Conditioning object-based models

To demonstrate the potential value of FAKTS as a tool for constraining object-based techniques, example work has been carried out with FLUVSIM v. 2.900 (Deutsch & Tran 2002), a public-domain object-based algorithm that was purposely developed for simulating the sedimentary architecture of fluvial systems. FLUVSIM generates stochastic channel centerlines and fits stochastic channel, levee and crevasse splay geometries to these centerlines in a floodplain background (Deutsch

& Tran 2002; Deutsch & Wang 1996). FLUVSIM simulations are run by a FORTRAN program that is conditioned by parameters stored in GSLIB (Geostatistical Software Library) parameter files (Deutsch & Tran 2002).

Although the Boolean objects that are simulated by the FLUVSIM program are designated as facies types (Deutsch & Tran 2002) or architectural elements (Pyrcz et al. 2008), FAKTS’ depositional elements and architectural elements would both be suitable genetic-unit types for providing input to FLUVSIM simulations (cf.

Deutsch & Tran 2002). At the FAKTS’ depositional-element scale, channel-complex and floodplain-segment data can be used to generate FLUVSIM simulations that would simply model the distribution of channel-complexes (possibly filtered in order to correspond with 5^th and/or 6^th order channel-belts) in a floodplain matrix.

Alternatively, to include in the simulations all the FLUVSIM facies types comprising levee and crevasse splay objects, object constraints can be derived by either of the following methods:

1) working at the FAKTS’ architectural-element scale whereby it would be appropriate to consider FLUVSIM channels as properly described by either FAKTS CH elements or by material units (see below) themselves composed of neighbouring FAKTS’ in-channel elements (CH, DA, LA, DLA, HO; see table 6.1 for code explanation) and to identify FLUVSIM levees with FAKTS’ LV elements and FLUVSIM crevasse splays with either FAKTS’ CS elements or combinations of stacked CS and CR elements; FLUVSIM floodplain proportions would be derived by either FAKTS’ FF element proportions or cumulative FF+SF proportions;

2) combining depositional-element information, which is used to constrain the dimensional and geometrical properties of the FLUVSIM channel facies type, with architectural-element information, which is used to constrain all FLUVSIM facies type proportions as well as the dimensional parameters of the levee and crevasse splay FLUVSIM facies types.

In the first instance, database-derived architectural-element proportions results are useful for determining what type of fluvial depositional contexts can be properly modelled by using all the facies types available for the FLUVSIM code (i.e.

employing FAKTS’ information derived at the architectural-element scale or combined architectural- and depositional-element scale). Secondly, both depositional- and architectural-element proportions can be used to condition FLUVSIM facies type proportions, working at the depositional- or architectural-element scale respectively.

Thus, working at the depositional-element scale, modelling the distribution of channel-complexes in a floodplain background, the simulation would be satisfactorily conditioned by specifying proportions of channel and floodplain deposits and channel-complex geometrical parameters, as derived from FAKTS.

Ideally, it would be desirable to obtain volumetric proportions of genetic units, but in practice, only very rarely are data recording 3D geometries available, as most of FAKTS’ data originates from 2D architectural panels, 2D/pseudo-3D borehole- or log-correlation diagrams, and 1D logs. Using an architectural panel dataset purposely acquired from a 300-m-wide section of the Kayenta Formation and characterized at the facies-unit scale, it has been possible to test the sensitivity of FAKTS’ genetic-unit proportions to the method of estimation, whose choice depends on available data types and dataset completeness. Where there exists high palaeocurrent variability, proportions based on cross-sectional areal extents can be considered as good estimators of volumetric proportions, as the sizes of the genetic bodies intersected by the cross-section (e.g. lateral extent of architectural element cropping out along an architectural panel) are expected to be representative of their anisotropy. By comparison with cross-sectional areal proportions, we have observed that, the sum of unit thicknesses corrected according to average lateral dimensions (product of individual-unit thickness, mean unit-type width and mean unit-type length) also return accurate estimations of volumetric proportions, when working with 2D or pseudo-3D datasets. Proportions computed as summed thicknesses would be used when working with datasets based on 1D logs. The FAKTS-derived proportion of channel deposits would then be entered in the FLUVSIM parameter file at line 22 (Deutsch & Tran 2002).

