SUMMARY INTRODUCTION WHICH WAY?

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1 Apparent horizontal in timelapse seismic images Dae Hale 1, Barbara Cox 2 and Paul Hatchell 2 1 Center for Wae Phenomena, Colorado School of Mines 2 Shell International E&P SUMMARY In addition to ertical time shifts commonly obsered in timelapse seismic images, horizontal are apparent as well These apparent horizontal may be small relatiely to seismic waelengths, perhaps only 5 m at depths of 5 km, but they consistently suggest an outward lateral expansion of images away from a compacting reseroir It is well known that apparent ertical are caused mostly by a decrease in seismic wae elocities aboe compacting reseroirs Those same elocity changes contribute to horizontal This contribution can be computed from the elocity changes that, in turn, can be estimated from measured ertical Horizontal computed in this way are similar to those measured, and this similarity suggests that horizontal as well as ertical may be largely due to elocity changes INTRODUCTION Physical of rocks during reseroir compaction cause apparent in timelapse seismic images Figures 1a and 1b illustrate an example of apparent ertical (time shifts) measured from two seismic images of a highpressure hightemperature reseroir in the North Sea Figure 1a shows three orthogonal slices from a 3D seismic image acquired in 2002 Lines in each of the three slices indicate where they intersect in 3D The one point where all three slices intersect lies just beneath the target reseroir To monitor changes in that reseroir, a second 3D seismic image (not shown) was acquired in 200 By crosscorrelating these two 3D images for many oerlapping windows, we obtain estimates of apparent ertical δt like those shown in Figure 1b These measured apparent ertical δt are mostly positie; that is, ertical twoway reflection times generally increase from 2002 to 200 Hatchell and Bourne (2005a, 2005b) show that such increases are caused mostly by a decrease in seismic wae elocity in rocks aboe the reseroir as those rocks are stretched by reseroir compaction In this sense, Figure 1b is an image of a lowelocity lens And if not accounted for in seismic migration (as it was not here), this lens aboe the reseroir will cause apparent horizontal that may obscure any concurrent physical horizontal of subsurface rocks Displacements in 3D are ectors with three components ertical, inline and crossline and with careful processing we can measure all three Figures 1c and 1d show measured inline (δx) and crossline (δy) components of apparent corresponding to the same two images acquired in 2002 and 200 Like the ertical in Figure 1b, these apparent lateral are not constant Both δx and δy ary as functions of ertical time t, inline distance x and crossline distance y Together the three components δt, δx and δy comprise a 3D apparent displacement ector field Figures 1c and 1d suggest that apparent in the inline and crossline directions are less consistent than those in the ertical direction Most measured lateral are less than 5 m, which is relatiely small compared with horizontal sampling interals (inline and crossline trace spacings) of 25 m But the largest of these measured lateral appear to be spatially correlated with the reseroir location Specifically, they imply that, near the reseroir, the seismic image is expanding horizontally In this paper we show that much of this apparent horizontal expansion can be explained by the lowelocity lens aboe the reseroir in 200 Using the concept of image rays, we show that horizontal like those in Figures 1c and 1d are consistent with an expected expansion outward, away from the center of the reseroir where ertical compaction is largest Moreoer, from the measured ertical displayed in Figure 1b, we can estimate the location, size and shape of the lowelocity lens and then compute expected magnitudes of corresponding horizontal We show below that those computed magnitudes are approximately 5 m near the reseroir, with a spatial pattern that is consistent with measured WHICH WAY The processing used to measure the apparent shown in Figures 1b 1d began with local 3D predictionerror filtering of the two 3D seismic images (Hale, 2007) This processing was local in that for each image sample we computed a different 3D predictionerror filter from a 3D autocorrelation of only nearby samples When applied to the 3D seismic image of Figure 1a, local 3D predictionerror filtering yields the less coherent image displayed in Figure 2 As expected, local predictionerror filtering has attenuated laterally coherent features, while presering