Enhancing the resolution of CSEM inversion using seismic constraints Peter Harris*, Rock Solid Images AS Lucy MacGregor, OHM Surveys Ltd Summary The vertical resolution of inverted CSEM data remains an important issue for its optimal exploitation. In this paper we use a modified simulated annealing (SA) algorithm to remap the inverted CSEM data, in the form of resistivity profiles in depth, into the seismic resolution. Our modification of the SA algorithm solves not only for a best-fitting model, but also for parameters describing the probability density functions for the resistivity in each layer. This allows us to monitor the uncertainty of our resistivity estimates within the layers. In fact we find that the expected value of the shows better agreement with the well log than the best-fit model, although the latter has a lower misfit when compared with the surface EM data. In application to the Nuggets-1 field, we find that the method correctly locates the anomaly associated with the gas sand. The seismic layer is thicker than the gas sand as determined from the well logs, and therefore our estimate of resistivity remains lower than the well log values. Introduction It is widely recognised that the vertical resolution of CSEM data inverted to resistivity with depth is poorer than that of seismic data, due to the diffusive nature of EM energy propagation. In order to investigate rock and fluid properties at seismic resolution, we would like to sharpen the resistivity image before combining it with the seismic information. Separating the resolution enhancement from the process of combination allows us to calibrate the rock physics models used in the latter, as described by Harris and MacGregor (26). Our starting point is a resistivity profile in depth, inverted from the recorded CSEM data using the methods of MacGregor et al (26), and a set of seismic events. These may be picked automatically, by interpretation, or by a combination of both. In this study we used an automatic technique for event identification from seismic attributes developed by M.T.Taner (pers. comm.). The resistivities are then mapped into the seismically-derived layers. This process is justified by the observation that the product of thickness and resistivity is well-resolved by the CSEM inversion (MacGregor et al, 26) even though the individual factors of thickness and resistivity are not. To deal with the high degree of non-uniqueness in this process, we use a modified simulated annealing algorithm to perform the remapping. The result of the remapping is a probability density function () for the resistivity within each layer, allowing us to investigate the uncertainties in the result. In theory this method does not require any well data. However, in practice the seismic events must be mapped from time to depth and this has to be verified by a well-tie. In addition, the resistivity inversion may require depth constraints in order to fix the absolute depths at which anomalies occur. Thus in practice well information is a requirement, although our remapping does not use it explicitly. The Remapping Technique The simulated annealing (SA) algorithm is described in many publications, for example Kirkpatrick et al (1983). In order to understand the uncertainties, we generate models and test for acceptance in the usual way; if the model exhibits a lower misfit than our current best model it is accepted unconditionally, whereas if it results in a higher misfit then it may be accepted with a probability dependent on the current temperature. Figure 1 shows the number of 5 45 4 35 3 25 2 15 1 5 Number of models accepted 5 1 15 2 Figure 1: Number of models accepted per temperature iteration of the simulated annealing. The red curve is the number of accepted models causing the objective function to increase. This decreases as the temperature decreases. The blue curve is the number of accepted models causing a decrease in the objective function. The number remains more or less constant. SEG/San Antonio 27 Annual Meeting Downloaded 21 Feb 212 to 216.198.85.26. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 64
accepted models at each temperature from one run. The blue curve, the number of models where the misfit decreases, is more or less constant, whereas the red curve, which plots the number of accepted models where the misfit increases, starts high but finally drops down to a very small value at low temperatures. At each temperature in the SA cooling schedule, we use the ensemble of accepted models to construct an explicit lognormal for the resistivity in each layer. These s are then sampled at the next, lower temperature step of the SA optimisation. At the start, the s have a constant low expected value (1.5 Ωm in this example) and a very wide spread, but their variances decrease as the iterations proceed thus sharpening the estimates. The sampling strategy also reduces the number of unacceptable models generated, thus improving the run time. Figure 2 shows an example of the evolution of the s in one layer over the course of the cooling schedule..7.6.5 Example We illustrate the method using data from the Nuggets-1 field, described in a previous publication by MacGregor et al (26). We concentrate on the data at the well location in order to verify the method. Figure 3 shows the results at the well location. The magenta curve is the original resistivity from the