Marschallinger GeoInformatik, 5201 Seekirchen, Austria; ** BBT SE, 6020 Innsbruck, Austria; ***geozt gmbh, 6060 Hall, Austria. Multiple Point Geostatistics ...
Multiple Point Geostatistics for the 3D-modeling of geological formations
A new paradigm to realistically portray categorical and numerical rock properties in 3D Robert Marschallinger *, Georg Orsi **, Ulrich Burger **, Gerhard Poscher *** * Marschallinger GeoInformatik, 5201 Seekirchen, Austria; ** BBT SE, 6020 Innsbruck, Austria; ***geozt gmbh, 6060 Hall, Austria.
Multiple Point Geostatistics (MPS) MPS is a new paradigm for the threedimensional simulation of the geological substrate (e.g., Remy et al. 2009, Caers 2011). As compared with 3D design approaches, model update is straightforward and reproducible. In contrast to traditional, variogram-based geostatistical modeling and simulation, MPS incorporates geological expert knowledge via a Training Image (TI). The TI permits geologists the intuitive formulation of geometrically complex geological structures plus their genetic relationships like cross-cutting joint generations or mutually eroding sediment types. MPS derives conditional probabilities for the grid node to be simulated from the TI, which can be two- or three-dimensional and is a purely conceptual depiction of geological context without any local accuracy. In MPS the patterns lifted from the TI replace the 2-point structure provided by the variogram in classical 2-point geostatistics. During MPS simulation, patterns are conditioned to hard or soft primary data like outcrops, drillings or geophysics. MPS simulation yields equally probable realizations, enabling scenario modeling at the voxel-level. In a processing pipeline, MPS results convey to FE or particle modeling (hydrological, rock mechanical) as 2D or 3D grids.
An example from soft rock As a result of driving the Brenner Basement Tunnel, the Padaster Valley (a side branch of the Wipptal, Austria) is currently being covered with excavation material. A geological model of the quarternary infill of the Padaster Valley was derived by MPS as a basis for hydrogeological considerations. Available primary data are ALS, boreholes, pits, geological surface mapping and seismic sections. The TI of the Padaster valley quarternary sequence is based on orthoimagery of comparable actuo-geologic sites and on above borehole data. The final 3D-TI (Figure 1) was assembled with an object-based training image generator. It consists of five sediment classes and incorporates mutual erosion relations: gravel channels, gravel-sand mixtures, sand benches, silt and clay ponds.
Figure 1: 3D TI of the Padaster Valley sedimentary infill. Color coding: Gravel channels: white; gravel-Sand mix: yellow; sand benches: orange; silt ponds: green; clay ponds: violet.
To yield local probabilities for each rock class, fifty MPS runs (Figure 2) were realized (about 100mio voxels/simulation, 20hrs computing).
Position of profile section in Figure 3.
Figure 2: One MPS realization of the Padaster Valley sedimentary infill with position of Figure 3. Slant view to NE , size approx. 1200*600*300m, 4*4*2m voxel size.
Figure 4: Slant NE view of model volume showing the resultant post-processed 3D models with probabilites of rock-classes 1-3 > 67% (one sigma).
Figure 3: 200m long, vertical profile section through MPS realization. Position see Figure 1.
Moreover, in Figure 5 the model has been cut along a vertical plane that parallels the galleries: here, the gravitative sliding process is clearly indicated by a left-shift of the hanging (moving) part.
Figure 3, a profile extracted from the voxel array in Figure 2, gives a good impression of the very natural style of MPS simulation: sediment layering is reproduced as are general dip and extension and thickness ranges of the individual sediment classes.
Terrain surface
Old hydro gallery
New hydro gallery
An example from hard rock In the course of a hydro power gallery project, MPS was used to simulate the hard rock substrate above and below a sliding plane. The sliding plane cross-cuts an existing gallery, necessitating its replacement. Input data for MPS were ALS, boreholes, geological mapping, documentation from the existing gallery and seismics. The 3D-TI comprises rounded to block-shaped carbonate bodies, folded layers of Gypsum-bearng schists and Phyllites as well as folded Calc-schists. Rock class proportions and geometrical relationships like main strike/dip directions, fold amplitudes and wavelengths were derived from geological mapping and gallery documentation. For both the stable (below sliding plane) and moving (above sliding plane) simulation volumes, 50 MPS simulations were run yielding rock-classes Gypsum-bearing rock (1), Phyllite (2), Carbonate (3) and two types of Calc-schist (4,5). The 50 MPS simulations were post-processed to derive pervoxel probabilities for each of the above rockclasses. This provides the basis for a statistical 3D-model of rock classes: Figure 4 shows all voxels with > 67% (one sigma) probability to belong to classes Gypsum-bearing rock (red), Phyllite (yellow) and Carbonate (blue). In the model, the general strike and dip of rocks is reproduced as is a large folded structure within the Phyllites. The complete post-processed 3D model is shown in Figure 5. For better orientation within the 3D model, terrain surface and the sliding plane are indicated there.
Carbonate
Sliding plane Calc-schists
Phyllite Gypsum bearing rock
Figure 5: post-processed model, cut along NW-SE plane. Rock types, sliding plane and terrain surface indicated for reference. Slant view to NE, size about 1900*1100*1000m, 5*5*5m voxels.
Summary MPS is a modern approach to simulate both categorical and metric rock properties. Due to its flexiblity in handling complex structures and incorporating hard and soft data, it is considered a universal component in a timely geoengineering work flow.
References Caers, J. 2011. Modeling uncertainty in the Earth Sciences. Wiley-Blackwell: 229pp. Remy, N, Boucher, A., Wu, J. Applied Geostatistics with SGeMS. A user’s guide. Cambridge University Press 2009; 264pp.
