modeling terrains and subsurface geology · interpretation several commercial tools exist for...
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Modeling Terrains and Subsurface Geology
M. Natali, E. Lidal, J. Parulek, I. Viola, D. Patel
Vienna University of Technology, Austria
University of Bergen, Norway
Christian Michelsen Research, Norway
● Part 1: Introduction and Taxonomy (I. Viola 20 min)
● Part 2: Surface Creation and Representation (M. Natali 40 min)
● Part 3: Solid models(D. Patel 40 min)
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Presentations and Presenters
Introduction and TaxonomyPart 1
Ivan Viola
● Rapid modeling in computer graphics● Procedural modeling: fractals, erosion● Sketch-based modeling directing procedure● Surface modeling predominantly● Domain: Film and gaming industry● User group: artists, content creators
Ebert et al.: Texturing and Modeling: A Procedural Approach
● Geosciences● Developed their own methods (Kriging ~ RBF)● Time-consuming modeling of complex structures
(e.g. GoCAD)● Dedicated interpolation methods of sparse data● Users: Geoscientists, geologists
Mallet: Geomodeling
● Rapid modeling in geoscience is needed!● Intellectual crosspollination of CG and Geo
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Modeling of Terrains and Subsurface
● Uniformitarianism● Layer-cake model
● Sedimentation,horizons, faulting,folding, igneous processes, erosion
● Relevant for Oil&Gas● Structural model (geo-bodies)● Reservoir model (hydrocarbon flow)
● Complex geological model● Mineralogy and metal
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Geological Background
● Man-made objects● Architecture (orthogonal, regular)● CAD (simple shapes, identical instances)
● Natural objects● Vegetation, Animals, Terrain (complex
shapes, individual instances, clear boundaries)
● Subsurface (unclear boundaries, unfamiliar shapes, complex 3D arrangement)
Turner: Challenges and trends for geological modelling and visualisation
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Modeling Complexity
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Geological Interpretation
● Measurements● Boreholes● Remote sensing● Seismic slices● Vertical outcrop analysis
● Simulations● Forward simulation● Inversion
● Palaeoclimate and Palaeogeography● Uncertainty
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Taxonomy According to Origin
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TaxonomyAccording toWorkflow
Surface Creation and Representation
Part 2M. Natali
Workflow Taxonomy
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Fractal and Erosion
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Synthetic terrains from:
● Fractal landscape modelling
● Physical erosion simulation (Thermal or Hydraulic)
● Images or terrain patches
[Belhadj et al. 2007] [Stava et al. 2008]
Fractal Example I
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Stachniak and Stuerzlinger, An algorithm for automated fractal terrain deformation, 2005
More user control than previous techniques Constraints to the created model according to user Fractal approximation of terrain + function defining
user constraints
Fractal Example II
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Schneider et al., Realtime editing, synthesis, and rendering of infinite landscapes on GPUs, 2006
Reduction of parameter setting
Interactive fractal landscape synthesizer
Erosion Example I
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Benes and Forsbach, Visual simulation of hydraulic erosion, 2002
Physically-based approach with high level control
Fast and stable
Erosion Example II
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Benes et al., Hydraulic erosion, 2006
Fully based on fluid mechanics (Navier-Stokes)
Voxel grid representation
Erosion Example III
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Stava et al., Interactive terrain modeling using hydraulic erosion, 2008
Interactive physically-based erosion Implemented on GPU Subdivision in tiles (height-maps)
Erosion Example IV
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Kristof et al., Hydraulic Erosion Using Smoothed Particle Hydrodynamics, 2009
Smoothed Particle Hydrodynamics (SPH) employed
Works on large terrains
Erosion Example V
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Hnaidi et al., Feature based terrain generation using diffusion equation, 2010
Constrained modelling process
Curves with properties (elevation, slope angle, ...)
