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1 A new parameterization for anisotropy update in full waeform inersion Nuno V. da Sila*, Andrew Ratcliffe, Graham Conroy, Vetle Vinje, Geoff Body, CGG Summary Full Waeform Inersion (FWI is now used regularly by the industry to update elocity models. These algorithms often take into account anisotropy but do not update it. We introduce a set of parameters, new in the scope of FWI, which hae better orthogonal properties in comparison to other equialent sets. This was done in an attempt to mitigate the existing ambiguity when jointly estimating anisotropy and elocity from FWI. After demonstrating the properties of this new parameter set, a practical application to a North Sea field dataset is then presented. Our FWI result reeals interesting elocity and anisotropy details associated with features in the near surface geology; an associated improement in the seismic image is also obsered. Introduction Seismic anisotropy (Thomsen, 1986 plays a key role in exploration seismology. In industry applications of FWI it is still common practice to update for ertical elocity only, while keeping the anisotropic parameters fixed during the inersion (see for example, Warner et al., 013. Such approaches mitigate the different sensitiity of the data to the parameters that characterize the subsurface and, in addition, circument the intrinsic ambiguity when estimating multi-parameters from surface seismic data. Howeer, fixing the anisotropic parameters imposes a constraint on the update of the ertical elocity, potentially leading to a sub-optimal, or een a biased, solution of the inerse problem. Anisotropic inersion, in the Vertical Transerse Isotropy (VTI sense, aims to take into account the difference between ertical and horizontal elocities. Some recent efforts hae focused on deising strategies for updating the anisotropic parameters together with the acoustic wae elocity (see for example, Plessix and Rynja, 010; Gholami et al., 011; Wang et al., 01; Stopin and Plessix, 014. Incorporating the estimation of both elocity and anisotropic parameters together in the inersion scheme potentially allows us to determine an improed model from an initial estimate of the model parameters. In principle we obtain improed data fitting and an improed elocity model because of the extra degrees of freedom aailable compared to fixing the anisotropic parameters. Here we present a scheme for an FWI update of ertical elocity and epsilon from surface seismic data, assuming that a good model of the delta parameter is known a priori. It is known that when jointly estimating elocity and epsilon, there is an ambiguity, also commonly referred to as a trade-off, or cross-talk, between these two parameters (see Operto et al., 013, for an excellent reiew of multiparameter FWI. Based on the theory of kinematically equialent media (Stoas, 008, we introduce a new parameterization of the inerse problem that attempts to mitigate this ambiguity. We will refer to this parameter set as PTS parameters (from Presered Trael-time Smoothing as they hae been used preiously in the smoothing of elocity models (Vinje et al., 013. The paper is organized as follows: first we reiew the equations for the acoustic waes in VTI media, followed by a feasibility study on the orthogonality properties of the PTS parameters. This is followed by the computation of the gradients within the new parameterization of FWI. We then describe an inersion of a marine dataset from the North Sea, which contains a brief outline of the methodology, before the results and interpretation. VTI time-domain modeling In our FWI algorithm we use the acoustic wae equation and formalism of Zhang et al. (011: 1 A QL s (1 t where, (1 Q L and T p r h, x x h 1 ( 0 h z 0 1 ( p is the horizontal stress, r is the ertical stress (Dueneck et al., 008, the density, is the P-wae (ertical elocity, s the source term, and and the anisotropy parameters. Kinematically equialent media A problem that arises is how to parameterize the inersion scheme. This aspect is particularly important gien the inherent ambiguity when estimating anisotropy from surface seismic data due to an existing trade-off between the ertical elocity, epsilon and delta (Gholami et al., 011, Prieux et al. 011, Plessix and Cao, 011. FWI aims to fit all the eents in the seismic trace, which can be understood as fitting all the trael-times and amplitudes resulting from excitation of the subsurface, with the trael- 014 SEG SEG Dener 014 Annual Meeting DOI Page 1050