inverted CSEM data. The anomalous region extends over about 25 metres in depth. The red curve shows the best fitting model obtained from one run of the SA process, and the green curve is the expected value of the corresponding. The blue curve is the deep resistivity log from the well. The expected value curve, in green, seems to predict the well log better than the best fitting model. The anomalous peak in the best fitting model just before 16 metres depth is much higher in resistivity than the expected value in that layer. It seems to be associated with the asymmetry of the anomaly in the inverted CSEM data (magenta). The for that layer is plotted in figure 4. The wide spread of the at this depth indicating a high level of uncertainty in the result is most likely also a consequence of the asymmetry..4.3.2.1.1.9.8.7.6 Anomalous layer 1 2 3 4 5 Figure 2: Figure 2: s for one layer in the resistivity.2 model, plotted for every 2 th temperature. As the system cools, the s are sharpened, in this case converging on a.1 low value around 1Ωm. 1 2 3 4 5.5.4.3 In order to stabilise the inversion, the misfit function has three terms. One is of course the discrepancy between modelled and actual data. The second penalises deviations from an initial model. This is most important in the deepest few layers to ensure stability, and typically in most layers this term is heavily downweighted and not significant. The third term is an entropy measure designed to encourage sparseness, since we assume that the resistivity anomalies are localised within a few layers rather than spread over the entire depth range. Figure 4 Final for the anomalous layer at just above 16 m. The green point shows the expected value, and the red point marks the best fit model. The spread of this remains quite high. Figure 5 shows the for the gas sand layer. Again the spread of the is quite high, reflecting a degree of uncertainty in the value. It is also evident that the estimated value is less than the well-log resistivity. This may be partly because the seismic layer thickness, into which the SEG/San Antonio 27 Annual Meeting Downloaded 21 Feb 212 to 216.198.85.26. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 65
resistivity is mapped, is greater than the resistive anomaly determined from the log..25 Gas Sand Layer Discussion Vertical resolution is a key issue for CSEM data. Sharpening the data is an ill-posed deconvolution problem, which requires additional data to reduce the nonuniqueness of solutions. Here we use seismic relative impedance layering as a source of information. This assumes, of course, that seismic boundaries and resistivity boundaries coincide. In our experience to date, this assumption has held reasonably well..2.15.1.5 Generating s permits the exploration of the uncertainties associated with the results. A further important refinement, not shown here, is to analyse the posterior covariances between nearby layers. As expected, we find correlations over a depth range corresponding to the resolution of the inverted CSEM data going into the remapping process. 2 4 6 8 1 Figure 5: Final for the gas sand layer. The green point shows the expected value, and the red point marks the best fit model Having achieved this sharpening of the data, we are better positioned to obtain rock and fluid properties from combined CSEM and seismic data as described by Harris and MacGregor (26). The influence of the lower CSEM resolution may be seen in their gas saturation image as the speckle at levels above and below the gas sand. Acknowledgements The seismic data are shown by courtesy of TGS-Nopec. The authors would like to acknowledge the support of the ITF, and thank BP, Total, ENI and Shell for their support of the Nuggets CSEM project. We would also like to thank Total for access to the Nuggets-1 field, and their assistance in operating there. SEG/San Antonio 27 Annual Meeting Downloaded 21 Feb 212 to 216.198.85.26. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 66
1 9 8 7 6 5 4 3 2 1 14 15 16 17 18 19 2 21 22 23 24 Depth m Figure 3: Results of the remapping at the well. Magenta: original inverted CSEM data, Red: best fitting model from this SA run, Green: Expected value of the final in each layer, Blue: well log resistivity. The extent of the vertical resolution in the inverted CSEM data may be readily seen by comparing the magenta curve with the blue well log response. The green expected value curve does a reasonable job of mapping the inversion result into the seismic layer thicknesses. The asymmetry of the inversion response generates the high resistivity values above the true anomaly, SEG/San Antonio 27 Annual Meeting Downloaded 21 Feb 212 to 216.198.85.26. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 67
EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 27 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Harris, P. E., and L. MacGregor, 26, Determination of reservoir properties from the integration of CSEM and seismic data: First Break, 24, 15 21. Kirkpatrick, S., C. D. Gelatt Jr., and M. P. Vecchi, 1983, Optimization by simulated annealing: Science, 22, 671 68. MacGregor, L., D. Andreis, J. Tomlinson, and N. Barker, 26, Controlled source imaging on the Nuggets-1 reservoir: The Leading Edge, 25, 984 992. SEG/San Antonio 27 Annual Meeting Downloaded 21 Feb 212 to 216.198.85.26. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/ 68