Geo-physique Appliquée et Sismologie
  Utilisation de l’hodogramme comme un attribut AVO pour identifier les anomalies du gaz
 

 

Utilisation de l’hodogramme comme un attribut AVO pour identifier les anomalies du gaz
 DJEDDI* Mabrouk et Abdelkader KASSOURI* and DJEDDI Mounir
(*) Laboratoire de la physique de la terre (LABOPHYT), Faculté des hydrocarbures et de la chimie, Université de Boumerdes - Algérie
 
RESUME
Dans cet article, nous étudions les causes de l’anomalie d’amplitude observée sur la section sismique, traitée en amplitudes préservées, appartenant a un champ a gaz du sud algérien, en utilisant le crossplot AVO et l’analyse des hologrammes. Nous présentons un exemple correspondent a des grés a gaz d’âge carbonifère dans le basin de Sbaa.
Les deux facteurs importants qui déterminent la réponse AVO des réflexions des grés sont le coefficient de réflexion à incidence normale R(0) appelé l’intercepte et la variation relative de l’amplitude avec l’angle d’incidence et l’offset exprimée par le gradient (G) qui fortement dépend du contraste du coefficient de Poisson au niveau de réflecteur.
Les méthode classiques sont basées sur la déviation des grés a gaz de la tendance argiles/grès a eau dans un crossplot AVO tels que l’intercepte et le gradient. L’inconvénient de cette approche est qu’elle néglige l’ondelette sismique. Quand une ondelette est convoluée avec la série des coefficients de réflexion, chaque point sur le crossplot AVO devient une série de points, qui sont typiquement distribués sur tous les quatre quadrants du crossplot. Ce processus donne un hodogramme AVO dans lequel le mouvement de la particule AVO est polarisée avec la tendance générale de la subsurface dans le cas des événements non anomales, et est polarisée selon des angles différents de la tendance globale de la su surface dans le cas des événements anomales. Par conséquent, il devient apparent que le paramètre définissant un événement dans les hodogrammes est son angle de polarisation. Cette approche identifie directement les classes I-IV des anomalies AVO.
Liste des Figures (En Français et en Anglais):
Fig.1 : Convention utilisée pour l’angle de polarisation et les différentes classes AVO I-IV.
Fig.1 : Convention used for the polarization angle and different AVO classes I-IV.
 
Fig.2 : (a) Plot de l’Intercepte et le Gradient. (b) Crossplot de l’Intercepte avec le Gradient pour un seul réflecteur donne une ligne droite quand li n’y a pas de bruit. Figures (c)-(d) montrent un exemple d’un hodogramme résultant crossplot où un décalage de temps (phase) est ajouté à la courbe du Gradient.
Fig.2 : (a) Plot of Intercept and Gradient. (b) Crossplot of Intercept and Gradient for a single reflector falls along a straight line when there is no noise. Figures (c)-(d) show a sample hodogram resulting from a crossplot where a time shift (phase) is added to the Gradient curve.
 
Fig.3 : Stack du profil sismique S100 dans la région de Sbaa (Sud Ouest de l’ Algérie). Le rectangle entourait la zone d’intérêt.
Fig.3 : Stack from a seismic line S100 in Sbaa area (South West of Algeria). The box enclosed the zone of interesr.
 
Fig. 4 : Agrandissement de l’échelle de temps de la zone entourée par le rectangle dans la figure 3.
Fig. 4 : View on an expanded time scale of the zone enclosed by the box in figure 3.
 
Fig.5 : Stacks des attributs AVO de l’objectif. (a)Intercepte. (b)Gradient. (c)Produit Intercepte * Gradient. (d)Signe (Intercepte) * Gradient. (e) Facteur fluide.
Fig.5 : AVO attributes stacks of the target. (a)Intercept. (b)Gradient. (c)Product Intercept * Gradient. (d)Sign (Intercept) * Gradient. (e) Fluid Factor.
 
Fig.6 : Crossplot AVO de R(0)-G de la zone d’intérêt dans une fenêtre de temps=300ms.
Fig.6 : AVO time-Window R(0)-G crossplot of the zone of interest. Time–Window= 300ms width.
 
