3D S wave statics from direct VSP arrivals Michael J. O'Brien, Allied Geophysics, and Paritosh Singh, Colorado School of Mines

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1 3D S wave statics from direct VSP arrivals Michael J. O'Brien, Allied Geophysics, and Paritosh Singh, Colorado School of Mines Summary We observe that direct S wave arrivals in 3D VSP data contain the information needed to find the S wave statics solution for 3D surface seismic. This solution is independent of P wave data. We show S wave statics computed from VSP data can improve the alignment of shear reflections seen on 3D surface seismic shot records, making these events easier to analyze and process with common flat earth assumptions. Introduction The derivation of source statics from VSP first breaks is not new. It has commonly been done for walkaway VSPs (Kragh et al., 1991; Liu and Owusu, 2005; Libin et al., 2009), and also for 3D VSPs (Paulsson et al., 2004). In these prior works, the statics found from VSP data were applied only to VSP data. It is also well known that VSPs and surface seismic have many complementary attributes, including statics (Constance et al., 1999). Kragh et al. (1991) showed that, by using downhole sources in a so called hole to surface geometry, a receiver Figure 1. Field data (top) show discontinuity in the S wave first arrivals of a VSP. Similar discontinuities are seen in S wave model data (bottom). The difference between a smooth predicted first break surface and the discontinuous picked surface is the basis for a statics solution. (a) is inline source, inline receiver and (b) is xline source, xline receiver. Figure 2. The surface to hole geometry at left is used to determine source statics for 3D surface seismic data. The holeto surface geometry at right is used to determine receiver station statics. statics solution is also available. An example of applying P wave statics derived from VSP data to surface shot records was shown by Tabakov and Baranov (2007). Here we propose to combine the ideas of Tabakov and Baranov with those of Kragh et al., to find a complete S wave statics solution for 3D surface seismic data. Method Since we have limited field data, the examples shown in this study come from a 3D, anisotropic, elastic model; however, the field data we do have has the same character that we exploit with model data examples (Figure 1). In order to get a complete statics solution, two VSPs are needed. First we record data from surface sources into downhole receivers, and then from downhole sources into surface receivers (Figure 2). The 3D source and receiver line geometry we modeled is shown in Figure 3. We acquired 16 source lines and 16 orthogonal receiver lines. Both source and receiver lines are separated by 200 m; stations along the lines are separated by 33 m. The underlying map in Figure 3 is a color contour map of one way S 2 wave (slow shear wave) time through the near surface of the model. The differential static across the map area is sec. In addition to building a near surface problem into the model, HTI anisotropy has also been added. The Thomsen parameter gamma and the azimuth of HTI isotropy planes vary in space (O'Brien, 2010). Our current work emphasizes S wave statics only, though much more could be learned by analyzing the many other facets of the 3D 9C data. Our method is straight forward: fit a least squares hyperboloid to the S wave first break picks and apply the time differences between picks and the hyperboloid as a statics solution for surface seismic data. If necessary, a more sophisticated fit

2 could be used. The closer the fitting method is to the real problem, the more accurate the surface fit will be. We picked first break on raw data and no effort was made to align source and receiver components to the principal anisotropy axes of the model. The equation for a hyperboloid can be expressed as t 2 = S x 2 x 2 S y 2 y 2 S z 2 z 2, where S x,s y, S z is a slowness vector, x, y, z are spatial coordinates and t 2 is the hyperbolic surface. Since each first break pick is characterized by t, x, y, z, minimizing the squared error between squared pick times and the t 2 surface produces coefficients of squared slowness in three directions (Figure 4). This means that aside from a statics solution, information about the maximum horizontal stress direction in the HTI medium is also available. Discussion Figure 3. Modeled 3D source lines are shown in red. 3D receiver lines are shown in blue, and the VSP well is at the black dot near the center. The color contours beneath show the one way vertical S 2 wave (slow shear wave) times in the model. Differential statics across the map area are as high as sec. Figure 4. For a source at depth, straight rays that intersect the surface at a given time will form an ellipse. The shape and size of the ellipse change as members of the slowness vector S x, S y, S z change. Figure 5 shows an example of how the least squares hyperboloid (blue) fits the first break picks (red) for source lines 3 and 9. The difference between the two surfaces can be called the relative static for the surface position of the data (either a source or receiver station). Using surface to hole and hole to surface VSP datasets, source statics and receiver statics can be computed independently or simultaneously. Maps of independently computed source and receiver statics are shown in Figures 6a and 6b. Similarities in the shapes of the anomalies are a good indication that the solutions are consistent and correct. It is also possible to use source and receiver statics together to find a unified, surface consistent solution. To compute the surface consistent solution, our method of least squares surface fitting requires a single location for both source and receiver. This might be achieved Figure 5. Red points in the two upper graphs show first break picks for source lines 3 and 9. The blue points show the least squares hyperbolic fit to picks. The difference between picks and fit represent the relative statics solution. That relative statics solution is plotted in green points in the bottom part of the figure.

