The integrated model of VS from the surface to the base of the North Sea Supergroup is a combination of three different VS models, each with its own depth range. The top part of the model ranges from the surface to NAP-50 m and is constructed from the combination of the high resolution 3D geological voxel model GeoTOP constructed by TNO—Geological Survey of the Netherlands and Groningen specific VS data. The VS model for this depth range has been derived from seismic cone penetration tests (SCPT) that were linked to the geological units of the GeoTOP model. This VS model is referred to as the GeoTOP VS model.
The intermediate depth interval ranges from approximately NAP-40 m to NAP-120 m. Extensive reflection seismic surveys were conducted in the 1980s for imaging purposes of the reservoir. The legacy data were reprocessed using surface waves information to retrieve a VS model based on the Modal Elastic Inversion (MEI) method (Ernst 2013). This model is referred to as the MEI VS model.
The deepest depth interval ranges from approximately NAP-70 m to the base of the North Sea Supergroup, providing overlap with the MEI VS model. The VS model for this depth range is based on the pre-stack-depth-migration model (PSDM) of compression-wave velocity (VP) used to image the reservoir. The VP model is based on 70 sonic logs and well markers in 500 wells. The VP model is converted to a VS model using relationships for the VP/VS ratio based on Groningen-specific data. This model is referred to as the Sonic VS model. The following sections describe each of these models in more detail.
GeoTOP VS model
GeoTOP describes the subsurface in voxels measuring 100 by 100 by 0.5 m (x, y, z) to a maximum depth of NAP-50 m. The model provides estimates of stratigraphy and lithology, including sand grain-size classes. The estimates are calculated using Sequential Gaussian Simulation (SGS) and Sequential Indicator Simulation (SIS) (Goovaerts 1997; Chilès and Delfiner 2012). These stochastic techniques allow the construction of multiple, equally probable 3D subsurface models as well as the evaluation of model uncertainty (Stafleu et al. 2011). The “most likely” subsurface model was determined from the multiple subsurface models, using the averaging technique described by Soares (1992). This “most likely” model is used in the construction of the GeoTOP VS model. The GeoTOP model (version 1.3) is publically available at https://www.dinoloket.nl/en/subsurface-models (Stafleu and Dubelaar 2016).
The GeoTOP model of the north-eastern part of the Netherlands, including the Groningen region, was constructed using some 42,700 digital borehole descriptions from DINO, the national Dutch subsurface database operated by the Geological Survey. The largest part of these boreholes consists of manually-drilled auger holes collected by the Geological Survey during the 1:50,000 geological mapping campaigns. Most of the other borehole data comes from external parties such as groundwater companies and municipalities. Because of the large share of manually-drilled boreholes, borehole density decreases rapidly with depth.
An example of a cross section through the GeoTOP model is presented in Fig. 3, showing the stratigraphic units in the top panel and the lithological classes in the bottom panel. From top to bottom there are in this example Holocene Naaldwijk clays, the Holland and Basal Peat, sands of the Boxtel Formation and clays of the Peelo Formation.
The GeoTOP VS model associates each of the voxels of the GeoTOP model to a VS value. The various constituents of the Groningen subsoil have different geological histories, as described above, and consequently have different geomechanical characteristics. A Holocene clay will have a different VS than a Pleistocene clay that has experienced loading by ice sheets. Therefore, different VS statistical distributions were derived for each of the stratigraphic and lithological combinations that are found in the Groningen field. In the following, the combination of stratigraphy and lithology is referred to as “unit”.
A data set of 88 SCPTs in Groningen provided the input for these statistical distributions. The VS measurements from the SCPTs at each depth were associated with a stratigraphy, inferred from GeoTOP, and lithological class, inferred from cone resistance and friction ratio of the accompanying cone penetration test (CPT). The effective isotropic confining stress, \(\sigma_{o}^{'}\) (i.e., the average of the vertical and two horizontal components of the effective stress) for each depth is computed using the unit weight of the overlying sediments and assuming a mean water table of 1 m below the surface. For brevity, the effective isotropic confining stress is hereafter simply referred to as “confining stress”. Next, VS values from the SCPTs were clustered for each unit and \(\ln Vs\) was plotted versus the natural logarithm of the confining stress. The clustered VS values were then used to develop models to assign VS values to each of the GeoTOP voxel-stacks. A voxel-stack is a vertical sequence of voxels at a particular (x,y)-location in the GeoTOP grid. This approach enhances the inclusion of geological information in the VS profiles generated for this depth range.