those features in our images that best enable us to resole all three components of displacement Without this filtering, are well defined in only those directions perpendicular to features that (in seismic images) tend to be planar or linear within small crosscorrelation windows Local 3D predictionerror filtering attenuates such locally predictable features, thereby leaing only a less predictable, more random texture from which we can measure three components of displacement Furthermore, by highlighting pointlike features that tend to scatter seismic waes in all directions, this filtering simplifies our analysis of lateral We need not be concerned with specular reflections from subsurface interfaces dipping at arious angles Instead, we need only consider diffractions from scattering points Figure 3 illustrates diffractions in 2002 and 200 for a single stationary point in the subsurface In this example, we assume that the point is located on the left side of a compacting reseroir Compaction causes a dilation of rocks aboe the reseroir and a corresponding decrease in elocity, so that elocity in 200 tends to decrease from left to right aboe this point This lefttoright decrease in elocity will cause a righttoleft displacement of diffractions Velocities directly aboe the diffracting

2 Apparent horizontal ertical (time) δt(t, x, y) (ms) image 2002 (b) (a) inline δ x(t, x, y) crossline δ y(t, x, y) 6 (c) (d) Figure 1: Slices (a) of a 3D seismic image recorded in 2002 A second image (not shown) was recorded in 200 Vertical (b) components of apparent displacement are measured in ms; inline (c) and crossline (d) components are measured in m Crosshairs in each slice show the locations of the other two slices point are lower in 200, so that seismic waes propagating there will arrie at the surface later than they did in 2002 The shortest twoway traeltime in 200 corresponds to an image ray (Hubral, 1975, 1977; Larner et al, 1981) that emerges to the left of the diffracting point, where elocity is higher Therefore, where elocity decreases from left to right, the peaks of diffractions will shift from right to left Now imagine the effect of migration on these two diffractions, where the same migration elocities (the 2002 elocities) are used for both We would typically use the same elocities, in part because we might not yet know how elocities hae changed in 200 Migration will collapse the diffractions to construct pointlike features in migrated images In migrated time sections, each imaged point will appear at the apex of its corresponding diffraction cure The point in 200 will be imaged to the left of the point in 2002 Assuming that the point in Figure 3 was correctly imaged in 2002, then that same point will be incorrectly imaged in 200 to the left of its true location On the opposite side of the reseroir, where elocity in 200 decreases from right to left, pointlike features in 200 will be imaged to the right of their true locations Therefore, the effect of the lowelocity lens aboe the reseroir in 200 is an apparent expansion of the image beneath that lens Of course, the horizontal displacement of diffractions in Figure 3 is greatly exaggerated Recall that measured are roughly 5 m at depths of 5 km This illustation explains only the direction, not the magnitude, of the of diffractions and imaged points that we may expect as elocity aboe a compacting reseroir decreases HOW FAR To quantify apparent horizontal, we must first quantify the change in elocity from 2002 to 200, and then compute image rays for 200 like the one shown in Figure 3 We can estimate the change in elocity from the apparent ertical in time δt shown in Figure 1b Let dz = dt denote the distance that a seismic wae in 2002 traels ertically downward with elocity in time t Assuming that changes δ z, δ and δt from 2002 to 200 are small, we hae d(δ z) = δ dt + d(δt) and d(δ z) δ d(δt) εzz = + (1) dz dt Here εzz d(δ z)/dz denotes ertical strain The quantity d(δt)/dt is sometimes called time strain (eg, Rickett, 2006) An alternatie