Dimensional parameters of FLUVSIM channels are specified in the form of triangular distributions – defined by minimum, mode, and maximum values – of channel thickness and width/thickness ratios, with along-channel variability in thickness and width optionally expressed by undulation parameters and by the correlation length of such undulation (Deutsch & Tran 2002). FAKTS provides channel-complex thickness (figure 6.3) and width/thickness ratio (figure 6.4a)

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information that can be straightforwardly input in FLUVSIM parameter file (lines 33 and 36). When values are assigned for the undulation-parameter, FAKTS-derived minimum and maximum values for triangular distributions of dimensional parameters should be corrected in order to account for the maximum undulation; in such cases at least maximum thickness input values should always be corrected to account for channel-complex thicknesses being generally entered in the FAKTS database with values representative of their maximum thickness.

Figure 6.3: frequency distribution of all FAKTS channel-complex thicknesses and best-fit probability density function.

Channel sinuosity is not a direct input to FLUVSIM simulations; however geometrical input parameters related to channel sinuosity are the channel deviation from its axis (departure) and the correlation length of the sinusoidal departure.

Thus, FAKTS-derived channel-complex sinuosity values can be used to obtain departure and length scale values, for example by referring to the relation depicted in Pyrcz et al. (2008, their figure 7). Additionally, the triangular distribution function that describes the orientation of FLUVSIM channels (line 30 of parameter file) can be informed by FAKTS channel-complex palaeocurrent variability within subsets, qualitatively assigned as ‘High’, ‘Intermediate’, or ‘Low’.

As FAKTS channel-complexes represent channel-clusters defined on the basis of clearly defined geometrical rules, FLUVSIM channels – which can stack on each other themselves generating channel-clusters – would more appropriately embody 5^th and/or 6^th order (sensu Miall 1996) channel-belts. Since FAKTS allows storing information on the order of the lower bounding surface of depositional elements, it

is possible, for example, to filter the database in order to obtain parameters relating to the geometry of 5^th-order surface bounded channel-clusters (figure 6.4b) with which to constrain the object-based simulation. A visual depiction of the sensitivity of FLUVSIM realizations to the choice of the type of channelized genetic units is offered in figure 6.5.

Figure 6.4: (A) scatter-plot of all FAKTS channel-complex width vs. thickness (W/T), classified according to observation completeness classes by Geehan & Underwood (1993); (B) scatter-plot of 5th order-bounded FAKTS channel-belt width vs. thickness;

(C) scatter-plot of 4th order FAKTS channel-fill (CH) architectural elements.

Working at the architectural-element scale (i.e. including levee and crevasse splay objects in the FLUVSIM simulations), FLUVSIM channels can be described by FAKTS 5^th-order channel-complexes, FAKTS 4^th order CH architectural elements (cf. figure 6.4b for width/thickness ratios), or by material units (see below) composed of neighbouring FAKTS in-channel elements (CH, DA, LA, DLA, HO).

Levee and crevasse splay proportions can be constrained by FAKTS-derived proportions as outlined above. The FLUVSIM levee and crevasse splay dimensional parameters are partly specified as triangular distribution functions (levee width and splay planform area), which can be readily derived from FAKTS output, and partly entered as a relative dimension (levee height and depth and splay thickness), expressed as a fraction relative to the thickness of the adjacent channel (Deutsch & Tran 2002).

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Figure 6.5: example FLUVSIM realizations modelling the distribution of channelized bodies in a floodplain background; the simulations were conditioned on geometrical data from (left to right): FAKTS channel-complexes, channel-complexes bounded by 5th-order lower bounding surfaces (5th-5th-order channels), and CH architectural elements (channel-fills).

As the FAKTS database allows a full storage of the relationships of spatial adjacency between genetic units belonging to the same scale (Colombera et al.

2012a; Chapter 2), it is possible to query the database to derive dimensional parameters of laterally juxtaposed units, thereby yielding the relative dimensional parameters required by FLUVSIM (but also employed by widely used commercial software with programs for object-based simulations of fluvial depositional systems;

e.g. PETREL by Schlumberger). An example of this type of query is presented in figure 6.6a, where the interrogation that returns the thicknesses of juxtaposed 4^th order CH and CS architectural elements is shown. Since the containment of genetic units within larger-scale genetic units is also properly represented in FAKTS, it is also possible to derive relative dimensional parameters associated to genetic units belonging to different scales (figure 6.6b); for example it is possible to submit a query to return the thickness of all the crevasse splay architectural elements (CS) neighbouring 5^th-order channel-cluster depositional elements (channel-complexes bounded by 5^th-order lower bounding surfaces) and the thickness of the channel-clusters themselves in order to derive their relative thicknesses, in cases where FLUVSIM channels are described by FAKTS’ 5^th-order channel-complexes.

In a similar fashion, the same type of FAKTS output (proportions, absolute and relative dimensional parameters) can be used to constrain mixed object/process-based simulation methods of fluvial architecture, like ALLUVSIM (Pyrcz et al. 2008).