Fig.7: Hodogramme AVO. L’anomalie à 1270ms dans le CDP 250 est représentée en rouge (j=136°). L’hodogramme bleu représente la tendance de la fenêtre du temps (j0 = 64°).
Fig.7: AVO Hodogram. The 1270ms anomaly in CDP 250 is red (j=136°). The Blue Hodogram gives the time-window trend (j0 = 64°).
 
 
Fig.8: Hodogramme AVO. L’anomalie à 1200ms dans le CDP 323 est représentée en rouge (j = 85°). L’hodogramme bleu représente la tendance de la fenêtre du temps (j0 = 64°).
Fig.8: AVO Hodogram. The 1200ms anomaly in CDP 323 is red (j = 85°). The Blue Hodogram gives the time-window trend (j0 = 64°).
 
Fig. 9: Angle-plot des données incluses dans la figure 6. L’anomalie AVO est représentée (coloriée) en noir.
Fig. 9: Angle-plot of data included in figure 6. AVO anomaly is highlighted black.
 
 
 
 
 


Using the hodogram as an AVO attribute to identify anomalies of gas
Pr. M. DJEDDI* and A. KASSOURI*
(*) Laboratoire de la physique de la terre (LABOPHYT), Faculté des hydrocarbures et de la chimie, Université de Boumerdes - Algeria
 
ABSTRACT
In this paper we study the causes of amplitude anomaly observed on true amplitude stacked seismic data in southern Algerian gas field using AVO crossplot and hodograms analysis. We present an example associated with Carboniferous gas sandstones in Sbaa basin.
 
The two factors that strongly determine the AVO behavior of sandstones reflections are the normal incidence reflection R(0) called the intercept and the relative change in amplitude with incidence angle and offset expressed by the gradient (G) that mostly depends on the contrast of Poisson’s ratio at the reflector.
 
Traditional methods are based on the deviation of gas sands from the wet-sand/shale trend in an AVO crossplot such as intercept and gradient. An inconvenience of this approach is that it neglects the seismic wavelet. When a wavelet is convolved with the reflection coefficients, each point on the AVO crossplot becomes a series of points, which typically spread across all four quadrants of the crossplot. This process gives an AVO hodogram in which the AVO particle motion is polarized along the background trend for nonanomalous events, and is polarized at angles different from the background trend for anomalous events. Consequently, it becomes apparent that the parameter defining an event in the hodogram is its polarization angle. This approach directly identifies class I-IV of AVO anomalies.
 
 


INTRODUCTION
The use of hodograms in interpretation of AVO crossplots is a relatively recent innovation [T. Keho, 2001]. Often, when comparing models of attributes to the actual seismic attributes, we find that anomalous zones are much closer to the background trend than the model indicates. One reason for this concerns wavelet effect. The AVO hodogram takes wavelet effects into account and can better isolate anomalies that are otherwise difficult to distinguish from the background trend by calculating the polarization angle of the hodogram for the series of points.       
 
THEORY
For small changes in layer properties and for small angles of incidence q, usually less than 300, Shuey [1985] has given an approximation of P-wave reflection coefficient variation with incidence angle: 
                                                                                  (1)
Where R(0) is the intercept or the value of the reflection coefficient at normal incidence, and G is the gradient. For small perturbations in elastic properties at the reflecting interface, D. J. Foster (1999) gave an approximation of the gradient by the following equation:
                                                                 (2)
Where g = Vsa/Vpa and Dg/g = (DVs/Vsa) – (DVp/Vpa). Vpa, Vsa and ra are respectively the averages of the P-wave velocity (Vp), S-wave velocity (Vs) and density (r) at the reflecting interface. DVp, DVs and Dr are the differences in P-wave velocity, S-wave velocity and density between the layer below and the layer above the reflector.
If the ratio g is close to 0.5, we obtain the equation
                                                                                 (3)
 
 
Equation (3) describes a family of lines parallel to the line given by the equation (4):
                                                                                                       (4)
This line is called the ‘’fluid line’’, where the slope (1-8g2) depends on the background Vp/Vs ratio. The fluid line trend rotates counterclockwise as background Vp/Vs increases. When Vp/Vs decreases, the gradient–intercept pair falls on a trend displaced below the fluid line by an amount proportional to the change in Vp/Vs ratio, and an increase in Vp/Vs will cause the gradient–intercept pair fall on a trend above the fluid line. 
For a time-windowed reflection and at a given reflector, AVO intercept and gradient have a certain trend in the R(0)–G crossplot. Non anomalous events related to shales and brine sandstones fall on fluid line. So, events with trends different from the fluid line can be considered anomalous (e.g hydrocarbon-filled sandstones). Therefore, the polarization of crossplots can help AVO anomalies identification.
 
