Modeling Terrains and Subsurface Geology M. Natali, E. Lidal, J. - - PowerPoint PPT Presentation

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)

2

Presentations and Presenters

Introduction and Taxonomy Part 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

4

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

5

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

6

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

8

Taxonomy According to Origin

9

Taxonomy According to Workflow

Surface Creation and Representation

Part 2

• M. Natali

Workflow T axonomy

2

Fractal and Erosion

3

 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

4

 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

5

 Schneider et al., Realtime editing, synthesis, and rendering

• f infinite landscapes on GPUs, 2006

 Reduction of parameter setting  Interactive fractal landscape synthesizer

Erosion Example I

6

 Benes and Forsbach, Visual simulation of hydraulic

erosion, 2002

 Physically-based approach with high level control  Fast and stable

Erosion Example II

7

 Benes et al., Hydraulic erosion, 2006  Fully based on fluid mechanics (Navier-Stokes)  Voxel grid representation

Erosion Example III

8

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

9

 Kristof et al., Hydraulic Erosion Using Smoothed Particle

Hydrodynamics, 2009

 Smoothed Particle Hydrodynamics (SPH) employed  Works on large terrains

Erosion Example V

10

 Hnaidi et al., Feature based terrain generation using

diffusion equation, 2010

 Constrained modelling process  Curves with properties (elevation, slope angle, ...)

Erosion Example VI

11

 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 T errains

12

 Rapid modelling  Expressive  Intuitive  No need to set parameters

[Gain et al. 2009]

Sketching T errains - Example I

13

 Watanabe and Igarashi, A sketching interface for terrain

modeling, 2004

 Noise after surface deformation  Local minima and maxima for area of influence

Sketching T errains - Example II

14

 Gain et al., Terrain Sketching, 2009  Sketch-based procedural generation  Elevation + area of influence  Noise where required

Sketching T errains - Example III

15

 Vital Brazil et al., Sketching Variational Hermite-RBF

Implicits, 2010

 3D closed surfaces using implicit functions  General tool, adaptable to geology

Sketching T errains - Example IV

16

 Sketches combined with exemplar-based technique  Height-map sketching  Zhou et al., Terrain synthesis from digital elevation

models, 2007

By-example - Example I

17

 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

18

 Height maps  Implicit surfaces  Meshes

[de Carpentier and Bidarra 2009]

[Brazil et al. 2010]

Workflow T axonomy

19

Sparse- and Dense-data

20

 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

21

 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

22

 Orientable surfaces  Implicit surfaces imply validity conditions  Caumon et al., Surface-Based 3D Modeling of Geological

Structures, 2009

Interpolation

23

 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

25

 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

26

 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

27

 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

28

 B-spline  Inverse distance  Kriging  Discrete Smooth Interpolation (DSI)  Natural Neighbor Interpolation  The natural neighbors of any node are those in the

neighboring Voronoi cells, or equivalently, those to which the node is connected by the sides of the Delaunay triangle

• N. Sukumar, UCDAVIS

Surface Representations

29

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

31

 Weathering simulation  Natural appearance of top surface  No discontinuity  Hard to control  Low storage, high processing

Exemplar-based

32

 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

33

 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

34

 From a set of control points with normal  No fault (continuity of surface)  Parametric form facilitates computation and visualization  Ordered list of points

Kriging

35

 T

errain realism

 Statistical interpolation  Incorporates domain knowledge  Fills gaps in input dataset  Completely automatic

[Siska and Hung 2001]

Discrete Smooth Interpolation

36

 Computes missing information  Iterative minimization algorithm (high complexity)  Efficient in iterative modelling (adjust existing model)  No multi-scale representation  Automatic method

Part 3

Daniel Patel

Solid models

1

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

5

Solid Assembly Natali et al. 2012

 Assembling

geological layer-cake models

 Sketch 2D

curves

 Extrude and

triangulate

 Conformal

texturing

 Cut

6

Time with Natali et

• al. Method to create

3D model Time in Adobe Illustrator by a geologic illustrator to create 2D image

7

Solid Assembly Natali et al. 2012

Solid Representations (data free)

In the following we consider three solid representations:

 Semisolid representation using voxelization

Arches - Peytavie et al. 2009 Solid representations with spatially varying properties :

 Diffusion surfaces by

T akayama 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

9

Diffusion surfaces T

akayama 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

10

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

11

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

14

 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

Organic material layering Burial with pressure and heat Migration from source, through porous material to trap Porous material

15

Seismic objects

Objects which can be detected in the collected data and can help indicate presence of hydrocarbons: Horizons Faults Channels

16

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

19

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

20

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.

21

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

22

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

24

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

• perations 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

• uter borders.

29

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

30

Solid Representations 3-G Map

31

 . A 3-G-map Lienhardt [Lie91] is defined as a set of

darts D and three functions on them

Solid Representations 3-G Map

32

• 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. T
• 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

33

 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)

34

 Siggraph 2001 paper on fast

RBfs

 Cowan et al. 2003. Practical

Implicit Geological Modelling

 Leapfrog: Commercial

Geological Modelling Software

Solid Representations comparison

35

• 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

36

 + 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

37

 ++ 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. T

riangle meshes

 o Storage requirements. Store geometry and topology  + Multiscale. Details at arbitrary level using triangulations

Voxel Representation

38

 + Layer. Simply assign segmentation mask to voxel  + Channels/Cavities. T

ag 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

39

Geosciences

Computer 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

40

Geosciences

Computer 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

41

Thank you!

42

“Modeling Terrains and Subsurface Geology”

Mattia Natali, Endre M. Lidal, Július Parulek, Ivan Viola, Daniel Patel