Erosion Example VI
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Hudak and Durikovic, Terrain Models for Mass Movement Erosion, 2011
Long time period erosion
Particle system adopted
Discrete Element Method
SPH for water simulation
Sketching Terrains
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Rapid modelling
Expressive
Intuitive
No need to set parameters
[Gain et al. 2009]
Sketching Terrains - Example I
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Watanabe and Igarashi, A sketching interface for terrain modeling, 2004
Noise after surface deformation
Local minima and maxima for area of influence
Sketching Terrains - Example II
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Gain et al., Terrain Sketching, 2009
Sketch-based procedural generation
Elevation + area of influence
Noise where required
Sketching Terrains - Example III
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Vital Brazil et al., Sketching Variational Hermite-RBF Implicits, 2010
3D closed surfaces using implicit functions
General tool, adaptable to geology
Sketching Terrains - Example IV
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Sketches combined with exemplar-based technique
Height-map sketching
Zhou et al., Terrain synthesis from digital elevation models, 2007
By-example - Example I
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Brosz et al., Terrain synthesis by-example, 2007
Realistic terrains from reference examples
Rough base + target (small-scale characteristics)
Brush operation or procedural synthesis
Surface Representations
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Height maps
Implicit surfaces
Meshes
[de Carpentier and Bidarra 2009]
[Brazil et al. 2010]
Workflow Taxonomy
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Sparse- and Dense-data
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Geological measured data as input:
Seismic 2D or 3D (reflection of sound waves) Collection of well logs (material samples and
measurements) Outcrop scan (combination of laser and photography,
LIDAR)
University of Idaho
Sparse-/Dense-data Example I
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Geometric surfaces for each stratigraphic layer No holes Shared vertices for intersecting surfaces
Caumon et al., Terrain synthesis from digital elevation models, 2007
Sparse-/Dense-data Example II
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Orientable surfaces Implicit surfaces imply validity conditions
Caumon et al., Surface-Based 3D Modeling of Geological Structures, 2009
Interpolation
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B-spline Inverse distance Kriging Discrete Smooth Interpolation (DSI) Natural Neighbor Interpolation
Interpolation
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B-spline Inverse distance Kriging Discrete Smooth Interpolation (DSI) Natural Neighbor Interpolation
A spline is a pw-defined smooth polynomial function A B-spline is a linear combination of spline functions with minimal support wrt a given degree, smoothness, and domain partition
Weisstein, Eric W. "B-Spline." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/B-Spline.html
Given m+1 knots n+1 control points P0 , … , Pn
Interpolation
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B-spline Inverse distance Kriging Discrete Smooth Interpolation (DSI) Natural Neighbor Interpolation
Data points closer to the grid points have more effect than those which are further away
Estimates the values of an attribute at unsampled points using a linear combination of values at sampled points
B-spline Inverse distance Kriging Discrete Smooth Interpolation (DSI) Natural Neighbor Interpolation
Jin Li and Andrew D. Heap, A Review of Spatial Interpolation Methods for Environmental Scientists
Interpolation
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B-spline Inverse distance Kriging Discrete Smooth Interpolation (DSI) Natural Neighbor Interpolation
Data points and their spatial variance are used to determine trends which are applied to the grid points
Jin Li and Andrew D. Heap, A Review of Spatial Interpolation Methods for Environmental Scientists
Interpolation
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B-spline Inverse distance Kriging Discrete Smooth Interpolation (DSI) Natural Neighbor Interpolation
Interpolation of a function f known at some data points (n dimensional)
Most classical methods find a function defined everywhere, DSI produces values only at grid points
Interpolation
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B-spline Inverse distance Kriging Discrete Smooth Interpolation (DSI) Natural Neighbor Interpolation
The natural neighbors of any node are those in theneighboring Voronoi cells, or equivalently, those to whichthe node is connected by the sides of the Delaunay triangle
N. Sukumar, UCDAVIS
Surface Representations
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Fractal and Noise-based
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Realistic appearance of the surface
Self-similarity of fractals like in nature
(Height-maps) Do not allow discontinuities
Not intuitive, no local control
No multi-z values
Erosion
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Weathering simulation
Natural appearance of top surface
No discontinuity
Hard to control
Low storage, high processing
Exemplar-based
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Surface reconstruction (geometry and texture) through a collection of data from photography and laser
Computational expensive to create a terrain
Little control on the process
High storage requirements
Radial Basis Functions
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Interpolation of a set of n points with their normal vector
Unordered points (unlike splines)
Cn continuity