METHODOLOGY
Seismic data is bandlimited, so reflections that are identified on a crossplot do not come from single point, but from a series of points that result when convolving a wavelet with the reflectivity sequence of the earth. At any given seismic horizon, AVO intercept and gradient for a time-windowed reflection have a preferred orientation in the crossplot space. So the angle defining any preferred orientation in the intercept-gradient crossplot is called the polarization angle.
Nonanomalous events related to shales and brine sands can exhibit a well-defined orientation (Background angle). Seismic events at angles different from the background angle can be considered anomalous. Therefore, a main benefit of this method is enhancing seismic anomalies that are small or embedded in the background trend. For example, an event corresponding to a gas sand whose points are close to the background trend on the intercept-gradient crossplot may be obscured by the spread of background points. However, such an event can show up as a large anomaly based on polarization angle and related attributes.
The main advantage of the AVO hodogram is that it provides a preferred orientation of a seismic event in the R(0)-G space within a time window instead of a deviation or separation from any well-defined trend (fluid line trend). To describe the relationship between AVO hodograms and wavelet effect, a simple example is shown below.
Figure 1 shows the convention used for the polarization angle. Instead of computing the angles relative to the positive R(0) axis, they are computed relative to the background trend. Figure 2a shows a sample of the intercept and gradient amplitudes for a single reflector.
When the two attributes are free of noise, the crossplot of the amplitudes for the single interface maps onto a straight line (figure 2b). Adding noise (random, phase, etc.) creates what many recognise as a hodogram, an apparently non-systematic curve (figures 2c-d). The hodogram will have a dominant angle, called the polarization angle, which defines the dominant vector of the crossplot for the single reflector.

Fig.1: Convention used for the polarization angle and different AVO classes I-IV.

 
Fig.2: (a) Plot of Intercept and Gradient. (b) Crossplot of Intercept and Gradient for a single reflector falls along a straight line when there is no noise. Figures (c)-(d) show a sample hodogram resulting from a crossplot where a time shift (phase) is added to the Gradient curve.

 

  
 
 
Often when cross-plotting AVO attributes derived from seismic data, some anomalies may reside on the edge of what would be defined as the background trend. These anomalies, however, will have a very different polarization angle from the rest of the background trend, providing another means to help in the identification of AVO anomalies. This same calculation can be applied to real seismic data to create another attribute to which can be used as an aid to identify subtle AVO anomalies by the polarization angle of the hodogram.    
 
The AVO crossplot is compared to the AVO hodogram results and corresponding attributes. Also, by using the hodogram, we can derive a filter that can be applied to AVO attributes to derive enhanced AVO attributes which better identify the anomaly. By analyzing the angle of the hodogram derived in crossplot space from a series of amplitudes, it is possible to better distinguish AVO anomalies from the background trend. This crossplot angle attribute can produce a variety of various attributes, indicating a polarization filter. This filter, when applied to the AVO attributes used to derive the hodogram, can produce a more recognizable AVO anomaly, providing a means of data-derived anomaly accentuation.    
 
CASE STUDY
The seismic line S100 is processed with true amplitude recovery from onshore 2-D survey, in Sbaa syncline (south-west of Algeria). The result is shown in Figure 3. The area presents two principal reservoirs: the sandstone of Ordovician and Tournaisian. The reservoir in this prospect presents a porosity around 12% and a good permeability. The gas column is important and the average production is about 230,000m3/day. The seismic line shows a strong amplitude anomaly at 1200ms two-way time at Tournaisian level. The data enclosed by the box are seen on an expanded scale in figure 4. In all figures, red denotes a peak and blue denotes a trough. 
 
 
 
Figure 5 shows AVO attributes of this anomaly. The quantities plotted with attributes stacks are based on a simple analysis of the prestack data. At each time sample of an NMO-corrected CMP gather, a straight line least squares fit is used for a limited range of reflected angles.
The linear fit generates two attributes at each time sample: the intercept and the gradient. Figure 6 represents the crossplot of the intercept and the gradient in a 300ms width time-window centered on the target. 
 
