geomodeller inversion workflow details

Details of the Inversion

workflow

Des Fitzgerald

August 2007

Geology Constrained Inversion

Simple Slab Tutorial

Part 1 Background

A statistical approach

2007

Objectives

Demonstrate new approaches to inversion

Use all available geology, gravity and magnetics to constrain the result

Limit the infinite possibilities to a set that is consistent with all the facts

Bring latest inversion & probability thinking to geoscience

Constraining Your Geology

Geomodeller has a set of geological rules to resolve and constrain the initial model Contacts Dip/Strike Pile, erode/onlap Fault network

Inversion does not make direct use of these. Instead, it uses a framework of geological units, important for producing realistic property models allows simultaneous inversion of multiple

geophysical data types

Commonality Possessing like and interchangeable

characteristics

The number of voxels in common between the proposed models and the

reference model is controlled

statistically using a Commonality

constraint jRefjSame

j yCommonalit

Geological Commonality Misfit

Say you want 90%

Shape Ratio "Shape" is the square-root of surface area

divided by the cube-root of volume (to mimimize any scale dependence).

"ShapeRatio" is the Shape of the formation in the proposal divided by the Shape of the formation in the ReferenceModel.

Shape of a sphere = 2.2 No scale dependency

Shape of a cylinder h = r, Shape = 2.42 h = 2r, Shape = 2.35 h = 4r, Shape ~ 2.41

h = 20r, Shape ~ 2.89 Some aspect ratio dependency !

Cube Shape ~ 2.45

Prism square base r*r , height r/4 - Shape ~ 2.75

Geophysical Grid Preparation

Detrending

Need to be able to fit the anomalies caused by signal in your model

External influences or deeper sources are not relevant

Geomodeller does this on demand,

either just once at the beginning

Or on a regular basis as inversion continues

Grids continued

You create a Measured Grids List

Type, (eg Gravity)

Mean Elev., (eg 50m )

Precision, (eg 0.5 mGals)

Detrend, (eg Yes/No)

Detrend degree, (eg 0,1,2 etc)

detrend freq., (eg 0, or 100000)

grid URL (eg c:/data/bouguer.ers)

Geophysical Precision

An estimation of the standard deviation of the measurement error in your geophysical data

All observed data has inherent error due to a variety of factors

Typically, ground gravity would be good to about 0.5 mGals

Airborne Total Magnetic Intensity to about 1 nT

Overview of Cases

1. Forward Model Propose a start model, compute gravity response

2. Prior Only Propose a geological model, explore probability

space implied by the geological constraints

3. Fixed Geometry Solve for properties using a bounded least-squares

fit

4. Bi-Modal Property Only No proposed body, just a proposed density contrast

5. Constrained Geology Use gravity to constrain result

Overview continued

7. Constrained Geology

Use magnetics assuming induced response only


Joint gravity and magnetics


Use magnetics with the possibility of remanence


Use observed tensor gradients

Property Uncertainty

vs

Geological Modelling By default, we give equal importance to

these two differing aspects

You can speed convergence of your inversion, if you have a high confidence

in your properties and there in no

spread of values

Simply adjust all the effort towards the geological uncertainty

Tools & Status

The Geomodeller Tool as used for creating your 3D geological model, can also perform Forward Modelling functions

The ManageLithoInversion Tool is a Batch Processing tool only at V1.2 This is used for all other aspects of Inversion

Voxets Can be examined by Voxler, other thirdparty tools

Movies Standard thirdparty products



Part 2 Practical


2007

Test Problem

Find Buried Object Unknown dip / strike

Unknown density contrast

Unknown magnetic susceptibility

Observed Geophysics Vertical component of gravity

Total magnetic intensity

No remanence

Observed Gravity

Observed Magnetics

Make initial Geology Model

Propose a simple vertical slab as a

starting model

Buried 100 m

Dimension of 100 * 200 * 400

Make model

Save project

Initial Plan view of model

200m below surface

Test Properties

Slab density 3.67

Host density 2.67

Slab susceptibility 0.001

Host susceptibility 0.000001

Optional Extras

Slab remanence (0.05,0.00,100,25,115)

Host remanence (0.00,0.00,100,0,00)