3 Apparent horizontal tions is too lengthy to proide here, but is analogous to that used to obtain equation 1 Combining those perturbations with equation 2, we obtain the following expressions for horizontal δ x(t, x, y) and δ y(t, x, y): image 2002 after local predictionerror filtering t R 1+R 0 Z t R δy = 1+R 0 Z δx = 2 2 (δt) dt, x (δt) dt y (3) In both of these expressions, t denotes the same twoway ertical traeltime labeled in Figures 1 As suggested by Cox and Hatchell (2008), we may express both lateral and ertical in terms of a single timeshift potential function φ = φ (t, x, y) defined by Figure 2: Slices of the image of Figure 1a after local 3D predictionerror filtering to highlight scattering points (Note that the amplitude scale is ten times smaller in this figure) The same filtering was also applied to a second image (not shown) recorded in 200 φ Z t 2 0 () δt dt, so that x δx δx = elocity decreasing in 200 diffractions z, t R φ, 1+R x δy = R φ, 1+R y δt = φ 2 t (5) Equations and 5 proide rather simple relationships between apparent horizontal δ x(t, x, y) and δ y(t, x, y) and apparent ertical δt(t, x, y) Because we hae measured all three components of displacement (displayed in Figures 1b 1d), we can test these relationships TESTING Figure 3: Image rays and diffractions in 2002 and 200 for a single diffracting point located below and left of a lowelocity lens present only in 200 Aboe this point, elocity in 200 decreases from left to right Horizontal displacement δ x here is greatly exaggerated All image rays are ertical at the surface phrase that extends well to three components of apparent displacement is apparent strain Hatchell and Bourne (2005a, 2005b) show that the fractional change in elocity is well approximated by δ / = Rεzz, where R 5 for rocks aboe many different compacting reseroirs around the world With equation 1, we see that this same fractional change in elocity is also proportional to apparent ertical strain: δ R d(δt) = 1 + R dt (2) In other words, gien measured apparent δt(t, x, y) like those in Figure 1b and interal elocities (t) measured in 2002, we can estimate changes in elocity δ (t, x, y) With δ (t, x, y), we may then use image ray tracing to estimate apparent horizontal δ x(t, x, y) or δ y(t, x, y) This ray tracing is greatly simplified by the obseration that, because elocity changes δ (t, x, y) are small, image rays ertical at the surface remain essentially ertical in the subsurface Apparent δ x and δ y are small fractions of reseroir depths, and are well approximated by small perturbations to ertical image rays Our deriation of timelapse perturbations to image ray tracing equa Equations and 5 enable us to test the hypothesis that apparent horizontal, like apparent ertical, are caused mostly by decreases in seismic elocities aboe a compacting reseroir If this hypothesis is alid, then δ x(t, x, y) and δ y(t, x, y) that we compute ia equations and 5 from measured δt(t, x, y) should be comparable to our measured δ x(t, x, y) and δ y(t, x, y) Discrepancies might suggest other explanations not considered here, such as physical horizontal or changes in seismic anisotropy, as well as errors in our measurements Any δ x(t, x, y) and δ y(t, x, y) that we compute from measured δt(t, x, y) will of course hae errors In this respect, the integration oer time t in equation has both adantages and disadantages On the one hand, this integration performs a smoothing that will tend to attenuate errors in δt(t, x, y) that are amplified by lateral deriaties φ / x and φ / y On the other hand, integration enables errors in δt(t, x, y) for small times to alter the δ x(t, x, y) or δ y(t, x, y) computed for all times Unfortunately, errors in δt(t, x, y) can be large for small times t, where image quality is often degraded as seismograms recorded with large sourcereceier offsets are muted In timelapse imaging, any ariations in seismic acquisition or muting patterns hae a more significant effect on earlier reflections than on later ones Therefore, we should generally aoid integrating from time t = 0 in equation Although not displayed in Figure 1b, measured ertical δt for times t = 0 to 2 s are negligible in this example, except for a brief range (less than 100 ms) of small times t where the errors cited aboe are largest Therefore, when computing φ ia equation, we replaced the lower limits of integration t = 0 with t = 2 s, the beginning of the time window displayed in Figures 1

4 Apparent horizontal computed inline δx(t,x,y) computed crossline δy(t,x,y) (a) (b) Figure : Computed (a) inline and (b) crossline components of apparent displacement ectors, in m Compare with Figures 1c and 1d In addition to measured apparent ertical δt, application of equations and 5 requires estimates for interal elocities (t) and R We estimated the function (t) using depths and times measured in a checkshot surey The parameter R is more difficult to estimate, but for large alues of R 5 the ratio R/(1 + R) is fairly insensitie to uncertainties in R We assumed a constant R = 5 For the sampled images in this example, we used a simple sum to approximate the integral oer time t in equation, and a twosample centered finitedifference approximation to the