No gap in the surface
Overhangs feasible
Splines
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From a set of control points with normal
No fault (continuity of surface)
Parametric form facilitates computation and visualization
Ordered list of points
Kriging
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Terrain realism
Statistical interpolation
Incorporates domain knowledge
Fills gaps in input dataset
Completely automatic
[Siska and Hung 2001]
Discrete Smooth Interpolation
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Computes missing information
Iterative minimization algorithm (high complexity)
Efficient in iterative modelling (adjust existing model)
No multi-scale representation
Automatic method
Part 3Daniel Patel
Solid models
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Solid models A solid object divides space into two parts – interior and
exterior
A solid representation provides a point membership predicate that tells if a point is inside or outside the solid
Interactive clipping techniques for texture-based volume visualization and volume shading. Weiskopf et al.2003 2
Solid models in the Geosciences Opens up for more advanced visualization and analysis
Is the first step in producing physical simulations of liquid or gas flow inside the model
The output from the surface-creation stage can be input to to the solid-creation methods
Often called a sealed model
Multiscale Vector Volumes by Wang et al. 2011 3
Data Free Scenario for Solids In the data-free scenario
we will discuss now, there is no ground truth (measured) data
Models are created from scratch, driven by imagination or concept ideas and domain knowledge
In geosciences: For sketching hypotheses and for education
In computer graphics : For games and art 4
Solid Assembly (data free)
By solid assembly, we refer to the process of assembling boundary surfaces or basic solid building blocks into a complete solid object.
Such a work process is supported by CAD based tools
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Solid Assembly Natali et al. 2012
Assembling geological layer-cake models
Sketch 2D curves
Extrude and triangulate
Conformal texturing
Cut
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Time with Natali et al. Method to create 3D model
Time in Adobe Illustrator by a geologic illustrator to create 2D image
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Solid Assembly Natali et al. 2012
Solid Representations (data free)
In the following we consider three solid representations:
Semisolid representation using voxelizationArches - Peytavie et al. 2009
Solid representations with spatially varying properties : Diffusion surfaces by
Takayama et al. 2010
Multiscale Vector Volumes by Wang et al. 2011
Voxel representation Peytavie et al. 2009
[PGGM09a] Peytavie et al.. Arches: a Framework for Modeling Complex Terrains
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Diffusion surfaces Takayama et al. 2010 An extension of diffusion curves [Orzan et al. 2008] to
3D volumes A set of coloured surfaces describing the model’s
volumetric colour distribution A smooth volumetric colour distribution that fills the
model is obtained by diffusing colours from these surfaces Colours are interpolated only locally at the user-defined
cross-sections using a modified version of the positive mean value coordinates algorithm
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Multiscale Vector Volumes Wang et al. 2011
Objects are represented as implicit functions using signed distance functions
Composite objects are created by combining implicit functions in a tree structure
This makes it possible to produce volumes made of many smaller inner components
This multi-structure framework makes it possible to produce models irrespective of resolution
More compact than CSG and adaptively sampled distance fields
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Measured Data (sparse/dense data) data) When modelling an actual subsurface volume,
measurements are taken and a model that fits the measurements is created.
Relevant for analyzing the stability of the ground for identifying subsurface resources such as
Ground water Minerals Hydrocarbons
Examples of data for creating a solid model are Volumetric measurements such as seismic
reflection, gravity, electromagnetism (dense) 2D slices of seismic (sparse) 1D measurements of well logs from bore holes
(sparse)
Expensive to perform subsurface measurements 12
Measured Data (sparse/dense data) data) Seismic reflection data is collected by sending sound
waves into the ground and analyzing the echoes.
When the sound waves enter a new material with a different impedance, a fraction of the energy is reflected
Therefore, various layer boundaries of different strength are visible as linear trends in the seismic data
geomaticsolutions.com 13
Interpretation
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Seismic slice
Vertical axis is depth
Up to 5 km
Seismic is shown in gray-scale. Sometimes with blue and red in
interpretation in color Faults are red Important
horizons in other colors
Source, Reservoir and Trap for hydrocarbons
Figures from
http://resources.schoolscience.co.uk
Organicmaterial layering
Burial with pressure and heat
Migration from source, through porous material to trap
Porous material
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Seismic objects
Objects which can be detected in the collected data and can help indicate presence of hydrocarbons:
Horizons
Faults
Channels
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Seismic objects: horizons and faults
http://mpgpetroleum.com/ 17
Seismic objects: channels
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Interpretation Several commercial tools exist for interpreting 3D seismic data.
