Seismic Tomography

Time-lapse analysis, required to detect small changes in the reservoir due to fluid movements, often has the problem that the seismic data has been collected with different acquisition configurations and technologies, and thus special processing aimed at rendering the different data sets equivalent is required (e.g. Magesan et al., 2005). Another problem that may mask the velocity variations in the reservoir are the seasonal changes of the overburden (the sea-water layer in marine surveys or the water table on-land). The use of 3D time-lapse tomography has proven to be a flexible and powerful tool in solving both problems, enabling the removal of the related small velocity variations and giving a set of coupled models to highlight the reservoir changes (Vesnaver et al., 2003).

The tomographic inversion consists of minimizing the differences between the observed and calculated travel times, thus allowing to obtain the wave velocities. The travel time of seismic waves recorded by a geophone is obtained by integrating the slownesses along the ray path. The integral is replaced by a summation over the voxels, since a discrete blocky model is usually adopted. The travel time difference can be expressed as to = tOBS _ (CALC Au. . 1

In practice, the tomographic inversion follows the scheme of Figure 1. The rays are first traced on an initial model, using the same acquisition geometry of the real experiment, and the obtained travel times are subtracted from those of the real experiment. The residuals are minimized to upgrade the velocity and geometrical features of the reflecting/refracting interfaces, until the model does not change compared to the previous one. The separate inversion of the velocity and interface depths and geometry makes the procedure less sensitive to cross talk between velocity and depth errors (Bishop et al., 1985; Bickel, 1990; Delprat-Jannaud and Lailly, 1992; Docherty, 1992; Lines, 1993; Tieman, 1994). The non-uniqueness of the solution is reduced by finding the optimal grid for the velocity field via adaptive irregular or staggered grids (e.g. Vesnaver and Bohm, 2000).

/Initial model\ V set-up J

Null space analysis

Grid update

Ray tracing

Velocity update f TraveltimeA '^picking J

Interfaces update

Figure 1. Scheme of the three main loops of the tomographic inversion. A) Update of the velocity field and interface depth; B) Picking and comparison with travel times from the tomographic model; C) Grid upgrading, based on velocity field and reliability.

The final result of the seismic tomography is therefore a velocity model in depth, where the geologic complexities are preserved. This output can be an optimal input for pre-stack depth migration to obtain an accurate imaging of the various geological features.

In the case of time-lapse analysis we can impose the additional constraint that the geometry and velocity of most of the model does not change over time, while leaving free the reservoir and the shallowest layer (which may be affected by seasonal variations). This procedure constitutes the basis of "Time-lapse tomography", successfully applied to different vintages acquired offshore Norway (Vesnaver et al., 2003). The data was acquired in 1989, with a single vessel towing two streamers and a central air gun, and in 1992, using one vessel with three streamers and a sleeve gun as source while a second vessel towed two additional streamers. In 1989 the hydrophone spacing was double that of 1992. These acquisition differences made a direct comparison of the seismic profiles difficult in the time domain, however the use of 3D tomography made it possible to overcome these difficulties (Vesnaver et al., 2003).

Figure 2. Vertical sections of the 1989 and 1992 3D tomographic models, obtained by a coupled time-lapse inversion.

After independently estimating the velocity models of the two vintages, both the velocities and geometries of the layers were assumed constant in time. They were averaged and used as initial models to improve the velocity fields within the overburden and the reservoir, resulting in two coupled models (see Figure 2). These models have been used as input for a pre-stack depth migration, obtaining the images shown in Figure 3. These sections and the velocity models allow us to verify the changes which occurred within the reservoir during production time.

Figure 3. Pre-stack depth-migrated images of the reservoir for the 1989 and 1992 vintages, using coupled velocity models.

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