Geophysics Observations

Data Collection height : 50m

Gravity Data

normal ground observations

Magnetic Data

Field Intensity: 50000

Inclination: -65

Declination: 25

Conditioning the Geophysics

For both Gravaity and Magnetics, we recommend you turn detrending ON

A first order trend should be fine, so choose 1

Gravity detrending should not need to be repeated as the inversion evolves

Sometimes Magnetic data can benefit from a further detrending adjustment of the misfit say every 100000 iteration

Actual Body

Preparing a case NewCase Command

Create an Inversion Case

Within this case the following are treated as constant

The voxet resolution and extent

The reference geological model

The physical property laws

The voxels to hold fixed

The geological constraints

The observed geophysical grids

Preparing a Run

Create an Inversion Run

Within this run the following are treated as constant

The Case

The number of iterations

The initial lithology and physical properties

The starting or initial geological model can be varied

Case 1 - Forward Modelling

Before starting the inversion, run forward model first

This is done via the Geomodeller Tool

This way we check that the starting geological model is reasonable

The assumed physical properties can be checked

Case 1 Instructions

Start Geomodeller

Load Simple slab

Geophysics menu

3d Forward/Inversion

Choose G00 (gravity)

Constant grid

Choose apply

Gravity Grids

Observed Initial

Forward

Not bad but missing some plunge??

Case 2 Prior Only

This is always recommended before full inversion

Do you have good geological control of proposed models ie are your geological models viable?

Methodology Ignore the geophysics

Constrain the geological arrangements with respect to a reference geology

Randomly perturb, evaluate model geologically using one or more of:

1. Shape ratio constraint

2. Commonality of new with reference

3. Volume ratio

Prior Only is an expression of geological uncertainty

Load start litho- & property models

Modify models

Test against geology model criteria

(Modification accepted) (Modification rejected)

Test against geophysics dataset

criteria

Continue?

Finish

Start

Fails

Fails

PRIOR ONLY

computational scheme

No Geophysics used

Mechanics

You describe your process via the file : Inversion.xml

This is both human and machine readable Try internet explorer on it!

A copy of Your Geomodeller Project is also made for each case this is also mostly an XML file

Current interface is via batch scripts

An inversion run can take time to complete

A voxet of 50m x 50m x 50m is produced

A voxel change log for every viable model is kept so that it is possible to reconstruct the evolving state after the event.

Inversion.xml -

Run Parameters 1

Iterations 100000

Commonality: Y

Slab Commonality Weibull(0.02,1.0)

Host Commonality Weibull(0.05,1.0)

Shape Ratio: Y

Slab ShapeRatio LogNormal(0.1,0.05) Host ShapeRatio LogNormal(0.0,0.05)



Part 3 Reporting


2007

Recommended Discipline for

Project layout

Querying Inversion Outputs

Once the inversion itself is complete various visuals can be produced to analyse the

results

Images along sections

Movies along sections

Geophysical grids of the computed geophysics

Surface mesh representing isovalues

Probability of lithology voxets

Available Queries MakeSummaryStats

Work out the summary statistics of all models between a start and end iteration. From this we can derive products such as the probability of a given lithology at a given cell

MakeHistogram Generates a histogram of densities and/or susceptibilities for each

Formation in a Voxel dataset

MakeSectionImage Generates a section through a Voxel dataset and presents it as a jpg

image that can then be displayed from within 3D GeoModeller

MakeDerivedVoxet Various operations on Voxel datasets. Ex. Searches though a list of

Sujmary stats datasets and can find the most probable formation

MakeEvolutionMovie On a nominated section can create an avi movie of the evolution of

the lithology model though the iterations

Example of 2 SuperSummary Stats Outputs

The names of the various queried output properties are defined in the voxet

header: eg 85% & 95% probabilty effects only property 5 below.

SuperSummaryStats_Case_4_Run_1_iterations_3000000_1000000_85_super.vo,

AND identically also in:

SuperSummaryStats_Case_4_Run_1_iterations_3000000_1000000_95_super.vo

Property 1 = Change Count

Property 2 = Mean Density

Property 3 = Std Dev Density

Property 4 = Most Probable

Property 5 = Most Probable Thresholded

Property 6 = probability 0 (First lithology from model)

Property 7 = probability 1 (Second lithology from model)

Property 8 = probability 2





Definition: Most probable thresholded

means

For the entire inversion after burn in, and considering

all of the accepted, proposed geology models Report back all the voxets which remain a single lithology for a given %, or more, of the total # of

proposals.