One example is Petrel by Schlumberger Horizon interpretation from 3D seismic
The user sets seed points and/or interpolation curves. Then the system grows out a surface. The user can change the growing criteria or the seed
points/curves until a satisfactory surface is extracted. This can be time consuming.
Editing surface is hard
Some papers have suggested a faster interpretation procedure Creating surfaces:
Kadlec et al. 2010: Interactive growing Patel et al. 2010: Growing performed in a preprocess
Editing surfaces: Parks 2009: Freeform editing of grown surfaces Amorim et al. 2012 Freeform editing and snap-to-data
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Interpretation Kadlec et al. [KTD10] present a system where the user
interactively steers the growing parameters to guide the segmentation instead of waiting until the growing is finished before being able to investigate it.
Growing is based on level set methods
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Interpretation Fast extraction of horizon surfaces is the focus of Patel et al.
[PBVG10]. Preprocessing for extracting possible structure candidates in
3D seismic reflection volume (hours). After preprocessing, user can quickly construct horizon
surfaces by selecting candidates from the preprocessed data. Compact storage of surface candidates using a single
volumetric distance field representation (assuming surfaces do not intersect).
Fast picking and integrated volume rendering Editing existing surfaces is not possible.
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Interpretation Editing is addressed by Parks [Par09]. He presents a
method that allows to quickly modify a segmented geologic horizon and to cut it for modeling faults.
Free-form modelling is achieved using boundary constraint modelling [Botch & Kobbelt 04]. This is simpler and more direct than Spline modelling, which requires manipulation of many control points.
Discontinuities arising from faults are created by cutting the mesh
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Interpretation Amorim et al. [ABPS12] allow for more advanced surface
manipulation Surfaces with adaptive resolution can be altered and cut
with several sketch-based metaphors. Also, the sketching takes into account the underlying 3D
seismic so that it can automatically detect strong reflection signals which may indicate horizons and automatically snap the sketched surface into position.
[Amorim et al. 2012]23
Solid Assembly (based on measured data) Surfaces that have been interpreted or grown may
be inaccurate Caumon et al. 2004 [CLSM04] present rules for
creating a correct and sealed model from inaccurate input surfaces:● Horizons can not cross each other
Only faults can have free borders, horizon borders must terminate into other surfaces
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Solid Assembly (based on measured data)
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Four horizons and three faults which are connected Quickly gets complex Criteria are satisfied. Horizons are connected, faults
can have free borders
Solid Assembly (based on measured data) Additional rules in follow-up - Caumon et al.
[CCDLCdV*09] Geological surfaces are always orientable - no
twists, Möbius ribbon topology or self-intersections Using implicit surfaces instead of triangulated surfaces
directly enforce several validity conditions as well as making model updates easier, however at the cost of larger memory consumption.
For simple fault structures: Model faults and their connectivity first. This partitions space into fault blocks then introduce horizons.
For complex fault structures: Model horizons first, then introduce faults.
Important to be aware of the varying degree of uncertainty in the different measured data modalities and somehow encode it in the model. They suggest to use triangulations of different coarseness. 26
Solid Assembly (based on measured data)
Baojun et al. [BBZ09] generate solid model from borehole data using commercial tools and standards.
They use ArcGIS for creating interpolated surfaces from the sparse data.
Baojun et al. 2009
Interpolation such as Inverse Distance Weighted, Natural Neighbor, or Kriging to create a collection of height-maps which are imported into 3D Studio Max and stacked into a layer cake model .
Then Constructive Solid Geometry is used to create holes at places where data is missing in the well logs.
The model is then saved as VRML enabling widespread dissemination since it can be viewed in web browsers 27
Solid Assembly (based on measured data)
Lemon and Jones 2003. Generating solid model from borehole data
For creating a closed model, they show that CSG together with set operations can be problematic as the set operation trees grow quickly with increased model complexity 28
Solid Assembly (based on measured data)
They simplify the model construction by representing horizons as triangulated surfaces while letting all horizon vertices have the same set of (x; y) positions and only varying the z positions.
