3D curvature analysis of seismic waveform & its interpretational

implicationsHaibin Di, Motaz Alfarraj, and Ghassan AlRegib

Center for Energy & Geo Processing (CeGP)Georgia Institute of Technology

{hdi7, motaz, alregib}@ece.gatech.eduSeptember 25, 2017

INT E-P1: Attribute Applications @ SEG 2017

Outline• Motivation• Waveform curvature vs. geometric curvature• Three implications• Application to horizon modeling• Conclusions

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Motivation• Curvature analysis is useful for measuring the reflector geometry to

depict the surface morphology and highlight the potential faults and fractures caused by anticlinal bending (e.g., Roberts, 2001);

• The reflector geometry is only partial information offered in a seismic cube, and the reflection waveform is also of significant importance for interpreting the seismic signals;

• What if applying the curvature analysis to the reflection waveforms?

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Curvature

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𝑘𝑘2𝐷𝐷(x, z) =𝑧𝑧′′

1 + 𝑧𝑧′2⁄3 2

𝑘𝑘3𝐷𝐷𝑚𝑚𝑚𝑚𝑚𝑚 𝑥𝑥,𝑦𝑦, 𝑧𝑧 = MAX(𝑘𝑘3𝐷𝐷𝜑𝜑 𝑥𝑥,𝑦𝑦, 𝑧𝑧 , 𝜑𝜑=[0o, 360o))

𝑘𝑘3𝐷𝐷𝑚𝑚𝑖𝑖𝑖𝑖 𝑥𝑥,𝑦𝑦, 𝑧𝑧 = MIN(𝑘𝑘3𝐷𝐷𝜑𝜑 𝑥𝑥,𝑦𝑦, 𝑧𝑧 , 𝜑𝜑=[0o, 360o))

where 𝑘𝑘3𝐷𝐷𝜑𝜑 𝑥𝑥, 𝑦𝑦, 𝑧𝑧 = 1

1+𝐴𝐴12+𝐴𝐴22⁄1 2 �

𝐵𝐵1+𝐵𝐵2 tan2 𝜑𝜑+2𝐵𝐵3𝑡𝑡𝑚𝑚𝑖𝑖𝜑𝜑1+𝐴𝐴12 + 1+𝐴𝐴22 𝑡𝑡𝑚𝑚𝑖𝑖2𝜑𝜑+2𝐴𝐴1𝐴𝐴2𝑡𝑡𝑚𝑚𝑖𝑖𝜑𝜑

Waveform Curvature: 1D trace

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𝑘𝑘2𝐷𝐷(z, w) =𝑤𝑤′′

1 + 𝑤𝑤′2 ⁄3 2

where z: vertical coordinatew: waveform amplitude

2nd-order derivative resolution enhancement

Waveform Curvature: 2D section

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Take inline section for example:

𝒌𝒌𝟑𝟑𝟑𝟑𝒎𝒎𝒎𝒎𝒎𝒎 𝒎𝒎, 𝒛𝒛,𝒘𝒘 = MAX(𝒌𝒌𝟑𝟑𝟑𝟑𝝋𝝋 𝒎𝒎, 𝒛𝒛,𝒘𝒘 , 𝝋𝝋=[0o, 360o)) (in blue)

𝒌𝒌𝟑𝟑𝟑𝟑𝒎𝒎𝒎𝒎𝒎𝒎 𝒎𝒎, 𝒛𝒛,𝒘𝒘 = MIN(𝒌𝒌𝟑𝟑𝟑𝟑𝝋𝝋 𝒎𝒎, 𝒛𝒛,𝒘𝒘 , 𝝋𝝋=[0o, 360o)) (in red)

where x: crossline coordinatez: vertical coordinatew: waveform amplitude

Crossline No.

SampleNo.

Waveform Curvature

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Geometric curvature Waveform curvatureObject Curvature analysis of seismic signals

Information for analysis

a. Structural depth/timeb. Reflection amplitude Reflection waveform

Computation direction

Horizontal(the 𝑥𝑥-𝑦𝑦 plane)

Vertical(the 𝑥𝑥-𝑧𝑧 and/or 𝑦𝑦-𝑧𝑧 plane)

Implications

Structure analysis:a. Fault detectionb. Fracture characterizationc. Reflector morphology

delineation

Waveform analysis:a. Resolution enhancementb. Dip estimation c. Reflector decomposition

Table: Geometric curvature vs. waveform curvature

Implication #1: Resolution enhancement

8Original amplitude section Maximum waveform curvature

a. Curvature: 2nd-order derivative better resolutionb. Maximum curvature: Normal to the reflection more reliable analysis

Implication #2: Dip estimation

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Minimum curvature: Parallel to the reflection reflector dip

Orientation of Minimum waveform curvature Dip-guided horizon tracking

More in my next presentation at 3:05 pm

Implication #3: Reflector decomposition

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Peaks Troughs

S-crossings Z-crossings

Application to horizon modeling

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Peak decomposition Thinning

Seed picking and sortingSeeded horizon trackingHorizon model

Seismic image

Limitations• Sensitivity to high-frequency components• Sensitivity to vertical window size• Sensitivity to seismic noises

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Limitation #1: Sensitivity to high-frequency components

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Maximum waveform curvature

Original amplitude

-15000 +15000

-0.5 +0.5

Take Ricker wavelet for example𝑤𝑤 𝑡𝑡 = 𝐴𝐴 � 1 − 2𝜋𝜋2𝑓𝑓𝑀𝑀

2𝑡𝑡2 𝑒𝑒−𝜋𝜋2𝑓𝑓𝑀𝑀2𝑡𝑡2

Waveform curvature:𝑘𝑘 0,𝑤𝑤 = 6 � 𝐴𝐴 � 𝜋𝜋2𝑓𝑓𝑀𝑀

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• Linear to amplitude A• quadratic to frequency f

Limitation #2: Sensitivity to vertical window size

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Z

Window size = 7

Window size = 3

Window size = 9

Window size = 5

-0.5 +0.5

Window size no larger than half of the waveform period

Limitation #3: Sensitivity to seismic noise

15-0.5 +0.5

From smoothed seismic

From original seismic

For resolution enhancement: use original amplitude

For dip estimation :Apply smoothing first

For horizon interpretation:Apply smoothing first

Conclusions• Curvature analysis is extended to seismic waveforms;• Several implications:

• Resolution enhancement along the direction normal to seismic reflectors• Dip estimation• Reflector decomposition to peaks, troughs, and z/s-crossings;

• Potentials for horizon interpretation and modelling

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More information (e.g., recent research, publications, tools, and codes) is available by:Visit our booth: #2109Visit our center: http://www.ghassanalregib.comVisit my webpage: https://sites.google.com/site/dihaibin/