Assumptions of the intra-survey modelling workflows in Section 4.3.3 and Section 5.2

The spatio-temporal binning workflow (Figure 4-13 ) and 1D convolution seismic modelling workflow (Figure 5-2, Section 5-2) are geometric CMP-based (Figure 4- 15) approaches, and, as such, are a crude way of analysing the intra-survey problem. Propagation effects of the seismic wavefield (amplitude loss, attenuation/absorption, diffractions, scattering, Amplitude Variation with Offset (AVO)), intrinsic noise of data acquisition contributed mostly by acquisition geometric non-repeatability, other noise such as multiples and statics, and effects of seismic data processing, especially migration, are not considered. In real seismic experiments and processing, all of these effects including the intra-survey reservoir fluctuations combine to affect the acquired 4D seismic data, and it is difficult to separate one from the other. The assumptions described below highlight the limitations of the modelling workflows adopted in this chapter and in Chapter 4. However, these workflows (Figure 4-13 and Figure 5-2) achieve the main aim of the analysis, which is to study purely the intra-survey problem outside other effects mentioned above.

(1) Homogeneous overburden earth model:

To perform 1D convolution, seismic reflectivity from the surface down to the reservoir (the overburden), in the reservoir, and below the reservoir (the underburden) is required at each bin location. The reflectivities are computed using Zoeppritz equations (Aki and Richards, 2008) which require a 3D earth model containing the elastic properties (P-wave velocity, VP, S-wave velocity, VS and

density, ). These are calculated using the rock-physics equations in Section 2.2, with some simplifications. The overburden and underburden consist only of shale with homogenous elastic properties i.e. a single VP, VS and  (see Table 5-2). The

overburden remains unchanged during production. The reservoir sands remain heterogeneous, with lateral variations in VP, VS and  provided by the static and

dynamic properties of the simulation model. It is also only the reservoir (with a thickness of 28 m and at a depth 4500 m) that is affected or changed during production.

(2) Horizontal reflectors (no dipping layers):

As the interest is the reservoir’s response, the overburden and underburden are not just homogenous (with no diffractors), but are also flat. This implies a horizontal and continuous overburden/reservoir interface, and the reservoir is structurally simple such that the dip is negligible. As seen in Figure 4-8(a), the reservoir layer is not flat, but is dipping at angles of 0° to 10°, but mostly at 4° which should not be neglected. In addition, abrupt discontinuities due to faulting will cause diffractions and scattering. The 1D convolution to be performed here handles only reflected energy, and not diffracted energy.

(3) Common-midpoint (CMP) maps directly to common-depth point (CDP) (or common-reflection point (CRP) or common-image point (CIP)):

The assumptions in (1) and (2) imply straight ray-paths from source to reflector and back to the receiver at the surface. So, the recorded location which is the point at the surface halfway between the source and receiver is shared by numerous source- receiver pairs, and is called the common midpoint. Thus, a CMP location recorded at the surface is assumed to be the same CMP location in depth vertically down to the reservoir reflector (Figure 4-15). This allowed the development and implementation of the spatio-temporal binning workflow (Figure 4-13).

In the real earth, strata are dipping with complex geology including faulting, folding, (some) fracturing, salt bodies, different lithology/rock type and unconformities, and other velocity anomalies in the overburden. Where dip is present, the CMP method breaks down since traces do not all reflect from the same mid-point location, likewise, where other geological complexities exist. As is the case with imaging the real subsurface, multi-channel processing techniques such as Dip Move out (DMO) and Migration are required to accurately reposition/move the seismic data from the recorded surface locations to the locations in depth with the correct CMP. This correctly located CMP is otherwise called common-depth point (CDP) or common-reflection (CRP) or more appropriately, common-image point (CIP). Migration corrects the flat-geological-layer assumption by a numerical, grid- based spatial convolution of the seismic data to account for dipping events (where geological layers are not flat) and collapse diffractions (Yilmaz, 2001). Such

imaging techniques work by combining many traces from different CMP locations. This contradicts the 1D convolution method applied in Section 5-2, which embodies a single channel seismic reflection system. Although, a migration operator (see Figure 5-4) based on Chen and Schuster’s (1999) equations is applied on the post-stack seismic data obtained after 1D convolution, it only crudely emulates the smoothing effect of migration (see Figure 5-6), and the reservoir’s dip is ignored (assumptions (1) and (2) above). It is simply the spatial impulse response of the migration operator and is applied to all image points (i.e. in this case, CMP bin locations) irrespective of where the reflections are generated.

(4) Perfect geometric repeatability between baseline and monitor acquisition:

This implies source and receiver positions (Figure A-2) are the same in the baseline and monitor acquisition, which is not always the case. Source positioning errors, ΔSource, between the baseline and monitor PRM survey (Figure 4-6) are +/-5 m or lower, but with permanently installed sensors on the seabed, the receiver positioning error, ΔReceiver, is zero. However, for the towed streamer acquisitions in Figure 4-7, the monitor and baseline positioning errors combined, ΔSource +ΔReceiver, are a maximum of 180 m, but on average around 65 m (calculated from the 1500 m to 3000 m mid-offset locations). The influence of such degree of non-repeatable acquisition geometry in the intra-survey analysis in Section 5.3 is not modelled and is considered negligible for two reasons. The first is that a common grid with a large CMP bin size (i.e. grid size) of 67.5 x 50.25 m is used, which was found to be the optimum for both the PRM and towed streamer acquisition data (see Table 4-1). The second and most important is that a horizontal, homogenous and non-changing overburden is modelled based on the assumptions in (1) to (3). In the real subsurface, the overburden can be very complex and near-surface velocity variations including sea tide, water bottom and weathering layer changes occur, making even the smallest positioning errors between baseline and monitor acquisition cause high non-repeatable noise (non- production-induced time-shifts, amplitude and phase changes), which is problematic for imaging the true 4D seismic response at the reservoir interval.

for processed 4D seismic data acquired in several North Sea fields (Figure 5-9). The NRMS error was computed above the reservoir and away from any intervals affected by production.

