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 Velocity Model Depth Migration Interpretation Seismic Acquisition Time Migration SCRF 2

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

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? 5 Canyons? Reflector ? Faults?

Interpretation Aids Artifact Uncertainty 6 Positional Uncertainty Best Guess Truth

Extension to Existing Workflow 7

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:  Generate representative realizations  Account for uncertainty of reference  Computationally fast One approach: Fractals 9

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 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

Identify Salt Body  Find the salt body in the reference  Contour detection:  Hough Transform  Radon Transform 12

Characterizing Roughness 13  Find local roughness of salt body  Compute fractal dimension in sliding window along contour  Minkowski–Bouligand dimension

Characterizing Roughness 14

Defining Uncertainty Buffers 15

Generate Anchor Points 16  Sample portion of points (~5%) from original  Perturb by a noise proportional to uncertainty buffer in that region

Fractal Interpolation 17

Resulting Realizations 18

How Do We Use These Realizations?  Migration  Discuss later how to decrease cost  Analyze variation of resulting seismic images  Different metrics measure different types of uncertainty 19

Euclidean Distance Map  Euclidean map indicates where pixels/voxel values are changing the most  Indicates regions of high positional uncertainty  Relatively fast to compute 20

Procrustes Analysis 21  Four Step Procedure: 1.Find centroids and translation 2.Find size of shapes, and scale ratio 3.Find optimal rotation between shapes 4.Apply transformation and compute Squared Sum Difference Dissimilarity = Real #2 Real #1 Real #2 Transformed

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 22

Model Selection  Proxy distances  Norm of difference between models  Procrustes distance of contour of salt bodies  Construct distance matrix for all realizations 23

Multi-Dimensional Scaling 24

Conclusions Workflow  Migration uncertainty  Multiple velocities using fractal approach  Interpretation uncertainty  Uncertainty maps to aid interpreter Applications  Extension to 3D, multiple bodies, real data  Collaboration with Stanford Exploration Project (SEP)  Quantitative measure of uncertainty buffer  Integration with structural uncertainty 25

Bonus Slides: CCSIM Based Velocity Modeling 26