Generally, VS increases with confining stress (e.g. Hardin 1978; Jamiolkowski et al. 1991; Yamada et al. 2008). Therefore, we checked for confining stress dependence within each group of VS data. A typical model for VS dependence on confining stress is:
$$\ln Vs = \ln Vs_{1} + n\ln \left( {\frac{{\sigma_{o}^{'} }}{{p_{a} }}} \right)$$
(1)
where \(\sigma_{o}^{{\prime }}\) is the confining stress, \(p_{a}\) is atmospheric pressure, \(\ln Vs_{1}\) is a parameter that represents the shear-wave velocity at a confining stress equal to one atmosphere, and n is the slope that defines confining stress dependence (Sykora 1987). The parameters n and \(\ln Vs_{1}\) and their statistics were determined for each unit. Shear-wave velocity values are assumed to be log-normally distributed; hence the ln-mean and the standard deviation fully define the distribution. The development of the confining stress-dependent VS models considered three different cases. The first case is when the confining stress-dependence is fully defined by the SCPT data. A second case is for units that do not show confining stress dependence. The last case is for units where the data is insufficient to define the confining stress-dependence, but such dependence is to be expected based on analogy to similar sediments elsewhere in the field. For these units, the parameters of Eq. 1 are based on existing literature and expert judgment.
Two examples of VS data for typical units with numerous observations are shown in Fig. 4. The mean VS at a certain confining stress is described by the slope n and the intercept lnV
S1
, while the standard deviation depends on the number of observations, mean \(ln\left( {\sigma_{0}^{{\prime }} /p_{a} } \right)\), the sum of squares of \(ln\left( {\sigma_{0}^{{\prime }} /p_{a} } \right)\) and the total variance of VS (Montgomery et al. 2011). As indicated previously, the VS profiles also need to be randomised (described in Sect. 4.1), for which the above described mean VS and standard deviation will be used. There were sufficient observations (a minimum of 20) for 10 units to derive a confining stress-dependent relation based on SCPT data. The parameters describing the confining stress dependence defined by the SCPT data are given in Table 1. The values of the slope n for Groningen clay (including sandy clay and clayey sand) range from 0.18 to 0.43 with an average of 0.28. This compares well with literature values for clay, which are generally given as n = 0.25 (Hardin 1978; Jamiolkowski et al. 1991; Yamada et al. 2008). The slope n depends on the type of sediment (Fig. 4): clays of the Peelo Formation (Pleistocene glacial deposits) have a stronger confining stress dependence (larger n) than clays of the Naaldwijk Formation (Holocene tidal deposits) which is generally present at much shallower depths and thus lower confining stresses.
Table 1 Look-up table summarising parameters for the confining stress dependent VS (Eq. 1) from SCPTs
For several units, confining stress dependence is not apparent in the SCPT data, showing an n close to 0 or even slightly negative. Figure 5 shows VS data for medium sand from the Boxtel Formation. Since the slope in this case is very close to 0 (0.07), no confining stress dependence was imposed for this unit. In some other cases, the geological history implies that confining stress dependence is not expected. For example, the clay from the Drente Formation formed under varying glacial conditions and the effect of spatially varying loading is much larger than the confining stress dependence. The distributions of these constant VS units are defined by the mean and standard deviations of \(\ln Vs\). These are summarised in Table 2. A minimum standard deviation of 0.2 is imposed. This lower limit was used in the past as measurement uncertainty in VS profiles (Coppersmith et al. 2014). A standard deviation 0.27 is imposed on all peats, based on the observations from the SCPT data set for Nieuwkoop Holland Peat.
