Uncertainty Maps for Seismic Images through Geostatistical Model

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 2

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 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

Interpretation Aids Artifact Best Guess Truth Uncertainty Positional Uncertainty 6

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: 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 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 ¡Find local roughness of salt body ¡Compute fractal dimension in sliding window along contour ¡Minkowski–Bouligand dimension 13

Characterizing Roughness 14

Defining Uncertainty Buffers 15

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

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 Dissimilarity = 0. 090519010066215 ¡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 Real #2 Transformed Real #1 21

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 3 D, 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