This simplifies intersection testing between horizons and makes it trivial to pairwise close horizons by triangulating around their outer borders.
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Solid Assembly (based on measured data)
Complexity increases when models must incorporate discontinuities in the layers due to the faults.
Wu and Xu 2003, describe the spatial interrelations between faults and horizons using a graph with horizons and faults as nodes. The graph is used to find relevant intersections and bounding surfaces which are Delaunay triangulated to form closed bodies
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Solid Representations 3-G Map
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. A 3-G-map Lienhardt [Lie91] is defined as a set of darts D and three functions on them
Solid Representations 3-G Map
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• The 3- G-map is a simple yet powerful structure for defining the topology, in such a way that it is easy to traverse the space between connected or neighbouring vertices, surfaces and solids
• For 3-G-maps, topology must be described very detailed. To relieve the user from this task, several abstractions have been suggested. By letting the user instead define the relation and cuts between horizons and faults in a graph or tree datastructure, a system can then generate a detailed topology description from this
Solid Representations 3-G Map
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For automated topology in 3-G-maps
Perrin et al. 05 [PZRS05], specifies a graph of chronological order for when the surfaces have been physically created
In addition a graph describing the fault network using the relation “fault A stops on fault B”, is specified
This seems to be more like theoretical work
Solid Representations Implicit (not in paper)
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Siggraph 2001 paper on fast RBfs
Cowan et al. 2003. Practical Implicit Geological Modelling
Leapfrog: Commercial Geological Modelling Software
Solid Representations comparison
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• Categories are not ideal, not mutually exclusive. Based on papers• CSG can use implicits or B-reps (3-G maps)• Vector volumes use implicits and some form of space partitioning
(voxel representation)
Implicit Solids
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+ Layer support by combination of implicit primitives or by RBFs + Channel/Cavity support by implicit functions + Ease of modeling: Interactive and sketch-based modeling
[Brazil et al. 10 rbfs, Karpenko et al. 02] -- Processing requirements: evaluate and transform to mesh or
raycast ++ Storage requirements: only the functions + Multiscale (Shapeshop [Schmidt et al. 06])
3-G-maps
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++ Layer support. Can represent topological fault information
+ Channels/cavities. Due to boundary representation + Ease of modelling. Supports triangle meshes o/+ Processing requirements . Faster than CSG. Triangle
meshes o Storage requirements. Store geometry and topology + Multiscale. Details at arbitrary level using triangulations
Voxel Representation
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+ Layer. Simply assign segmentation mask to voxel + Channels/Cavities. Tag voxel as empty - Ease of modelling. Unpractical to model directly on
voxels + Processing requrements. Direct access from position to
content -- Storage. Very space demanding -- Multiscale. Scale is bound by resolution.
+ Layer support. Possible using tree of signed distance functions + Channel support. Possible using tree of signed distance functions - Ease of modelling. Converting mesh into vector volumes o Processing requirements. Faster than implicit due to voxel lookup -/o Storage. Grid of voxel lookups and set of implicit functions ++ Multiscale. Interior and exterior stored in a hierarchical fashion
Vector Volumes
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GeosciencesComputer Graphics
Better knowledge transfer between computer graphics and geosciences
Geoscience technology is lagging behind
With current modelling technology, uncertainty is difficult to express, and models are hard to update
Current tools focus on precise modelling rather than rapid modelling as the latter is more challenging
Combine different representations in one model
Challenges and Trends
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GeosciencesComputer Graphics
Caumon et al. [CCDLCdV*09] state that beginners with 3D modeling too often lose their critical sense about their work, mostly due to a combined effect of well-defined graphics and nonoptimal human-machine communication.
Interesting research directions:
Procedural geological modelling that takes advantage from sparsely defined acquired information about the subsurface
Consideration of the temporal aspect in geology
Challenges and Trends
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Thank you!
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“Modeling Terrains and Subsurface Geology”
Mattia Natali, Endre M. Lidal, Július Parulek, Ivan Viola, Daniel Patel