Table 2 Look-up table summarising parameters for units with constant VS
The last class of VS consists of units for which confining stress dependence of VS is to be expected, but there are not enough data in the SCPT data set to constrain this relationship. In that case, we estimate n from literature. We use n = 0.25 for clay, for all lithoclasses within Nieuwkoop Basal Peat and for peats within Pleistocene Formations following Hardin (1978), Jamiolkowski et al. (1991) and Yamada et al. (2008). For sand, we use measured coefficients of uniformity Cu from Groningen to estimate n using Menq (2003). This results in values for n varying between 0.25 and 0.29. In this case, no average VS estimates were available from the SCPT data set. Therefore, we used judgement to infer average VS for these units. Next, the intercept \(\ln Vs_{1}\) was determined such that the estimate of VS occurs at the average depth of occurrence in the region and consistent with the slope n. In the Groningen region, the intercept at \(\ln \left( {\frac{{\sigma_{o}^{{\prime }} }}{{p_{a} }}} \right) = 0\) corresponds to a depth of approximately 13 to 14 m. The parameters describing the confining stress dependence in this fashion are given in Table 3. A standard deviation of 0.27 for \(\ln V_{S}\) is imposed for all peats, and a value of 0.20 for all other lithologies, consistent with the values from Table 1 and Table 2.
Table 3 Look-up table summarising parameters for the confining stress dependent VS (Eq. 1) from estimates
Not all units present in the Groningen region are represented in the SCPT data set. In those cases, either representative relations from similar units or expert estimates were used (e.g. Table 3). For example, all members from the Naaldwijk Formation were represented by the Naaldwijk VS distributions in Table 1 and 3. Additionally, the VS distributions of Nieuwkoop Holland Peat are assumed to be representative for all Holocene peats.
MEI VS model
Three-dimensional seismic reflection data was acquired in the 1980s by NAM for the purpose of imaging and characterisation of the Groningen gas reservoir. This legacy data set was used to constrain the VS model in the intermediate depth range. Surface waves are generally regarded as noise in the process of seismically imaging deep reflectors. Therefore, they are attenuated during acquisition of seismic data and suppressed during processing. The surface (and guided) waves, however, propagate along the surface and therefore contain useful information of the elastic properties of the near-surface. Survey techniques have been designed that use these types of waves (e.g. Park et al. 1999). Hence, inversion of these surface waves was used to derive a VS model.
The Modal Elastic Inversion (MEI) method was used for the elastic near-surface model building. In essence, the MEI method is an approximate elastic Full Waveform Inversion method, in which the elastic wavefield is approximated by focusing on waves that propagate laterally through the shallow subsurface. These waves include the fundamental mode of the Rayleigh wave, its higher modes and guided waves. A limited number of horizontally propagating modes, characterized by lateral propagation properties and depth-dependent amplitude properties, are taken into account to represent the near-surface elastic wavefield (Ernst, 2013). The objective in the MEI approach is to find a model that minimizes the difference between the observed data (Rayleigh waves) and the forward modelled data.
The pre-processing applied to the data prior to Modal Elastic Inversion was restricted to applying a high-cut filter and data selection of those data traces that contain the Rayleigh waves. For efficiency, the data set was split in large overlapping rectangular areas, which were inverted independently. Within one area, all data are inverted simultaneously. The resulting VS models are merged afterwards. The starting model was a laterally invariant vertical gradient, which was subsequently updated during the inversion. All lateral variations in the resulting VS model were introduced by the inversion. Generally, the uncertainty in VS values in the resulting VS model is estimated to be 5–10%.
The vertical resolution of the resulting VS model is limited and the maximum depth range to which VS in this case can be reliably estimated is approximately 120 m below the surface. This is due to the seismic data acquisition design and consequently the narrow frequency band in which the surface waves are unaffected and still present in the data. The surface seismic data was acquired in 1988 with mostly (buried) dynamite sources and to a lesser extent with vibroseis sources (in cities) or airgun sources (in lakes and offshore), and recorded with 10 Hz vertical geophones. The seismic data acquisition was designed for deep imaging of the Groningen reservoir with a typical orthogonal geometry with line spacing of 250–500 m and group spacing of 50 m. The receiver group arrays were designed to suppress and distort Rayleigh waves with wavelengths less than approximately 80 m. The effect of the geophone arrays on the surface waves is illustrated in Fig. 6, in which a typical seismic record is displayed with full frequency band and with a frequency high-cut filter applied to 3 Hz. Above 3 Hz the receiver arrays have distorted and aliased the Rayleigh waves, and below 1 Hz the Rayleigh waves have become too weak to be observed on the seismic records. The application of the MEI method to the data was therefore restricted to the bandwidth from 1 to 3 Hz, and to those recorded traces on which the Rayleigh waves were recorded.