 
 
 
 
 
 
 
 

The intercept attribute exhibits strong negative amplitude values and the gradient gives strong absolute value implying that amplitude increases with reflected angle. The product R(0)*G presents a strong amplitude in a portion of the target. The product sign[R(0)]*G shows an important amplitude and changes in sign due to the heterogeneity of the reservoir. The anomaly is more significant in the fluid factor stack. It matches to characteristics of sandstones filled with gas.       
The time-window crossplot in figure 6 shows an ellipse (blue points) concentrated in the third quadrant. The background trend corresponding to shales and brine filled rocks is represented by the yellow points. The pairs of R(0) and G, inside the black polygon, give trends corresponding to hydrocarbon accumulation at the top of reservoir (black points) and define lateral extension of the anomaly of about 5 Km.       
 
By analyzing the angle of the hodogram derived in crossplot space, it is possible to better distinguish AVO anomalies from the background trend. The polarization angle can be computed for every sample on every seismic CMP using a sliding time window with a length of about one-half to one wavelength. This angle must be compared to the background trend angle.
The trend angle of background changes with depth as the Vp/Vs ratio decreases [Castagna et al., 1998]. Deviations from this background are indicative of hydrocarbons or unusual lithology.
 
Figures 7 and 8 show the polarization angle and the AVO hodogram in two different locations of CDPs situated respectively in the left and in the right of the anomaly. The angles are measured from the positive R(0) axis. The polarization angle j0 of the background trend (blue points), computed by eigenvector analysis, is approximately 64°, corresponding to Vp/Vs ratio of about 1.61.
 
The zone of gas sandstone is very large with a polarization angle (red points) of about 136° at CDP 250 and 85° at CDP 323. Thus, as measured by polarization angle, the class of the anomaly varies from class III to class II along the horizon target.
 

Fig.8: AVO Hodogram. The 1200ms anomaly in CDP 323 is red (j = 85°). The Blue Hodogram gives the time-window trend (j0 = 64°).

 
G
R(0)
Fig.7: AVO Hodogram. The 1270ms anomaly in CDP 250 is red (j=136°). The Blue Hodogram gives the time-window trend (j0 = 64°).
G
R(0)
 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 


Figure 9 presents the angle-plot (angle difference Dj between polarization angle of each sample of data and the background angle versus AVO length) that corresponds to the crossplot presented in figure 6. The dataset includes a gas prospect showing a distinct class II and class III of AVO anomaly (black points). Note that, in the angle plot space the AVO events are clearly separated. The dominant polarization-angle difference of the anomaly is about 25° to 155°.

Dj

 
AVO Length
Fig. 9: Angle plot of data included in figure 6.
AVO anomaly is highlighted black.
 

 

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The Angle-plot has added robustness and stability to the crossplots and hodogram analysis, as well as enabling AVO anomaly classification.

According to the results of crossplot and hodograms polarization, the anomaly is better identified and can be interpreted as an AVO anomaly of several classes (classes 3 and 2 are dominant) associated to porous and gas sandstone reservoir.
 
Conclusion
In the past, AVO indicators have been designed using AVO crossplots of intercept versus gradient; this approach neglects the effect of the wavelet. The wavelet can be incorporated by crossploting attributes to produce an AVO hodogram. The key parameter defining an event in the hodogram is the polarization angle. .
 
Intercept and gradient crossplots are useful for interpreting AVO anomalies and explaining the effects of changes in rock and pore fluid properties.
 
For good enhancement of AVO interpretation, AVO crossplot analysis was combined with polarization attributes computed from the AVO hodogram which allowed us to have more details about the amplitude anomaly.
 
Concerning the example presented here, the study has confirmed the result obtained from a nearest well which shows a good productive Tournaisian reservoir associated to gas sandstone with a good porosity.
 
References
[1] Castagna J.P and Backus M., 1993 "Offset dependent reflectivity - Theory and practice of AVO analysis ", Investigation in geophysics N°. 8, SEG, TUSLA.
[2]. R. Simm and al., “the anatomy of AVO crossplots”, the leading edge, February2000.
[3]. T. Keho and al., The AVO hodogram: Using polarization to identify anomalies, the leading edge, November 2001.
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