Uncertainty Maps for Seismic Images through Geostatistical Model

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Uncertainty Maps for Seismic Images through Geostatistical Model Randomization Lewis Li, Paul Sava, &

Uncertainty Maps for Seismic Images through Geostatistical Model Randomization Lewis Li, Paul Sava, & Jef Caers 27 th SCRF Affiliates’ Meeting May 8 -9 th 2014

Motivation: Assessing Seismic Uncertainty Seismic Acquisition Velocity Model Time Migration Depth Migration SCRF Interpretation

Motivation: Assessing Seismic Uncertainty Seismic Acquisition Velocity Model Time Migration Depth Migration SCRF Interpretation 2

Velocity Uncertainty ¡Iterative migration and velocity updating ¡ Expensive ¡ Single “best guess” model

Velocity Uncertainty ¡Iterative migration and velocity updating ¡ Expensive ¡ Single “best guess” model ¡Clapp (2004)1 generate multiple smoothly varying velocity models in 1 D ¡Goal: 3 D and account for deposits and discontinuities 1. Clapp, Robert G. "Velocity uncertainty in tomography“ Stanford Exploration Project, Report 115, May 22, 2004, pp. 233 -248 3

Interpretation Uncertainty ¡ 412 expert interpretations, 21% correct (Bond et al. , 2007) ¡Dealing

Interpretation Uncertainty ¡ 412 expert interpretations, 21% correct (Bond et al. , 2007) ¡Dealing with uncertainty ¡Multiple experts, multiple interpretations ¡Tools to aid interpreter ¡Uncertainty map indicate to interpreter regions of high uncertainty 4

What Do You Think This Is? Reflector ? Faults? Canyons? 5

What Do You Think This Is? Reflector ? Faults? Canyons? 5

Interpretation Aids Feature Best Guess Shape Uncertainty Truth Positional Uncertainty 6

Interpretation Aids Feature Best Guess Shape Uncertainty Truth Positional Uncertainty 6

Extension to Existing Workflow 7

Extension to Existing Workflow 7

Stochastic Salt Modeling • Target reservoir under salt body • Salt has higher velocity

Stochastic Salt Modeling • Target reservoir under salt body • Salt has higher velocity • Acts a lens • Sub-salt plays can be productive, ex: Gulf of Mexico • Capture uncertainty in salt boundary 8

Stochastic Generation Workflow Given a reference velocity image: q Generate representative realizations q Account

Stochastic Generation Workflow Given a reference velocity image: q Generate representative realizations q Account for uncertainty of reference q Computationally fast One approach: Fractals 9

What Are Fractals? ¡Mathematical set that displays self-similar patterns ¡ Looks the same/similar from

What Are Fractals? ¡Mathematical set that displays self-similar patterns ¡ Looks the same/similar from up close/far away ¡Discovered by Benoit Mandelbrot in 1967 ¡Natural phenomena exhibit fractal properties 10

Characterizing Fractals By Dimensions ¡The fractal dimension is measure of detail in the pattern

Characterizing Fractals By Dimensions ¡The fractal dimension is measure of detail in the pattern change with the scale it is being measured at ¡Consider fractal coastline of England ¡ What is it’s length? ¡ Depends on how we are measuring it… ¡Mandelbrot termed it a measure of “roughness” 11

Characterizing Roughness ¡ Find local roughness of salt body ¡ Compute fractal dimension in

Characterizing Roughness ¡ Find local roughness of salt body ¡ Compute fractal dimension in sliding window along contour ¡Contour detection ¡ Minkowski–Bouligand dimension 12

Characterizing Roughness Local Surface Roughness 13

Characterizing Roughness Local Surface Roughness 13

Defining Uncertainty Buffers Illumination Human Defined. Map Buffer 14

Defining Uncertainty Buffers Illumination Human Defined. Map Buffer 14

Generate Anchor Points ¡ Sample portion of points (~5%) from original ¡ Perturb by

Generate Anchor Points ¡ Sample portion of points (~5%) from original ¡ Perturb by a noise proportional to uncertainty buffer in that region 15

Fractal Interpolation 16

Fractal Interpolation 16

Resulting Realizations 17

Resulting Realizations 17

How Do We Use These Realizations? ¡Migration ¡Discuss later how to decrease cost ¡Variation

How Do We Use These Realizations? ¡Migration ¡Discuss later how to decrease cost ¡Variation of seismic images ¡Different metrics = different types of uncertainty 18

Euclidean Distance Map ¡ Euclidean map indicates where pixels/voxel values are changing the most

Euclidean Distance Map ¡ Euclidean map indicates where pixels/voxel values are changing the most ¡ Indicates regions of high positional uncertainty ¡ Relatively fast to compute 19

Procrustes Analysis Euclidean Distance: Voxel Comparison Real #1 Dissimilarity = 0. 09 Procrustes Distance:

Procrustes Analysis Euclidean Distance: Voxel Comparison Real #1 Dissimilarity = 0. 09 Procrustes Distance: Shape Analysis, Artifact Detector Real #2 Four Step Procedure: 1. Find centroids, translation Real #2 2. Find size, scale ratio 3. Find optimal rotation 4. Compute Squared Sum Difference Real #2 Transformed Real #1 20

Procrustes Distance Map ¡ Pre-process images to binary ¡ Compute map as before ¡

Procrustes Distance Map ¡ Pre-process images to binary ¡ Compute map as before ¡ Procrustes map shows where shapes are changing the most ¡ Indicates regions of high structural uncertainty ¡ Slower to compute 21

Model Selection ¡“Proxy” distances ¡Norm of difference between models ¡Procrustes distance of salt contour

Model Selection ¡“Proxy” distances ¡Norm of difference between models ¡Procrustes distance of salt contour ¡Construct distance matrix for all realizations 22

Multi-Dimensional Scaling 12 Realization Procrustes Map 50 Realization Procrustes Map MDS Projection of Velocity

Multi-Dimensional Scaling 12 Realization Procrustes Map 50 Realization Procrustes Map MDS Projection of Velocity Model Distance 23

Conclusions Workflow ¡Migration uncertainty ¡Multiple velocities using fractal approach ¡Interpretation uncertainty ¡Uncertainty maps to

Conclusions Workflow ¡Migration uncertainty ¡Multiple velocities using fractal approach ¡Interpretation uncertainty ¡Uncertainty maps to aid interpreter Future Steps ¡Extension to 3 D, multiple bodies, real data ¡Collaboration with Stanford Exploration Project (SEP) ¡Quantitative measure of uncertainty buffer ¡Integration with structural uncertainty 24

Bonus Slides: CCSIM Based Velocity Modeling 25

Bonus Slides: CCSIM Based Velocity Modeling 25

Uncertainty Maps for Seismic Images through Geostatistical ModelUncertainty Maps for Seismic Images through Geostatistical Model
SEISMIC HAZARD Seismic risk versus seismic hazard SeismicSEISMIC HAZARD Seismic risk versus seismic hazard Seismic
Seismic Wave Propagation What are Seismic Waves SeismicSeismic Wave Propagation What are Seismic Waves Seismic
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