Figure 5-9 Geometry repeatability for towed streamer surveys. The relationship between NRMS values and the average positioning error in source plus receiver location, ΔSource +ΔReceiver, for 4D surveys in the North Sea. Each blue dot represents one acquired 4D survey. Arrows connect repeat surveys shot over the same field. The dashed red line marks the trend of the data (after Smit et al. (2005)).

Each dot in Figure 5-9 represents one 4D seismic survey. Black lines connect points corresponding to the same field in cases where multiple surveys are acquired over the same field. A clear trend of decreasing NRMS values with decreasing positioning errors (Figure 8-3, dashed red line) can be observed. This is evident for the three fields (black lines) where multiple 4D seismic surveys are shot. For the latter case, however, it is assumed that all 4D seismic surveys acquired over the same field are reprocessed so that the decrease in NRMS is solely attributable to the decreasing positioning error and not to an improvement in the data processing. An important observation is that mispositioning of source and receiver locations during 4D seismic acquisition is a controlling parameter which affects the overall NRMS measure.

This NRMS error due to geometric non-repeatability is rather high (Figure 5-9), compared to the resulting NRMS error caused by intra-survey reservoir fluctuations causing genuine production induced 4D signals in the reservoir - up to 7.5% is observed between the near and far offset stacks (Table 5-4, see Section 5-

3). However, positions of sources and receivers are increasingly well controlled now, such that geometric non-repeatability can lead to an NRMS of as low as 2 to 5% (for example, in PRM acquisitions; see also Figure 3-1). If such is the case, then the problem of intra-survey reservoir fluctuations in stacked 4D seismic data is likely to be dominant at the reservoir level.

(5) Planar wave assumption and no attenuation:

Geometrical spreading which causes amplitude loss with distance, and attenuation does not occur. This is not true of the seismic energy which behaves as spherical waves that spread-out over a spherical surface of ever increasing size as they propagate through the earth from the point source. In addition, as with elastic wave propagation, high frequencies are absorbed rapidly than low frequencies because of the intrinsic attenuation in rocks. So that deeper reflectors are of much lower resolution and lower amplitude than shallower reflectors. In addition, scattering attenuation which causes the energy of the seismic wavefield to be scattered in different phases when it encounters different rock properties does not occur. This also leads to amplitude loss and dispersive effects. This assumption of a planar wave is however not far-fetched. One of the fundamental techniques in processing is True Amplitude Recovery which accounts for amplitude loss (using a scaling function of velocity, offset and time), in an attempt to recover the true amplitude. Deconvolution, time-variant spectral whitening and inverse-Q filtering are also routine methods that try to remove the effect of attenuation by modifying the amplitude spectrum of the seismic signal (Yilmaz, 2001).However such effects cannot be completely compensated for in processing.

(6) Fixed Amplitude Variation with Offset response:

In typical angle-dependent seismic modelling, the incidence angle (equivalent of offset) is used to calculate the amplitude variation with angle (AVA) or offset (AVO) response. However, in the seismic modelling (Section 5.2) of the results from the spatio-temporal binning workflow in Figure 4-13, the amplitude dependency on the angle of incidence is omitted by calculating the reflectivity using the same angle of incidence as further discussed in Section 5.2. This is done so as to separate the intra-survey effect from the 4D AVO response. The workflow

(Figure 4-13) reconstructs the reservoir changes in pressure and saturation according to the acquisition geometry (source-receiver midpoint and offset) and timings of shots, based on the many assumptions above. As a result, the reconstructed pressure and saturation changes could be obtained for all midpoints at each CMP bin for a range of offsets from the acquisition geometry. Therefore any differences between the computed reflectivity (and convolved seismic traces) for the range of offsets at a CMP bin is solely due to their different time of shots. Different time shots imply different pressure and saturation changes as these are fluctuating during the acquisition (in Section 4.4 the results of implementing the workflow in Figure 4-13 are shown). If the AVO response was to be modelled by including different angle of incidence with respect to the different offset groups from the acquisition, then this will amplify the resulting NRMS measure of the intra-survey effect between offset stacks in Section 5.3. As real acquisitions and seismic wave propagation are naturally designed for the AVO effect, it is not possible to separate the intra-survey fluctuation problem from such effects in the acquired 4D seismic data. This is perhaps one of the perks of being able to study such a problem through a fixed-angle 1D convolution seismic modelling.

Based on the above assumptions, the intra-survey modelling results in this chapter provide only a rough estimate of the magnitudes of the 4D seismic response obtained through 1D convolution seismic modelling. A comprehensive scheme for modelling the seismic data as the reservoir changes during the acquisition using finite difference (FD) modelling, and including the effects of data processing is discussed in Chapter 8 (Section 8.2.3). The FD modelling is performed only once for the baseline survey as it is assumed to be acquired pre-production. For the monitor, this will need to be repeated for as many shot times acquired (Figure 8-3). This is because intra-survey reservoir fluctuations occur during the monitor acquisition, and the reservoir might be changing at each shot time. Seismic shot gathers for the entire survey area are output from the FD scheme for the baseline, but for the monitor, these should be obtained for each shot time. Typical 4D seismic processing workflows (Figure 8-5(b)) can then be applied on the modelled shot gathers, and the shot timestamp preserved for the reconstruction of the acquired 4D seismic data through spatio-temporal binning. Applying the full scheme (Section 8.2.3) is beyond the scope of this thesis and it recommended for future studies.