modeling terrains and subsurface geology · interpretation several commercial tools exist for...

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