ondes P et S à l'aide de la matrice spectrale avec informations à priori

### The Separation of P and S Waves Using the Spectral Matrix with a Priori Information

Institut Français du Pétrole

Classiquement, la technique de filtrage utilisant la matrice spectrale proposée par Mermoz ne permet une séparation automatique des ondes au sens des indicatrices sismiques que dans certains cas particuliers, à savoir lorsque les ondes à séparer sont naturellement alignées sur les vecteurs propres de la matrice spectrale. Dans les autres cas, nous montrons que l'introduction d'information a priori sur la vitesse apparente de quelques ondes et une limitation de la durée temporelle de ces dernières permettent d'estimer leurs vecteurs d'ondes. L'utilisation de ces vecteurs et une technique de projection au sens des moindres carrés conduit à une extraction optimale de ces ondes, sans dégrader les autres ondes. La technique de filtrage proposée a été appliquée sur des données sismiques de type PSV (profil sismique vertical) déporté. Le PSV a été enregistré dans un puits entre les cotes 1050 m et 1755 m; la source est déportée de 654 m par rapport à la tête de puits. L'outil utilisé est un géophone de puits à trois composantes. Le puits traverse une structure géologique complexe. Le traitement réalisé a mis en évidence des réflexions sismiques d'ondes de compression et de cisaillement, associées à des marqueurs fortement pentés (10 à 25°). Après estimation des champs de vitesse et des pendages à l'aide d'abaques, la migration en profondeur des horizons temps pointés a permis d'obtenir un modèle structural faillé.

Abstract

Detailed structural analysis can be achieved by using 3-component vertical seismic profiling method which gives structural information at several hundred meters from the wellhead. The use of an offset VSP on the Auzance structure has led to obtain a structural model composed by faulted dipping reflectors. This is due to the robust nature of the wave separation method which is based on the spectral matrix and uses an a priori information. This method preserves the true amplitude and the local apparent velocity of the reflected waves. The proposed filtering technique was applied to seismic waves of the offset VSP type. The VSP was recorded in a well between the depths of 1050 and 1755 m. The tool used was a well geophone with three components. The well crossed a complex geological structure. Processing revealed seismic reflections of compressional and shear waves, associated with steeply sloping markers (10 to 25 degrees). Once we have estimated the velocity fields and the dips by means of charts, the depth migration of the picked time horizons provided a faulted structural model. Wave Separation Method - Generally speaking, the filtering technique using the spectral matrix proposed by Mermoz only allows an automatic separation of the waves in the sense of seismic time/distance curves in a number of specific cases, namely when the waves to be separated are naturally aligned with the eigenvectors of the spectral matrix. In the other situations, the introduction of an a priori information on the apparent velocity of some waves and a limitation of their time duration enable to estimate their associated wave vectors. The use of these vectors and a least square projection method lead to an optimal extraction of these waves, without degrading the other waves. In the Fourier domain, for seismic data D (f) composed of N recordings, the spectral matrix M consists in N x N components Mk,1(f). This term represents the cross-spectrum averaged between the recordings dk(t) and d1(t). The average is introduced to decorrelate the waves. Two types of averaging are routinely used, frequency averaging and distance averaging. Frequency averaging implies a local stationarity of the signals and favors the waves with very high apparent velocities. Distance averaging favors the signals that are coherent on several recordings, regardless of their apparent velocity. We propose a matrix calculated from the recordings modified to optimize the extraction of the desired wave Wi(f). Optimization is carried out in two steps: (a) First step: Realignment of the data, according to an apparent velocity model given a priori or introduced by picking, to give to the wave Wi(f) an infinite apparent velocity. (b) Second step: Limitation of the recording time in a time window centered on the wave to be extracted so as to minimize the interference of the other waves. The average applied to calculate the matrix is a high frequency average and a low distance average to preserve the variation in the character of the wave (phase and amplitude). The first eigenvector of the spectral matrix thus estimated represents the wave vector Si(f) of the desired wave Wi (f). To extract p waves, it is necessary to calculate p matrices. This gives a set of normalized vectors Si(f) for i = 1 to p. We shall apply this type of treatment to seismic data of the VSP type, recorded in a well drilled on a complex geological structure. Presentation of the data - The VSP consists in 48 measurement points located between the depths of 1050 and 1755 m, at intervals of 15 m. The source is a vertical vibrator, transmitting a vibroseismic signal in the frequency band 14 to 125 Hz, over a duration of 8 s. The source is offset 654 m from the wellhead. The average number of vibrations per measurement point is 3. The well geophone is the Schlumberger SAT. C probe, equipped with a system of three gimbal-mounted geophones, the time sampling interval is 2 ms, for a recording time of 2 s after correlation. Data preprocessing includes correlation, printing, stacking of the unit recordings at each level, and the re-orientation of the horizontal components, designed to compensate for the rotation of the tool and to obtain a seismic recording located in the plane passing through the well and the source. Figures 1 and 2 show the vertical component Z of the VSP and the horizontal component X after re-orientation. Wave separation. Separation is aimed to extract the downgoing and upgoing P compressional waves and the SV shear waves, using the multi--component data (X and Z). Separation is carried out in three steps :(a) estimation of the wave vectors Sp and Ssv associated with the downgoing P and SV waves. (b) Extraction on each component (Z and X ) of the downgoing P (Figs. 3 and 6) and SV waves (Figs. 4 and 5), by least square projection on the vectors Sp and Ssv. (c) Analysis of the residues Rz and Rx (Figs. 7 and 8). On the residue Rz, the poorly estimated part of the downgoing P field is observed in a time window centered on the direct P arrival, as well as two P type reflections clearly individualized in depth. The poorly estimated part of the downgoing SV field interferes very little with the reflected upgoing P waves in the depth interval analyzed. In order to improve the quality of these reflections, the residual downgoing P field was subsequently filtered. The enhanced upgoing P waves are shown on Fig. 13, for the Z components. On the residue Rx, the poorly estimated part of the downgoing SV field is significant and requires supplementary filtering (Fig. 14). The VSP section (Fig. 13) shows three markers denoted A, B and C. Interpretation. Geophysical interpretation by means of charts (Fig. 18) conducted to an estimation of the structural dips, and led to the proposal of a faulted geological model (Fig. 20). Conclusion. It has been demonstrated that the acquisition, processing and interpretation of 3-component offset VSP data on the Auzance structure have led to such an improved structural interpretation with an accurate fault location. This is due to the recording of the complete wavefield and the efficiency of the wave separation method which preserves the true amplitude and the local apparent velocity of the reflected waves. The filtering technique uses a spectral matrix proposed by Mermoz and consists in estimating separately the wave vector associated with each wave in a limited time window, by introducing its apparent velocity. The separation is then achieved by least square projection of the initial data on the different vectors.

*© IFP, 1990*