Overview of SomeOverview of Some Coherent Coherent Noise Filtering MethodsNoise Filtering Methods

Jianhua Yue, Yue Wang, Gerard SchusterJianhua Yue, Yue Wang, Gerard SchusterUniversity of UtahUniversity of Utah

Problem: Ground Roll Degrades SignalProblem: Ground Roll Degrades SignalOffset (ft)Offset (ft)

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003500350020002000

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ReflectionsReflections

Ground Ground RollRoll

Problem: PS Waves Degrade SignalProblem: PS Waves Degrade SignalT

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c)T

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PP ReflectionsPP Reflections

Converted S WavesConverted S Waves

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ReflectionsReflections

Converted S WavesConverted S Waves

31003100Depth (ft)Depth (ft)2000200000

TimeTime(s)(s)

0.140.14

Problem: Tubes Waves Obscure PPProblem: Tubes Waves Obscure PP

ReflectionsReflections

Aliased tube wavesAliased tube waves

• Radon Filtering MethodsRadon Filtering Methods• ARCO Field Data ResultsARCO Field Data Results• Saudi Land DataSaudi Land Data• Multicomponent Data ExampleMulticomponent Data Example• Conclusion and DiscussionConclusion and Discussion

OutlineOutline

Two Classes of CoherentTwo Classes of CoherentNoise FilteringNoise Filtering

Model Noise and Adaptive SubtractionModel Noise and Adaptive Subtraction

Filter that Exploit Moveout DifferencesFilter that Exploit Moveout Differences

F-K Dip FilteringF-K Dip Filtering

Filtering Methods:Filtering Methods:Moveout SeparationMoveout Separation

Filtering in Filtering in - p - p domaindomain linear linear - p - p parabolic parabolic - p - p hyperbolic hyperbolic - p - p local+adaptive subtractionlocal+adaptive subtractionLeast Squares Migration FilterLeast Squares Migration Filter

DistanceDistance

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NOISENOISE

SIGNALSIGNAL

WavenumberWavenumber

Fre

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Fre

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Separation Principle: Exploit Differences in Separation Principle: Exploit Differences in Moveout & Part. Velocity DirectionsMoveout & Part. Velocity Directions

SIGNALSIGNAL

NOISENOISETransformTransform

Overlap Overlap Signal & NoiseSignal & Noise

DistanceDistance

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V=1/PV=1/P

Tau

TauTransformTransform

SumSum

Tau-P TransformTau-P Transform

DistanceDistance

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Tau-P TransformTau-P Transform

Tau

Tau

V=1/PV=1/P

DistanceDistance

Tim

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ime TransformTransform Mute NoiseMute Noise

Tau-P TransformTau-P Transform

Tau

Tau

V=1/PV=1/P

Tau

Tau

DistanceDistance

Tim

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ime TransformTransform

Problem: IndistinctProblem: IndistinctSeparation Signal/NoiseSeparation Signal/Noise

V=1/PV=1/P

Tau-P TransformTau-P Transform

Tau

Tau

DistanceDistance

Tim

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V=1/PV=1/P

Tau-P TransformTau-P Transform Hyperbolic TransformHyperbolic Transform

Distinct SeparationDistinct Separation Signal/Noise Hi res.Signal/Noise Hi res.

DistanceDistanceT

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Breakdown of Hyperbolic Breakdown of Hyperbolic AssumptionAssumption

vv vv vv vv vv vv vv vv vv**Irregular MoveoutIrregular Moveout

DistanceDistance

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Filtering by LSMF Filtering by LSMF

PSPS

d =d = L m L m pp pp

d =d = L m L m ++ L mL mssss

P-reflectivityP-reflectivityKirchhoffKirchhoffModelerModeler

Invert for Invert for mm & & mmpp ss

ddPPPP

S-Refl. KirchhoffS-Refl. KirchhoffModelerModeler

LSMF MethodLSMF Method

2.2. Find Find mm by conjugate gradient by conjugate gradientpp

d =d = L m L m ++ L mL msssspp pp

1.1.

datadata unknownsunknowns

dd = = L m L m pp pp

3. Model Coherent Signal3. Model Coherent Signal

OutlineOutline• Radon Filtering MethodsRadon Filtering Methods• ARCO Surface Wave DataARCO Surface Wave Data• Saudi Land Data: Local Adapt.+Subt.Saudi Land Data: Local Adapt.+Subt.• Multicomponent Data ExampleMulticomponent Data Example• Conclusion and DiscussionConclusion and Discussion