partial deriaties φ/ x and φ/ y in equations 5 The apparent horizontal computed in this way are displayed in Figures Computed horizontal displayed in Figures a and b are clearly not the same as the measured horizontal in Figures 1c and 1d In particular, computed horizontal are noticeably smoother in time than measured horizontal Still, the spatial patterns of the larger are comparable Both computed and measured imply an apparent lateral expansion And near the reseroir magnitudes of computed horizontal are approximately 5 m, consistent with measured horizontal Moreoer, although our deriation and computations here are different, the computed horizontal shown in Figures a and b are generally consistent with those shown by Cox and Hatchell (2008) They also show that δx and δy computed from measured δt are comparable to those computed by raytracing for a elocity function + δ estimated from a geomechanical model CONCLUSIONS This research began with the unexpected obseration that timelapse seismic images appear to expand laterally away from a compacting reseroir The simplest explanation for these apparent horizontal is that they are caused primarily by a decrease in seismic wae elocities aboe the reseroir That decrease in elocities is well understood to be largely responsible for the apparent ertical that we today measure routinely in timelapse imaging The concept is simple Waes that trael through thick layers of rocks with elocities that hae decreased slightly will arrie slightly later in time The extension of this concept to horizontal is only a bit more complex, requiring only an understanding of how waes are focused by a lowelocity lens, and how that focusing alters seismic images that hae not been processed to account for it To account for changes in elocity, we must first quantify them The method presented in this paper uses lateral deriaties of measured apparent ertical to estimate releant lateral changes in elocity Image ray approximations then proide a simple method for computing apparent horizontal in timelapse seismic images Our ability to compute apparent horizontal caused by elocity changes leads to an interesting question If we subtract any horizontal that we compute from those we measure, are we left with physical horizontal Before we can answer this question, we must better understand the accuracy with which we can measure from seismic images, as well as the spatial resolution of those measurements The processing used here was tuned to enable measurements of all three components of, and care was taken to maximize the fidelity of each step in this processing But the we measure may be small fractions of seismic waelengths, and a tradeoff between accuracy and resolution is unaoidable The results shown in this paper suggest that future work to improe our understanding of accuracy and resolution in timelapse seismic imaging is worthwhile We should ideally measure from unstacked seismic images, because the effects of a lowelocity lens will ary for different sourcereceier offsets We might also consider additional contributions to apparent lateral, such as those resulting from changes in seismic anisotropy Similarities and differences like those shown here between computed and measured horizontal are interesting It remains to be seen whether they can be made meaningful ACKNOWLEDGMENTS We thank Shell UK Limited and the Shearwater partnership (Shell, BP, and ExxonMobil) for proiding access to their timelapse seismic images and permission to publish results deried from them

5 Apparent horizontal REFERENCES Cox, B and P Hatchell, 2008, Straightening out lateral shifts on timelapse seismic data: First Break, May, 2008 (submitted) Hale, D, 2007, A method for estimating apparent displacement ectors from timelapse seismic images: 77th Annual International Meeting, SEG, Expanded Abstracts, Hatchell, P and S Bourne, 2005a, Measuring reseroir compaction using timelapse timeshifts: 75th Annual International Meeting, SEG, Expanded Abstracts, Hatchell, P and S Bourne, 2005b, Rocks under strain: Straininduced timelapse time shifts are obsered for depleting reseroirs: The Leading Edge, 2, Hubral, P 1975, Locating a diffractor below plane layers of constant interal elocity and arying dip: Geophysical Prospecting, 23, Hubral, P 1977, Time migration Some ray theoretical aspects: Geophysical Prospecting, 25, Larner, KL, L Hatton, BS Gibson, and I Hsu, 1981, Depth migration of imaged time sections: Geophysics, 6, Rickett, JE, L Duranti, T Hudson, and N Hodgson, 2006, Compaction and D time strain at the Genesis Field: 76th Annual International Meeting, SEG, Expanded Abstracts,