175 7. Integrated seismic study 7.3 Depth conversion A geostatistical approach for time-to-depth conversion of seismic horizons is often used in many geo-modelling projects. The more appropriate kriging method for this problem is the Bayesian Kriging method (Sandjivy and Shtuka, 2009). The Bayesian approach provides an excellent estimation, which is more general than the traditional kriging with external drift(s) and fits very well with the requirements for time-to-depth conversion of seismic horizons. For each selected horizon, Bayesian Kriging (BK) provides its estimated depth Z associated with its time t, in agreement with all the calibration points (well tops depth…). BK depth conversion also provides the underlying interval velocity model (trend and residual), and associated quantified uncertainties. The BK depth conversion simultaneously updates the estimated depths of all the seismic horizons. Figure 7.10 illustrates the time-to-depth conversion of seismic horizons by the BK method, using the UDOMORE depth software developed by Seisquare. The advantage of using the Bayesian Kriging (BK) for estimations compared to other approaches is that we can simultaneously manage the uncertainty on the trend velocity model and the local uncertainty defined by the uncertainty of interpreted time maps and local fluctuations of interval velocities. The input information required for BK consists of: • two-way-time (TWT) maps for interpreted horizons, • well markers for each horizon, • prior velocity model and associated uncertainty for each layer, • local uncertainty definition for each time map (picking uncertainty, and spatial variogram definition), • local uncertainty definition of interval velocity for each layer (local velocity fluctuations around the trend model, and spatial variogram definition). Like any kriging-based estimation approach, the Bayesian Kriging (BK) provides: • the estimated variable (estimated depth for each horizon), • variance of estimation (associated uncertainty of estimated depth). The advantage of using BK in depth conversion is that it provides the ability to combine the prior knowledge of the velocity model with a certain degree of uncertainty and the well data. All sources of uncertainty (velocity and time) are integrated in a consistent way in a unique probabilistic model used for estimation or simulation. For each selected horizon, the Bayesian Kriging provides its estimated depth Z associated with its time t. The “Z versus t” data set is interpolated in the whole space (3D block) at the time sampling rate (1 ms) to obtain a time-to-depth conversion model, using the impedance sections to estimate the short wavelength variations of the velocity model.
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