The narrow temporal bandwidth results in a narrow range of wavelengths (roughly between ~70 m and ~500 m). The penetration depth of the Rayleigh wave depends on the wavelength: the short wavelengths are sensitive to the shallow subsurface velocities, whereas the long wavelengths are more sensitive to the deeper velocities. The narrow range of wavelengths and especially the lack of short wavelengths therefore results in limited resolving power for the very shallow subsurface velocities. A typical depth resolution kernel of the fundamental mode of the Rayleigh wave is shown in Fig. 7. The high frequencies (right side of the plot) are more sensitive to the shallow layers, while the low frequencies (left side of the plot) are more sensitive to the deeper layers. The maximum penetration depth is ~120 m and there is a limited resolving power of velocities in the shallow layers of the model (0–20 m).
The convergence of the inversion is verified using the normalized root-mean-square (RMS) misfit between the model and the data for each seismic shot (Fig. 8). The normalized RMS misfit ranges from 0 (excellent convergence) to 100 (very poor convergence). Generally, Fig. 8 shows that the normalized RMS misfit is good, but there are several areas with large misfits (denoted by red outlines). These larger misfits are linked to the source types used during the seismic acquisition. In and around cities or highways vibroseis sources were used and airguns were used in lakes. Both source types do not contain the low frequencies required for the inversion. The estimation of the shear-wave velocity model in these areas might be hampered by these conditions. In other areas, the seismic records were acquired using buried dynamite sources and show a much better RMS. The area in the north is characterized by a high ambient noise level that cannot be modelled and therefore shows up as a relatively large RMS misfit.
The inversion resulted in a VS model over the area where 3D seismic data was available, and therefore does not cover the full extent of the area of interest. Horizontally, the VS model is gridded on the same 100 m × 100 m grid as the GeoTOP model. Vertically, the VS model is defined at 10 m depth intervals. An example of a depth slice at 65 m depth is shown in Fig. 9. The MEI VS model shows distinct zones of relatively high and relatively low VS values in patterns that resemble geological features, such as buried valleys. These structures can also be recognized in a cross-section from West to East in the centre of the field (Fig. 10). The cross-section also shows the vertical smoothness of the model.
Sonic VS model
For larger depths, VS is derived from the seismic data that was collected to image the reservoir. One component of the processing of seismic data for imaging is the application of pre-stack depth migration (Yilmaz 2001), which among others moves dipping reflectors to their true positions. This procedure requires a velocity model, the so-called Pre-Stack Depth Migration Velocity model (PSDM velocity model). There are more than 500 wells in the Groningen field. Data from these wells were available for this project. Sonic logs, providing VP, were measured in 70 of them. In several wells, VS was measured as well over a limited depth range. In two wells both VP and VS were measured over the entire North Sea Supergroup. Sonic logs and well markers for key horizons are used to construct a depth-calibrated, high-resolution P-wave (VP) model over the entire field. There is sufficient coverage of sonic logs for depths larger than 200 m, but for shallower depths, the accuracy of the VP model is reduced.
The PSDM velocity model is used as input VP model for the North Sea Supergroup. Site response calculations, however, require information in terms of VS instead of VP. Hence, the PSDM VP values are converted to VS using VP/VS relations from the two well logs where both VP and VS were measured over the entire North Sea Supergroup (Fig. 11). The measurements of VP and VS start below the depth of the conductor in the well, at ~60–75 m. The ratio between VP and VS shows a linear decrease with depth in the Upper North Sea Group, while it is more or less constant in the Lower North Sea Group (Fig. 11). The linear relationship to convert VP into VS for the Upper North Sea Group is given by:
$$V_{S} = \frac{{V_{P} }}{{\left( {4.7819 {-} 0.0047 * {\text{Z}}} \right)}}$$
(2)
where Z is the depth in metres. The corresponding Poisson’s ratio in the Upper North Sea Group generally varies between 0.45 and 0.47. The constant relation to convert VP into VS for the Lower North Sea Group is given by:
$$V_{S} = \frac{{V_{P} }}{3.2}$$
(3)
This corresponds to a Poisson’s ratio of 0.446.
The Sonic VS model was discretised in layers of 25 m thickness and on a grid identical to the 100 m × 100 m cells of the GeoTOP model. A cross section of the sonic VS model through the centre of the field is shown in Fig. 12. The VS inversion which is present in the Lower North Sea Group at depths of ~500 m is caused by the Brussels sand. Locally, this sand is cemented, leading to high VS.