Copyright 000 by the Society of Exploration Geophysicists ANISOTROPIC PRESTACK DEPTH MIGRATION: AN OFFSHORE AFRICA CASE STUDY Philippe Berthet *, Paul Williamson *, Paul Sexton, Joachim Mispel * * Elf Exploration Production, Elf Geoscience Research Centre Abstract. Prestack depth migration is widely used as the best tool for imaging and velocity model QC and refinement, but is mostly applied isotropically, even when there is evidence of anisotropy. We outline a methodology of model-building and imaging for use in anisotropic contexts and apply it to a line of data from offshore West Africa dominated by massive shales. The results show that the anisotropy in the shale increases with depth, along with the velocity. The prestack migrated data are sufficiently sensitive to the anisotropy that a thin layer of sand showing little or no anisotropy can be detected, and they must be included in the model to get flat common image gathers everywhere. This suggests that the use of anisotropy as a lithologydiscriminating attribute may be feasible on a depth scale of only a few wavelengths. In any case anisotropy determination is important for precise application of other lithoseismic methods such as AVO. 1 Introduction Prestack depth migration is the most powerful imaging tool currently applied by the oil industry when a good velocity model is available. Conversely, the prestack migrated data are very sensitive to the quality of the velocity model and contains information which can be inverted to improve unsatisfactory models (Stork, 199; Kosloff et al., 1994). An iterative migration and model-updating loop should eventually converge to an optimum. However, most applications of this methodology to date have been for isotropic models, which often give results which are inconsistent with other data, e.g., from wells, and may fail to be satisfactory across the full range of offsets. The exploration provinces offshore West Africa are known to contain strongly anisotropic shales (Ball, 1995; Toldi et al., 1999). The anisotropy may affect the quality of imaging, accuracy of positioning, uncertainty estimation and attribute extraction if it is not correctly taken into account. These shales are commonly considered to be transversely isotropic, usually with a vertical symmetry axis (TIV), so that the kinematic properties of qpwaves are governed by the three parameters proposed by Thomsen (1986), V p0, δ and ε, in place of the elastic tensor components. We have developed a model-based inversion method to determine these interval parameters. This method may invert stacking velocities and well data only (Williamson et al., 1997; Sexton, 1998) or include prestack data in the time (Sexton and Williamson, 1998) or migrated depth domains (Williamson et al., 1999). In this paper we apply this method to a line from offshore Africa. Whereas our previous studies were essentially structural, in this case the tectonics are relatively calm, and our interest is more in the stratigraphic and lithoseismic aspects of a sand reservoir embedded in massive shale layers. The possibility of using anisotropy as a lithologic attribute was raised by Alkhalifah and Rampton (1997), and our results confirm that with high-quality data this may indeed be possible. Anisotropy 000: Fractures, converted waves and case studies Published by The Society of Exploration Geophysicists P.O.Box 70740, Tulsa, OK 74170-740 1
Anisotropic Migration Figure 1: The inversion loop: Interpreted horizons from an initial migration are demigrated and then map-migrated through the current velocity model; stacking velocities, well marker depths or image gathers are modelled and the model parameters updated if necessary. Method We work with layer-cake models, using the modelbuilding method summarized in figure 1: first, a set of interfaces is interpreted, typically in a timemigrated block, and demigrated into the stack (time) domain. These stack times are independent of the velocity fields in the layers between the interfaces and so remain constant during the inversion unless one or more interfaces are reinterpreted. Trial velocity fields are then inserted, and the interfaces are map-migrated into depth by normal ray-tracing. The interval velocity for each layer, assumed to be TIV, is defined by ( V ( x, y) kz) A( ε, δ, θ ) V = + (1) 0 where A is the anisotropy factor defined by the phase angle θ, and the Thomsen anisotropy parameters, ε and δ; and V0(x,y) is a polynomial function of the horizontal coordinates. ε, δ, and the vertical velocity gradient, k, are constant for each layer. The data is forward-modelled within the resultant velocity depth model, and the data misfits are inverted to calculate an update to the velocity parameters. The range of data types which can be inverted has evolved from stacking velocities and well marker depths (Williamson et al., 1996; Sexton, 1998) to include well seismic travel times (Williamson et al., 1997) and prestack time or depth residuals (Sexton and Williamson, 1998; Williamson et al., 1999). Thus the objective function has the general form D( m) DV Dt st Dz w + + + = σ σ σ σ V z t u Du () where V st is a stacking velocity misfit, z is the misfit between the depth of the horizon at a well and the corresponding marker depth, t w is the time misfit for a well seismic arrival and u is a prestack time or depth residual. The σ s are the corresponding variances. Note that the stacking velocity term may also contain parameters corresponding to a higher-order moveout such as the η parameter pro-