3 A B C Figure 6. Statics solutions can be computed from source data alone (A), receiver data alone (B) or from source and receiver data simultaneously (C). In these images, the least squares fit of all three data combinations results in statics maps with the same overall structural features. The structural similarity of maps A, B, and C with times computed in the model (Figure 3) give us confidence that the data derived solutions are of high quality. in cased wells using non destructive downhole sources. A statics map that represents such a solution is shown in Figure 6c. An example of applying the statics from Figure 6c to 3D surface seismic data is shown in Figure 7. The upper half of Figure 7 shows common shot data without statics applied, and the lower half shows the same traces after VSP derived S wave statics were applied. The statics corrected data in the lower half of Figure 7 shows a marked increase in continuity of S wave reflections. Using the model for QC Since these data were calculated in a model we can QC our data derived statics by comparing them to vertical times computed directly from the model. Figure 8 shows a comparison between data derived statics (green) and vertical S wave time from the model to a depth of 250 m (magenta). Results for far offset and near offset source lines (Lines 3 and 9 respectfully) are shown in this figure. We observe that at the nearest offsets of Line 9, the data derived statics are a good match to statics taken directly from the model. But we also note that as offset increases toward the ends of Line 9, the data derived static increases relative to those from the model. We also note that on Line 3, which is ~1100 m away from the VSP well, the data derived solution has longer statics delays for the entire source line. We call the extra time seen in the data derived statics a time delay relative to vertical time from the model. Figure 7. S wave 3D surface seismic data without statics applied (top), and with VSP derived S wave statics applied (bottom). After statics are applied, the shallowest high amplitude event has the continuity and hyperbolic shape that will facilitate analysis and processing with common flat earth methods often used.

4 Figure 8. Statics computed vertically to a depth of 250 m in the known model are shown in magenta. Data derived statics are shown in green. The VSP well position is projected onto Line 9 at the arrow. Data derived statics match model statics at the nearest offsets but deviate systematically as offset increases along Line 9 and as source line offset from the VSP well increases (Line 3). To show the cause of this systematic increase in time delay with offset, we extracted a 2D slice, diagonally through the model. That slice starts at the northwest corner of the survey, passes through the VSP well, and ends near the southeast corner of the survey. From the locations where the 2D slice intersects 3D source lines, we traced 2D rays to a downhole receiver (Figure 9). We then accumulated time along ray paths to a depth of 250 m and converted those to time delays relative to vertical time. For the 15 source line intersections we analyzed, we plot the ray traced time delay and the dataderived time delay in the bottom part of Figure 9. While imperfect, there is a general agreement between the two datasets. This suggests that as offsets increase, the assumption that static time delays follow vertical paths is less accurate. Conclusions We have extended the ideas of others to develop an S wave statics solution that is independent of P wave data. The method uses direct arrival S waves from surface to hole and hole tosurface VSP acquisition. We have shown that statics computed in this way can increase the continuity of S wave reflections in 3D surface shot records, making them easier to analyze and process with common tools. Our solution is simplistic in that it uses a least squares hyperbolic fit to a first break time surface. This type of fit assumes horizontal layering and a constant, but directionally variable, velocity field. A more general solution is available if the time surface is created by forward modeling through a heterogeneous model. Finally, because we can compare our solution with vertical times computed in the known model, we are able to show that vertical path assumption of statics corrections becomes less accurate with increasing offset. Acknowledgments We are grateful for support from the Reservoir Characterization Project at the Colorado School of Mines and thank BP for the use of their finite difference modeling tools. Figure 9. Rays traced from surface source lines to a downhole receiver are used to find travel time to a depth of 250 m. Differences between ray time to 250 m and vertical time to 250 m (blue) are plotted along with the discrepancies between dataderived statics and vertical S wave times to 250 m (red). The agreement between ray information and data derived statics indicates that the statics assumption of vertical propagation breaks down at far offset. References Constance, P. E., M. B. Holland, S. L. Roche, P. Bicquart, B. Bryans, S. Gelinsky, J. G. Ralph, and R. I. Bloor, 1999, Simultaneous acquisition of 3 D surface seismic data and 3 C, 3 D VSP data: 69th Annual International Meeting, SEG, Expanded Abstracts, Kragh, J.E., N.R. Goulty, and M.J. Findlay, 1991, Hole tosurface seismic reflection surveys for shallow coal exploration: First Break, 9, Libin, Cao, Wu Furong, and Li Zhiring, 2009, The application of walk away VSP in reef & oolitic reservoir characterization: CPS/SEG Beijing International Geophysical Conference, ID Liu, Qinglin, and John Owusu, 2005, Near surface velocity and static model estimation from downgoing VSP multiples: The Leading Edge, 24, O'Brien, Michael J., 2010, Mounting an offense against poorquality shear data: 80th Annual International Meeting, SEG, Expanded Abstracts,

5 Paulsson, Björn, Martin Karrenback, Paul Milligan, Alex Goertz, Alan Hardin, John O'Brien, and Don McGuire, 2004, High resolution 3D seismic imaging using 3C data from large downhole seismic arrays: First Break, 23, Tabakov, Alexander A. and Konstantin V Baranov, 2007, Integrated land seismic and VSP survey geometries offer improved imaging solution: First Break, 25, D S wave statics from direct arrivals