RAW DATA OF ARCORAW DATA OF ARCO

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1.8 3.6X (kft)

Raw Data

ARCO DATAARCO DATAT

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X (kft) X (kft)

FKFK LSMFLSMF

A

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ZOOM VIEW OF WINDOW “ A”ZOOM VIEW OF WINDOW “ A”T

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2.0 3.0X (kft)

FK LSMF

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2.0 3.45X (kft)

FK LSMF

ZOOM VIEW OF WINDOW “ B”ZOOM VIEW OF WINDOW “ B”

OutlineOutline• Radon Filtering MethodsRadon Filtering Methods• ARCO Surface Wave DataARCO Surface Wave Data• Saudi Land Data: Local Adapt.+Subt.Saudi Land Data: Local Adapt.+Subt.• Multicomponent Data ExampleMulticomponent Data Example• Conclusion and DiscussionConclusion and Discussion

4.0s

Aramco Saudi Land Data Aramco Saudi Land Data

0.0s

Local tau-pLocal tau-p

N SS++

N SS++~~~~

Tau-pTau-p

Tau-pTau-p -1-1

N N SS++-- == SS

Adaptive SubtractionAdaptive Subtraction

Input After Noise ReductionInput After Noise ReductionInput After Noise ReductionInput After Noise Reduction

INPUT LOCAL TAU-PINPUT LOCAL TAU-P

(courtesy Yi Luo @ Aramco)(courtesy Yi Luo @ Aramco)4.0s

0.0s

Input FKInput FK

Signal FKSignal FK

FF

KK

FF

KK

• Radon Filtering MethodsRadon Filtering Methods• ARCO/Saudi Field Data ResultsARCO/Saudi Field Data Results• Multicomponent Data ExampleMulticomponent Data Example Graben ExampleGraben Example

Mahagony ExampleMahagony Example

• Conclusion and DiscussionConclusion and Discussion

OutlineOutline

Graben Velocity ModelGraben Velocity Model

05000

Dep

th (

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3000

0 X (m)

V1=2000 m/s

V2=2700 m/s

V3=3800 m/s

V4=4000 m/s

V5=4500 m/s

Synthetic DataSynthetic Data

1.4

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0 Offset (m)5000

Horizontal ComponentHorizontal Component Vertical ComponentVertical Component

PP1 LeakPP1 Leak

PP2 PP2 LeakLeak

PP3 PP3 LeakLeak

PP4 PP4 LeakLeak

PP1PP1

PP2PP2

PP3PP3

PP4PP4

LSMF SeparationLSMF Separation

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Offset (m)Offset (m) 5000

0

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Horizontal ComponentHorizontal Component Vertical ComponentVertical Component

PP1PP1

PP2PP2

PP3PP3

PP4PP4

True P-P and P-SV ReflectionTrue P-P and P-SV Reflection

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Horizontal ComponentHorizontal Component Vertical ComponentVertical Component

PP1PP1

PP2PP2

PP3PP3

PP4PP4

F-K Filtering SeparationF-K Filtering Separation

1.4

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Horizontal ComponentHorizontal Component Vertical ComponentVertical Component

PP1PP1

PP2PP2

PP3PP3

PP4PP4

PP1 LeakPP1 Leak

PP2 PP2 LeakLeak

PP3 PP3 LeakLeak

PP4 PP4 LeakLeak

• Radon Filtering MethodsRadon Filtering Methods• ARCO/Saudi Field Data ResultsARCO/Saudi Field Data Results• Multicomponent Data ExampleMulticomponent Data Example Graben ExampleGraben Example

Mahagony Field DataMahagony Field Data

• Conclusion and DiscussionConclusion and Discussion

OutlineOutline

CRG1 Raw DataCRG1 Raw Data

CRG1 (Vertical component) CRG1 (Vertical component)

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4PSPS PSPS

PSPS

CRG1 (Vertical component) CRG1 (Vertical component)

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CRG1 Data after Using F-K FilteringCRG1 Data after Using F-K Filtering

PSPS PSPS

PSPS

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CRG1 Data after Using LSMFCRG1 Data after Using LSMF

PSPS PSPS

PSPS

Local tau-p and adaptive subtractionLocal tau-p and adaptive subtraction

LSMF computes moveout and particleLSMF computes moveout and particle velocity direction based on true physics.velocity direction based on true physics.