Anisotropic Migration 3 posed by Alkhalifah and Tsvankin (1995), although this is not used in this case. We may also include a priori constraints, derived, for example, from log information or even core measurements (see Williamson et al., 1997). The presence of the various terms obviously reflects the availability of the data but can also depend upon the current stage of the model-building. The prestack residuals are analysed only at the interpreted events defining the model interfaces. The derivatives of the modelled data with respect to the parameters, and indeed some of the data themselves, are calculated using raytracing. For example, stacking velocities are estimated by regression analysis of the travel times of a fan of reflected rays, found by a bending algorithm. Their derivatives are then calculated by applying the chain rule to the derivatives of the times with respect to the model parameters and the derivatives of the regression with respect to the individual times. The data derivatives are used in turn to estimate the first and (approximate) second derivatives of the objective function, and, from these, a Gauss- Newton update to the model parameters. The process of map migration, modelling and model update is iterated until convergence, either in a layerstripping mode or, if a good initial model is available, working with all the model parameters at once ( global inversion ). Layer-stripping is particularly relevant if it seems likely that (depth) migration and reinterpretation of some of the interfaces may be appropriate as the inversion proceeds. 3 Example We applied the above inversion scheme to a line from offshore West Africa with the following methodology. In the first phase of the modelbuilding we constructed an isotropic depth model by inversion of the stacking velocity field only. We then applied a D Kirchhoff prestack depth migration (PSDM) in the common offset domain to a line of the data. Part of the result of this migration is shown in Figure, which contains a portion of the image obtained by stacking the common-offset sections over the first half of the offset range (i.e., the shorter offsets). We also show three common image gathers (CIGs), each of which comprises the set of migrated traces from the specified horizontal location for the whole range of offsets. Figure : Prestack depth migration result from an isotropic model built using stacking velocity inversion.
Anisotropic Migration 4 The residual moveout of events in a CIG is indicative of errors in the velocity model. We analyzed this moveout at regularly sampled locations along the line for the events defining the interpreted model interfaces. Picks were made either by automatic semblance analysis or by hand (Figure 3); the presence of anisotropy is indicated by nonhyperbolic residual moveout. Typically events initially move to greater depth with increasing offset and then move back to lower depths at the far offsets when the stacking velocity picks were accurate. The residual picks are added into the inversion as extra terms in the objective function, as shown in equation () above. The derivative information is calculated by shooting a fan of rays upward from each reflector at each analysis location. We initially used this technique to refine the isotropic model with the aim of flattening the near-offset traces. For events in which residual (nonhyperbolic) moveout persists on the far offsets, or for anomalous dips, we added the anisotropy parameters ε and δ to each layer and inverted for a TIV model. In this case, without well information, δ is at best weakly constrained, so we fixed it at 0 everywhere and interpreted the inverted values of ε as the parameter η. We used an anisotropic PSDM code (Mispel et al., 1998) to iterate this phase of the model-building, which continued until the CIGs appeared satisfactorily flat along all the reflectors, and to obtain a final depth image. The corresponding portion of this final image, along with the same three CIGs as in Figure, is shown in Figure 4. Note that the image is, overall, rather cleaner than that in figure, although the differences are relatively minor. These differences are only indirectly caused by the anisotropy, being attributable to the fact that the full-offset stacking velocities are slightly larger than the NMO (shortspread) velocities; thus, as can be seen in Figure, the events on the CIGs from the initial isotropic model tend to have a slight downward moveout on the near offsets. The corresponding η section, superposed upon the seismic image, is shown in Figure 5. Figure 3: Picking illustrated for three layers. The main window, on the left, shows the model in depth and the rays for the analysis points; the three central windows show sections from the CIG centered on the three reflectors and the picked residuals, and the three windows on the right show semblance analyses. 4 Resolution The isotropic layer, which is the second deepest in the section of Figure 5, is considerably thinner (its maximum thickness is less than 150 m) than most layers used in layer-based velocity models. Despite its geological interest (it is thought to correspond to a potential reservoir zone), we might ask whether its inclusion in the model is justified/useful. We therefore compared results from the best models obtained from inversion with and without the horizon at the base of this layer (denoted h). Over most of the line the resulting differences are indeed small but CIGs through the central bulge (at location B in Figures and 4) showed quite a marked change at the h level, suggesting that, there at least, this horizon was important. Specifically, Figure 6a shows that although the event at the top of the bulge is flat, those around the h level from the migration using the model without this horizon show significant downward curvature resulting in a depth residual of up to 80-90m at far offsets. But near the bottom of the section, at the lowest picked interface, the events are again flat, showing that the interval η value for this layer, as a