Report back the location and lithology of those voxets.

Black volumes indicate areas of greater changeability

of lithology, such that the threshold % was not met.

Section 130_000_N: Most probable geology

Section 130_000_N: Most probable geology Thresholded 85%

Section 130_000_N: Most probable geology Thresholded 95%

Example section

Each type of output statistic generated by MakeSuperSummaryStats

ProbabilityResults

Run1 - All random changes allowed

Run 2 - Body constrained by commonality and shape ratios

Mean Density

Predicted density

distributions

based purely

on geology

constraints

Raw Statistics of Prior Only Run

AcceptanceCount="73365 AcceptanceRatePerHour="434214" CommonalityRejectCount="12969" CommonalityTestCount="99999" ComputerName="RAYS-PC" Counter="100000" FinishedDateTime="24/ 8/2007 9:24:18.122000"

InterAcceptanceDifferentFormationCount="8926" InterAcceptanceSameFormationCount="64439" InterProposalDifferentFormationCount="35560" InterProposalSameFormationCount="64439

ProposalRatePerHour="591849" ShapeRejectCount="13665" ShapeTestCount="87030" StartedDateTime="24/ 8/2007 9:14:9.443000

Super Summary Stats

Statistical History of each voxel

Change count

Mean property

Standard deviation

Probability for each lithology

Most probable lithology over certain threshhold ( say > 90%)

Visualise via a voxet viewer or sectional images or movies

Run Parameters 2

We can show how the predicted bodies can be tightened up to honour the original shapes by changing the commonality

Iterations 100000

Commonality: Y Slab Commonality Weibull(0.1,1.0) Host Commonality Weibull(0.1,1.0)

Shape Ratio: Y Slab ShapeRatio LogNormal(0.10,0.05) Host ShapeRatio LogNormal(0.0,0.05)

Case 3 - No Geology Body Shape

Bi-Modal Properties

Another case to show the tool working in a way that is closest to existing

deterministic methods

Prepare a voxet with no buried geological body

Propose the existing of a second population via a bi-modal property law

Create Physical Properties 1

Create Bi-Modal Density for Host

80%

background

20% more

dense

Gravity Inversion of Bi-Modal

Case Final Density Section Image Since we

have no

geological

control the

density

anomaly is

biased to the

near surface

NB takes

500000

iterations

Case 4 - Gravity Inversion

Enforce commonality

Enforce Shape Ratio

Use observed ground gravity

Run for 100000 iterations


Modify models

Test against geological model


Test against gravity dataset

Continue?

Finish

Start

Fails

Fails

Gravity plus geology

constraints

computational scheme

Dipping Slab

Gravity Grids

Final

Observed

Initial

Case 5 Magnetics Inversion

Assume a small vertical slab body as a starting model

Constrain the geology via commonality and shape ratio

Use observed magnetic data to refine aspects of the bodys geometry and properties

Assume the magnetics is induced only

Dipping Slab

Magnetic Grids

Final

Observed

Initial


Modify models

Test against model criteria


Test against dataset criteria

Continue?

Finish

Start

Fails

Fails

Overview of the

computational

scheme

Case 6 - Joint Inversion

We have shown the dipping slab case using the observed gravity

Now we add observed magnetics to our case and run joint inversion

Run for 300000, with a burn-in of 200000

Most Probable Lithology

Joint Miss-fit evolution

Gravity and magnetic misfit during inversion

0

1

2

3

4

5

6

7

8

9

10

0 1000000 2000000 3000000 4000000 5000000 6000000

# iterations

mis

fit

(nT

/mG

al)

gravity

magnetic

Comments

This shows good adaption to the expected outcome

Both Mag. And Gravity contribute

Over-view of Outcomes

Gravity Only inversion

does not do depth estimates well

Volume/mass of geological anomaly is quite good

Induced Magnetics inversion

Depth to top of body is good

Orientation of body is also good

Poor estimate of body volume

Joint Magnetic & Gravity

Get both depth and volume OK

geomodeller inversion workflow details

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