Don’t use a shotgun to kill a flyDon’t use a shotgun to kill a fly

ConclusionsConclusions Filtering signal/noise using: moveoutFiltering signal/noise using: moveout difference & particle velocity directiondifference & particle velocity direction

FKFK LinearLinearTau-PTau-P

ParabolicParabolicTau-PTau-P

LSMFLSMF

Simple FilteringSimple Filtering YESYES YESYES YESYES YESYES

Complex FilteringComplex Filtering NoNo YES/YES/NoNo YES/YES/nono YESYES

User InterventionUser Intervention YesYes YesYesMildMild YesYes

CostCost cc $$ $$ $$$$$$$$

ProvenProven YESYES YESYES YESYES Yes/Yes/NoNo

SUMMARYSUMMARY

SAUDI DATASAUDI DATA

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Raw Data

SAUDI DATA AFTER FK & LSMFSAUDI DATA AFTER FK & LSMFT

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88 2988X (m)

FK LSMF

A AB B

CRG2 (Vertical component) CRG2 (Vertical component)

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CRG2 Data after Using F-K Filtering (vertical component)CRG2 Data after Using F-K Filtering (vertical component)

CRG2 (Vertical component)

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CRG2 Data after Using LSMF (vertical component)CRG2 Data after Using LSMF (vertical component)

ZOOM VIEW OF WINDOW A ZOOM VIEW OF WINDOW A T

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(s)

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2.0

890 2088X (m)

FK LSMF

890 2088X (m)

ZOOM VIEW OF WINDOW B ZOOM VIEW OF WINDOW B T

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2.0

186 1189X (m)

FK LSMF

186 1189X (m)

SAUDI DATASAUDI DATA

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Raw Data

SAUDI DATA AFTER FK & LSMFSAUDI DATA AFTER FK & LSMFT

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88 2089X (m)

FK LSMF

B B

A A

ZOOM VIEW OF WINDOW “A” ZOOM VIEW OF WINDOW “A” T

ime

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2.0

327 1370X (m)

FK LSMF

327 1370X (m)

ZOOM VIEW OF WINDOW “B” ZOOM VIEW OF WINDOW “B” T

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(s)

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186 621X (m)

FK LSMF

186 621X (m)

Overview of SomeOverview of Some Coherent Noise Coherent Noise Filtering MerthodsFiltering Merthods

OverviewOverviewThere are a number of different coherent noise filtering There are a number of different coherent noise filtering methods, including FK dip filter, Radon transform, methods, including FK dip filter, Radon transform, hyperbolic transform, and parabolic transform methods. hyperbolic transform, and parabolic transform methods. All of these methods rely upon transforming the signal All of these methods rely upon transforming the signal into a new domain where the signal and noise are more into a new domain where the signal and noise are more separable. We will show that LSM filtering is another separable. We will show that LSM filtering is another coherent filtering method, but is more precise in defining coherent filtering method, but is more precise in defining a transform that separates signal and coherent noise a transform that separates signal and coherent noise according to the physics of wave propagation. Examples according to the physics of wave propagation. Examples show that this is sometimes a more effective ilter, but it is show that this is sometimes a more effective ilter, but it is more costly.more costly.

DistanceDistance

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PPPP

Multicomponent Filtering by LSMF Multicomponent Filtering by LSMF

ZZ

PPPPPSPS

ssssd =d = L m L m ++ L mL mpp ppxx

ssssd =d = L m L m ++ L mL m

pp ppzz

Signal FK

Problem: Out-of-Plane Ground RollProblem: Out-of-Plane Ground Roll

Ground RollGround Roll

DistanceDistance

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PPPP

Filtering by LSMF Filtering by LSMF

MM11MM22

ZZ

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LL-1-1pp

LL-1-1

ss

CRG2 (Vertical component) CRG2 (Vertical component)

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CRG2 Raw Data (vertical component)CRG2 Raw Data (vertical component)

DistanceDistance

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AA

BB

V=1/PV=1/P

Tau

Tau

Filtering by Parabolic Filtering by Parabolic - p - p

Signal/NoiseSignal/NoiseOverlap Overlap

F-X Spectrum of ARCO DataF-X Spectrum of ARCO DataOffset (ft)Offset (ft)

Fre

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z)F

req

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cy (

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003500350020002000

5050

S. of LSM Filtered Data (V. S. of LSM Filtered Data (V. Const)Const)

S. of F-K Filtered Data (13333ft/s)S. of F-K Filtered Data (13333ft/s)

SummarySummary

TraditionalTraditional coherent filtering based on coherent filtering based on approximate moveoutapproximate moveout

LSMF filtering operators based onLSMF filtering operators based on actual physics separating actual physics separating signalsignal & & noisenoise

Better physics --> Better focusing, more $$$Better physics --> Better focusing, more $$$