2 A new parameterization for anisotropy update in full waeform inersion times generally being the dominant factor. Hence, it makes sense to study the sensitiity of trael-times with respect to perturbations in the model parameters and we show how trael-time ambiguity relates to the inersion parameter space. For simplicity and clarity we define a model with one layer and a single reflector at a depth of 1000 m, as shown in figure 1. Figure 1 One dimensional reference model for inestigating the sensitiity of trael-time with model parameterization. We study four different parameterizations for the solution of the inerse problem: (a ertical and horizontal slowness, (b ertical elocity and epsilon, (c ertical elocity and eta, and (d PTS (Stoas, 008, Vinje et al., 013: 1 1 ( (1 (1 8 6 a b c d Figure Plot of the misfit of trael-time with percentage of model perturbation for different parameterizations: a ertical and horizontal slowness, b ertical elocity and epsilon, c ertical elocity and eta, and d PTS parameters. ( The trael-times are computed using: t ( x t where, 0 x z t 0 (1 nmo (1 S x 4 4 nmo 4 nmo 8( S In this study is left unchanged because it is assumed it is known a priori. In the case of the PTS parameterization, it is sufficient to use a subset of the three parameters, and the obious choice is η -1 and η 3. Each parameter is perturbed up to a maximum of 4% from its true alue and the misfit is quantified using the square of the residuals between the trael-time in the true medium and the trael-time in the perturbed medium: E ( t p t i, i 0, i where, t p,i is the trael-time in the perturbed medium for the i-th receier and t 0,i is the trael-time at the i-th receier for the true medium. The offset for the receier position ranges between 00 and 5000 m. Figure shows the plot of the misfit with the perturbation of the model parameters for each one of the four parameterizations. By inspection of figure, one can immediately conclude that the PTS parameterization is the one that has the best orthogonal properties, thus the one that should be more robust to ambiguity between the parameters considered here. Full waeform inersion problem The inerse problem is formulated as the minimization of a least squares problem: min f : [ u( m, x, x, t d( x, x, t] dt m s, r T s r where u is the synthetic data, d is the obsered data, m represents the model parameters, x s is the source position and x r is the receier position. The non-linear inerse problem is soled with a preconditioned steepest-descent method. The inerse problem is formulated in terms of the new parameterization, and the gradient for each one of the PTS parameters is obtained through the chain rule: f J (,, f (,, where J is the Jacobian matrix and, f s r (3 (4 (5 (6 014 SEG SEG Dener 014 Annual Meeting DOI Page 1051

3 A new parameterization for anisotropy update in full waeform inersion T f f f f f f f T f ; Finally, the gradient of the misfit function with relation to a elocity, delta and epsilon are computed using the adjointstate method (see, for example, Plessix, 006. North Sea dataset example We apply the anisotropic FWI update to a ariable-depth streamer dataset acquired in the North Sea (Jupp et al., 01 with PTS. In this case a VTI model is appropriate and the ertical elocity, epsilon and delta parameters are discretized with a 56.5 m grid. In the inersion we consider three frequency bands with high frequency cut-off filters applied at 5, 6 and 7 Hz, respectiely, and the algorithm iterates 8 times in each frequency band. The inerted data set comprises ~116,000 sources and ~186 million traces, coering a total area of oer 1000 km. We use the same pre-processing for FWI as described in Jupp et al. (01. Figure 3a-d shows an oerlay of a Kirchhoff migrated section, used here for QC only, with the starting elocity, inerted elocity, starting epsilon and inerted epsilon models, respectiely. The inerted elocity model shows ery good agreement with geological structures such as the shallow channels, the de-watering faults (i and the low elocity anomaly thought to be a small gas cloud (ii aboe a salt diapir. The inerted epsilon model also captures the gas cloud (iii, showing a significant decrease here. The inersion also builds anomalies with higher epsilon in the centre of the contourites (i. This is in agreement with the expectation that these geological features are filled with a more shale rich sediment than the neighbouring areas. Figures 4a-d, show depth slices at 90 m of the starting elocity, starting epsilon, inerted elocity and inerted epsilon models, respectiely, oerlaid with a Kirchhoff migration (note the data oid due to infrastructure in the area. As one can see, the FWI captured the structural details associated with the contourites in both the elocity and epsilon models. The waelength of the anomalies in the epsilon model appears larger than the waelength of the inerted anomalies in the elocity model. In addition, one can obsere regions where elocity and epsilon both increase or decrease together, as well as regions where they increase or decrease in opposition to one another. While not a definitie conclusion, this does gies some eidence of mitigation in the parameter cross-talk. Finally, in figure 5 we show sections that hae been Kirchhoff migrated using the starting and inerted models. Here we see a clear uplift in the image quality (see red arrows as the FWI model has fixed the pull-up and pushdown distortions caused by the shallow channels, as well as improing the strength of the reflectors in places. (i (ii (iii (i Figure 3 Vertical sections of: (a starting elocity model, (b inerted elocity model, (c starting epsilon model, and (d inerted epsilon model. 014 SEG SEG Dener 014 Annual Meeting DOI Page 105