Anisotropic Migration whole, is correct. Part of this downward curvature can be explained by a contrast in vertical velocity of around 10%, the effect of which can be seen on the near offsets. But the residual moveout accelerates quite sharply at about 75% of the maximum offset, and we ascribe this to the strong anisotropy contrast (the η value in the bottom layer is around 0.35). In 5 fact, due to a favourable offset/depth ratio we have ray angles of more than 45 degrees at the far offsets, so we calculate that the anisotropy contrast contributes more than half of the depth residuals at these offsets. These residuals seem to justify including the extra horizon in the model. Figure 4: Prestack depth migration result using final anisotropic depth model. Note the improvement in the focusing, particularly in the lower part of the section around location C, and the overall flatness of the CIGs. Figure 5: Final η section through model superposed on seismic. Note the thin isotropic zone between horizons h1 and h.resolution
Anisotropic Migration 6 On the other hand, at locations away from the bulge (e.g., locations A and C in figures and 4) the layer is too thin to have a significant effect indeed it is hard to distinguish separate top and base events on the seismic, and there appears to be no particular reason for the additional horizon (Figure 6b). It is thought that the bulge corresponds to a stack of channel sands and the rest of the layer contains floodplain deposits, or sheet facies, probably comprising relatively thin layers of sand with interspersed shale. The combination of the relative thinness of the layer and the change in lithology explains the low impact of this part of the layer on the migration through the simplified model and the slight overcorrection when h is introduced and the overlying layer is isotropic. Nonetheless the inclusion of the extra layer appears justified, on the CIGs at least, by the response at the channel zone. 5 Discussion and Conclusions The estimated anisotropy profile is interesting because it conforms with the lithology variations the isotropic layer is thought to be a sand layer between two massive shale layers. The inclusion of this isotropic layer is prompted by the inversion process the combination of good data quality, a large offset/depth ratio, and a relatively calm tectonic context makes the CIGs very sensitive to velocity anomalies of all kinds, including those due to (the presence or absence of) anisotropy. In this case the anomalous sandy layer is strongly detectable and appears effectively isotropic in a zone thought to be a stack of channel sands in a background of strongly anisotropic shales. Outside the channel zone, where the lithology is different (probably more shaly and therefore more anisotropic) and the layer thinner, its impact is marginal. However, we conclude that overall the inclusion of this layer in the model is mandated by the data; i.e., the acquisition and processing may resolve layers of thicknesses down to around 100 m. thick. This study thus appears to confirm the possibility of using anisotropy as a direct lithology indicator. Even when it does not greatly change the image, taking the anisotropy into account should also improve the reliability of more conventional lithoseismic studies based on AVO, if only because it allows the use of longer offsets. Figure 6: (a) CIGs at location B from inversions with and without the horizon h ( base reservoir ); (b) CIGs at location C from the same inversions.
Anisotropic Migration 7 Acknowledgments The authors thank Elf Exploration Production for permission to publish this paper References Alkhalifah, T., and Tsvankin, I., 1995, Velocity analysis for transversely isotropic media, Geo physics, 60, 1550-1566. Alkhalifah, T., and Rampton, D, 1997, Seismic anisotropy in Trinidad: processing and interpretation, SEG 67 th Internat. Mtg., Expanded Abstracts, INT6.. Ball, G., 1995, Estimation of anisotropy and anisotropic 3D prestack migration, offshore Zaire, Geophysics, 60, 1495-153. Kosloff, D., Koren, Z., Meshbey, O., Sherwood, I.W.C., 1994, Velocity determination by tomography of prestack CRP (Common reflection point) depth gathers, EAEG 56 th. Internat. Mtg., Expanded Abstracts, P061. Mispel., J., Williamson, P., and Berthet, P., 1998, Ray-based D anisotropic prestack depth migration on synthetic and real data, Proceedings of the 8IWSA, Revue de l IFP, 53, 595-607. Sexton, P.A., 1998, 3D velocity-depth model building using surface seismic and well data, Ph.D. Thesis, University of Durham. Sexton, P.A., and Williamson, P.R., 1998, 3D anisotropic velocity estimation by model-based inversion of prestack traveltimes, SEG 68 th Internat. Mtg., Expanded Abstracts, ST14.3. Stork, C., 199, Reflection tomography in the postmigrated domain, Geophysics, 57, 680-69. Thomsen, L.A., 1986, Weak elastic anisotropy: Geophysics, 51, 1954-1966. Toldi, J., Alkhalifah, T., Berthet, P., Arnaud, J., Williamson, P., Conche, B., 1999, Case study of estimation of anisotropy, The Leading Edge, 18, 588-594. Williamson, P.R., Sexton, P.A., and Xu, S., 1997, Integrating observations of elastic anisotropy: Constrained inversion of seismic kinematic data, SEG 67 th Internat. Mtg., Expanded Abstracts, ST9.6 Williamson, P.R., Sexton, P.A., Mispel, J., and Berthet, P., 1999, Anisotropic velocity model construction and migration: an example from West Africa, SEG 69 th Internat. Mtg., Expanded Abstracts, SRC.1.