4 A new parameterization for anisotropy update in full waeform inersion Figure 4 Depth slices at 90 m of: (a starting elocity model, (b starting epsilon model, (c inerted elocity model, and (d inerted epsilon model. Note the data oid due to infrastructure in the area on the left-middle of eery image. Figure 5 Stack sections obtained with Kirchhoff pre-stack migration for: (a the starting model, and (b the anisotropic inerted FWI model. Red arrows point to significant uplift. Conclusions We hae presented a new parameterization in the context of FWI for the automatic building of ertical elocity and epsilon models in VTI anisotropy. These parameters hae better orthogonal properties in comparison to other kinematically equialent sets. This is an attempt to reduce the ambiguity when jointly estimating anisotropy and elocity from surface seismic data using FWI. A real data example from the North Sea shows that our approach is suitable for obtaining both elocity and epsilon models from FWI. This approach can be extended naturally to other types of anisotropy scenarios, for example tilted transerse isotropy (TTI. Acknowledgements We thank CGG for permission to publish this work and to show the data from the UKCS Cornerstone 3D surey. We would also like to thank Stee Thompson in the CGG Crawley office for his geological interpretation of our FWI results. 014 SEG SEG Dener 014 Annual Meeting DOI Page 1053

5 EDITED REFERENCES Note: This reference list is a copy-edited ersion of the reference list submitted by the author. Reference lists for the 014 SEG Technical Program Expanded Abstracts hae been copy edited so that references proided with the online metadata for each paper will achiee a high degree of linking to cited sources that appear on the Web. REFERENCES Dueneck, E., P. Milcik, P. M. Bakker, and C. Perkins, 008, Acoustic VTI wae equations and their application for anisotropic reerse-time migration: 78 th Annual International Meeting, SEG, Expanded Abstracts, Gholami, Y., R. Brossier, S. Operto, V. Prieux, A. Ribodetti, and J. Virieux, 011, Acoustic VTI fullwaeform inersion: sensitiity analysis and realistic synthetic examples: Presented at the 81 st Annual International Meeting, SEG. Jupp, R., A. Ratcliffe, and R. Wombell, 01, Application of full-waeform inersion to ariable -depth streamer data: Presented at the 8 nd Annual Meeting, SEG. Operto, S., Y. Gholami, V. Prieux, A. Ribodetti, R. Brossier, L. Metiier, and J. Virieux, 013, A guided tour of multiparameter full-waeform inersion with multicomponent data: From theory to practice: The Leading Edge, 3, , Plessix, R.-E., 006, A reiew of the adjoint-state method for computing the gradient of a functional with geophysical applications : Geophysical Journal International, 167, no., , Plessix, R.-E., and Q. Cao, 011, A parameterization study for surface seismic full waeform inersion in an acoustic ertical transersely isotropic medium: Geophysical Journal International, 185, no. 1, , Plessix, R.-E., and H. Rynja, 010, VTI full waeform inersion: A parameterization study with a narrow azimuth streamer data example: 80 th Annual International Meeting, SEG, Expanded Abstracts, , Prieux, V., R. Brossier, Y. Gholami, S. Operto, J. Virieux, O. I. Barked, and J. H. Kommedal, 011, On the footprint of anisotropy on isotropic full-waeform inersion: The Valhall case study: Geophysical Journal International, 187, no. 3, , Stopin, A., and R. E. Plessix, 014, Land seismic data multi-parameter waeform inersion: Presented at the 76 th Annual International Conference and Exhibition, EAGE. Stoas, A., 008, Kinematically equialent elocity distributions : Geophysics, 73, no. 5, VE369 VE375, Thomsen, L. A., 1986, Weak elastic anisotropy: Geophysics, 51, , Vinje, V., A. Stoas, and D. Reynaud, 013, Presered-traeltime smoothing: Geophysical Prospecting, 61, , Wang, C., D. Yingst, R. Bloor, and J. Leeille, 01, VTI waeform inersion with practical strategies: Application to 3D real data: Presented at the 8 nd Annual International Meeting, SEG. 014 SEG SEG Dener 014 Annual Meeting DOI Page 1054

6 Warner, M., A. Ratcliffe, T. Nangoo, J. Morgan, A. Umpleby, N. Shah, V. Vinje, I. Stekl, L. Guasch, C. Win, G. Conroy, and A. Bertrand, 013, Anisotropic 3D full-waeform inersion: Geophysics, 78, no., R59 R80, Zhang, Y., H. Zhang, and G. Zhang, 011, A stable TTI reerse-time migration and its implementation: Geophysics, 76, no. 3, WA3 WA11, SEG SEG Dener 014 Annual Meeting DOI Page 1055